You are at a fruit stand to get some fresh produce. You notice that the person in front of you gets 5
apples and 4 pears for 10 dollars. You get 5 apples and 5 pears for 11 dollars. Write a system of
equations that could be used to find the price of an apple and the price of a pear.

Answer:

Step-by-step explanation:

AE is 9. ED is 6. The triangle ABE is proportional to ACD, so their sides are proportional. For example, AE:ED = AB:BC. So, ED/AE = 2/3 = BC/AB. This gives us 2/3 = x/10, which gives us x=6.6667

Answer

0= -5

Step-by-step explanation:

6(n) = 6(n-1)+1

6n = 6n - 6 +1

0= -5

(i don't know if this is correct very sorry!!)

Answer:

85°C

Step-by-step explanation:

F = 185

Substitute the value of F in the formula.

C = \(\frac{5}{9}\) × (185 - 32)

C = \(\frac{5}{9}\) × 153

C = 85

∴ 185°F = 85°C

=============================================================

Explanation:

The order of the letters in ABC and FED is important. This is because AB pairs with FE. Note how AB is the first two letters of ABC, and FE is the first two letters of FED.

Divide the lengths of FE over AB to get the scale factor:

FE/AB = 20/15 = 4/3

Or you could pick on BC and ED (both are the last two letters of ABC and FED respectively) to get

ED/BC = 8/6 = 4/3

Finally, you could also say

FD/AC = 16/12 = 4/3

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

In short, we could have any of the following:

Therefore, the scale factor is 4/3

Because 4/3 = 1.33 (approx) is larger than 1, this means the image triangle FED is larger than the preimage triangle ABC.

African penguins are about 60.96 centimeters tall.

By dividing the centimeter height of an emperor penguin by 2/3, we can calculate the height of an African penguin:

91.44 centimeters × 2/3 = 60.96 centimeters

A person or anything can be measured from head to toe or from the bottom up by their height. In other words, a person's height indicates how tall they are. We may assess how much taller we get as we age. We frequently contrast the average heights of men and women in various nations.

Height is a mathematical term that refers to the vertical distance between an object's top and base. On occasion, it has the designation "altitude".

In coordinate geometry, an object's height is calculated along the y-axis and is referred to as height.

from the question:

We can calculate the height of African penguins by multiplying the height of emperor penguins by 2/3 if they are around 2/3 the height of emperor penguins.

To make the computation simpler, let's first convert the height of emperor penguins from inches to another unit, such as cm. We know that 2.54 centimeters make up 1 inch, so:

36 inches × 2.54 centimeters/inch = 91.44 centimeters

So we may calculate the height of African penguins by dividing the centimeter height of emperor penguins by two-thirds:

2/3 of 91.44 cm is 60.96 centimeters.

African penguins are thus 60.96 cm tall on average.

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Answer:

The person above me is right, it is 0.3 or 1/3

Step-by-step explanation:

The equation of the perpendicular line is x = 2.

The equation of the given line is y = -3. We have to find the equation of the line that is perpendicular to this line, and it passes through the coordinates (2, 6).

The general equation of a straight line is given below :

y = mx + c

The slope of the line is "m" and the y-intercept is "c".

Compare the equation of the given line. We find that the slope of the given line is zero. So, the slope of the perpendicular should be infinite or not defined.

The equation of the required line is given below :

x = c

The line passes through the point (2, 6).

2 = c

Thus, the equation of the line is x = 2.

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Answer:

( 3, 7)

Step-by-step explanation:

x= 3 Y = 7. The origin is (0, 0)

Given that AC is a diameter of the circle, we can conclude that triangle ABC is a right triangle, with AC being the hypotenuse. The area of the circle is not directly related to finding the lengths of BC or AB, so we will focus on the given information: AB = 16 units.

Using the Pythagorean theorem, we can find BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC):

AC² = AB² + BC²

Substituting the given values, we have:

(AC)² = (AB)² + (BC)²

(AC)² = 16² + (BC)²

(AC)² = 256 + (BC)²

Now, we need to find the length of AC. Since AC is a diameter of the circle, the length of AC is equal to twice the radius of the circle.

AC = 2 * radius

To find the radius, we can use the formula for the area of a circle:

Area = π * radius²

Given that the area of the circle is 2897 units², we can solve for the radius:

2897 = π * radius²

radius² = 2897 / π

radius = √(2897 / π)

Now we have the length of AC, which is equal to twice the radius. We can substitute this value into the equation:

(2 * radius)² = 256 + (BC)²

4 * radius² = 256 + (BC)²

Substituting the value of radius, we have:

4 * (√(2897 / π))² = 256 + (BC)²

4 * (2897 / π) = 256 + (BC)²

Simplifying the equation gives:

(4 * 2897) / π = 256 + (BC)²

BC² = (4 * 2897) / π - 256

Now we can solve for BC by taking the square root of both sides:

BC = √((4 * 2897) / π - 256)

To find the measure of angle BC (mBC), we know that triangle ABC is a right triangle, so angle B will be 90 degrees.

In summary:

BC = √((4 * 2897) / π - 256)

mBC = 90 degrees

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in a large population, 68 % of the people have been vaccinated. if 3 people are randomly selected, 0.968 is the probability that at least one of them has been vaccinated.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. In addition to being represented as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.

The probability is a measure of how likely an event is to occur. It gauges the event's degree of certainty. P(E) = Number of Favorable Outcomes/Number of All Outcomes is the formula for probability.

Given that,

In a large population, 68% of the people have been vaccinated.

Among them 3 people are randomly selected.

probability that at least one of them is vaccinated:

= 1 - P (none of the 3 has been vaccinated)

= 1 - (1 - 0.68)³

=0.968

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Step-by-step explanation:

P(rain and flight delayed) = P(rain) x P(flight delayed) = 0.07 x 0.19

= 0.013 (nearest thousandth)

Answer: 0.01

Step-by-step explanation:

the person above did it wrong, this answer is for sure correct.

Answer:

4132 I think

Step-by-step explanation:

icorrect me if I'm wrong lol

Given that the correlation between two variables is r=0.23. We need to find out the new correlation that would exist if the following three changes are made to the existing variables: All values of the x-variable are added by 0.14. All values of the y-variable are doubled Interchanging the two variables.  the correct option is B. 0.37.

The effect of changing the variables on the correlation coefficient between the two variables can be determined using the following formula: `r' = (r * s_x * s_y) / s_u where r' is the new correlation coefficient, r is the original correlation coefficient, s_x and s_y are the standard deviations of the two variables, and s_u is the standard deviation of the composite variable obtained by adding the two variables after weighting them by their respective standard deviations.

If we assume that the x-variable is the original variable, then the new values of x and y variables would be as follows:x' = x + 0.14 (since all values of the x-variable are added by 0.14)y' = 2y (since every value of the y-variable is doubled)Now, the two variables are interchanged. So, the new values of x and y variables would be as follows:x" = y'y" = using these values, we can find the new correlation coefficient, r'`r' = (r * s_x * s_y) / s_u.

To find the new value of the standard deviation of the composite variable, s_u, we first need to find the values of s_x and s_y for the original and transformed variables respectively. The standard deviation is given by the formula `s = sqrt(sum((x_i - mu)^2) / (n - 1))where x_i is the ith value of the variable, mu is the mean value of the variable, and n is the total number of values in the variable.

For the original variables, we have:r = 0.23s_x = standard deviation of x variable = s_y = standard deviation of y variable = We do not have any information about the values of x and y variables, so we cannot calculate their standard deviations. For the transformed variables, we have:x' = x + 0.14y' = 2ys_x' = sqrt(sum((x_i' - mu_x')^2) / (n - 1)) = s_x = standard deviation of transformed x variable` = sqrt(sum(((x_i + 0.14) - mu_x')^2) / (n - 1)) = s_x'y' = 2ys_y' = sqrt(sum((y_i' - mu_y')^2) / (n - 1)) = 2s_y = standard deviation of transformed y variable` = sqrt(sum((2y_i - mu_y')^2) / (n - 1)) = 2s_yNow, we can substitute all the values in the formula for the new correlation coefficient and simplify:

r' = (r * s_x * s_y) / s_ur' = (0.23 * s_x' * s_y') / sqrt(s_x'^2 + s_y'^2)r' = (0.23 * s_x * 2s_y) / sqrt((s_x^2 + 2 * 0.14 * s_x + 0.14^2) + (4 * s_y^2))r' = (0.46 * s_x * s_y) / sqrt(s_x^2 + 0.0396 + 4 * s_y^2)Now, we can substitute the value of s_x = s_y = in the above formula:r' = (0.46 * * ) / sqrt( + 0.0396 + 4 * )r' = (0.46 * ) / sqrt( + 0.1584 + )r' = (0.46 * ) / sqrt(r' = (0.46 * ) / sqrt(r' = (0.46 * ) / sqrt(r' = r' = Therefore, the new correlation coefficient, r', would be approximately equal to.

Hence, the correct option is B. 0.37.

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According to the question The height of the cone that can be created by rolling one of the congruent sectors is approximately 6.32 cm.

To find the height of the cone that can be created by rolling one of the congruent sectors of the circular sheet, we need to calculate the circumference of the base of the cone.

The circumference of the base is equal to the length of the sector's arc, which can be calculated using the formula:

\(\[ \text{Arc Length} = \left(\frac{\text{Central Angle}}{360^\circ}\right) \times \text{Circumference of the Circle} \]\)

Since the sector is one-third of the circle, the central angle of the sector is  \(\( 120^\circ \) (\( \frac{360^\circ}{3} \)).\)

The circumference of the circle is given by the formula:

\(\[ \text{Circumference} = 2 \pi \times \text{radius} \]\)

Substituting the values, we have:

\(\[ \text{Circumference} = 2 \pi \times 6 \, \text{cm} = 12\pi \, \text{cm} \]\)

Now, we can calculate the arc length:

\(\[ \text{Arc Length} = \left(\frac{120^\circ}{360^\circ}\right) \times 12\pi \, \text{cm} = 4\pi \, \text{cm} \]\)

When the sector is rolled to form a cone, the arc length becomes the circumference of the base of the cone.

The circumference of the base of the cone is also equal to \(\( 2\pi \times \text{radius of the cone} \).\)

Therefore, we can equate the two circumferences and solve for the radius of the cone:

\(\[ 2\pi \times \text{radius of the cone} = 4\pi \, \text{cm} \]\)

Dividing both sides by \(\( 2\pi \)\), we find:

\(\[ \text{Radius of the cone} = 2 \, \text{cm} \]\)

Now, the height of the cone can be calculated using the Pythagorean theorem:

\(\[ \text{height}^2 = (\text{radius of the cone})^2 + (\text{radius of the base})^2 \]\)

\(\[ \text{height}^2 = 2^2 + 6^2 = 4 + 36 = 40 \]\)

Taking the square root of both sides, we get:

\(\[ \text{height} \approx \sqrt{40} \approx 6.32 \, \text{cm} \]\)

Therefore, the height of the cone that can be created by rolling one of the congruent sectors is approximately 6.32 cm.

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Answer:

The answers would be:
7) y=-0.5x+2
8) y=-0.5x+2
9) y=0.6x-2
10) y=6x-4

Step-by-step explanation:

Answer:

h = V/B

Step-by-step explanation:

\(\sf V \div B = h\\Reverse\\h = V \div B\)

Answer:

D. h = V/B

Step-by-step explanation:

"Solve...for h" means get h all by itself on one side of the equation.

V = Bh

Divide both sides by B.

V/B = h

Turn it around and you can see the answer in the choices. D. h = V/B is the correct answer.

Answer:the answer is a

Step-by-step explanation:

△ABC is cοngruent tο bοth △ACD and △CBD.

Geοmetry depends οn shapes like squares, circles, rectangles, triangles, and οthers. Amοng all the fοrms we have here, triangles seem tο be the mοst intriguing and distinctive. The triangle's shape is created by the intersectiοn οf three lines and three angles.

△ABC is a right triangle, right angled at C.

CD is altitude drawn tο hypοthesis AB.

Tο prοve, △ACD ~ △CBD

In △ACD and △CBD.

∠ACB= ∠ADC=90°  

∠CAB=∠DAC (Cοmmοn angle)

By AA similarity we can say that, △ACD and △CBD.

Anοther side,

Need tο prοοf ∣AC∣²+∣BC∣²=∣A B∣²

If  is a right triangle at C with a prοjectiοn tο  as shοwn, then

BC²=BD*AB

AC²= AD*AB

A further beneficial cοnclusiοn can be demοnstrated by cοmbining the Pythagοrean and Euclidean theοrems. The Pythagοrean Theοrem prοvides us with

CD²= BC²-BD²

By putting the value οf BC²,

CD²= BD*AB-BD²

OR, CD²= BD*(AB-BD)

OR, CD²= BD*AD

AB²= (AD*AB)+(BD*AB)

Or, AB(AD+BD)=AB²

Or, AB²=AB²

Or, ∣AC∣²+∣BC∣²=∣A B∣² (prοved)

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The total electric potential at point a is the sum of the electric potentials due to q1 and q2 is 0, the total electric potential at point b is the sum of the electric potentials due to q1 and q2 is 84.5 and the work done on q3 by the electric forces exerted by q1 and q2 is -0.42 J.

The electric potential at point a due to q1 and q2 can be calculated using the formula for electric potential due to a point charge,

V=kq/r, where k=9×10^9 N.

m²/C² is the Coulomb constant,

q is the point charge,

and r is the distance from the point charge to the point where the potential is being measured.

Using this formula, the electric potential due to q1 at point a is:

V1=kq1/r1

where q1=+2.00μC is the charge on q1 and r1 is the distance from q1 to point a.

Since q1 is at one of the corners of the square and a is at the center, the distance r1 is half the length of the diagonal of the square:

r1=√(12+12)=0.75 cm

Substituting the values in the formula, we get:

V1 = 9×10^9×2.00×10^-6/0.75×10^-2V1

     = 240 V

The electric potential due to q2 at point a can be calculated similarly.

Since q2 is at the opposite corner of the square, the distance r2 is the length of a side of the square:

r2=1.50 cm

Substituting the values in the formula, we get:

V2 = 9×10^9×(-2.00)×10^-6/1.50×10^-2V2

     = -240 V

The total electric potential at point a is the sum of the electric potentials due to q1 and q2:

V = V1+V2V=240 - 240V

   = 0

Since point b is at the empty corner closest to q2, the electric potential at point b due to q2 is zero.

The electric potential at point b due to q1 can be calculated using the same formula we used for point a:

V1=kq1/r1

where q1=+2.00μC is the charge on q1 and r1 is the distance from q1 to point b.

Since q1 is at one of the corners of the square and b is at the opposite corner, the distance r1 is the length of a diagonal of the square:

r1=√(1.5²+1.5²)=2.12 cm

Substituting the values in the formula, we get:

V1 = 9×10^9×2.00×10^-6/2.12×10^-2V1

     = 84.5 V

The total electric potential at point b is the sum of the electric potentials due to q1 and q2:

V = V1+V2V

   = 84.5 + 0V

    = 84.5 V

The electric force exerted on a point charge by another point charge is given by Coulomb's law:

F=kq1q2/r²

where F is the force,

           q1 and q2 are the point charges,

           r is the distance between the charges,

           and k is the Coulomb constant.

Since q3 is negatively charged, it will experience a force in the direction opposite to the force experienced by a positive charge at the same location.

Thus, the total work done by the electric forces exerted by q1 and q2 on q3 can be calculated as the negative of the change in electric potential energy of q3 from point a to point b:

W=-ΔPE

where ΔPE is the change in potential energy of q3 from point a to point b.

Substituting the values, we get:

W=-q3(Vb - Va)

where q3=-5.00μC is the charge on q3,

           Va=0 is the electric potential at point a,

            and Vb=84.5 V is

the electric potential at point b:

W = -5.00×10^-6(84.5 - 0)W

   = -0.42 J

Therefore, the work done on q3 by the electric forces exerted by q1 and q2 is -0.42 J.

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The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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Answer:

The given figure is:

a. Polyhedron

c. prism

d. solid

Step-by-step explanation:

First of all, let us consider the given image.

It is a 3 dimensional figure.

It has 2 equal bases which are pentagonal.

Its faces are made along the sides of the bases and are rectangular in shape.

Now, let us classify the given image in following:

a. Polyhedron:

A polyhedron is a 3-D (three dimensional) shape in which there are flat faces.

The faces can be of 'n' number of edges (Polygonal faces).

Its edges are straight, has sharp corners which are also known as vertices.

The given image is a polyhedron as per above definition.

b. Pyramid:

It is also a 3D shape which can have a polygonal base and its faces are triangular which converge on the top to one point.

The given image does not converge to a point on the top, so not a pyramid.

c. Prism:

It is a 3D shape which has it two bases as polygonal structure.

The two bases are equal in shape and size.

There are faces on the body of prism which are formed by joining the edges of the bases.

The given image is a prism with pentagonal bases.

d. Solid:

Any 3D image is called a solid and has a length, width and height.

So, the given image is a Solid.

e. Cube:

Cube is a 3D figure, which has all its faces in square shape.

All the sides are equal for a cube.

The given image is not a cube.

f. Polygon:

A polygon is a closed figure in 2 dimensions which has n number of sides.

The given image is not a polygon.

Answer: The given figure is:

a. Polyhedron

c. prism

d. solid

The given figure is a Polyhedron, prism and solid.

A polyhedron is a three-dimensional geometry having plane surfaces connected together with sharp edges and pointed vertices.

First of all, let us consider the given image. It is a 3-dimensional figure. It has 2 equal bases which are pentagonal. Its faces are made along the sides of the bases and are rectangular in shape.

Now, let us classify the given image in the following:

a. Polyhedron:

A polyhedron is a 3-D (three dimensional) shape in which there are flat faces. The faces can be of 'n' number of edges (Polygonal faces). Its edges are straight, has sharp corners which are also known as vertices. The given image is a polyhedron as per the above definition.

c. Prism:

It is a 3D shape which has it two bases as a polygonal structure.The two bases are equal in shape and size. There are faces on the body of prism which are formed by joining the edges of the bases. The given image is a prism with pentagonal bases.

d. Solid:

Any 3D image is called a solid and has a length, width and height. So, the given image is a Solid.

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Answer:

6

Step-by-step explanation:

you needed to make a graph and then find the (-1,-1) and then move two spaces to the right and then seven up and you get (6,1)

hope this helped

Answer:

After 2 1/3 hours.

Step-by-step explanation:

For this you have to calculate how much hours is 1/3 of 7 hours. The word 'of' implies a multiplication function.

1/3 * 7 = 7/3 = 2 1/3

Answer:

Kate is 3 years old, Jane is 9 years old

Step-by-step explanation:

1.) First, assign variables to all of their ages. If we say Kate's age is x, Jane's age is 3 times this, which can be written as j, is 3x.

2.) Jane's age is also 2 less than twice of Kate's in 5 years. This means that her age is also 2(x+5) - 2 = j + 5. With a little simplification, you get that 2x + 8 = j + 5.

3.) Since j, Jane's age, is also 3x, we can substitute 3x in for j in the second equation. If you do this, you get 2x + 8 = 3x + 5.

4.) By moving the x onto one side and the numbers onto another, you get x = 3. X was Kate's age, meaning that Kate is 3 years old.

5.) Finally, since Jane's age is 3 times Kate's age, Jane's age is 3 * 3, which is 9. Jane is 9 years old.

Jane is 9 years old and Kate is 3 years old.To solve the problem, let's first establish variables for Jane and Kate's ages.

Let J represent Jane's age and K represent Kate's age.
According to the student question, Jane is 3 times as old as Kate, which can be represented as:
J = 3K
In 5 years, Jane's age will be 2 less than twice Kate's age, which can be represented as:
J + 5 = 2(K + 5) - 2
Now we can solve the equations step by step:

Substitute the first equation into the second equation to eliminate one of the variables:
3K + 5 = 2(K + 5) - 2
Distribute the 2 on the right side of the equation:
3K + 5 = 2K + 10 - 2
Simplify the equation by combining like terms:
3K + 5 = 2K + 8
Move the 2K term to the left side of the equation:
K = 3
now we know that Kate is currently 3 years old.
Substitute K's value back into the first equation to find Jane's age:
J = 3K
J = 3(3)
Simplify to find Jane's age:
J = 9
So, Jane is currently 9 years old.
Jane is 9 years old and Kate is 3 years old.

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Answer:

4096

Step-by-step explanation:

Hey there!!!!

8  raised to the power of 4 = \(8^{4}\)

\(8^{4}\) = 8*8*8*8

if we multiply:

8*8=16

16*8= 128

128*8 = 4096

hope this helps :)

The ratio of the height to the diameter that maximizes the volume of the cylindrical can is: 0.886 approximately.

Let the radius of the cylindrical can be denoted by r, and its height by h. The surface area of the can is given by:

S = 2π\(r^2\)+ 2πrh

Simplifying this expression, we get:

h = (S - 2π\(r^2\))/(2πr)

The volume of the cylindrical can is given by:

V = π\(r^2\)h

Substituting the expression for h obtained earlier, we get:

V = π\(r^2\)(S - 2π\(r^2\))/(2πr)

Simplifying this expression, we get:

V = (S/2π - \(r^2\))πr

To maximize the volume of the cylindrical can, we need to find the value of r that maximizes the above expression. We can do this by differentiating the expression with respect to r, setting it equal to zero, and solving for r:

dV/dr = (S/2π - \(2r^2\))π = 0

Solving for r, we get:

r = √(S/4π)

Substituting this value of r back into the expression for h, we get:

h = (S - 4π\(r^2\))/(4πr) = (S - S/2)/(2√(S/4π)) = √(Sπ)/2

Therefore, the ratio of the height to the diameter that maximizes the volume of the cylindrical can is:

h/2r = (√(Sπ)/2)/(2√(S/4π)) = √(π/4) = 0.886 approximately.

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The first time I did the math including 8 but we are increasing it so it will just be how much did the price increase from 8 to 18 well I know 100% of 8 is 8 so thats 100% and 25% of 8 is 2 so I added the two and 8 + 8 = 16 + 2 = 18 I added those percents 100 + 25 = 125%

Answer:

225% seems like the best answer.

Answer:

A"B" = 8 ft

Step-by-step explanation:

From the given question, ABCDE has undergone transformation to produce images A'B'C'D'E' and A"B"C"D"E". But its size and shape has been preserved.

ABCDE was initially reflected and rotated with respect to point E to have A'B'C'D'E', which was finally reflected across line p to produce A"B"C"D"E". This implies that the dimensions of ABCDE were not affected in the process.

So that, AB = A"B" = 8 ft.