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2 years ago

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Devin wants to buy some t-shirts from a store in the mall. He has $20 in his pocket and the t-shirts cost $5 each. The situation

can be modeled by the function F(t) = 5t, where F(t) represents the total cost of t t-shirts. State a reasonable domain and range for this situation.

1 answer:

avanturin [10]2 years ago

7 0

Answer:20-5t+=

Step-by-step explanation:

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A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

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2 years ago

What is 0. 72 [REPEATING] as a fraction in simplest form?

Nostrana [21]

The answer is 13/18 because it is congruent to 0.7(2).

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2 years ago

Could you please answer this precisely. Thank you!

OleMash [197]

The mathematical functions (equations) are matched to their graph line respectively as follows:

y = 960 - 78x: purple straight line.
y = 8·3^x: violet line curve that slopes to the left.
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<h3>What is a linear function?</h3>

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate. Mathematically, a linear function is given by this equation:

y = mx ± c.

<h3>What is an exponential function?</h3>

An exponential function can be defined as a type of mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:

f(x) = keˣ

Next, we would match each of the mathematical functions (equations) to their graph line respectively as follows:

y = 960 - 78x: purple straight line.
y = 8·3^x: violet line curve that slopes to the left.
y = 960·(1/2)^x: green line curve that slopes to the right.

Read more on graphs here: brainly.com/question/24298987

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Solve the equation. 12x+3=51

Zinaida [17]

$12x + 3 = 51 \\ 12x = 48 \\ x = 4$

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3 years ago

-3(5x + 6) + 2 = 2(8 + 8x) - 1

bija089 [108]

So first, we multiply out the brackets.
-15x - 18 + 2 = 17 + 16x -1
Then, bring all the terms onto one side so you can solve.
-15x-18+2-17-16x+1=0
Then, we simplify this.
-31x-32=0
Then, isolate x
-31x=32
x=32/-31 or -1.03 (nearest hundredth )

6 0

2 years ago