Show that p(0,7), q(6,5), r(5,2) and s(-1,4) are the vertices of rectangular

Answers

Answer 1

Answer:

Step-by-step explanation:

P(0,7), Q(6,5), R(5,2), and S(-1,4) form the vertices of a rectangle. To prove this, we need to show that the opposite sides of the quadrilateral are parallel and that the diagonals are equal in length and bisect each other.

To explain this solution in more detail, we can start by finding the slopes of the line segments connecting each pair of points. The slope of a line segment can be calculated using the formula:

slope = (change in y) / (change in x)

For example, the slope of the line segment connecting P and Q is:

slope PQ = (5 - 7) / (6 - 0) = -2/6 = -1/3

We can calculate the slopes of the other line segments in a similar way. If the opposite sides of the quadrilateral are parallel, then their slopes must be equal. We can check that this is true for all pairs of opposite sides:

slope PQ = -1/3, slope SR = -1/3

slope QR = (2 - 5) / (5 - 6) = -3/-1 = 3, slope PS = (4 - 7) / (-1 - 0) = -3/-1 = 3

Next, we can calculate the lengths of the diagonals using the distance formula:

distance PR = sqrt[(5 - 0)^2 + (2 - 7)^2] = sqrt(5^2 + (-5)^2) = sqrt(50)

distance QS = sqrt[(6 - (-1))^2 + (5 - 4)^2] = sqrt(7^2 + 1^2) = sqrt(50)

If the diagonals are equal in length, then we should have distance PR = distance QS, which is indeed the case.

Finally, we need to show that the diagonals bisect each other. This means that the midpoint of PR should be the same as the midpoint of QS. We can calculate the midpoint of each diagonal using the midpoint formula:

midpoint of PR = [(0 + 5)/2, (7 + 2)/2] = (2.5, 4.5)

midpoint of QS = [(6 + (-1))/2, (5 + 4)/2] = (2.5, 4.5)

Since the midpoints are the same, we have shown that the diagonals bisect each other.

Therefore, we have shown that the points P(0,7), Q(6,5), R(5,2), and S(-1,4) form the vertices of a rectangle.

To know more about vertices of a rectangle refer here:

https://brainly.com/question/16071215#

#SPJ11


Related Questions

Need this fast
A) -24 Solve lim 69²-24 B) 4 a+2 2-a C) 24 D) - 4

Answers

The limit of (69²-24) as x approaches infinity is equal to infinity.

As x approaches infinity, the value of (69²-24) becomes very large, and it goes to infinity. Therefore, the limit of (69²-24) as x approaches infinity is infinity.

B) The limit of (4a+2)/(2-a) as a approaches 2 from the left is equal to -6 and as a approaches 2 from the right is equal to 6.

As a approaches 2 from the left, the denominator (2-a) approaches zero from the negative side, and the numerator (4a+2) approaches -6. Therefore, the limit of (4a+2)/(2-a) as a approaches 2 from the left is -6.

As a approaches 2 from the right, the denominator (2-a) approaches zero from the positive side, and the numerator (4a+2) approaches 6. Therefore, the limit of (4a+2)/(2-a) as a approaches 2 from the right is 6.

For more questions like Limit click the link below:

https://brainly.com/question/12211820

#SPJ11

The temperature at a point (x, y, z) is given byT(x, y, z) = 10e¯2x² − y² − 3z².In which direction does the temperature increase fastest at the point (1, 3, 1)?Express your answer as a UNIT vector.

Answers

The direction of fastest increase in temperature at the point (1, 3, 1) is given by the unit vector (-5/sqrt(10) , -3/sqrt(10) , -9/sqrt(10)).

To find the direction of fastest increase in temperature at the point (1, 3, 1), we need to find the gradient of the temperature function T(x, y, z) at that point.

The gradient of a function is a vector that points in the direction of steepest increase, and its magnitude is the rate of change in that direction. So, we can find the gradient vector ∇T(x, y, z) as follows:

∇T(x, y, z) = ( ∂T/∂x , ∂T/∂y , ∂T/∂z )

=[tex]( -20xe^(-2x^2-y^2-3z^2) , -2ye^(-2x^2-y^2-3z^2) , -6ze^(-2x^2-y^2-3z^2) )[/tex]

Therefore, at the point (1, 3, 1), the gradient of T(x, y, z) is:

∇T(1, 3, 1) = [tex]( -20e^(-8) , -6e^(-8) , -18e^(-8) )[/tex]

To find the direction of fastest increase, we need to normalize this vector to a unit vector. The magnitude of the gradient vector is:

|∇T(1, 3, 1)| = sqrt( (-[tex]20e^(-8))^2 + (-6e^(-8))^2 + (-18e^(-8))^2 )[/tex]

= sqrt( 640e^(-16) )

= 8e^(-8) sqrt(10)

So, the unit vector in the direction of fastest increase is:

( -20e^(-8) / (8e^(-8) sqrt(10)) , -6e^(-8) / (8e^(-8) sqrt(10)) , -18e^(-8) / (8e^(-8) sqrt(10)) )

= ( -5/sqrt(10) , -3/sqrt(10) , -9/sqrt(10) )

Therefore, the direction of fastest increase in temperature at the point (1, 3, 1) is given by the unit vector (-5/sqrt(10) , -3/sqrt(10) , -9/sqrt(10)).

To learn more about unit vector visit: https://brainly.com/question/30279109

#SPJ11

In the coordinate plane, the point X(1,4) is translated to the point X(0,6) . Under the same translation, the points Y(-1,2) and Z(-3,1) are translated to Y and Z , respectively. What are the coordinates of Y and Z ?
Help!!!!!! URGENT

Answers

Thus, the coordinates of Y and Z after the translation is obtained as :

Y'(-2,4) and Z'(-4, 3).

Define about the translation:

A figure is translated when it is moved from one point to another without changing in size, form, or rotation.

A figure can be translated to move it up, down, left, or right while maintaining the same size. This is carried out using a coordinate system in order to be done properly and accurately.The pre-image is the original object that needs to be translated, and the image is the translated object.

Given translation:

Point X(1,4) --->  point X'(0,6)

There is 1 unit shift to left as 1 is subtracted to x coordinate to get 0.

There is 2 unit shift to upward as 2 is added to y coordinate to get 6..

Translation:

(x,y) --->(x - 1, y + 2)

Applying same on points Y and Z,

Y(-1,2)  --> Y'(-2,4)

Z(-3,1)  --> Z'(-4, 3)

Thus, the coordinates of Y and Z after the translation is obtained as :

Y'(-2,4) and Z'(-4, 3).

Know more about the translation

https://brainly.com/question/1574635

#SPJ1

A student usally saves $20 a month. He would like to reach a goal of saving $350 in 12 months the students writes the equation 350=12(x + 20) to represent this situation

Answers

Answer: x=55/6 or 55 over 6

Step-by-step explanation: Step 1: Distribute:

- 350= 12(x+20)

- 350= 12x + 240

Step 2: Subtract 240 from both sides:

- 350-240= 12x+240-240

Step 3: Simplify:

Subtract the numbers: 350-240= 12x+240-240= 110=12x+240-240

Subtract again: 110=12x+240-240= 110=12x

Step 4: Divide both sides by the same factor:

110=12x= 110/12= 12x/12

Step 5: Simplify:

- Divide the numbers: 110/12=12x/12= x=55/6=12x/12

- Cancel terms that are in both the numerator and denominator: 55/6=12x/12= 55/6=x

- Move the variables to the left: 55/6=x = x=55/6

Answer: x=55/6 or 55 over 6

!!!HELPP ME ASAP!!!! Claude is reading a science fiction book in which aliens have dropped a fungus on a 10 square mile section of a planet. The fungus spreads rapidly, increasing the area it covers by 50% every hour. The total


area of the planet is 200 million square miles. Claude created an equation and determined that it will take approximately 41 hours for the fungus to cover planet What is the equation that Claude created?

Answers

The equation Claude created is: 10 * (1.5)^t = 200,000,000, where t represents the number of hours.

Let A be the initial area of the fungus that covers the 10 square mile section of the planet.

After 1 hour, the fungus increases in size by 50%, which means it multiplies by 1.5. Thus, the area covered by the fungus after 1 hour is:

A + 1.5A = 2.5AAfter 2 hours, the fungus increases again by 50%, so its area becomes:

2.5A + 1.5(2.5A) = 6.25A

In general, after n hours, the area of the fungus becomes: A(1.5)^n

Since we want the fungus to cover the entire planet, we need to solve the following equation: A(1.5)^41 = 200,000,000

Simplifying, we get:

A = 200,000,000 / (1.5)^41

Therefore, the equation that Claude created is:

A(1.5)^n = 200,000,000

where n is the number of hours it takes for the fungus to cover the planet.

To learn more about “area” refer to the https://brainly.com/question/25292087

#SPJ11

According the April 12, 2017 Pew Research survey, 58% of Americans approve of U. S. Missile strikes in


Syria in response to reports of the use of chemical weapons by Bashar al-Assad's government (the


Syrian government). A sample of 50 Americans are surveyed. Let o be the sample proportion of


Americans who approve the U. S. Missile strikes.


1. What is the population proportion?


(decimal form)


2. What is the sample size?


3. Can the normal approximation be used with this distribution?



4. What is the mean of the sampling proportion?

Answers

Answer:

The population proportion is given as 58% or 0.58 in decimal form.

The sample size is given as 50 Americans.

Yes, the normal approximation can be used with this distribution because the sample size is sufficiently large (n=50) and the underlying population is assumed to be large enough to satisfy the independence requirement.

The mean of the sampling proportion (o) can be calculated using the formula:

mean = population proportion = 0.58

Therefore, the mean of the sampling proportion is 0.58 or 58%.

To know more about decimal refer here

https://brainly.com/question/30958821#

#SPJ11

Mai drew the design shown below. Each
rectangle in the design has the same
area. Each rectangle is what fraction of
the area of the complete design?

Answers

Each rectangle is 1/3 of the area of the complete design.

What fraction of the area of the complete design?

A fraction represents the parts of a whole or collection of objects e.g. 3/4 shows that out of 4 equal parts, we are referring to 3 parts.

Looking at the design, you will be notice that the main (bigger) rectangle is divided to three smaller rectangles. Thus, each rectangle is one out of three  rectangles i.e. 1/3.

Therefore, each rectangle is 1/3 of the area of the complete design.

Learn more about fraction on:

brainly.com/question/11562149

#SPJ1

Complete Question

Check attached image

find the general solution of the following linear system. y′ = [2 2 −4 2 −1 −2 4 2 −6] y with λ = −1,−2,−2

Answers

To find the general solution of the linear system y' = [2 2 -4; 2 -1 -2; 4 2 -6] y, we need to first find the eigenvectors and eigenvalues of the coefficient matrix A = [2 2 -4; 2 -1 -2; 4 2 -6].

Using the characteristic equation, we can find the eigenvalues:

det(A - λI) = 0

=> det([2-λ 2 -4; 2 -1-λ -2; 4 2 -6-λ]) = 0

=> (2-λ)[(-1-λ)(-6-λ) - 4] - 2[(-2)(-6-λ) - 8] + 4[2(-1-λ) - 4] = 0

=> λ^3 -  + 8λ - 4 = 0

=> (λ-1)(λ-2[tex])^2[/tex] = 0

Thus, λ = 1, 2 (with multiplicity 2). For each eigenvalue, we need to find a corresponding eigenvector.

For λ = 1, we need to find the null space of the matrix (A - λI):

A - λI = [1 2 -4; 2 -2 -2; 4 2 -7]

=> R2 <- R2 - 2R1, R3 <- R3 - 4R1

[1 2 -4; 0 -6 6; 0 -6 9]

=> R3 <- R3 - R2

[1 2 -4; 0 -6 6; 0 0 3]

So, we have a basic eigenvector of the form [4,-2,1]^T. To obtain a linearly independent eigenvector, we use the method of generalized eigenvectors. We need to find a vector v such that (A - λI) v = u, where u is the basic eigenvector.

(A - λI) v = u

=> [1 2 -4; 2 -2 -2; 4 2 -7] v = [4; -2; 1]

=> R2 <- R2 - 2R1, R3 <- R3 - 4R1

[1 2 -4; 0 -6 6; 0 -6 9] v = [4; -2; 1]

=> R3 <- R3 - R2

[1 2 -4; 0 -6 6; 0 0 3] v = [4; -2; 1]

=> -6v2 + 6v3 = -2

=> 3v3 = 1

=> 2v2 - 4v3 = -2

=> v2 = 0

So, we have v = [0; 1/3; 2/3[tex]]^T[/tex] as the second eigenvector corresponding to λ = 1.

For λ = 2, we need to find the null space of the matrix (A - λI):

A - λI = [0 2 -4; 2 -3 -2; 4 2 -8]

=> R1 <-> R2

[2 -3 -2; 0 2 -4; 4 2 -8]

=> R3 <- R3 - 2R1

[2 -3 -2; 0 2 -4; 0 8 -12]

Learn more about general solution,

https://brainly.com/question/12641320

#SPJ4

Math geometry question please help

Answers

Answer:

LP is a raym∠LMO = 90°m∠LPO = 90°m∠MLP = 26°arc MP = 154°arc MNP = 206°

Step-by-step explanation:

You want various angle and arc measures in the given figure.

Relationships

The relevant angle relationships are ...

a radius to a point of tangency makes a right angle with the tangentan arc has the same measure as its central anglethe sum of the arcs of a circle is 360°the sum of angles in a quadrilateral is 360°an angle is formed from two rays whose endpoints are the vertex of the angle

These answer the given questions as follows:

  LP is a ray.

  The angle at M is 90°.

  The angle at P is 90°.

 The angle at L is 360° -90° -90° -154° = 26°

  Arc MP has the same measure as angle MOP, 154°

  Arc MNP completes the circle, so is 360° -154° = 206°

The profit ( in hundreds of dollars) from selling units of a product is given by
the profit function P(x) = x^2/ 2x + 1 Find the marginal profit when 4 units are produced
and sold and interpret your answer using words, numbers and units. Be very specific.
(Round the number part of your answer to the nearest cent.)

Answers

the marginal profit when 4 units are produced and sold is approximately -$69.14. This means that when producing and selling the 4th unit, the profit will decrease by $69.14.

To find the marginal profit when 4 units are produced and sold, we first need to find the derivative of the profit function P(x) with respect to x. The given profit function is:

P(x) = (x^2) / (2x + 1)

Now, let's find its derivative, which represents the marginal profit function:

dP/dx = (d/dx(x^2))/(2x + 1) - (x^2)(d/dx(2x + 1))/((2x + 1)^2)

First, find the derivative of x^2 and 2x + 1:

d/dx(x^2) = 2x
d/dx(2x + 1) = 2

Now, substitute these values into the marginal profit function:

dP/dx = (2x)/(2x + 1) - (x^2)(2)/((2x + 1)^2)

Next, we'll find the marginal profit when 4 units are produced and sold. So, let's substitute x = 4 into the marginal profit function:

dP/dx(4) = (2 * 4)/(2 * 4 + 1) - (4^2)(2)/((2 * 4 + 1)^2)

dP/dx(4) = (8)/(9) - (32)(2)/(81)

dP/dx(4) = (8 - 64)/(81)

dP/dx(4) = -56/81

Since the profit is in hundreds of dollars, we need to multiply the marginal profit by 100 to get the value in dollars. Then, round to the nearest cent:

Marginal profit in dollars = (-56/81) * 100 ≈ -$69.14

So, the marginal profit when 4 units are produced and sold is approximately -$69.14. This means that when producing and selling the 4th unit, the profit will decrease by $69.14.

to know more about marginal profit click here:

https://brainly.com/question/29785280

#SPJ11

The area of the triangle below is \frac{2}{25}

25

2



square feet. What is the length of the base? Express your answer as a fraction in simplest form.

1/5 f

Answers

The length of the base of the given triangle can be simplified as 2√2/5 feet, which is equivalent to √8/5 feet.

What is the length of the base of a triangle if its area is (2/25) * 252 square feet and the height is twice the length of the base?

We are given that the area of the triangle is (2/25) * 252 square feet.

Let the length of the base be x. Then, the height of the triangle can be expressed as (2/5)x, since the base divides the triangle into two equal parts.

The area of the triangle is given by the formula A = (1/2)bh, where b is the length of the base and h is the height of the triangle.

Substituting the given values, we get:

(1/2)x(2/5)x = (2/25)*252

Simplifying this equation, we get:

(1/5)x²= 20.16

Multiplying both sides by 5, we get:

x² = 100.8

Taking the square root of both sides, we get:

x =√(100.8)

Simplifying this expression, we get:

x = √(25*4.032)x = 5*√(4.032)x = (5/5)*√(4.032)x = 1*√(4.032)

Therefore, the length of the base is √(4.032) feet, which can be expressed as a fraction in simplest form as 2√(2)/5 feet.

Learn more about triangle

brainly.com/question/2773823

#SPJ11

16. Justin is joining a gym. The gym is currently offering a discount on the fee to join and on the monthly rate.
The discounted price,in dollars,the gym charges can be represented by the equation y=10x+5
a. What are the slope and the Y-intercept of the equation? What do the slope and the Y-intercept each represent in this equation?

Answers

Answer:

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.Slope (m) = 10

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.Slope (m) = 10Y-intercept (b) = 5

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.Slope (m) = 10Y-intercept (b) = 5The slope represents the rate of change of the monthly rate with respect to the fee to join. For every increase of $1 in the fee to join, the monthly rate increases by $10.

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.Slope (m) = 10Y-intercept (b) = 5The slope represents the rate of change of the monthly rate with respect to the fee to join. For every increase of $1 in the fee to join, the monthly rate increases by $10.The y-intercept represents the initial cost of joining the gym. It is the amount that the gym charges even if the fee to join is $0. In this case, the gym charges $5 to join.

The slope is 10 which represents the monthly rate. The Y-intercept is 5 which represents the joining fee.

What is 3x-(2x+9) + 4x?
Please help^^

Answers

Answer:

5x-9

Step-by-step explanation:

Distribute: 3x-(2x+9) + 4x

3x - 2x - 9 + 4x

Combine Like Terms: 3x - 2x - 9 + 4x

5x-9

3x-(2x+9)+4x
first distribute the negative
3x-2x-9+4x
combine like terms
5x-9

A tank in the shape of a hemisphere has a diameter of 8 feet. If the liquid that fills the tank has a density of 86 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?

Answers

Answer:

209.07 pounds

Step-by-step explanation:

radius= 8÷2=4 feet

volume of hemisphere=((4/3)×(22/7)×r^3)/2

=134.09 cubic feet

Mass=density × volume

=86×134.09

=209.07 pounds

Calculate d²y/d²x y= -5x2 + x d²y/d²x= Calculate d²y/dx² y= 7/x d²y/dx²=

Answers

To calculate the second derivative of a function, we need to take the derivative of the first derivative. The second derivative gives us information about the curvature of the function. A positive second derivative indicates that the function is concave up, while a negative second derivative indicates that the function is concave down. A second derivative of zero indicates that the function has no curvature at that point.

In the first example given, y = -5x^2 + x, we first find the first derivative by taking the derivative of the function with respect to x. This gives us dy/dx = -10x + 1. To find the second derivative, we take the derivative of dy/dx with respect to x. This gives us d²y/d²x = -10. This indicates that the function has a constant negative curvature, meaning it is concave down everywhere.

In the second example given, y = 7/x, we first find the first derivative by taking the derivative of the function with respect to x. This gives us dy/dx = -7/x^2. To find the second derivative, we take the derivative of dy/dx with respect to x. This gives us d²y/dx² = 14/x^3. This indicates that the function is concave up for positive values of x and concave down for negative values of x. The second derivative is undefined at x = 0, indicating a point of inflection.

Overall, the second derivative gives us important information about the behavior of a function and can help us identify points of inflection and concavity.
MORE PROBLEM ON DERIVATIVES : https://brainly.com/question/23819325

#SPJ11

KAP


1 IN PU


1. Luis parents give him x dollars for his monthly allowance. Each month, he must


pay $35 for his cell phone. One-sixth of the remaining money can be spent on


entertainment. Which function can be used to find the amount in dollars Luis can


spend on entertainment?


A f(x) =*735


B. F(x) = 35x - 3


C. F(x) = 35 - $


D. F(x) = § - 35

Answers

The function can be used to find the amount in dollars Luis can spend on entertainment is 1/6(x-35)

Total amount of money luis get from his parent = x dollars

The amount luis has to pay to his parents for his cell phone is $35

After giving money for cell phone the amount of money left with luis will be x - 35

so, remaining money with luis = x - 35

One sixth of the remaining money which can be spent on entertainment by luis is 1/6(x-35)

The function can be written in the form of

f(x) = 1/6(x-35)

To know more about function click here :

https://brainly.com/question/12431044

#SPJ4

Small baskets of tomatoes are sold at a vegetable stand for $3 per basket. Large


baskets of tomatoes are sold at the stand for $5 per basket. Only whole numbers of


baskets may be purchased.


A customer purchases a total of 8 baskets of tomatoes and pays $36.


A. Write and solve a system of equations that models the number of small


baskets (x) and the number of large baskets () that the customer purchases.


Show or explain all your work.

Answers

The customer purchased 2 small baskets and 6 large baskets.

Let x be the number of small baskets and y be the number of large baskets that the customer purchases.

We can set up a system of two equations based on the information given:

Equation 1: x + y = 8 (The total number of baskets purchased is 8)

Equation 2 3x + 5y = 36:  (The total amount paid for the baskets is $36)

To solve this system, we can use either substitution or elimination method.

Using substitution method:

From Equation 1, we have x = 8 - y.

Substitute this into Equation 2:

3(8 - y) + 5y = 36

24 - 3y + 5y = 36

2y = 12

y = 6

Now, we can substitute y = 6 back into Equation 1 to find x:

x + 6 = 8

x = 2

Therefore, the customer purchased 2 small baskets and 6 large baskets.

Using elimination method:

We can multiply Equation 1 by 3 and subtract it from Equation 2 to eliminate x:

 3x + 5y = 36

- (3x + 3y = 24)

   2y = 12

    y = 6

Now, we can substitute y = 6 back into either Equation 1 or Equation 2 to find x. Let's use Equation 1:

x + 6 = 8

x = 2

To know more about basket refer here

https://brainly.com/question/54060245#

#SPJ1

Shandra has $760 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. ⢠She buys a new bicycle for $433. 54. ⢠She buys 2 bicycle reflectors for $18. 41 each and a pair of bike gloves for $10. 76. ⢠She plans to spend some or all of the money she has left to buy new biking outfits for $66. 40 each. Write and solve an inequality which can be used to determine o, the number of outfits Shandra can purchase while staying within her budget. â

Answers

We can use an inequality to determine the number of biking outfits Shandra can purchase while staying within her budget.

Let o represent the number of outfits she can purchase. Here are the given terms and costs:
- Initial budget: $760
- Bicycle cost: $433.54
- 2 reflectors cost: 2 * $18.41 = $36.82
- Bike gloves cost: $10.76
- Outfit cost: $66.40 each

Now, we can set up the inequality:
760 >= 433.54 + 36.82 + 10.76 + 66.40 * o

First, combine the constants:
760 >= 481.12 + 66.40 * o

Now, subtract 481.12 from both sides:
278.88 >= 66.40 * o

Finally, divide both sides by 66.40:
o <= 4.2

Since Shandra can only purchase whole outfits, the maximum number of outfits she can buy is 4. So the inequality representing this situation is o <= 4.

To know more about inequality refer here:

https://brainly.com/question/30231190?#

SPJ11

Penny decided to travel to Palawan. The airplane flew at an average rate of 300 miles per hour and covered 1500 miles. How long will the flight will take? *

A. 3 hours

B. 4 hours

C. 5 hours

D. 6 hours

Answers

The time it will take the flight is C) 5 hours.

To solve this problem, we can use the formula: distance = rate x time. In this case, we know that the distance is 1500 miles and the rate (or speed) is 300 miles per hour. We can rearrange the formula to solve for time: time = distance / rate. Plugging in the values we have, we get:

time = 1500 miles / 300 miles per hour
time = 5 hours

Therefore, the correct answer is C. It will take Penny 5 hours to fly from her starting point to Palawan at an average speed of 300 miles per hour. This calculation assumes that the plane maintains a constant speed throughout the entire flight, which may not be the case due to factors such as wind and turbulence.

Learn more about speed here: https://brainly.com/question/27888149

#SPJ11

The prism shown has a surface area of 1,500 mm squared. What is the height, h, of the prism?

Answers

The height of the triangular base prism is 10 mm.

How to find the surface area of a prism?

The prism above is a triangular base prism. The surface area of the prism can be calculated as follows:

surface area of the triangular prism = (a + b + c)l + bh

where

a, b, and c are the side of the triangular basel = height of the prismb = base of the triangleh = height of the triangle

Therefore,

surface area of the triangular prism = (20 + 30 + 40) + 20 × 30

1500 = 90l + 600

1500 - 600 = 90l

90l = 900

divide both sides by 90

l = 900 / 90

l = 10 mm

Therefore,

height of the prism = 10 mm

Learn more on surface area here: https://brainly.com/question/31223288

#SPJ1

The angle of depression from the top of a 150m high cliff to a boat at sea is 7°. How much closer to the cliff must the boat move for the angle of depression to become 19°?

Answers

The boat must move 785.82 m closer to the cliff  for the angle of depression to become 19°.

We need to find how much closer to the cliff the boat must move for the angle of depression to change from 7° to 19°.

Calculate the distance from the boat to the base of the cliff at 7° angle of depression.
Using the tangent function, we have:
tan(angle) = height/distance
tan(7°) = 150m/distance
distance = 150m/tan(7°)

distance=1221.49

Calculate the distance from the boat to the base of the cliff at 19° angle of depression.
Using the tangent function, we have:
tan(angle) = height/distance
tan(19°) = 150m/distance
distance = 150m/tan(19°)

distance=435.6665

Calculate the difference between the two distances to find out how much closer the boat must move.
difference = distance at 7° angle of depression - distance at 19° angle of depression

Plugging in the values from Steps 1 and 2, we get:
difference = (150m/tan(7°)) - (150m/tan(19°))

difference=1221.49-435.6665

difference=785.8235



After calculating, we find that the boat must move approximately 785.82 meters closer to the cliff for the angle of depression to change from 7° to 19°.

To learn more about angle of depression refer here

https://brainly.com/question/13514202#

#SPJ11

PLEASE HELP (40 POINTS)

Answers

The coordinates of the points N and L are N = (-2d, 0) and L = (-4f, g)

Calculating the coordinates of N and L

From the question, we have the following parameters that can be used in our computation:

M = (-2d - 4f, g)

O = (0, 0)

ON = 2d

Given that

ON = 2d

Then it means that

N = (-2d, 0)

For the point L, we have

LO = MN

Where

LO = √[(x - 0)² + (y - 0)²] i.e. the distance formula

LO = √[x² + y²]

Next, we have

MN = √[(-2d - 4f + 2d)² + (g - 0)²] i.e. the distance formula

MN = √[(-4f)² + g²]

So, we have

LO = MN

√[x² + y²] = √[(-4f)² + g²]

By comparison, we have

x = -4f and y = g

This means that the coordinates of point L = (-4f, g)

Read more about distance at

https://brainly.com/question/28551043

#SPJ1

Hallar la altura de una asta bandera, si un estudiante la observa desde un punto a, con un ángulo de 30° y entre el estudiante y la asta hay una distancia de 10m.

Answers

Answer:

The height of the flagpole is approximately 5.774 meters.

Step-by-step explanation:

Let's call the height of the flagpole h. We can use trigonometry to set up the following equation:

tan(30°) = h/10

Simplifying this equation, we get:

h = 10 tan(30°)

Using a calculator, we find that tan(30°) ≈ 0.5774, so:

h ≈ 5.774 meters

Therefore, the height of the flagpole is approximately 5.774 meters.

To know more about flagpole refer here

https://brainly.com/question/31296662#

#SPJ11

For each pair of numbers, decide if lines with these gradients are perpendicular or not. a) 5 and 1/ 5 b) 2/3 and -1/3 c) and -1/1 d) - and 3​

Answers

The pair of numbers  3/5 and -5/3,  -1/3 and 3 are perpendicular because two lines are perpendicular if and only if the product of their gradients is -1.

Each pair of numbers, we have to decide if lines with these gradients are perpendicular or not

Two lines are perpendicular if and only if the product of their gradients is -1.

For 5 and 1/5

The product is 1 which is not -1, so these are not perpendicular.

For 3/5 and -5/3

The product is -1 so these are perpendicular

For 1/4 and -1/4

The product is -1/16 so these are not perpendicular.

For -1/3 and 3

The product is  -1 so these are perpendicular

Hence, the pair of numbers  3/5 and -5/3,  -1/3 and 3 are perpendicular.

To learn more on slope of line click:

https://brainly.com/question/16180119

#SPJ1

Aleks and Melanie used a protractor to measure the angle below. Aleks thinks the angle measures 50° but Melanie says it is actually 130°. Their teacher confirms that Melanie has the correct answer. What mistake did Aleks make while measuring the angle?

Answers

The mistake, Aleks made, while measuring the angle is, he measure the angle from the wrong side of the line.

Angle is a dimensionless vector quantity, that is, it is very important, to take care of the directions, while measuring the angle.

That is, to measure the angle, say ∠ABC, the 0°(reference) line of the protractor, must be on one either AB or BC, to measure the angle rightly.

And since the angles between two lines are supplementary in nature, that is, the two angles will add up to make 180°, that is why, the angle measure by Alek and Melanie, add up to make 180°.

Read more about angle at:

https://brainly.com/question/1309590

I have some coins in my pocket. Nickles and pennies I have a total of $. 41 I have 21 coins in total. How many Nickles and pennies do I have?​

Answers

The number of nickels and pennies in the pocket is 5 and 16 respectively.

How to find the number of coins?

To find the number of coins, Let's assume the number of nickels is x and the number of pennies is y.

According to the problem, we have two equations:

The total value of the coins is $0.41:

0.05x + 0.01y = 0.41

The total number of coins is 21:

x + y = 21

Now we can solve this system of equations to find x and y. One way to do this is to use substitution.

Solving the second equation for y, we get:

y = 21 - x

Substituting this into the first equation, we get:

0.05x + 0.01(21 - x) = 0.41

Simplifying:

0.05x + 0.21 - 0.01x = 0.41

0.04x = 0.2

x = 5

So we have 5 nickels.

Substituting this into the equation y = 21 - x, we get:

y = 21 - 5 = 16

So we have 16 pennies.

Therefore, the number of nickels and pennies in the pocket is 5 and 16 respectively.

Learn more about Coins counting

brainly.com/question/27681719

#SPJ11

What's 2x = 20 if 4y = 80

Answers

Answer:

x=10 and y=20, 2x=20=y

Step-by-step explanation:

2x=20 | Divide by 2 on both sides

x=10

4y=80 | Divide by 4 on both sides

y=20

Answer: 40

80 ÷ 2 = 20, so x = 40.

To check your answer;

40 x 2 = 80

Bob and two friends each were able to juggle with bean bags for 3/4 of a minute. How long did they juggle together? No decimals pls!

Answers

Answer:

Step-by-step explanation:

They each juggled for 3/4 of a minute

There were 3 people in total

3 people times 3/4 of a minute equals 2 1/4 minutes

fast pls
in When calculating 4-√x+15 what option you get x?-1 lim X>1 1 the process -1 A) lim (x + 1) (4 + V1 +15) -1 B) lim 21 (1+1) (4 - V1-15) C) lim 16 - 2 - 1)(4+r+15) D) lím 16-1 (12 - 1) (4 - Vr+15)

Answers

None of the options are correct, and the value of x is simply 1.

Start with the given expression: 4 - √x + 15

Substitute x with the limit value of 1: 4 - √1 + 15 = 18

Therefore, the limit of the given expression as x approaches 1 from the right is 18.

To verify this result using the provided options, we can simplify each option and check which one equals 18 as x approaches 1 from the right.

Option A simplifies to (2/√2) + 2, which equals √2 + 2, not equal to 18.

Option B simplifies to 2(4 - √15), which equals 2(4 - 3.87), approximately equal to 2.27, not equal to 18.

Option C simplifies to 3(4 + √15), which equals 3(4 + 3.87), approximately equal to 23.61, not equal to 18.

Option D simplifies to 3(3)(3), which equals 27, not equal to 18.

Therefore, none of the options are correct, and the value of x is simply 1.

none of the options are correct, and the value of x is simply 1.

For more questions like Limit click the link below:

https://brainly.com/question/12207539

#SPJ11

Please help with this question. I am offering 40 points. You can use the word box above to answer the questions.

Answers

We define [tex]9^{\frac{1}{2} }[/tex] to be the square root of nine. This means that [tex](9^{\frac{1}{2} })^{2}[/tex] must be equal to nine.

By using the properties of exponents to explain why [tex]8^{\frac{1}{3} }=2[/tex];

Statement                           Reasons_____________________

[tex]8^{\frac{1}{3} }=2[/tex]                                  Given

[tex](8^{\frac{1}{3} })^3=2^3[/tex]                        Exponent property of equality.

[tex]8^{\frac{1}{3} \times 3}=2^3[/tex]                        Exponent property of a power.

8 = 8                                simplify

What is an exponent?

In Mathematics, an exponent refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

the variables b and n are numerical values (numbers) or an algebraic expression.

n is referred to as a superscript or power.

By applying the multiplication and division law of exponents for powers to each of the expressions, we have the following:

[tex]9^{\frac{1}{2} }[/tex] = √9 (square root of nine)

[tex](9^{\frac{1}{2} })^{2}=(9^{\frac{1}{2} \times 2})=9^1 = 9[/tex]  

Read more on exponent here: https://brainly.com/question/27858496

#SPJ1

Other Questions
The seventh-grade class is selling boxes of votive candles as a fundraiser. The first box purchased costs $14. 00, and each additional box costs $10. 0. a. Is the relationship between the number of additional boxes of candles purchased and the total money spent linear?explainb. An equation that relates the total money spent on boxes of candles, C, to the number of additional boxes purchased,b,is,c. Using the equation from part (b), the total money spent by a person who bought 3 boxes of candles for the fundraiser would be $ The energy system predominantly involved during the whole duration of the race I need help on number 2 In this lab exercise we tried to predict what would be the limiting reagent in each beakerbased on observation of the amount (in mass) of reactant available. In determining thelimiting reagent in a chemical reaction, is it enough to just know the mass of each of thereactant? Explain. Image attached please help proof Two-year old James is watching his big brother jump rope. James really wants to do what his brother is doing. Which of the four parts of the observational learning process may interfere with James' learning to jump rope? Explain your choice unless he worked hard, he will fail the exam. check grammar A woman claims to have the ability to recognize by tasting it, whether tea was poured first and milk added after, or whether tea was added to milk. In order to test her powers, a set of 10 cups is brought to her and she is asked to taste them. She gets 7 out of 10 correct. Assuming each trial is independent, what is the probability that she would have done at least this well if she had no ability to recognize such difference A box is suspended by a rope. when a horizontal force of 100 n acts on the box, it moves to the side until the rope is at an angle of 20 degree with the vertical. the weight of the box is. which big us city just launched a new ad campaign to boost post-pandemic tourism? what is five term in 12,16,21,27 Write an equation (any form) for the quadratic graphed below A film distribution manager calculates that 9 % of the films released are flops. If the manager is correct, what is the probability that the proportion of flops in a sample of 407 released films would differ from the population proportion by less than 3% ? Round your answer to four decimal places. A student is planning to write a personal narrative about his first trip to the ocean.Which detail is most important for the student to include in his introduction?OA. the settingreflectionsB.O C.O D. dialoguea conflictResetNext A ship sailed from Port X to Port Y. It traveled 20 kilometers due north and then 25 kilometers due west. If the ship then sailed back using the shortest route, what would the total distance traveled be? Round to the nearest kilometer. Determine whether the series n - 5 na tn - 6 n=1 is convergent or divergent using the Limit Comparison Test. Larry's profit is maximized when he produces shirts. When he does this, the marginal cost of the last shirt he produces is $ , which is than the price Larry receives for each shirt he sells. The marginal cost of producing an additional shirt (that is, one more shirt than would maximize his profit) is $ , which is than the price Larry receives for each shirt he sells. Therefore, Larry's profit-maximizing quantity corresponds to the intersection of the curves. Because Larry is a price taker, this last condition can also be written as How does the frequency of a string affect its wavelength? Nicole has 28 nickels and dimes that amount to $1. 85 how many of each coin does she have A sheet of paper 82 cm-by-88 cm is made into an open box (i.e. there's no top), by cutting X-cm squares out of each corner and folding up the sides. Find the value of x that maximizes the volume of the box. Give your answer in the simplified radical form. X= is the max. Write a paragraph about the difference of federal local and state