For what value of x is the figure a​ rhombus?

For What Value Of X Is The Figure A Rhombus?

Answers

Answer 1

The value of x is -4.

We have,

(3x + 25) and (6x - 2) makes one angle.

So,

(9x + 23) is the angle.

Now,

It is bisected in two angles.

So,

9x + 23 = 1/2 x (6x - 2)

9x + 23 = 3x - 1

9x - 3x = -1 - 23

6x = -24

x = -4

Thus,

The value of x is -4.

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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.

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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.

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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

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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

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]

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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.
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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.

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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.

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.

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An airplane is circling an airport at a height of 500m. the angle of depression of the control tower of the aiport is 15 degrees. what is the distance between the airplane and the tower

Answers

The distance between the airplane and the tower is approximately 1864.5 meters.

To solve this problem, we can use trigonometry. Let's draw a diagram to help us visualize the situation:

```
   T
  /|
 / |
/  | 500m
/a  |
--------
  x
```

In this diagram, "T" represents the control tower, "a" represents the airplane, and "x" represents the distance between them. We know that the height of the airplane is 500m, and the angle of depression from the tower to the airplane is 15 degrees. This means that the angle between the horizontal ground and the line from the tower to the airplane is also 15 degrees.

Using trigonometry, we can set up the following equation:

```
tan 15 = 500 / x
```

We can solve for "x" by multiplying both sides by "x" and then dividing by tan 15:

```
x = 500 / tan 15
```

Using a calculator, we can find that tan 15 is approximately 0.2679. Therefore:

```
x = 500 / 0.2679
x ≈ 1864.5m
```

So the distance between the airplane and the tower is approximately 1864.5 meters.

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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)).

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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

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)

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!!!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.

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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.

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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

grade
Math
Z.1 Scale drawings of polygons WEA
Language
8
Polygon P is a scaled copy of polygon N.
10
4
Learn with an example
4
20
16
40
Polygon N
Polygon P
What scale factor takes polygon N to polygon P?
for
10
Watch a video ▸

Answers

To find the scale factor that takes polygon N to polygon P, you need to divide the corresponding side lengths of the two polygons.

How to Determine the Problem?

To find the scale factor that takes polygon N to polygon P, you need to divide the corresponding side lengths of the two polygons.

For example, if one of the sides of polygon N is 6 units long, and the corresponding side of polygon P is 9 units long, then the scale factor is 9/6 or 1.5. This means that polygon P is 1.5 times larger than polygon N in all dimensions.

To determine the scale factor for all the corresponding sides of the polygons, you can compare each pair of sides and divide the length of the corresponding side of polygon P by the length of the corresponding side of polygon N.

It's important to note that when finding the scale factor between two polygons, you must compare corresponding sides. That is, you can't just choose any two sides to compare; you must compare the sides that are in the same position in the two polygons.

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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).

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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

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3. What is the largest number that divides 626, 3127 and 15628 and leaves remainders of 1, 2 and 3 respectively?​

Answers

Answer:

Step-by-step explanation:

625

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.

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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.

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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)

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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°.

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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.

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Complete Question

Check attached image

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%.

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A magic square is shown below. Every row, column and long diagonal adds to the same total. Each number can only be used once. Copy the magic square into your book and complete it using the numbers provided. 2 Numbers to use 3 -1 0 3 X 2 4 Magic square -3 2 1 -4 -2​

Answers

Answer:

Here is the complete magic square:

-3 4 -1

2 0 -2

1 -4 3

Every row, column, and long diagonal adds to 0.

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

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]  

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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.

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