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3 years ago

Cassie’s book has 325 pages she read 155 pages yesterday and the rest today write an equation to express how many she read today

Mathematics

2 answers:

Andreas93 [3]3 years ago

8 0

Answer:170

Step-by-step explanation:

const2013 [10]3 years ago

7 0

So , first she read 155 pages so you would subtract;
325 pages - 155 pages.
325-155 equals to 170.
So you have 170 pages left to read for today.
So it can be 325 - 155 = x ,
Or, you can just put 325 - 155 = 170

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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>

3 0

3 years ago

Which statement is true about the value of (6)? A.(6) greater-than 6

Anvisha [2.4K]

Answer:

D. (6) is the distance between 6 and 0, and the distance is negative from 6 to 0

Step-by-step explanation:

(6) means the number exists in the negative state. It is -6.

Option A - As it is -6, it cannot be greater than positive 6. So, it is incorrect.

Option B - As it is -6, it cannot be less than negative 6. So, it is wrong.

Option C - As it is -6, its distance cannot be 0 to 6, and it should not be positive.

Option D - As it is -6, its distance should be negative and the distance is from 6 to 0. Therefore, it is the correct answer.

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3 years ago

What is the x-intercept and y-intercept of y=3x^2+6x+5

Eva8 [605]

There is no X But Y is (0,5)

5 0

3 years ago

You rolla fair 6-sided die.

Marizza181 [45]

Answer:dude just use a caculator

Step-by-step explanation:the answer is 200

3 0

3 years ago

How to find out the volume of a prism

slamgirl [31]

Answer:

The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm.

Step-by-step explanation:

1)Write down the formula for finding the volume of a rectangular prism. The formula is simply V = length * width * height.

2)Find the length.

3)Find the width.

4)Find the height.

5)Multiply the length, the width, and the height.

6)State your answer in cubic units.

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3 years ago

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