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2 years ago

Find the value of x so that the function has the given value.p(x) = 6x - 12; p(x) = 18

Mathematics

1 answer:

Kitty [74]2 years ago

6 0

k(x) = 6x - 12

k(x) = 18

substitute:

6x - 12 = 18 |+12

6x = 30 |:6

x = 5

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Raul has 56 bouncy balls. he puts three times as many balls into red gift bags as he puts into green gift bags. if he puts the s

Oksi-84 [34.3K]

Raul has 56 bouncy balls

he puts the balls into red gift bags and green gift bags

so lets say he puts x number of balls into green gift bags

then we are told that he puts three times as many balls into red gift bags as he puts into green gift bags

so the number of balls he puts into red gift bags is - 3 * x = 3x

the total number of balls = 56

so we can write the following equation

x + 3x = 56

4x = 56

x = 56/4

x = 14

therefore the amount of balls he puts into green bags is - 14 balls

6 0

2 years ago

Read 2 more answers

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

What is 20% of 5000

Dimas [21]

Answer:

1000

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Janet Fog's uncle, Pete Moore, promised her a gift of $30,000 upon her graduation from law school or $1500 every quarter for the

LenaWriter [7]

First calculate the future value of the annuity
The formula to find the future value of an annuity ordinary is
Fv=pmt [((1+r/k)^(kn)-1)÷(r/k)]
Fv future value?
PMT quarterly payment 1500
R interest rate 0.12
K compounded quarterly 4
N time 4 years
Fv=1,500×(((1+0.12÷4)^(4×4)
−1)÷(0.12÷4))
=30,235.32

Now compare the amount of the annuity with amount of the gift
30,235.32−30,000=235.32
So as you can see the amount of the annuity is better than the amount of the gift by 235.32

Second offer is better

Hope it helps!

5 0

3 years ago

1) A spinner is divided into equal red, blue, green,

Harlamova29_29 [7]

Answer:

1/18

Step-by-step explanation:

Probability of spinning red=2/6=1/3

Probability of spinning green=1/6

probability of spinning green and then red=(1/6)*(1/3)=1/18

3 0

2 years ago

Find the value of x so that the function has the given value.p(x) = 6x - 12; p(x) = 18​

Find the value of x so that the function has the given value.p(x) = 6x - 12; p(x) = 18