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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 $-16 \leq v \leq 30$.

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At a birthday party, Vivian counts 15 vanilla ice cream cups and 25 chocolate ice cream cups. Which properties can be used to de
o-na [289]

Answer:

62.5 %

Step-by-step explanation:

The percentage, p of the ice cream that is chocolate is p = total number of chocolate ice cream cups/total number of ice cream cups × 100%

Given that there are 25 chocolate ice cream cups and 15 vanilla ice cream cups, total number of ice cream cups  = 25 + 15 = 40

So, p = total number of chocolate ice cream cups/total number of ice cream cups × 100%

p = 25/40 × 100%

p = 25/4 × 10 %

p = 6.25 × 10 %

p = 62.5 %

4 0
3 years ago
Which point corresponds to the real zero of the graph of y = log3 (x+2) - 1?
brilliants [131]

Answer:

(1, 0 )

Step-by-step explanation:

using the rule of logarithms

log_{b} x = n ⇒ x = b^{n} , then

y = log_{3} (x + 2) - 1

to find the zero let y = 0 , that is

log_{3} (x + 2) - 1 = 0 ( add 1 to both sides )

log_{3} (x + 2) = 1 , then

x + 2 = 3^{1} = 3 ( subtract 2 from both sides )

x = 1

the zero is (1, 0 )

8 0
2 years ago
libon's new car can travel 45 miles on 1 gallon of of gas. at this rate how far can the car travel on 7 gallons
Setler [38]

Answer:

315

Step-by-step explanation:

If one gallon of gas can give you 45 miles, than multiple 45 ( the miles ) times 7 (the gallons of gas) and you will have your answer :)

4 0
2 years ago
There are 4 boys and 2 girls from the seventh grade and 3 boys and 5 girls from the eighth grade on the soccer team. Coach Foste
hodyreva [135]
1/2 because there is 7 girls and 7 boys in total
5 0
3 years ago
#9. Solve: 8x + 5 = 3x + 15<br><br> X = 4<br> x = 2<br> x = 20/11<br> x = 20
Jobisdone [24]

Answer:

x = 2

Step-by-step explanation:

8x + 5 = 3x + 15

8x - 3x + 5 = 3x - 3x + 15

5x + 5 = 15

5x + 5 - 5 = 15 - 5

5x = 10

5x / 5 = 10 / 5

x = 2

6 0
2 years ago
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