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2 years ago

Solve for x. 13 =(5x+ 6)/8 + (5x+4)/4

Mathematics

1 answer:

valkas [14]2 years ago

3 0

Answer: x=6

Step-by-step explanation:

To solve for x, we want to isolate the variable.

$\frac{5x+6}{8} +\frac{5x+4}{4} =13$ [get common denominator]

$\frac{5x+6}{8} +\frac{2(5x+4)}{8} =13$ [add fractions]

$\frac{5x+6+10x+8}{y} =13$ [combine like terms]

$\frac{15x+14}{8} =13$ [multiply both sides by 8]

$15x+14=104$ [subtract both sides by 14]

$15x=90\\$ [divide both sides by 15]

$x=6$

Now, we know that x=6.

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The two-way table below displays demographic data for the passengers aboard the Titanic.

meriva

Answer:

About 72%

Step-by-step explanation:

All you have to do is divide the number of children who traveled in third class (79) by the total number of children (109)

79/109=.724770642 OR 72%

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3 years ago

Read 2 more answers

Describe the overall shape of the histogram.

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Answer:How would you describe the shape of the histogram? Bell-shaped: A bell-shaped picture, shown below, usually presents a normal distribution. Bimodal: A bimodal shape, shown below, has two peaks. This shape may show that the data has come from two different systems.

Step-by-step explanation:i

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2 years ago

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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

480 stickers on 6 sheets or 120 stickers on 2 sheets? Which is the greater.

nlexa [21]

480 stickers on 6 sheets is greater because 480 divided by 6 is 80, whole 120 divided by 2 is 60

7 0

3 years ago

A club had some money to purchase new chairs. After buying 355 chairs at $199 each, there was $1,068 remaining. How much money d

Bumek [7]

Answer:

Explanation:

Find The Total Cost Of The 355 Chairs
355 Chairs - $199 Per Chair

355 · 199 = $70,645

Club Spent $70,645 And Had $1,068 Remaining

$70,645 + $1,068 = $71,713

<h2><em><u>The Club Had $71,713 At First</u></em></h2>

- PNW

7 0

3 years ago