MATHEMATICS MIDDLE SCHOOL

1. What is the solution to the system of equations?y = 5x - 7

-3x - 2y = -12

A. (2, 3)
B. (1, -2)
C. (-2, 9)
D. (3, 8)

What is the solution to the systems of equations represented by the 2 equations?
y = 4x + 3

y = -x - 2

A. (1, 7)
B. (-1, -1)
C. (2, -4)
D. (-3, -9)

A family went to an amusement park and paid $12 for each adult and $8 for each child. A group of 15 people went to the park and it cost $140. This system of equations models this situation, where x is the number of adults and y is the number of children.
How many children were in the group?

x + y = 15
12x + 8y = 140

Answers

Answer 1

Answer:

Answer: 1) A. (2, 3)

2) B. (-1, -1)

3) 10 children

Step-by-step explanation:

1) $\left \{ {{y=5x-7} \atop {-3x-2y=-12}} \right.$

Since the y is already isolated in the first equation, to solve the system you simply substitute that expression into the second equation and then solve, finding the value of x:

$-3x-2(5x-7)=-12\n-3x-10x+14=-12\n-13x=-12-14\n-13x=-26\nx=(26)/(13)=2$

And then you substitute that value into the first equation and solve to find the value of y:

$y=5(2)-7\ny=10-7\ny=3$

So, the solution of the system is (2, 3).

2) $\left \{ {{y=4x+3} \atop {y=-x-2}} \right.$

Since the y is already isolated in both equations, to solve the system you simply equalize the first and the second expression and then solve, finding the value of x:

$4x+3=-x-2\n4x+x=-2-3\n5x=-5\nx=-1$

And then you substitute that value into the first or the second equation (whichever you like) and solve to find the value of y:

$y=-(-1)-2\ny=1-2\ny=-1$

So, the solution of the system is (-1, -1).

3) $\left \{ {{x+y=15} \atop {12x+8y=140}} \right.$

To solve the system, the easiest way is to isolate the y in the first equation and then substitute the expression obtained into the second equation, finding the value of x.

From the first equation: $y=15-x$

Substituting:

$12x+8(15-x)=140\n12x+120-8x=140\n4x=140-120\n4x=20\nx=5$

And then you substitute that value into the first equation and find the value of y:

$y=15-5\ny=10$

So, there were 10 children in the group.

Answer 2

Answer: y=5x-7 -3x-2y=-12 (2,3)

y=4x+3 y=-x-2 (-1,-1)

12x+8y=140 5 adults 10 children
12(5)+8(10)=140
60+80=140

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7*10^8 is estimated as the product

Does the point (25,75) lie on the straight line y=3x

Answers

yes

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It costs $6 per pound for peanuts at the Blessed Food Market. Which of the following represent the range of the function in ferms of cost per pound?A. $6
B. Amount of Peanuts
C. Cost of Peanuts Purchased
D. Peanuts Purchased

Please answer. I will give you 11 points.

Answers

I think it's the cost of peanuts since the range is the y axis and the x axis shows the # of pounds of peanuts

Name a pair of fractions that use the least common denominator and are equivalent to 9/10 + 5/6

Answers

The smallest common denominator is 30 in so
9/10=27/30 and 5/6=25/30 are your answers ; ]

The pair of fractions needed are $(27)/(30)$ and $(25)/(30)$

Given sum of fraction is:

$(9)/(10) + (5)/(6)$

To find: pair of fraction using least common denominator and summing equal to given sum of fraction.

Calculations:

Why do we need to find least common denominator?

It is because summing(or subtracting) fractions with common denominators is very easy as compared to those with unlike denominators.

When denominators are same, the sum or subtraction operation can directly work on the numerator values and their result will be putted on top of the denominator.

For example:

$(3)/(5) + (2)/(5) = (3+ 2)/(5) = (5)/(5) = 1$

The least common denominator of 10 and 6 is 30 since:

6 , 12, 18, 24, 30

10, 20, 30

The least number that is common in both 6's and 10's multiple's list is 30.

Rewriting both the fractions using least common denominator:

$(9)/(10) = (3 * 9)/(3 * 10) = (27)/(30)$

and

$(5)/(6) = (5 * 5)/(5 * 6) = (25)/(30)$

Since both the new fractions are of same value as of old pair, thus their sum would be same, as shown here:

$(9)/(10) + (5)/(6) = (27)/(30) + (25)/(30) = (52)/(30)$

Thus, the pair of fractions needed are $(27)/(30)$ and $(25)/(30)$ .

Learn more about fraction addition here:

brainly.com/question/17544795

What is 3-3 x 6+2=?????????????????????????????????

Answers

-13 is what I came up with, and believe me, it is what the answer is

3-3 x 6+2= -13
The answer= -13

Joanna split three pitchers of water equally among her eighth plants. What fraction of a pitcher did each player get? A.1/8 of a pitcher

B.1/7 of a pitcher

C.3/8 of a pitcher

D.8/3 of a pitcher

Answers

C. Since 3÷8=3/8. You could also multiply 3/8×8 which is simply adding 3 eight times.

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