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2 years ago

14

Two angles form a linear pair. The measure of one angle is twice the measure of the other angle. Find the measure of each angle.

1 answer:

Flauer [41]2 years ago

6 0

Answer:

The smaller angle measures = 60º

The larger angle measures = 120º

Step-by-step explanation:

The sum of angles in linear pair is 180

The measure of one angle is twice the measure of the other angle.

x + 2x = 180

Combine like terms

3x = 180

Divide both sides by 3

x = 60º

2x = 120º

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Step-by-step explanation:

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A publisher sells 10⁶ copies of a new book. Each book sells 10² pages. How many pages total are there in all of the books sold?

KatRina [158]

Answer:

10^12.

Step-by-step explanation:

You need to solve 10^6 * 10^2 without using standard notation. As with variables, if you had x^6 * x^2 you would add the exponents. Replace x with 10. Your answer is 10^8. As a sidenote, only multiply exponents when raising a power to another power, e.g. (10^6)^2 = 10^12.

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2 years ago

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You have been asked to design a can shaped like right circular cylinder that can hold a volume of 432π-cm3. What dimensions of t

rosijanka [135]

Answer:

$Height = 12cm$

$Radius = 6cm$

Step-by-step explanation:

Given

Represent volume with v, height with h and radius with r

$V = 432\pi$

Required

Determine the values of h and r that uses the least amount of material

Volume is calculated as:

$V = \pi r^2h\\$

Substitute 432π for V

$432\pi = \pi r^2h$

Divide through by π

$432 = r^2h$

Make h the subject:

$h = \frac{432}{r^2}$

Surface Area (A) of a cylinder is calculated as thus:

$A=2\pi rh+2\pi r^2$

Substitute $\frac{432}{r^2}$ for h in $A=2\pi rh+2\pi r^2$

$A=2\pi r(\frac{432}{r^2})+2\pi r^2$

$A=2\pi (\frac{432}{r})+2\pi r^2$

Factorize:

$A=2\pi (\frac{432}{r} + r^2)$

To minimize, we have to differentiate both sides and set $A' = 0$

$A'=2\pi (-\frac{432}{r^2} + 2r)$

Set $A' = 0$

$0=2\pi (-\frac{432}{r^2} + 2r)$

Divide through by $2\pi$

$0= -\frac{432}{r^2} + 2r$

$\frac{432}{r^2} = 2r$

Cross Multiply

$2r * r^2 = 432$

$2r^3 = 432$

Divide through by 2

$r^3 = 216$

Take cube roots of both sides

$r = \sqrt[3]{216}$

$r = 6$

Recall that:

$h = \frac{432}{r^2}$

$h = \frac{432}{6^2}$

$h = \frac{432}{36}$

$h = 12$

Hence, the dimension that requires the least amount of material is when

$Height = 12cm$

$Radius = 6cm$

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2 years ago

A carton has a length of 2 2/3, width of 1 1/3, and height of 1 1/2 feet. What is the volume of the carton?

Phantasy [73]

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2 years ago

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Misha Larkins [42]

Answer:

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Q= y=-2x+2.5

Step-by-step explanation:

the formula is y=mx+b

M=slope

B=y-intercept

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The slope is two ordered pairs where you use the formula rise over run to find your slope.

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2 years ago