Can someone please help me solve this? and explain how you got the answer? Thank you

What’s the solution

xz_007 [3.2K]

Answer:

±5

±25

Step-by-step explanation:

5 0

2 years ago

What is the slope of the line that passes through (2,6) and (6,9)

Alenkasestr [34]

Answer:

3,3

Step-by-step explanation:

6 0

2 years ago

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>

3 0

2 years ago

Unit rate of 1/2 hour:$1.25

GREYUIT [131]

What I would do with is just multiply the 125 by half an hour yeah or just multiply the ones we five by in half an hour and get your final answer I multiply the 1.25 by 1.2 and I got 1.5 + If I multiply the 1.25 + 2i would get 2.5

4 0

2 years ago

Como se multiplican polinomios

seraphim [82]

I hope you speak english, because although i understood your question I don't know enough spanish to respond in it. You multiply polynomials by multiplying each part of one polynomial by all the other parts of the others, and then adding it all. For example: (ax+b) * (x+c) = (ax*x)+(ax*c)+(b*x)+(b*c) = $a x^{2} + acx + bx+bc$

Comprehende?

7 0

2 years ago

Can someone please help me solve this? and explain how you got the answer? Thank you​

Can someone please help me solve this? and explain how you got the answer? Thank you