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3 years ago

5

3/9 in simplest form

1 answer:

Molodets [167]3 years ago

4 0

It is 1/3
3:3 =1
9:3 = 3
make sure that the top and bottom numbers divide with the same number :)

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Robert drives 45 miles in 3 hours from New York City to New Jersey. How far will he drive in 5 hours?

fenix001 [56]

Ok so the awnser is 75 because 45 ÷ 3 is 15 and so 2 more hours so I added 30 to the 45 and I got 75 I think that's right please correct me

3 0

3 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

3 years ago

Help me plz its algebra 1

kvv77 [185]

Answer:

C. x > -7 and x <= 3

Step-by-step explanation:

-3 < x + 4 <= 7

Subtract 4 from the three expressions.

-7 < x <= 3

-7 < x means x > -7.

Then you have x <= 3.

Answer: C. x > -7 and x <= 3

5 0

3 years ago

The cost of three dozen of eggs at thirty pesos per dozen in numerical expression<br>

evablogger [386]

3 x 30

It cost 30 pesos per dozen and they are buying 3 dozen

3 x 30 = 90

4 0

3 years ago

Where did you get 22/7?

aleksley [76]

Pie value written in fraction form

8 0

3 years ago

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