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5 0

3x^3 - 12x has a greatest common factor of 3x.

3x(x^2 - 4) is one other way to write it. It was created by factoring out the GCF of 3x.

3x(x+2)(x-2) is another form which is created by factoring the (x^2 - 4) from the last form.

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The measures of the angles of a triangle are shown in the figure below. Solve for x.

Liula [17]

Answer:

Step-by-step explanation:

x=180-59-41

x=80

3 0

2 years ago

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The equation x^3+x^2+ax-4=0 has one root equal to -2. Find the value of a.

Vedmedyk [2.9K]

Answer:

a = - 4

Step-by-step explanation:

Given x = - 2 is a root then f(- 2) = 0

f(x) = x³ + x² + ax - 4, thus

f(- 2) = (- 2)³ + (- 2)² - 2a - 4 = 0, that is

f(- 2) = - 8 + 4 - 2a - 4 = 0, thus

- 8 - 2a = 0 ( add 8 to both sides )

- 2a = 8 ( divide both sides by - 2 )

a = - 4

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3 years ago

A pulley is used to pull a boat to the dock. The rope is attached to the boat 7 feet below the level of the pulley. What is the

Svetradugi [14.3K]

Answer: 24 ft

Step-by-step explanation:

By the Pythagorean theorem,

$7^{2}+x^{2}=25^{2} \\ \\ 49+x^{2}=625 \\ \\ x^{2}=576 \\ \\ x=\boxed{24 \text{ ft}}$

7 0

1 year ago

I am having trouble with mean absolute deviation and whisker box plots. I try looking at examples, but it keeps stressing me out

Arada [10]

Answer:

Mean absolute deviation is a statistical measure of dispersion. Whisker box-plot is a graphical method of quartile based divided data

Step-by-step explanation:

Mean Absolute Deviation is a statistical measure of dispersion or variability in data. It denotes average level of deviation of observations from the central mean.

It is calculated using following formula : ( Σ | X - X' | ) ÷ N ; where X = individual observations, X' = mean, N = no. of observations

Whisker Box-plot is a graphical method of representing group of numerical data through their quartiles. This also consists line extensions from boxes, showing scatter beyond lower & upper quartile.

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2 years ago

A cone and a sphere both have a radius of 1. If you fill the cone with liquid, and pour it into the sphere, it fits exactly. Wha

PtichkaEL [24]

Answer and Step-by-step explanation:

First, solve for the volume of the sphere, then solve for the height of the cone using the volume of the sphere (which is said to be equal to the volume of the cone) and the radius given.

Volume formula of Sphere

V = $\frac{4}{3} \pi r^2$