Ineed this for an exam
i have multiple try to answer at least 4? (or all it would me alot if you can answer
1: maurice runs 5 km in 15 mins. he plans to run a 20 km race. how long will it take him to complete the race?
2: emily bought 8 pounds of ground beef for $12.80, how much would 20 pounds of beef cost at the same price per pound?
3: the wingspan of a ghost bat is 10 more than twice that of a vampire bat. suppose a ghost bat has a wingspan of 25 inches. which equation can be used to find the wingspan of a vampire bat?
4: a true crab has 4 fewer than twice the number of legs than a hermit crab has. the hermit crab has 6 legs. how many legs dose the true crab have?
5: twice the sum of x and 5?
6: petra was given 12 yards of fabric to make costumes for the school play. if each costume requires 1 1/2 yards, how many costumes can she make?
7: a bag of potatoes weighs 4 1/2 pounds. at the first meal, 1 2/3 pounds are eaten. at the second meal, 1 3/4 pounds are eaten. how many pounds of potatoes are left in the bag?
8: the record high temperature for detroit, michigan was 101f. the record low was -32f. what is the difference between these two temperatures?
9: your score on a game show is -200. you answered the final question incorrectly, so you lost 500 points. which expression does not represent your final score.

1) maurice runs 5 km in 15 mins.

→ 5 km = 15 mins

→ 20 km = ? mins

we must try to find "?"

- this is pretty easy, i will show you both ways to solve this.

first way

-> 5 x 4 = 20. so, if you multiply 5 by 4, you must multiply 15 by 4 as well.

-> 15 x 4 = 60 mins or 1 hour.

second way

proportions!

- set two fractions equal to each other.

-> 5/20 = 15/x    (x = ? , i just made it less confusing)

-> use cross multiplying. multiply x by 5, and 15 by 20.

-> now you have 5x = 300

divide 5 on both sides. now, you have x = 60 (minutes)

2) this time, we can divide.

-> $12.80 for 8 pounds, divide 12.80/8 = $1.60 per pound

-> so, we have $1.60 per pound for 20 pounds.

-> 1.60 x 20 = $32 for 20 pounds

3) wingspan of ghost bat = 2x + 10   (let x = wingspan of vampire bat)

-> a ghost bat is 25 inches in this case.

equation: 2x + 10 = 25

4) true crab = 2x - 4   (let x = number of hermit crab legs, y = true crab legs)

-> the hermit crab has 6 legs. let's plug in 6 for x.

y = 2x - 4

y = 2(6) - 4     (do not add 2 and 6, multiply!)

y = 12 - 4

y = 8

the true crab has 8 legs.

5) twice the sum of x and 5

-> "the sum" means to add =  x + 5

-> now, twice means to multiply by 2.

2(x + 5)

! never do 2x + 5 unless it says "twice x plus 5"! these problems can be very confusing, you must add x + 5 first and then multiply.

6) 12 yards of fabric for petra, each costume requires 1 1/2 yards

-> in this problem, we divide.

-> 12 ÷ 1 1/2

   12 ÷ 3/2

   12/1 ÷ 3/2

   12/1 x 2/3    

(the KCF rule is to keep the first fraction, change the sign, and flip the second)

    12/1 x 2/3 = 12 x 2/ 1 x 3 = 24/3 = 8 costumes

7) a bag of potatoes = 4 1/2 pounds

first meal: 1 2/3 pounds eaten

second meal: 1 3/4 pounds are eaten

-> i'd rather add the first meal and second meal, then subtract it from 4 1/2

1 2/3 + 1 3/4

- we need a common denominator for 3 and 4 = 3 x 4 = 12.

1 2/3 + 1 3/4  ->  1 8/12 + 1 9/12  

(when multiplying, multiply the numerator with it!)

1 8/12 + 1 9/12 = 1 17/12 = 2 5/12

-> now, we subtract 2 5/12 from 4 1/2

4 1/2 - 2 5/12  

-> for the common denominator, we don't have to multiply 12 and 2 because 2 is already a factor of 12.

4 1/2 - 2 5/12 = 4 6/12 - 2 5/12 = 2 1/12

2 1/12 pounds of potatoes left in the bag

8) michigan high: 101 ° F

   michigan low:  -32 ° F

difference = subtraction

-> 101 - - 32  

(we have double negatives now! double negatives = positive!)

-> 101 - - 32 = 101 + 32 = 133

the difference is 133 ° F.

9) your score: -200

   lost final: lost 500 points, -500

which does not represent final score?

-> correct equation = -200 - 500

we find the opposite, so the answer is -200 + 500

✧ hope this helped! good luck on your exam and do well!

- aure

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3