What is the range of f(x) ? A B C D Graph and answer choices are above

How do I solve this algebra problem: 2(4a-12)+3a=6a+1

umka21 [38]

$2(4a-12)+3a=6a+1 \\\\ 8a-24+3a=6a+1 \\\\ 11a-24=6a+1 \\\\ 11a-6a=1+24 \\\\ 5a=25 \\\\ \boxed{a=\frac{25}{5}=5}$

6 0

3 years ago

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Simplify Rewrite the expression in the form 5 ^ n. (5/10)/(5/12) =

Amiraneli [1.4K]

Answer:

$5^{-2}$

Step-by-step explanation:

$5^{(10-12)}$

5 0

3 years ago

(x + y + 3)(x + y - 4) multiplying polynomials

Yuliya22 [10]

X^2 + 2xy + -x + y^2 + -y + -12

4 0

3 years ago

Two teams of movers are lowering a piano from the window of a 10 floor apartment building. The rope breaks when the piano is 30

GuDViN [60]

By solving the motion equations for the piano, we will see that they have 0.7 seconds to react.

<h3>How to find the motion equation for the piano.</h3>

So the piano is in a free fall from a height of 30m.

The motion equations will be given by:

The only force acting on the piano will be the gravitational one, thus the acceleration of the piano is the gravitational acceleration: a(t) = -9.8m/s^2 (Where the negative sign is because it is falling down).
To get the velocity we integrate over time, because the piano has no initial velocity, the constant of integration is zero: v(t) = (-9.8m/s^2)*t
To get the position equation we integrate again, here the initial position is 30 meters above the ground, so that will be our constant of integration: p(t) = (1/2)*(-9.8m/s^2)*t^2 + 30m

<h3>How long takes to fall?</h3>

We want to find the value of t such that the position is equal to zero, so we need to solve:

0 = (1/2)*(-9.8m/s^2)*t^2 + 30m

30m = (1/2)*(9.8m/s^2)*t^2

2*30m/(9.8m/s^2) = t^2

6.1 s^2 = t^2

√(6.1 s^2) = 2.5s = t

This means that the piano falls to the ground in 2.5 seconds.

But the workes notice it when the piano is 14 meters above the ground, it happens when:

p(t) = 14m = (1/2)*(-9.8m/s^2)*t^2 + 30m

Solving that we get:

30m - 14m = (1/2)*(9.8m/s^2)*t^2

2*16m/(9.8m/s^2) = t^2

3.27s^2 = t^2

√(3.27s^2) = t = 1.8s

So the piano falls in 2.5 seconds, and the works notice it 1.8 seconds after it starts falling, meaning that they have:

2.5 - 1.8 = 0.7 seconds to react.

If you want to learn more about motion equations, you can read:

brainly.com/question/2473092

4 0

2 years ago

Find x(3x+72) triangle

Alinara [238K]

Answer: x = -4 ; Angle = 60°

Concept:

The given figure is a triangle with 3 arc signs on each angle. This arc sign stands for the corresponding angles are congruent, which in this question, it shows that all three angles are congruent. Sometimes, if the figure has multiple angles and there are different groupings of congruent angles, then we use different numbers of arcs or symbols.

Solve:

Given information

An angle = 3x + 72

Total measure of angles = 180 (triangle angle sum theorem)

Total number of congruent angles = 3

Given expression

Total measure = Total number of congruent angles × An angle measure

Substitute values into the expression

180 = 3 (3x + 72)

Divide 3 on both sides

180 / 3 = 3 (3x + 72) / 3

60 = 3x + 72

Subtract 72 on both sides

60 - 72 = 3x + 72 - 72

-12 = 3x

Divide 3 on both sides

-12 / 3 = 3x / 3

$\boxed{x=-4}$

Find the angle measure

3x + 72 = 3 (-4) + 72 = $\boxed{60}$

Hope this helps!! :)

Please let me know if you have any questions

6 0

2 years ago

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