Question

GRADUATING THIS WEEK NEED THIS ALL ANSWERED

5. Tanika drove 189 miles. She drove 63 miles per hour. For
how many hours did Tanika drive? t=. hours
6. -2x< 4
7. 5t+7< 32
t=
8. 12s-17 2s +33
SE
9. -8m >-24
m=
10. 8n+7 > 4n+35
n=​

Answer 1

Question 1:

For this case we can raise a rule of three:

63 miles ---------------> 1 hour

189 miles -------------> x

Where "x" represents the number of hours it takes Tanika to travel 189 miles.

`x = \frac {189 * 1} {63}\\x = 3`

So, Tanika takes 3 hours to travel 189 miles

Answer:

Three hours

Question 2:

For this case we must solve the following equations:

A)
`-2x <4`

Dividing between -2 on both sides of the inequality:

`x <\frac {4} {- 2}\\x <-2`

B)
`5t + 7 <32`

We subtract 7 on both sides of the inequality:

`5t <32-7\\5t <25`

Dividing between 5 on both sides of the inequality:

`t <\frac {25} {5}\\t <5`

C)
`12s-17 \geq2s + 33`

We subtract 2s on both sides of the inequality:

`12s-2s-17 \geq33\\10s-17 \geq33`

We are 17 on both sides of the inequality:

`10s \geq33 + 17\\10s \geq50`

We divide between 10 on both sides of the inequality:

`s \geq \frac {50} {10}\\s \geq5`

D)
`-8m> -24`

Dividing between -8 on both sides of the inequality:

`m> \frac {-24} {- 8}\\m> 3`

E)
`8n + 7> 4n + 35`

Subtracting 4n on both sides of the inequality:

`8n-4n> 35-7\\4n> 28`

Dividing between 4 on both sides of the inequality:

`n> \frac {28} {4}\\n> 7`

Answer:

`x <-2\\t <5\\s \geq5\\m> 3\\n> 7`

Answer 2

3 hours

Explanation:

We have the amount of miles that Tanika passed, 189 miles. We also have the speed at which Tanika was driving, 63 miles per hour. Basically, Tanika was passing 63 miles on every one hour of driving. In order to find out how much time was Tanika driving with that speed to pass those miles, we just simply need to divide the miles passed with the speed of driving:

189 / 63 = 3

So we have a result of 3, thus Tanika needed three hours with a speed of 63 miles per hour to pass 189 miles.