MATHEMATICS MIDDLE SCHOOL

Amelia can spend no more than $89 to rent a car for a day trip a rental cost $35 per day plus $.20 per mile right and solve an inequality to find the possible distance in miles M that amelia can drive without exceeding her budget

Answers

Answer 1

Answer:

Answer:

The possible distance in miles that Amelia can drive without exceeding her budget is 270 miles

Step-by-step explanation:

Given:

Amelia's budget for renting a car for a day trip = $ 89

Rental cost = $35

cost per mile = $0.20

To Find:

The possible distance in miles that Amelia can drive without exceeding her budget = ?

Solution:

Let M be the number of miles

The equation representing the situation can be

Total budget less than or equal to rental + (number of mile x cost per mile)

That is

$89 \leq 35 +(0.20 * M)$

Solving for M, we get

$89-35 \leq 0.20 M\n$

$54 \leq 0.20M\n$

$M \leq (54)/(0.20)$

$M \leq 270$

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Find the solution set of this inequality|10x+20| ≤10

Answers

Answer:

solution is

[-3,-1]

Step-by-step explanation:

we are given

$|10x+20|\leq 10$

Firstly, we will find critical values

so, let's assume it is equal

$|10x+20|= 10$

now, we can break absolute sign

For $|10x+20|= -(10x+20)$ :

$-(10x+20)= 10$

we can solve for x

$-10x-20= 10$

Add both sides by 20

$-10x-20+20= 10+20$

$-10x= 30$

Divide both sides by -10

and we get

$x=-3$

For $|10x+20|= (10x+20)$ :

$(10x+20)= 10$

we can solve for x

$10x+20= 10$

Subtract both sides by 20

$10x+20-20= 10-20$

$10x= -10$

Divide both sides by 10

and we get

$x=-1$

so, critical values are

$x=-3$

$x=-1$

now, we can draw a number line and locate these values

and then we can check inequality on each intervals

For $(-\infty,-3)$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=-5

$|10* -5+20|\leq 10$

$|-50+20|\leq 10$

$30\leq 10$

so, this is FALSE

For $[-3,-1]$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=-2

$|10* -2+20|\leq 10$

$|-20+20|\leq 10$

$0\leq 10$

so, this is TRUE

For $(-1,\infty)$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=0

$|10* 0+20|\leq 10$

$|0+20|\leq 10$

$20\leq 10$

so, this is FALSE

so, solution is

[-3,-1]

PLSSSS help me!!!!TEMPERATURE A thermometer is guaranteed to give a temperature no more than 1.2°F from the actual temperature. If the thermometer reads 28°F.
a. Write an equation to find the maximum and minimum temperatures t.

Answers

Answer:

26.8 ≤ t ≤ 29.2

Step-by-step explanation:

26.8 and 29.2 are the 2 numbers that are both 1.2 from 28. The equation explains that the temperature, t, is in between them, as it is greater than 26.8, and less then 29.2

Hope this helps!

Answer:

26.8°F≤x≤29.2°F

Step-by-step explanation:

If the thermometer reads 28°F, the range should be from 28°F to 29.2°F or 26.8°F to 28°F.

What is 10 percent of 80

Answers

to find 10per cent just divide by 10, the answer is 8

do you know how to do proportions?
X/80 = 10/100

so you cross multiply and get 100x = 800
divide by one hundred on both sides…
and your answer is 8

I have been stuck with this one, and i would like to how to solve this.In each case, determine whether line AB is parallel or perpendicular to CD.
(a) A(0, 0), B(0, 1), C(0, 0), D(1, 0).
(b) A(0, 1), B(2, 3), C(4, 5), D(6, 7).

Answers

a) AB is parallel CD from graphic;
b) m AB = (3-1)/(2-0) => m AB = 1; m CD = (7-5)/(6-4) => m CD = 1 => m AB = m CD => AB is parallel CD;

Joan walked 23 1/4 miles in a week. Her sister walked 69 3/4 miles during the same week. How many times farther did Joan’s sister walk than Joan?

Answers

joans sister walked 3 times farther.

23 1/4 * 3 = 69 3/4

joans sister walked 3 times farther.

A girl is half as old as her sister and is also two years younger than her brother. If the sum of the three children's ages is $34$ years, what is the product of their ages?

Answers

13 and a half 5 and half and 16

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