MATHEMATICS MIDDLE SCHOOL

Solve the system by substitution :y=2x+2
y=3x
a.) (3,9) b.) (1,4)
c.) (-2,-4)

Answers

Answer 1
Answer: So since we already have one of the unknowns equaling something, we start by substituting...

y= 3x so let's substitute 3x into the first equation where the y is...

y = 2x + 2
3x = 2x + 2
subtract 2x from each side
x = 2

So now we know x = 2 So we can now substitute it back into the equation but for x this time...

y = 2x + 2
y = 2(2) + 2
y = 4 + 2 = 6

So our solution set is

(2, 6)

You can check it by substituting x and y into both of the equations to see if you have a true statement...

y= 2x + 2
6 = 2×2 + 2
6 = 6

y = 3x
6 = 3×2
6 = 6

Both true so it checks!

*note- I noticed that my solution was not one of your options, but if you substitute the available option that you gave into the equations none of them work, so take a look at your possible answers and see if you didn't leave something out. ;)

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A truck can be rented from Company A for ​$80 a day plus ​$0.30 per mile. Company B charges ​$20 a day plus ​$0.50 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same

Answers

Write equations for both companies:

Company A = 80 + 0.30x

Company B = 20 + 0.50x

X = number of miles.

Set the equations to equal and solve for x:


80 + 0.30x = 20 + 0.50x

Subtract 0.30x from both sides:

80 = 20 + 0.20x

Subtract 20 from both sides:

60 = 0.20x

Divide both sides by 0.20:

x = 60 / 0.20

x = 300


The answer is 300 miles.

If 4 bags of corn can feed a herd of cows for 6 days, how many bags will feed the herd for 9 days ?

Answers

1 BAG= 4/6 days which is 2/3
4 BAGS= 6 days
? BAGS= 9 days
9 days =2/3 X 9 days
therefore 2 X 3 =6 BAGS
therefore 6bags = 9days

1 BAG= 4/6 days which is 2/3

4 BAGS= 6 days

? BAGS= 9 days

9 days =2/3 X 9 days

therefore 2 X 3 =6 BAGS

therefore 6bags = 9days

Which word best describes the degree of overlap between the two data sets?A.
high

B.
moderate

C.
low

D.
none

Answers

I think the answer is B-moderate.

So the law of order and the law of grouping apply to division

Answers

It depends on what you are grouping

You brought 1.5 dozen bagels to school. A dozen bagels cost $5.98. You used a coupon that took $1.00 off of the total. How much did you pay for the bagels?

Answers

Answer: He would pay $7.97 for the bagel.

Step-by-step explanation:

Since we have given that

Number of dozen bagels he brought to school = 1.5

Cost of a dozen = $5.98

Total cost of 1.5 dozen bagels he brought to school is given by

1.5* 5.98\n\n=\$8.97

According to question, he used a coupon that took $1.00 off of the total .

so, it becomes

\$8.97-\$1.00\n\n=\$7.97

Hence, he would pay $7.97 for the bagel.
1 Dozen = 12
1 Dozen = $5.98
1/2 Dozen = 6
1/2 Dozen = $2.99

Add 1 Dozen ($5.98) and 1/2 Dozen ($2.99) Which Equals= $8.97 then subtract the $1.00 Coupon So final answer is $7.97 for 1.5 dozen bagels.

A chef prepares apples for a fruit salad. She cuts each apple into 6 slices. The following patterns can be made: Pattern A: start with 1 apple and increase by 1 apple Pattern B: start with 6 slices and increase by 6 slices Which ordered pairs represent the number of apples from Pattern A and the number of apple slices from Pattern B?

Answers

Answer:

A: (1,1)

B: (6,6)

Step-by-step explanation:

Given:

A chef prepares apples for a fruit salad. She cuts each apple into 6 slices.

The following patterns can be made:

Pattern A: start with 1 apple and increase by 1 apple.

Pattern B: start with 6 slices and increase by 6 slices.

To find : ordered pairs which represent the number of apples from Pattern A and the number of apple slices from Pattern B

Solution :

Pattern A:

If a chef starts with one apple then increase by 1 apple then ordered pair which represent this pattern is (1,1)

Pattern B :

If a chef starts start with 6 slices and increase by 6 slices then ordered pair which represent this pattern is (6,6)
a is 1:1 and b is 6:6
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