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-Dominant- [34]

3 years ago

8

How to substitute x=-2 and x=5 into 2x^2+6-20=0 to check my work

1 answer:

Komok [63]3 years ago

4 0

First answer (x=-2)
...
(2)[(-2)^2]+6-20
2(4)+6-20
8+6-20
14-20
<em>-6 (answer)
</em><em>
</em><em />Second answer (x=5)
...
(2)[(-5)^2]+6-20
2(25)+6-20
50+6-20
56-20
<em>36 (answer)
</em>Hope this helps!

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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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Tanmayi wants to raise $175 for a school fundraiser,She has raised $120 so far. How much more does she need to reach her goal?

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3 years ago

What is the value of n in the diagram below?

IRINA_888 [86]

Answer:

n = 24

Step-by-step explanation:

(n + 18) and 2n are "complementary angles:" they add up to 90°.

Thus, n + 18 + 2n = 90. Combining the n terms results in 3n + 18 = 90.

Then 3n = 72. Dividing both sides by 3 results in n = 24.

n is 24, so n + 18 is 42 and 2n is 48. Note that 42 and 48 add up to 90.

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What’s this answer YALL IM STRUGGLING WITH MATH !!

saul85 [17]

Area: 4900

Perimeter: 280

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Moon Sporting Goods received a shipment of tennis rackets and marked them up 45%. The cost of the tennis rackets to Moon was $85

Komok [63]

Answer:

$123.25

Step-by-step explanation:

A selling price reflecting a 45% markup can be found by multiplying the wholesale price ($85) by (1 + 0.45), or 1.45:

1.45($85) = $123.25

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4 years ago