MATHEMATICS HIGH SCHOOL

Matthew is going to drive from Salt Lake City, Utah, to Las Vegas, Nevada. His car travels a consistentnumber of miles

per gallon of gasoline and he has some gasoline in his tank already. Matthew writes the

equation 25(x + 3) = 424, where x represents the number of gallons of gasoline he will need to purchase to

complete the trip.

Identify the meaning of each of the constants in Matthew's equation in the context of the problem, then solve

the equation to determine how many gallons of gasoline he must purchase.

Answers

Answer 1
Answer:

Answer: 14 gallons of gasoline.

Step-by-step explanation:

given data:

25(x + 3) = 424

where x is the number of gallon of gasoline needed to purchase.

Solution.

25(x + 3) = 424

first we open the bracket

25x + 75 = 424

collect like terms

25x = 424 – 75

25x = 349

divide both sides by 25

25x/25 = 349/25

x = 13.96

x = 14

mathew needs to get 14 gallons of gasoline.

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A line has this equation: y= -9x-2Write an equation for the parallel line that goes through (2, -3).

Answers

Answer:

y = - 9x + 15

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 9x - 2 ← is in slope- intercept form

with slope m = - 9

Parallel lines have equal slopes, thus

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To find c substitute (2, - 3) into the partial equation

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Jack is taking medications for a recent illness. Every 6 hours he takes an antibiotic, every 4 hours he takes a pain reliever, and every 3 hours he drinks a glass of water. If he starts this regime at 10 am, at what time will he be taking both medicines and a glass of water?

Answers

At 10p.m that is after 12 hours of time gap he be taking both medicines and a glass of water.

What is least common multiple?

" Least common multiple is defined as the smallest number which is a multiple of given set of numbers."

According to the question,

Given,

Time to start regime = 10am

Time to take antibiotic =Every 6hours

Time to take pain reliever =Every 4hours

Time to drink a glass of water =Every 3hours

Least common multiple of ( 6, 4, 3) = 12

After 12 hours Jack is taking both medicines and a glass of water.

Start regime at 10am

Time after 12hours is 10pm.

Hence, at 10p.m that is after 12 hours of time gap he be taking both medicines and a glass of water.

Learn more about least common multiple here

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he'd take the antibiotics at 4pm, the pain reliever at 2pm and water at 1pm

Write a possible recursive rule and then find a7 for { 7,12,17,22,27}

Answers

Start from 7, then add 5 each time.

a7 is 7 plus 30, or 37.

What is the measure of angle x?

Answers

Answer:

x = 96°

Step-by-step explanation:

96 and x are Alternate exterior angles and are congruent, thus

x = 96°

Bob, driving a new Ford, travels 330 miles in the same amount of time it takes John, driving an old Chevy and traveling 10 miles per hour faster, to travel 390 miles. How fast is Bob driving?

Answers

Answer:

  55 mph

Step-by-step explanation:

Let x represent Bob's speed. Then John's speed is x+10, and their respective times are found by ...

  time = distance/speed

  330/x = 390/(x+10) . . . . . . . the times are the same

  330(x +10) = 390x . . . . . . .  multiply by x(x+10)

  3300 = 60x . . . . . . . . . . . . . subtract 330x

  55 = x . . . . . . . . . . . . . . . . . . divide by the coefficient of x

Bob is driving at 55 miles per hour.

Find x when y=3 in the literal equation 3x+6y=24

Answers

when you plug in 3 in for y the equation is 3x + 6(3) = 24

3x + 18 = 24

subtract 18 from both sides

3x = 6

Isolate the x by dividing both side by 3

x = 2
6x3=18
24-18= 6
so 3x=6 therefore x=2
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