Factor the expression completely. 3x + 24

Mathematics

1 answer:

Umnica [9.8K]3 years ago

3 0

Answer:

3(x+8)

Step-by-step explanation:

In order to factor the expression completely, you need to find the greatest common factor of both numbers, which would be 3 because 3 fits in both numbers without leading to weird decimals or fractions.

3(x+8) is the answer.

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Karina is creating two pyramids with the nets below using construction paper. In both nets, all of the triangular faces of the p

sleet_krkn [62]

Answer:

144 sq in

Step-by-step explanation:

Face height=9, bases=6 in

#Assume the pyramid has a square base.

First we need to calculate the perpendicular height of the pyramid:

$#Pythagorean \ Theorem\\a^2+b^2=c^2\\9^2-(0.5\times 6)^2=h^2\\72=h^2\\h=\sqrt{72} \ in$

Now to find the surface area of each pyramid:

$A=lw+l\sqrt{(w/2)^2+h^2}+w\sqrt{(l/w)^2+h^2}\\\\\#w=l=6,h=\sqrt{72}\\\\A=6^2+6\sqrt{(6/2)^2+72}+6\sqrt{(6/6)^2+72}\\\\A\approx 144\ sq \ in$

Hence amount of construction paper needed to make each pyramid is 144 sq in

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3 years ago

Describe the two situations when you can use the Law of Cosines.

Tasya [4]

We use the law of Cosines to be able to find : 1. The measure of the third side, when the measure of two sides and the included angle of a triangle ABC are known. 2. The measure of any angle, when the measure of the three sides of a triangle ABC are known.

The Law of Cosines is c² = a² + b² - 2abcosΘ. It has four variables; a, b, c and Θ. Whenever you have a triangle with three of these variables known, use the Law of Cosines to calculate the unknown variable.

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3 years ago

Solve by the linear combination method.

wlad13 [49]

X=5/9

Y=0.65

See below the following picture for the solution