Helppp translation and reflection

Helppp Translation And Reflection

Answers

Answer 1

The images of points B and C are B'(x, y) = (- 2, 6) and C'(x, y) = (- 1, 7), respectively.

How to compute the image of a point by translation

In this problem we find must determine the image of two points by translation, whose formula is introduced below:

T(x, y) = P'(x, y) - P(x, y)

Where:

P(x, y) - Original point.P'(x, y) - Resulting point.T(x, y) - Translation vector.

First, determine the translation vector:

T(x, y) = (1, 4) - (0, 0)

T(x, y) = (1, 4)

Second, determine the images of points B and C:

B'(x, y) = (- 3, 2) + (1, 4)

B'(x, y) = (- 2, 6)

C'(x, y) = (- 2, 3) + (1, 4)

C'(x, y) = (- 1, 7)

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Related Questions

+
ent will
A circle with center (7,3) and radius of 5 is graphed below with a square inscribed in
the circle.
+
Dillon says to write the equation of the tangent line you need the opposite-reciprocal
slope of the slope of the radius and Chelsey says you need to use the same slope as
the radius. Who is correct and why? Write the equation of the tangent line.
Part B: Find the perimeter of BCDE.

Answers

Chelsey is correct.

The equation of the tangent line is y = 8

Perimeter of BCDE is 28.28

How to determine tangent line and perimeter?

Chelsey is correct. The tangent line at a point on a circle is perpendicular to the radius at that point.

Therefore, it has the same slope as the radius at the point of tangency.

To find the equation of the tangent line at point B(7,8), find the slope of the radius at B.

The radius at B passes through the center of the circle (7,3) and B(7,8), so its slope is:

m = (8 - 3) / (7 - 7) = undefined

This is because the radius is a vertical line. The slope of the tangent line at B is the negative reciprocal of the slope of the radius at B, which is 0.

The equation of the tangent line is:

y - 8 = 0(x - 7)

y = 8

Part B: To find the perimeter of BCDE, we need to find the length of one of its sides and then multiply by 4. Since the square is inscribed in the circle, its diagonal is equal to the diameter of the circle, which is 10 (twice the radius).

Therefore, the length of one side of the square is:

s = 10/√(2) ≈ 7.07

The perimeter of BCDE is:

4s = 4(7.07) ≈ 28.28

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i need to factor 1/2y-5 1/2 and i can't seem to get it

Answers

The factored form of the equation is 1/2(y - √5)

To factor this expression, we need to look for any common factors that can be pulled out of both terms. We can see that both terms contain a factor of 1/2, so we can factor that out:

1/2(y - 5 1/2)

Now we need to see if there are any further factors that we can find. The term inside the parentheses, y - 5 1/2, cannot be factored any further using real numbers. However, we can write the expression as y - √5, which shows that it involves the square root of 5.

So the final factored form of the expression is:

1/2(y - √5)

This means that if we multiply 1/2 by (y - √5), we get back the original expression 1/2y - 5 1/2.

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Complete each conversion by dragging a number to each box.


Numbers may be used once, more than once, or not at all.



1,20012012,00012


12,000 g =


kg



120 cm =


mm



1. 2 L =


mL



1,200 cm =


m



0. 12 m =


mm

Answers

The conversion each unit gives:

12,000 g =   12 kg    

120 cm = 1200 mm

1.2 L = 1200 mL

1,200 cm = 12 m

0. 12 m = 120 mm

How to convert from one unit to another?

Conversion of units is the process of converting between different units of measurement for the same quantity through conversion factors.

1000 g = 1 kg. Thus,

12,000 g =   12 kg    

1 cm = 10 mm. Thus,

120 cm = 1200 mm

1L = 1000 mL. Thus,

1.2 L = 1200 mL

100 cm = 1 m. Thus,

1,200 cm = 12 m

1 m = 1000 mm. Thus,

0. 12 m = 120 mm

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Please help it would be amazing if you knew this

Answers

The solution of the composite function, (f + g)(x)  is 8x + 7

How to solve function?

A function relates input and output. In other words, a function is a special relationship among the inputs (independent variable) and their outputs (dependent variable).

A composite function is a function that depends on another function.

Therefore, let's solve the composite function

f(x) = x + 3

g(x) = 7x + 4

Hence,

(f + g)(x) can be solved as follows:

(f + g)(x)  = f(x) + g(x)

(f + g)(x)  = x + 3 + 7x + 4

combine like terms

(f + g)(x)  = x + 7x + 3 + 4

(f + g)(x)  = 8x + 7

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f (x) = ¹4 - 6. Find the inverse of f(x) and its domain.
O A. f¹(x) =
6 + 4, where x #-6
O B. f¹(x) =
6 +4, where x #4
O c. f¹(x) =
¹6-4, where x 4
OD. f¹(x) = 2¹6-4, where x#-6

Answers

The correct option is the first one, and the domain is the set of real numbers except for x = -6.

How to find the inverse?

The inverse will be a function such that when we take the composition we get the identity, then we can write:

[tex]f(g(x)) = \frac{1}{g(x) - 4} - 6 = x[/tex]

We need to solve that for g(x), we will get:

[tex]\frac{1}{g(x) - 4} - 6 = x\\\\\frac{1}{g(x) - 4} = x +6\\\\g(x) - 4 = \frac{1}{x + 6} \\g(x) = \frac{1}{x + 6} + 4[/tex]

That is the inverse function, and notice that if x = -6 the denominator becomes zero, so that value is not in the domain.

Then the correct option is the first one.

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Solve for x (2-3) 67

Answers

-67x

x(2-3)•67
x(-1)•67
-67x

Area The measurement of the side of a square floor tile is 10 inches, with a possible error of 1/32 inch.
(a) Use differentials to approximate the possible propagated error in computing the area of the square. (b) Approximate the percent error in computing the area of the square.

Answers

The possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.

How to calculate the error propagation?

(a) Let A be the area of the square tile. The differential of A with respect to the side length x is dA/dx = 2x.

dA ≈ (dA/dx)dx

At the lower end of the possible range for x, we have:

x = 9 31/32 inches

dx = 1/32 inch

dA = (2x)(dx) = (2(9 31/32))(1/32) = 19/32 square inches

At the upper end of the possible range for x, we have:

x = 10 1/32 inches

dx = 1/32 inch

dA = (2x)(dx) = (2(10 1/32))(1/32) = 21/32 square inches

Therefore, the possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.

(b) The percent error in computing the area of the square is given by:

(percent error) = (error / actual value) x 100

(percent error) = [(21/32 - 100) / 100] x 100% = -79/1600 x 100% ≈ -4.94%.

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A, B, and C are points of tangency in the given Circle, a m equals 6, BK equals 4 in the perimeter of mkn is 34 ​

Answers

The perimeter of triangle MKN is 34 units.

How to find the length of segment KN?

Based on the information provided, we have a circle with three points of tangency: A, B, and C. Let's consider the triangle formed by these points: MKN.

We are given that the length of AM is 6 and the length of BK is 4. We need to find the perimeter of triangle MKN.

To find the perimeter, we need to know the lengths of all three sides. However, the length of side AC is not provided.

Without additional information, we cannot determine the lengths of sides MN and KN or calculate the perimeter of triangle MKN.

Therefore, with the given information, we cannot find the perimeter of triangle MKN or provide a numerical answer

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A point in the figure is chosen at random. Find the probability that the point lies in the shaded region of the circle. ​

Answers

To find the probability that the point lies in the shaded region of the circle, we need to compare the area of the shaded region to the total area of the circle. Let's say the radius of the circle is r.

The area of the shaded region can be found by subtracting the area of the unshaded region from the total area of the circle. The unshaded region is a square with side length equal to the radius of the circle. Therefore, its area is r^2. The total area of the circle is πr^2. So the area of the shaded region is:
πr^2 - r^2 = r^2(π - 1)

Now, if we choose a point at random from the circle, any point has an equal chance of being chosen. So the probability of choosing a point in the shaded region is equal to the area of the shaded region divided by the total area of the circle:

P(shaded) = (r^2(π - 1))/πr^2 = π - 1

Therefore, the probability of choosing a point in the shaded region of the circle is π - 1.

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The length of a rectangle is 4 m more than the width. if the area of the rectangle is 77 m2. how many meters long is the width of the rectangle?






answer choices d: -11 m: 7 z: 9

Answers

The width of the rectangle is approximately 5.39 meters.

Let's denote the width of the rectangle by x. According to the problem, the length of the rectangle is 4 meters more than the width, which means that the length can be represented as x+4.

The formula for the area of a rectangle is A = length x width. In this case, we know that the area of the rectangle is 77 square meters, so we can set up the following equation:

77 = (x+4)x

Expanding the brackets, we get:

77 = x² + 4x

Rearranging this equation into standard quadratic form, we get:

x² + 4x - 77 = 0

To solve for x, we can use the quadratic formula:

[tex]x = \frac{(-b ± sqrt(b^2 - 4ac))}{ 2a}[/tex]

Plugging in the values for a, b, and c, we get:

[tex]x = \frac{(-4 ± sqrt(4^2 - 4(1)(-77)))}{ 2(1)}[/tex]

Simplifying this expression, we get:

[tex]x = \frac{(-4 ± sqrt(336)} { 2}[/tex]

[tex]x = \frac{(-4 ± 4sqrt(21))}{ 2}[/tex]

x = -2 ± 2[tex]\sqrt{(21)}[/tex]

Since the width of a rectangle cannot be negative, we discard the negative solution and get:

x = -2 ± 2[tex]\sqrt{(21)}[/tex]

Therefore, the width of the rectangle is approximately 5.39 meters (rounded to two decimal places).

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At Kennedy High School, the probability of a student playing in the band is 0. 15. The probability of a student playing in the band and playingon the football team is 0. 3. Given that a student at Kennedy plays in the band, what is the probability that they play on the football team?

Answers

In order to find the probability of a student playing on the football team given that they play in the band, we'll use conditional probability.

The formula for conditional probability is P(A|B) = P(A and B) / P(B).

In this case, A represents playing on the football team, and B represents playing in the band.

Given:
P(B) = 0.15 (probability of playing in the band)
P(A and B) = 0.03 (probability of playing in the band and on the football team)

Now we can apply the formula:

P(A|B) = P(A and B) / P(B) = 0.03 / 0.15 = 0.2

So, the probability that a student at Kennedy High School plays on the football team given that they play in the band is 0.2 or 20%.

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Fries 420 grams = $2.77
How much if its 1kg?

Answers

420 grams = 2.77
1 gram = 2.77 divided by 420= 0.007 (to 3 decimal places)
1 kilogram= 0.007 x 1000 = $6.60 (2 decimal places)

Answer: $6.60 (i think)

(not too sure, so sorry if i’m wrong!!!!!!)

What are two different ways you can solve 2(x – 3) = 8?

Answers

Answer:

There are three methods used to solve systems of equations: graphing, substitution, and elimination.

Step-by-step explanation:

A regular hexagon is shown. What is the measure of the radius, c, rounded to the nearest inch? use the appropriate trigonometric ratio to solve. 6 in. 10 in. 14 in. 24 in.

Answers

The measure of the radius of the hexagon rounded to the nearest inch is 14 inches.

The problem presents a hexagon with a central angle of 60º, and the task is to calculate its radius. To do so, we can use the trigonometric relationship between the radius, apothem, and an angle. The apothem is a line segment from the center of a polygon perpendicular to one of its sides. For a regular hexagon, the apothem length is equal to the radius, which we want to find.

The trigonometric relationship for this case is cos(30) = a/c, where a is the apothem and c is the radius. By rearranging the equation to solve for c, we get c = a/cos(30).

Substituting the value of 12 inches for the apothem, we get c = 12/cos(30). Using a calculator, we can find that cos(30) = 0.866, so c = 12/0.866 = 13.855 inches.

To round to the nearest whole number, we get c = 14 inches.

Correct Question :

A regular hexagon is shown. What is the measure of the radius, c, rounded to the nearest inch? use the appropriate trigonometric ratio to solve. 6 in. 10 in. 14 in. 24 in.

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1. What is the volume of the sphere?
4

Answers

The volume of the given sphere having radius of 4 units is 267.94 units³.

Given the radius of the sphere (r) = 4 units

To find the volume of the given sphere, we have to substitute the radius in the below volume formula of the sphere,

the volume of the sphere = 4/3 * π * r³

the volume of the given sphere = 4/3 * 3.14 * (4)³        

[π  is approximately equal to 3.14]

the volume of the given sphere = 267.94 units³

So from the above analysis, we can conclude that the volume of the sphere having 4 units radius is 267.94 units³.

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Given question is not having complete information, the complete question is written below:

What is the volume of the sphere having 4 units radius?

A mover notes the weights of a table and 4 chairs and records t+4C >_100 on his invoice. What is he communicating?


The choices are,


A. The table and 4 chairs each weigh more than 100 pounds.


B. The table and 4 chairs weigh at most 100 pounds.


C. The table and 4 chairs weigh around 100 pounds, give or take a little.


D. The table and 4 chairs at


least 100 pounds

Answers

The mover is communicating that the weight of the table and 4 chairs combined, represented as t+4C, is greater than or equal to 100 pounds.

The expression t+4C represents the total weight of the table and 4 chairs. The mover's invoice states that this total weight is greater than or equal to 100 pounds, which means that the combined weight of the table and chairs is at least 100 pounds. Therefore, the correct answer is D, "The table and 4 chairs weigh at least 100 pounds."

To solve this mathematically, we can use algebraic inequalities. The inequality t+4C >_ 100 can be rearranged as t >_ 100-4C. This means that the weight of the table t must be greater than or equal to 100 minus four times the weight of a single chair C.

If each chair weighs less than 25 pounds, then the total weight of the table and 4 chairs combined will be at least 100 pounds. So D is correct answer.

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"When a contractor paints a square surface that has a side length of x feet, he needs to know the area of the surface in order to buy the correct amount of paint. Since the contractor always adds 25 square feet to the area, he buys extra paint. Which function can be used to find the totall area in square feet, Ax , that the contractor will use to determine how much paint he needs to buy?

Answers

The function that can be used to find the total area is: (x^2 + 25) sq. ft.

What is a square?

A square is a type of quadrilateral which has an equal length of sides. So then its area can be calculated as;

area of a square = length x length

We have from the question that; a square surface that has a side length of x feet. So that;

area of the square surface = length * length

                                            = x * x

                                            = x^2 square feet

But since the contractor always adds 25 square feet to the area, he buys extra paint, then the function required is:

total area = (x^2 + 25) sq. ft.

The function is (x^2 + 25) sq. ft.

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Answer:

A(x) = x² + 25

----------------------

In order to find the total area, we need to consider both the area of the square surface and the extra paint he always adds.

Find the area of the square surface:

A = x² (since the side length is x feet)

Add the extra 25 square feet of paint:

A(x) = A + 25

Combining these steps, the function is:

A(x) = x² + 25

Patricia bought 4 apples and 9 bananas for $12. 70. Jose bought 8 apples and 11 bananas for $17. 70 at the same grocery store. What's the price of one apple?

Answers

the price of one apple after solving the simultaneous equations is $1.45.

Let's denote the price of one apple by "a" and the price of one banana by "b". We can then set up a system of two equations to represent the given information:

4a + 9b = 12.70 (equation 1)
8a + 11b = 17.70 (equation 2)

To solve for the price of one apple, we want to isolate "a" in one of the equations. One way to do this is to multiply equation 1 by 8 and equation 2 by -4, which will allow us to eliminate "b" when we add the two equations together:

(8)(4a + 9b) = (8)(12.70) --> 32a + 72b = 101.60 (equation 3)
(-4)(8a + 11b) = (-4)(17.70) --> -32a - 44b = -70.80 (equation 4)

Adding equations 3 and 4 gives:

28b = 30.80

Solving for "b" yields:

b = 1.10

Substituting this value of "b" into equation 1 gives:

4a + 9(1.10) = 12.70

Solving for "a" yields:

a = 1.45

Therefore, the price of one apple is $1.45.

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A pathway made of slate tiles measures​ 5 1/3 ​yards long. A tile measuring ​2​ feet is added to the end of the pathway.

What is the total length of the pathway now?

1. 5 1/3 ft

2. 10 2/3 ft

3. 18 ft

4. 22 ft

Answers

Answer:

18 feet

Step-by-step explanation:

multiply 5 1/3 yards by 3 to find the measurement in feet.

16/3 x 3 = 16

16 + 2 = 18

Helping in the name of Jesus.

the answer to this question is (c)18 feet


Solve for x. Round to the nearest hundredth if necessary.
X
24°
14

Answers

Step-by-step explanation:

there is no explanation about x so wierd

Imagine that the price per gallon of gas with a $7 car wash is $3. 19 and the price without the car wash is $3. 39. When is it worth it to buy the car wash? When is it worth it if the car wash costs $2?

Answers

If we plan to buy more than 10 gallons of gas, it is worth it to buy the car wash, assuming that the cost of the car wash is $2.

The car wash costs $7, and the price per gallon of gas with the car wash is $3.19, while the price per gallon of gas without the car wash is $3.39. Let's assume that we buy x gallons of gas, then the total cost of buying gas with the car wash would be:

Total cost with car wash = 7 + 3.19x

The total cost of buying gas without the car wash would be:

Total cost without car wash = 3.39x

To determine when it is worth it to buy the car wash, we need to find when the total cost with the car wash is less than the total cost without the car wash:

7 + 3.19x < 3.39x

Solving for x:

7 < 0.2x

x > 35

This means that if we plan to buy more than 35 gallons of gas, it is worth it to buy the car wash.

Now, let's consider the scenario where the car wash costs $2. The total cost of buying gas with the car wash would be:

Total cost with car wash = 2 + 3.19x

To determine when it is worth it to buy the car wash in this scenario, we need to find when the total cost with the car wash is less than the total cost without the car wash:

2 + 3.19x < 3.39x

Solving for x:

2 < 0.2x

x > 10

This means that if we plan to buy more than 10 gallons of gas, it is worth it to buy the car wash, assuming that the cost of the car wash is $2.

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Data-Safe Company leases online data storage
space. A customer can store up to 750
gigabytes of computer files for an annual fee of
$19.95. If the number of gigabytes exceeds 750,
then the equation c=0.05(g - 750) + 19.95
determines the annual cost, c. in dollars in terms
of g, the total number of gigabytes of data
stored. Which statement best describes this
information?

Answers

The statement that best describes the information is:

-If the total number of gigabytes stored exceeds 750, then each gigabyte beyond 750 costs 5 cents.

How to make the correct statement based on the information

This is because the equation c = 0.05(g - 750) + 19.95 applies only when the number of gigabytes (g) exceeds 750. For every gigabyte over 750, an additional 5 cents is charged, while the base cost of $19.95 is for the first 750 gigabytes of storage.

If the customer needs to store more than 750 gigabytes, the annual cost is determined by the equation c = 0.0 ,5(g - 750) + 19.95, where c is the annual cost in dollars, and g is the total number of gigabytes of data stored

The statement that best describes this information is:

The Data-Safe Company offers online data storage services with an annual fee of ,$19.95 for up to 750 gigabytes of storage. If a customer requires more than 750 gigabytes of storage,. an additional fee of $0.05 per gigabyte is charged for the excess storage beyond the initial 750 gigabytes.

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Complete question

Data-Safe Company leases online data storage

space. A customer can store up to 750

gigabytes of computer files for an annual fee of

$19.95. If the number of gigabytes exceeds 750,

then the equation c=0.05(g - 750) + 19.95

determines the annual cost, c. in dollars in terms

of g, the total number of gigabytes of data

stored. Which statement best describes this

information?

-If the total number of gigabytes stored is

more than 750, then every gigabyte stored

costs 5 cents.

-If the total number of gigabytes stored

exceeds 750, then each gigabyte beyond

750 costs 5 cents.

B

-The first 750 gigabytes stored costs 5 cents

each, after which there is an additional cost

of $19.95

-Every gigabyte of data stored costs 5 cents

no matter how many gigabytes are stored.

Which one is it please help thank you.


The students who attend Memorial High School have a wide variety of extra-curricular activities to choose from in the after-school program. Students are 38% likely to join the dance team; 18% likely to participate in the school play; 42% likely to join the yearbook club; and 64% likely to join the marching band. Many students choose to participate in multiple activities. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors. If Event A = sophomore or junior, what is Event A'?

Answers

Event A' has a probability of 50% (25% for freshmen + 25% for seniors).

To determine Event A', we need to first identify what Event A represents. Event A is the probability that a student is a sophomore or junior. Since students have equal probabilities of being freshmen, sophomores, juniors, or seniors, the probability of Event A is 50% (25% for sophomores + 25% for juniors).
Event A' is the complement of Event A, which means it includes the other two grade levels not included in Event A, in this case, freshmen and seniors. Therefore, Event A' is the probability that a student is a freshman or a senior. Since students have equal probabilities of being in each grade level, Event A' also has a probability of 50% (25% for freshmen + 25% for seniors).

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A bag has 6 red marbles, 3 blue marbles, and 1 orange marble. In a game to raise money for a class trip, parents pay $5 and pull a marble randomly from the bag. The payout is $10 for pulling an orange marble, $4 for a blue marble, and $1 for a red marble. How much can the class expect to earn per game?

Answers

There are 6 red marbles.
There are 3 blue marbles.
There is 1 orange marble.

To pull a marble from the bag you have to pay $5.

Payout for an orange marble is $10.
Payout for a blue marble is $4.
Payout for a red marble is $1.


Total amount of marbles= 6+3+1
=10.

Multiply the amount of marbles by the amount required to pull a marble
$5^10=$50


Multiply the amount of marbles for each color by the payout.

Red Marbles: 6^1=6
Blue Marbles: 3^4=12
Orange Marbles: 1^10=10

Add the total
$6+$12+$10=$28

Subtract from the $28 from the $50
28-50=22

Therefore, the class can expect to earn approximately $22 per game

If 3r/c=126 what is the value of r/2c

please i have no idea what the hecc is going on.

Answers

Examining the expression the value of r/2c is

21

How to find  r/2c

We can use algebra to calculate the value of r/2c with 3r/c as the variable.

First, let's reduce the expression 3r / c = 126 by multiplying both sides by c / 3:

3r/c * c/3 = 126 * c/3

r/1 = 42c

Now we can obtain r / 2c by dividing both sides by 2c:

solving for the left hand side of the equation

r /2c = (r/1)/(2c)

solving for the right hand side of the equation

42c = (42c)/(2c) = 21

Equation the left hand side to the right hand side of the equation

r/2c = 21

Therefore, r/2c = 21.

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Find the slope of the points (-10, -52)
and (-70, -32)

Answers

Answer:

Slope= -1/3

Step-by-step explanation:

The slope is found using (y₂ - y₁) / (x₂ - x₁)

(y₂ - y₁)

So let's do the numerator first with the y. -52-(-32). The two negative signs  make 32 positive so -52 + 32= -20

(x₂ - x₁)

Now the denominator, x. -10-(-70). Same thing here, the two negative signs  make 70 positive so -10 + 70 = 60

(y₂ - y₁) / (x₂ - x₁)

Now put them together so -20/60 which equals -1/3 which the slope

evaluate the integral tan inverse v(x+2 ) dx by making substitution
and then table of integrals

Answers

To evaluate the integral of tan inverse v(x+2) dx, we need to make a substitution. Let u = x + 2, then du/dx = 1 and dx= du. Therefore, the final answer is: ∫ tan inverse v(x+2) dx = (x+2) tan inverse v(x+2) - tan inverse v(x+2) / v'(x+2) + C

Substituting this back into the integral, we get:
∫ tan inverse v(x+2) dx = ∫ tan inverse v(u) du
Using the formula from the table of integrals, we have:
∫ tan inverse v(u) du = u tan inverse v(u) - ∫ u / (1 + v(u)^2) du
Substituting back u = x + 2, we get:
∫ tan inverse v(x+2) dx = (x+2) tan inverse v(x+2) - ∫ (x+2) / (1 + v(x+2)^2) dx
Now, we can use another substitution, let t = v(x+2), then dt/dx = v'(x+2) and dx = dt / v'(x+2).
Substituting this back into the integral, we get:
∫ (x+2) / (1 + v(x+2)^2) dx = ∫ (x+2) / (1 + t^2) dt / v'(x+2)
Using the formula from the table of integrals, we have:
∫ (x+2) / (1 + t^2) dt = tan inverse t + C
where C is the constant of integration.
Substituting back t = v(x+2), we get:
∫ (x+2) / (1 + v(x+2)^2) dx = tan inverse v(x+2) / v'(x+2) + C
Therefore, the final answer is:
∫ tan inverse v(x+2) dx = (x+2) tan inverse v(x+2) - tan inverse v(x+2) / v'(x+2) + C
where C is the constant of integration.


To evaluate the integral of tan inverse v(x+2) dx using substitution, we'll first make a substitution:
Let u = x+2. Then, du = dx.
Now, we can rewrite the integral as:
∫tan^(-1)(v(u)) du
Next, we'll look up the integral of tan^(-1)(v(u)) in a table of integrals. Unfortunately, there isn't a direct formula for this specific integral. However, we can use integration by parts to proceed further.
Let I = ∫tan^(-1)(v(u)) du. Let's choose:
f(u) = tan^(-1)(v(u)) and df(u) = du,
g'(u) = 1 and dg(u) = u du.
Using integration by parts formula:
I = f(u)g(u) - ∫g(u)df(u)
I = u*tan^(-1)(v(u)) - ∫u(1/(1+v^2(u))) du
Now, we'll need to substitute back x+2 for u:
I = (x+2)*tan^(-1)(v(x+2)) - ∫(x+2)(1/(1+v^2(x+2))) dx
This integral doesn't have a simple closed-form solution, so the final answer will remain in the form shown above.

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Area of this shape irregular polygon the high is 4 and width 13


:)

Answers

The area of this irregular polygon is 344.5 square units.

To find the area of an irregular polygon, you can divide it into smaller, simpler shapes.

In this case, we can divide the polygon into a rectangle and a right triangle.

The rectangle has a height of 4 and a width of 13, so its area is 4 x 13 = 52 square units.

The right triangle has a base of 13 and a height of (110 - 4 x 13) / 2 = 45, since the total height of the polygon is 110.

Therefore, the area of the right triangle is (1/2) x base x height = (1/2) x 13 x 45 = 292.5 square units.

Adding the areas of the rectangle and the triangle, we get a total area of 52 + 292.5 = 344.5 square units.

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For evrey 500g of reactants, 3. 1 g of catalyst were required. How much catalyst was required for 900g of reactants

Answers

5.58g of catalyst is required for 900g of reactants.

How much catalyst for 900g reactants?

If 500g of reactants require 3.1g of catalyst, then for 900g of reactants, we can use the following proportion:

500g reactants / 3.1g catalyst = 900g reactants / x

Where x is the amount of catalyst required for 900g of reactants.

To solve for x, we can cross-multiply:

500g reactants * x = 3.1g catalyst * 900g reactants

Then, we can divide both sides by 500g reactants to isolate x:

x = (3.1g catalyst * 900g reactants) / 500g reactants

Simplifying this expression gives:

x = 5.58g catalyst

Therefore, 5.58g of catalyst is required for 900g of reactants.

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The volume of a pyramid is 51 cubic centimeters. The area of the base is 17 square centimeters What is its height?

Answers

To solve for the height of the pyramid, we need to use the formula for the volume of a pyramid, which is V = (1/3)Bh, where V is the volume, B is the area of the base, and h is the height. We are given that the volume is 51 cubic centimeters and the area of the base is 17 square centimeters, so we can substitute these values into the formula and solve for h.

51 = (1/3)(17)(h)

To solve for h, we can first simplify the right side of the equation:

51 = (17h)/3

Then, we can multiply both sides of the equation by 3 to isolate h:

153 = 17h

Finally, we can divide both sides of the equation by 17 to solve for h:

h = 9

Therefore, the height of the pyramid is 9 centimeters.
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