Solve and graph the absolute value inequality: |2x + 4| > 14

Answers

Answer 1

Answer: $|2x+4| > 14\n\n2x+4 > 14\ \vee\ 2x+4 < -14\n\n2x > 14-4\ \vee\ 2x < -14-4\n\n2x > 10\ \vee\ 2x < -18\n\nx > 5\ \vee\ x < -9\n\nsee\ a\ picture\n\nx\in(-\infty;-9)\ \cup\ (5;\ \infty)$

Answer 2

Answer: |2x + 4| > 14
2x+ 4 = 14 2x + 4 = -14
x = 5 or x = - 9
2*5 = 10 +4 = 14 Yes
2*-9 = -18 + 4 = - 14 Yes
2x > 10 2x < - 18
X > 5
X < -9

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Jessica wants to go on a school trip next month. The trip will cost $100 and she already has $10 and plans to babysit for $5 an hour to earn the rest of the money.A. Write an equation that could be used to determine h, the number of hours Jessica needs to babysit to earn $100.

B. From your equation, determine the number of hours she needs to babysit.

Answers

Answer:

Step-by-step explanation:

100=10+5x x is the hours she needs to babysit

90=5x

x=18

She needs to babysit for 18 hours at $5 an hour if she already has $10

Help with the following complete the square equation...

Answers

Answer: D) Add 64 to both sides

Why do this?

Because we want to be able to factor the left hand side into the form p^2, where p is some algebraic expression. This will help us ultimately solve for x.

Currently, the left hand side is x^2+16x which does factor to x(x+16), but that isn't in the form p^2. We want something like (x+1)^2 or (x+2)^2. The general form is (x+k)^2 where k is some fixed constant.

Let's expand out (x+k)^2 using the FOIL rule and we get x^2+2kx+k^2

The x coefficient is 2k. If we cut that in half, we get k. Squaring that result leads to k^2.

So we have this order: 2k cuts in half to k then square it to get k^2

For x^2+16x, we have the x coefficient as 16. That cuts in half to 8, then that squares to 64. We add 64 to both sides

Note how

x^2+16x = 9

x^2 + 16x + 64 = 9+64

(x+8)^2 = 73

From here, we apply the square root to both sides and then subtract 8 from both sides to fully isolate x. You would get two different solutions.

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I recommend you use the FOIL rule to confirm that (x+8)^2 expands out to x^2+16x+64, to help check your work.

If you divide an inheritance of $45,600.00 among 22 heirs, each heir will receive

Answers

It is simple
you do 45,600 divided by 22
which equals about 2,072.72

Each heir will receive 2072.72 inheritance.

We have to given that;

You divide an inheritance of $45,600.00 among 22 heirs.

And, To find each heir will receive inheritance.

Now, find each heir will receive inheritance as;

⇒ 45,600.00 divided by 22

⇒ 45,600 / 22

⇒ 2072.72

Thus, Each heir will receive 2072.72 inheritance.

Learn more about the divide visit:

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What is the surface area of the triangular prism? A triangular prism. The rectangular sides are 20 feet by 3 feet, 20 feet by 4 feet, and 20 feet by 5 feet.

Answers

Answer:

252 ft²

Step-by-step explanation:

A triangular prism has three rectangles and two triangles, to find the surface area, first find the surface area of thee rectangles and then the surface area of the triangles. After that add all the surface area.

For rectangle 1, surface area = 20 × 3 = 60 ft²

For rectangle 2, surface area = 20 × 4 = 80 ft²

For rectangle 3, surface area = 20 × 5 = 100 ft²

The triangle has height, base and hypotenuse. 5 ft is the hypotenuse and the height and base are 3 ft and 4 ft.

5² = 3² + 4²

For the triangle, the surface area = 1/2 × base × height = 1/2 × 3 × 4 = 6 ft²

Total surface are = 60 + 80 + 100 + 2(6) = 252 ft²

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