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steposvetlana [31]

2 years ago

7

Help 10 > -3(x + 4) - 5

1 answer:

Nina [5.8K]2 years ago

7 0

X>-9

See explanation

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What is the slope of the line that passed through (3,-4) and (4,9)

Advocard [28]

Step-by-step explanation:

<u>Step 1: Find the slope</u>

<u /> $m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{9-(-4)}{4-3}$

$m =\frac{9+4}{1}$

$m=13$

Answer: The slope is 13

5 0

3 years ago

What is 1 3/4 divided by 2/5

sveta [45]

Answer:

35/8

Step-by-step explanation:

1 3/4 = 1 + 3/4 = 4/4 + 3/4 = 7/4.

So 1 3/4 ÷ 2/5 = 7/4 × 5/2 = 35/8.

6 0

3 years ago

The total cost (in hundreds of dollars) to produce x units of a product is c(x) = (3x-2) / (8x+1), find the average cost for eac

olya-2409 [2.1K]

Answer:

a) $\frac{74}{10025}$

b) $\frac{3x-2}{x(8x+1)}$

c) $\frac{-24x^2+32x-2}{(8x^2+x)^2}$

Step-by-step explanation:

For total cost function $c(x)$ , average cost is given by $\frac{c(x)}{x}$ i.e., total cost divided by number of units produced.

Marginal average cost function refers to derivative of the average cost function i.e., $\left ( \frac{c(x)}{x} \right )'$

Given: $c(x)=\frac{3x-2}{8x+1}$

Average cost = $\frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}$

a)

At x = 50 units,

$\frac{c(50)}{50}=\frac{150-2}{50(400+1)}=\frac{148}{50(401)}=\frac{74}{10025}$

b)

Average cost = $\frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}$

c)

Marginal average cost:

Differentiate average cost with respect to $x$

Take $f=3x-2\,,\,g=8x^2+x$

using quotient rule, $\left ( \frac{f}{g} \right )'=\frac{f'g-fg'}{g^2}$

Therefore,

$\left ( \frac{c(x)}{x} \right )'=\left ( \frac{3x-2}{8x^2+x} \right )'\\=\left ( \frac{3(8x^2+x)-(16x+1)(3x-2)}{(8x^2+x)^2} \right )\\=\frac{24x^2+3x-48x^2-3x+32x+2}{(8x^2+x)^2}\\=\frac{-24x^2+32x-2}{(8x^2+x)^2}$

3 0

3 years ago

The half-life of a certain radioactive material is 36 days. An initial amount of the material has a mass of 487kg. Write an expo

Lubov Fominskaja [6]

Answer:

442.302 kg

Step-by-step explanation:

amount = 487 (1/2)^(t/36) where t is the number of days.

if t = 5

amount = 487(.5)^(5/36)

= 442.302 kg

4 0

2 years ago

Which is a true statement about an isosceles right triangle?

AnnyKZ [126]

Let $l$ be the length of a leg. Using the pythagorean theorem, the hypotenuse is

$h = \sqrt{l^2+l^2}=\sqrt{2l^2}=l\sqrt{2}$

So, the hypotenuse is $\sqrt{2}$ times as long as either leg.

6 0

3 years ago