MATHEMATICS COLLEGE

Solve the inequality for x. –8x + 16 > –72

Answers

Answer 1
Answer:

Answer:

x>11

Step-by-step explanation:

x needs to be alone so subtract 16 on both sides, making the equation -8x > -88, next simply make x positive amd alone by dividing -8 on both sides, ending in the result of × > 11

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Find the surface area and volume of a rectangular solid with length 10, width 7, height 12surface area______square inchesvolume_____cubic inches​
Julio is planning activities for a trip that lasts from Thursday to Sunday. He is interested in visiting a museum, hiking the trails, attending the food festival, riding a jet ski, exploring a famous park, or going shopping. each activity takes a full day, and he will not do any activity twice. Julio wants to either visit a museum or explore the park on Thursday, and he is definitely attending the food festival on Saturday. How many different ways can he plan activities for his trip?A)24B)30C)40D)120

A ramp 17 1/2 feet in length rises to a loading platform that is 3 1/2 feet off the ground. Find the angle that the ramp makes with the ground.

Answers

Answer:

The angle that the ramp makes with the ground is 11.54°

Step-by-step explanation:

From the image attached, we can see that the length of 17 1/2 ft corresponds to the hypotenuse in a right triangle, the length of 3 1/2 ft corresponds to the opposite side.

We can use the fact that the sin(θ) = (Opposite)/(Hypotenuse) to find the angle that the ramp makes with the ground.

sin(\theta)=(3.5)/(17.5)

The angle is equal to

\theta = sin^(-1)((3.5)/(17.5) )\n\theta = 11.54\°

Final answer:

The angle that the ramp makes with the ground can be found using the concept of tangent in trigonometry. By dividing the height of the loading platform by the length of the ramp and taking the inverse tangent of the result, we find the angle to be approximately 11.3 degrees.

Explanation:

This question can be solved by using trigonometric principles, specifically the tangent of an angle in a right triangle. The tangent of an angle θ (theta) can be defined as the ratio of the side opposite the angle to the side adjacent to it.

In this scenario, the ramp forms a right triangle with the ground and the vertical line from the loading platform to the ground directly below it. The height of the platform, or the 'opposite' side, is 3 1/2 feet, and the ramp, or the 'adjacent' side, is 17 1/2 feet.

Therefore, we can say that: tan θ = (3.5 / 17.5)

To find the value of θ, we take the inverse tangent (or arc tangent) of the quotient. Using a calculator to do this (remember to set your calculator to degree mode), we find θ to be approximately 11.3 degrees.

Thus, the angle that the ramp makes with the ground is about 11.3 degrees.

Learn more about Trigonometry here:

brainly.com/question/11016599

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a home has a triangular backyard. The second angle of the triangle is 6 more than the first angle. The third angle is 14 more than three times the first angle. Find the angles of the triangular yard

Answers

Answer: The first angle is 32 degrees

The second angle is 38 degrees

The third angle is 110 degrees.

Step-by-step explanation:

Let x represent the size of the first angle.

Let y represent the size of the second angle.

Let z represent the size of the third angle.

The second angle of the triangle is 6 more than the first angle. This means that

y = x + 6

The third angle is 14 more than three times the first angle. This means that.

z = 3x + 14

The sum of the angles in a triangle is 180 degrees. It means that

x + y + z = 180 - - - - - - - - - - - -2

Substituting y = x + 6 and z = 3x + 14 into equation 2, it becomes

x + x + 6 + 3x + 14 = 180

x + x + 3x = 180 - 14 - 6

5x = 160

x = 160/5 = 32

y = x + 6

y = 32 + 6 = 38

z = 3x + 14

z = 3×32 + 14 = 96 + 14

z = 110

Which fractions convert into repeating decimals? Select ALL that apply. 4/40. 12/100. 3/18. 1/5. 9/27​

Answers

9/27 & 3/18 are repeating decimals

Answer:

3/18     = 1.6666

9/27​    = 0.3333

Step-by-step explanation:

4/40    = 0.1

12/100 = 0.12

3/18     = 1.6666

1/5       = 0.2

9/27​    = 0.3333

triangle town wants to build a school that is equidistant from its three cities L,M, and N. Which construction correctly finds the best location of the school? A. Construction Y because point E is the incenter of triangleLMN B. Construction Y because point E is the circumcenter of triangleLMN C. Construction X because point C is the incenter of triangleLMN D. Construction X because point C is the circumcenter of triangleLMN

Answers

Answer:

A

Step-by-step explanation:

Construction Y because point E is the circumcenter of Triangle LMN

A sphere that has a diameter of 6 what is the volume of the sphere

Answers

Answer:

36 pi or 113.04

Step-by-step explanation:

The volume of a sphere is given by

V= 4/3 pi r^3

we know the diameter so we need to find the radius

r =d/2

r = 6/2 = 3

V = 4/3 pi (3)^3

V =36 pi

We can approximate pi by 3.14

V is approximately 36 *3.14 or 113.04

Answer:

113.1 (113.0973355...)

Step-by-step explanation:

1. Use the sphere volume formula of (4)/(3)πr^(3).

2. Divide 6 by 2 in order to get a radius of 3.

3. Substitute 3 in for r.

4. Cube the 3, you'll get 27.

5. Multiply 27 by Pi and 4/3.

6. You get 113.1 as a rough estimate, or 113.0973355... for a more exact number. If you leave it in Pi terms, it's 36π.

What is the value of -(3/4) to the power of -4

Answers

The answer would be -3 13/81 (simplified)
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