MATHEMATICS MIDDLE SCHOOL

"You and your friend leave your houses at the same time to meet at a restaurant. The distance (in miles) your friend is from the restaurant is given by y=−40x+200, where x is the number of hours since your friend left home. You live 100 miles from the restaurant and arrive at the same time as your friend. Write a linear equation that represents your distance from the restaurant."

Answers

Answer 1

Answer:

The equation will be:

$y=-20x+100$

Why?

Let's work with your friend equation in order to find the time from his house to the restaurant (is the same as yours).

We are given the following function:

$y=-40x+200$

When: $y=0$ our friend arrived, so, calculating "x", we have:

$0=-40x+200\n\n40x=200\n\nx=(200)/(40)=5h$

We have that it took 5 hours for our friend to arrive at the restaurant, and it's the same time for you. We know that you live 100 miles from the restaurant.

Your equation will have the following form:

$y=-k*x+distance$

Where,

y is the position

k is the rate distance/time

x is the time

Now, again, when $y=0$ , you will have arrived at the restaurant too, so:

$0=-k*x+100$

Using "x" equal to 5 hours, because you will have arrived at that time too, we have:

$0=-k*5+100\n\nk=(100)/(5)=20$

Your equation will be:

$y=-20x+100$

Have a nice day!

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A group of mountain climbers begin an expedition with 250 pounds of food. They plan to eat a total of 12 pounds of food per day. Write and solve a linear equation to find the number of days their food will last,

Answers

The 250 pounds of food will last for 20.83 days.

What is an equation?

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

Initial quantity of food = 250 pounds,

Since, mountain climbers begin to eat 12 pounds per day,

Let the food will last for x days,

The equation can be written as,

12x = 250

x = 20.833

The food will last for 20.83 days.

To know more about Equation on:

brainly.com/question/187506

#SPJ5

Use the equation y=mx+b where m is the slope (how much it increases each time) and b is the y intercept (starting point).

Your equation would be: y=12x+0 because they eat 12 pounds each day and they start out having eaten 0 pounds.

To solve the equation, plug in the total amount of food for y and use algebra to solve for x:
250=12x
(divide by 12)
(250/12)=x
X=20.833

Their food would last approximately 20 days. (Make sure you round if required)

I need help ASAP!Lainey is sliding down a water slide that is 387 feet long at a rate of 43 feet per second. How long will it take Lainey to travel from the top to the bottom of the slide?

9 seconds

344 seconds

-9 seconds

-344 seconds

Answers

set this up as a proportion. 43 ft/ 1 sec to 387 ft/ x sec. Now cross multiply to get:

43x = 387

now divide by 43 on each side to get:

x = 9 sec

Does a scalene always have to have unequal sides?

Answers

Yes. That's the definition of a Scalene triangle. If any two
of its sides are equal, then it's not a Scalene triangle.

Yes, a scalene's all sides have to be unequal always or it won't be a scalene.

What is the answer to 2x+4-3x=0

Answers

2x+4-3x=0
-4 -4
2x-3x=-4
-1x=-4
_ _
-1 -1
x=4
so the answer is x=4

2x + 4 -3x = 0

2x - 3x + 4 = 0
-x + 4 = 0
-4 = - 4
-x = - 4
x = 4

Ans : x = 4

There are 15 violinists in the orchestra this year. Next year, two violinists will leave and some new violinists will join the orchestra. If v is the number of violinists who will join the orchestra, which expression(s) represent the number of violinists in the orchestra next year.A 15−2+v15 minus 2 plus v

B 15−v15 minus v

C v−2v minus 2

D 13+v13 plus v

E v−15v minus 15

F v+13