1/2r+2(3/4r-1)=1/4+6

The area of a storage shed floor is 20 ft2. The length is 3 more than twice the width. Find the dimensions of the storage shed f

vladimir1956 [14]

Answer:

2.5 ft wide
8 ft long

Step-by-step explanation:

The given relation between length and width can be used to write an expression for area. The equation setting that equal to the given area can be solved to find the shed dimensions.

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<h3>Given relation</h3>

Let x represent the width of the shed. Then the length is (2x+3), and the area is ...

A = LW

20 = (2x+3)(x) . . . . . area of the shed

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<h3>Solution</h3>

Completing the square gives ...

2x² +3x +1.125 = 21.125 . . . . . . add 2(9/16) to both sides

2(x +0.75)² = 21.125 . . . . . . . write as a square

x +0.75 = √10.5625 . . . . . divide by 2, take the square root

x = -0.75 +3.25 = 2.50 . . . . . subtract 0.75, keep the positive solution

The width of the shed is 2.5 feet; the length is 2(2.5)+3 = 8 feet.

8 0

2 years ago

Find the equation of the linear function represented by the table below in slope-intercept form. x y 1 -3 2 -9 3 -15 4 -21

aleksley [76]

Answer:

The numbers:

1, -3, 2, -9, 3, -15, 4, -21,

are not linear.

Step-by-step explanation:

If it was linear:

4, 3, 2, 1, -3, -9, -15, -21

8 0

3 years ago

The graph of y=x^3 is transformed as shown in the graph below. Which equation represents the transformed function?

omeli [17]

Answer:

y = (-x)^3 - 4

Step-by-step explanation:

Ok, for the function:

y = x^3

When x = 0, we have:

y = 0^3 = 0

So the original graph passes through the point (0, 0)

If we look at the given graph, we can see that the y-intercept (the value of y when x = 0) is:

y = -4

So, this is the graph of y = x^3 moved down 4 units.

You can also see that the graph goes downward as x increases (and up as x decreases) while for the function:

y = x^3

as x increases, we should see that y also increases.

Then we have a reflection across the x-axis.

Ok, now let's describe a vertical shift.

For a general function f(x), a vertical shift of N units is written as:

g(x) = f(x) + N

if N is positive, the shift is upwards

if N is negative, the shift is downwards.

And for a function f(x), a reflection across the x-axis is written as:

g(x) = - f(x)

Here we first apply the reflection across the x-axis, so we get:

g(x) = -f(x)

now we apply the shift 4 units downwards

g(x) = - f(x) - 4

replacing f(x) by our function, x^3

we get:

g(x) = -x^3 - 4

And because of the odd power, we can write:

-x^3 = (-x)^3

Then the function is:

g(x) = (-x)^3 - 4

The correct option is the last one.

y = (-x)^3 - 4

3 0

3 years ago

Select the correct answer. Function f is an exponential function that has an initial value of 64 and decreases by 50% as x incre

lozanna [386]

9514 1404 393

Answer:

D. Both functions are decreasing at the same average rate on that interval

Step-by-step explanation:

The dashed lines on the attached graph of the two functions (f in red, g in purple) represent the average rate of change of each function on the interval. The lines are parallel, because the average rate of change is the same for each of the functions on that interval.

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Function f decreases by 60 units from f(0) = 64 to f(4) = 4 on the interval x = [0, 4]. Function g decreases by 60 units from g(0) = 75 to g(4) = 15 on the same interval. The average rate of change is the amount of decrease divided by the interval width. Those values are the same for both functions.

3 0

3 years ago

Read 2 more answers

Chapter 12 F

marshall27 [118]

Answer:

(m+n) -a = r

Step-by-step explanation:

first, you have to find what m+n is because that is their total budget, then you have to remove how much their apartment costs from their budget, because r is the amount of free cash they have. once A is subtracted from m+n, you have r

8 0

3 years ago