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2 years ago

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An in ground rectangular pool has a concrete pathway surrounding the pool. if the pool is 16 feet by 32 feet and the entire area

of the pool including the walkaway is 924 ft^2, find the width of the walkway

1 answer:

Anastasy [175]2 years ago

7 0

1. Let's call:

x: the width of the walkway.
b: 2x+16 (there is a widht "x" of the walkway on each side).
h: 2x+32 (there is a widht "x" of the walkway on each side).
A: 924 ft^2 ( the area of the pool of including the walkway).

2. The area of a rectangle is:

A=(b)(h)

b: the base of the rectangle (2x+16)
a: the height of the rectangle (2x+32)

3. Then, we have a quadratic equation:

924=(2x+16)(2x+32)
4x^2+64x+32x+512-924=0
4x^2+96x-412=0

4. We apply the quadratic formula to find the value of "x":

x=(-b±√(b^2-4ac))/2a

x=3.71

The answer is: The width of the walkway is 3.71 ft

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Consider functions f and g below.

lidiya [134]

<h2>Hello!</h2>

The answer is:

The statement A "Function f is increasing, but g is decreasing."

<h2>Why?</h2>

To solve the problem and select the true statement, we need to compare both functions, using the inputs and outputs of the function "f" and the graph of the function "g" and then, discard each option.

Discarding we have:

A - Function f is increasing but g is decreasing: True.

From the shown table, we can see that the outputs of the function "f" are increasing, starting from 1.25 to 5, so, we can se that the function is increasing.

From the graph, we can see that the function "g" is the opposite of the function "f" since its outputs are decreasing, meaning that the function is decreasing.

Hence, the function "f" is increasing, but g is decreasing.

So, the statement A. "Function f is increasing, but g is decreasing." is true.

B - Both functions have positive x-intercepts.: False.

When a function intercepts the axis "x" we should be able to appreciate at least one output (y) equal to 0. We must remember that when a function intercepts the x-axis the y-value tends to 0.

Hence, the function f does not intercept the x-axis, also, we can see from the graph of the function g that there is not any x-axis intercept.

So, the statement B. "Both functions have positive x-intercepts." is not true.

C - The average rate of change of f is slower than the average rate of change of g over the interval [0, 2].: False.

From the graph of the function g, we can obtain its inputs and outputs and express it as points, and then, calculate its average of change, so, calculating we have:

$average=\frac{y_2-y_1}{x_2-x_1}$

Using the points: (0,2) and (2,5) we have:

$average=\frac{5-2}{2-0}=-0.75$

We have that the average rate of change is negative since the function is decreasing, and it's equal to 0.75.

Now, calculating the average of rate of the function f for the same interval, we have:

$average=\frac{5-2}{2-0}=1.5$

We have that the average rate of change is positive since the function is decreasing. and it's equal to 1.5

Hence, we have that the average rate of change of f is faster than the average rate of change of g over the interval [0, 2].

So, the statement C. "The average rate of change of f is slower than the average rate of change of g over the interval [0, 2]." is false.

D - The y-intercept of f is greater than the y-intercept of g: False:

When a function intercepts the y-axis, the "x" coordinate of the interception point tends to 0.

For f, we have that the y-intercept is located at "2", we can find the y-intercept using the point (0,2) where "x" is equal to 0, and "y" is equal to 2.

For g, we also have that the y-intercept is located at "2", we can find the y-intercept using the point (0,2) where "x" is equal to 0, and "y" is equal to 2.

Hence, both y-intercepts are equal.

So, the statement D. "the y-intercept of f is greater than the y-intercept of g." is false.

Therefore, we have that correct answer is:

The statement A is true.

Have a nice day!

5 0

2 years ago

Read 2 more answers

A water trough has two congruent isosceles trapezoids as ends and two congruent rectangles as sides.

BlackZzzverrR [31]

Answer:

Part a) The exterior surface area is equal to $160\ ft^{2}$

Part b) The volume is equal to $240\ ft^{3}$

Part c) The volume water left in the trough will be $84\ ft^{3}$

Step-by-step explanation:

Part a) we know that

The exterior surface area is equal to the area of both trapezoids plus the area of both rectangles

so

<em>Find the area of two rectangles</em>

$A=2[12*5]=120\ ft^{2}$

<em>Find the area of two trapezoids</em>

$A=2[\frac{1}{2}(8+2)h]$

Applying Pythagoras theorem calculate the height h

$h^{2}=5^{2}-3^{2}$

$h^{2}=16$

$h=4\ ft$

substitute the value of h to find the area

$A=2[\frac{1}{2}(8+2)(4)]=40\ ft^{2}$

The exterior surface area is equal to

$120\ ft^{2}+40\ ft^{2}=160\ ft^{2}$

Part b) Find the volume

We know that

The volume is equal to

$V=BL$

where

B is the area of the trapezoidal face

L is the length of the trough

we have

$B=20\ ft^{2}$

$L=12\ ft$

substitute

$V=20(12)=240\ ft^{3}$

Part c)

<em>step 1</em>

Calculate the area of the trapezoid for h=2 ft (the half)

the length of the midsegment of the trapezoid is (8+2)/2=5 ft

$A=\frac{1}{2}(5+2)(2)=7\ ft^{2}$

<em>step 2</em>

Find the volume

The volume is equal to

$V=BL$

where

B is the area of the trapezoidal face

L is the length of the trough

we have

$B=7\ ft^{2}$

$L=12\ ft$

substitute

$V=7(12)=84\ ft^{3}$

4 0

2 years ago

Nikki used the calculations shown to determine whether a carton of 12 eggs or a carton of 18 eggs was the better buy. A carton o

Lemur [1.5K]

Given :

A carton of 12 eggs or a carton of 18 eggs was the better buy. A carton of 12 eggs cost $2.39, and a carton of 18 eggs cost $3.39. Unit price of the 12-egg carton = ($2.39)(12 eggs) = $28.68 per egg Unit price of the 18-egg carton = ($3.39)(18 eggs) = $61.02 per egg The 12-egg carton has the lower unit cost, so it is the better buy.

To Find :

What was her first error.

Solution :

Her first error is to find Unit price of egg in each carton.

To find, unit price we should divide total amount by number of units :

Unit price for carton of 12 eggs, $ (2.39)/12 = $0.199 .

Hence, this is the required solution.

4 0

2 years ago

Solve the following multiplication and division problems. a. 8 T. 1,398 lb. 14 oz. × 6 b. 349 lb. 6 oz. ÷ 130 c. 6 T. 294 lb. ÷

tester [92]

Answer: a) 278382 oz

b) 43 oz

c) 64.1 oz

Step-by-step explanation:

a) 8 T. 1,398 lb. 14 oz. × 6

First we need to change it in 'oz'.

As we know that

$1\ ton=32000\ oz\\\\1\ lb=16\ oz$

so, it becomes,

$8\times 32000+1398\times 16+14\ oz\\\\=278382\ oz$

8 T. 1,398 lb. 14 oz. × 6 becomes

$278382\times 6\\\\=1670292\ oz$

b) 349 lb. 6 oz. ÷ 130

It becomes,

$349\times 16+6\ oz\\\\=5590\ oz\\\\\text{ at last it becomes}\\\\=\frac{5590}{130}\\\\=43\ oz$

c) 6 T. 294 lb. ÷ 3,071

First it becomes,

$6\times 32000+294\times 16\ oz\\\\=196704\ oz$

At last it becomes,

$\frac{196704}{3071}\\\\=64.1\ oz$

Hence, a) 278382 oz

b) 43 oz

c) 64.1 oz

6 0

2 years ago

Read 2 more answers

Simplify sin θ / square root 1 - sin^2 θ

Soloha48 [4]

Recall that

$\cos^2\theta+\sin^2\theta=1$

which means

$\dfrac{\sin\theta}{\sqrt{1-\sin^2\theta}}=\dfrac{\sin\theta}{\sqrt{\cos^2\theta}}$

Now, $\cos\theta$ could be positive or negative, which means $\sqrt{\cos^2\theta}=|\cos\theta|$ . If we specifically knew the sign of $\cos\theta$ was positive, then we can simplify and write

$\dfrac{\sin\theta}{\sqrt{1-\sin^2\theta}}=\dfrac{\sin\theta}{\cos\theta}=\tan\theta$

or if it's negative,

$\dfrac{\sin\theta}{\sqrt{1-\sin^2\theta}}=\dfrac{\sin\theta}{-\cos\theta}=-\tan\theta$

7 0

2 years ago