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2 years ago

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Mr. And Mrs. Storey drove 3,200 miles in all during their vacation. Mr Storey drove 3 times as many miles as Mrs. Storey. Howany

miles did Mr. Storey drive? How many miles did Mrs. Storey drive?

1 answer:

umka21 [38]2 years ago

5 0

If the ratio of miles is
.. mr : mrs = 3 : 1
The total number of "ratio units" is 3+1 = 4, so each one stands for 3200/4 = 800 miles.

Mr Storey drove 3*800 = 2400 miles
Mrs Storey drove 1*800 = 800 miles

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Yen paid $10.50 for 2.5 pounds of pretzels. What price did she pay for each pound of pretzels?

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Answer:

The first step is to multiply by a power of 10, so the divisor is a whole number.

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

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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

$128 = x * y$

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

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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If LO = 15x+19 and QN = 10x+2 find PN

svet-max [94.6K]

Answer:

$PN=64\ units$

Step-by-step explanation:

<u><em>The complete question is</em></u>

Given the quadrilateral is a rectangle, if LO = 15x+19 and QN = 10x+2 find PN

see the attached figure to better understand the problem

we know that

The diagonals of a rectangle are congruent and bisect each other

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substitute the given values

$10x+2=\frac{1}{2}(15x+19)$

solve for x

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substitute the value of x

$LO=15(3)+19=64\ units$

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1 year ago

Annie is running a trail that is 4 1/2 miles long. She ran the first 2/3 of the distance. Then the trail became very steep, so s

qwelly [4]

Answer:

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Step-by-step explanation:

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= 9/2 - 2/3

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