1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Katyanochek1 [597]
1 year ago
5

For the following exercises, solve each inequality and write the solution in interval notation.

Mathematics
1 answer:
WARRIOR [948]1 year ago
4 0

Answer:

The solution to the inequality $2|v-7|-4 \geq 42$ in interval notation is given by $-16 \leq v \leq 30$.

Step-by-step explanation:

An absolute value inequality $2|v-7|-4 \geq 42$ is given.

It is required to solve the inequality and write the solution in interval form.

To write the solution, first solve the given absolute value inequality algebraically and then write it in interval notation.

Step 1 of 4

The given absolute value inequality is $2|v-7|-4 \geq 42$.

Add on both 4 sides,

$$\begin{aligned}&2|v-7|-4 \geq 42 \\&2|v-7|-4+4 \geq 42+4 \\&2|v-7| \geq 46\end{aligned}$$

Step 2 of 4

Divide by 2 on both sides,

$$\begin{aligned}&\frac{2|v-7|}{2} \geq \frac{46}{2} \\&|v-7| \geq 23\end{aligned}$$

The inequality can be written as $v-7 \leq 23$ and $v-7 \geq-23$

Step 3 of 4

First solve the inequality, $v-7 \leq 23$.

Add 7 on both sides,

$$\begin{aligned}&v-7 \leq 23 \\&v-7+7 \leq 23+7 \\&v \leq 30\end{aligned}$$

Step 4 of 4

Solve the inequality $v-7 \geq-23$.

Add 7 on both sides,

$$\begin{aligned}&v-7 \geq-23 \\&v-7+7 \geq-23+7 \\&v \geq-16\end{aligned}$$

The solution of the inequality in interval notation is given by $-16 \leq v \leq 30$.

You might be interested in
What is the distance between the points (-3,5) and (3,-8) in the standard (x,y) coordinate plane?
zlopas [31]
The vertical distance is 5 + 8 = 13
the horizantal distance is 3 +3 = 6
then just do pythag therom
6^2 + 13^2 = c^2
205 = c^2
<span>√205 = c
</span>
6 0
3 years ago
Read 2 more answers
Please help me! What is x and y? Thank you!
Ivahew [28]

Answer:

x=3. y=6

Step-by-step explanation:

So, to solve x and y, we need to take the equivelent sides of the two triangles, take their equations, and solve them.

So to find what x equals, we can take the 13, and make it equal to the 4x+1:

13=4x+1

Subtract the one from both sides:

12=4x

Divide both sides by 4:

3=x

Or

<u>x=3</u>

So we know the x value is 3.

Now lets solve for y using the bottom equations:

2x+y=8x-2y

Subtract 1y from both sides:

2x=8x-3y

Subtract 8x from both sides:

-6x=-3y

Divide both sides by -6:

x=1/2y

So we already know that x=3, lets plug that in for x, and solve for y:

3=1/2y

Or

1/2y=3

Multiply both sides by 2 to get 1y:

<u>y=6</u>

So we know that y is equal to 6.

Hope this helps!

7 0
2 years ago
Mathhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
kirill115 [55]

Question? i cant see again friend

8 0
2 years ago
What is 1,360/16 reduced to smallest form? (please hurry this assignment is due soon)
Keith_Richards [23]

Answer:

85/1

Step-by-step explanation:

because both numbers are divisible by 16

5 0
2 years ago
Read 2 more answers
Pllllllease help me asap
marishachu [46]

Answer & Step-by-step explanation:

When we see the phrase "rate of change" then it means that we are looking for the slope. So, we will need to know the formula for finding slope or the rate of change.

slope=\frac{y_2-y_1}{x_2-x_1}

Now, let's use this equation to solve for the rate of change of each question.

<u>Problem 1:</u>

Slope=\frac{2-\frac{4}{3}}{0-(-1)}\\\\Slope=\frac{\frac{2}{3}}{1}\\\\Slope=\frac{2}{3}

<em>The rate of change of this equation is 2/3</em>

<u>Problem 2:</u>

<u></u>Slope=\frac{4-2}{1-0}\\\\Slope=\frac{2}{1}\\\\Slope=2<u></u>

<em>The rate of change for this equation is 2</em>

<u>Problem 3:</u>

<u></u>Slope=\frac{10-4}{2-1}\\\\Slope=\frac{6}{1}\\\\Slope=6<u></u>

<em>The rate of change for this equation is 6</em>

4 0
3 years ago
Other questions:
  • GUYS HELP PLEASEEEE I HAVE AN EXAM
    7·2 answers
  • A squirrel in a long glide typically covers a horizontal distance of 16 m while losing 8.0 m in altitude. during this glide, wha
    5·2 answers
  • Sixty photos taken at a photo shoot are in black and white. If this represents 15 percent of the total number of photos taken, w
    11·1 answer
  • ∠xangle, x and \angle y∠yangle, y are supplementary angles. \angle y∠yangle, y measures 88^\circ88
    7·1 answer
  • As a motorcycle accelerates at 5.1 m/s2, its speed changes from 16 km/h to 118 km/h. How long does this take?
    9·2 answers
  • What is cube root of 27
    11·1 answer
  • What is the slope of the function
    8·1 answer
  • the mass of your new motorcycle is to 120 Kg on Earth. What is the mass of the motorcycle on the moon?​
    8·1 answer
  • GOOD MORNING! \(:0:)/
    12·2 answers
  • Three angles of a quadrilateral are 75°, 90° and 75°. What is the measure of the fourth angle?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!