MATHEMATICS MIDDLE SCHOOL

Which equation represents the linear relationship shown in the table? y=3x+4 y=3x+8 y=8x+3 y=4x+3 x y 0 3 2 11 4 19 6 27

Answers

Answer 1

Answer:

Answer:

The linear relationship is given by, y = 4x + 3

Step-by-step explanation:

The points given are ( as (x,y) pair)

x y

0 3

2 11

4 19

6 27

The given lines are ,

1) y = 3x + 4

2) y = 3x + 8

3) y = 8x + 3

4) y = 4x + 3

Now , by inspection or trial and error method only line (4) does satisfy all the points, so the linear relationship is given by,

y = 4x + 3

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The product shown is a difference of squares. What is the missing constant term in the second factor?(–5x – 3)(–5x +?

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) 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.

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

50 POINTS!!!!A company makes cylindrical cans for peaches. Each can has a radius of 4 centimeters and a height of 12 centimeters. The company plans to increase the
volume of each can by 25%.

a) What will be the height of the new can if the radius remains the same?

b) What will be the radius of the new can if the height remains the same?

*Please show your work*

Answers

Volume = πr²h

V = π × 4² × 12
V = π × 16 × 12
V = 192π

Original Volume = 192π

25% = 0.25
0.25 × 192 = 48

New Volume = Old Volume + 25% Old Volume
New Volume = 192π + 48π
New Volume = 240π

25% = 0.25
12 × 0.25 = 3

New Height = Old Height + 25% Old Height
New Height = 12 + 3
New Height = 15

V = πr²h
240π = π × r² × 15
240 = 15r²
16 = r²
√16 = √r²
4 = r

New Radius = 4

25% as a decimal is 0.25
multiply 12 and 0.25 12 X 0.25 = 3
add 2 and 3 2+3=5

So that makes the new height 15

the new radius is 4:46

What is the cube root of 216x18?

Answers

Answer:

The correct answer is 15.72 or 6 ∛18

Step-by-step explanation:

Let's calculate the cube root of 216 * 18

∛(216 * 18)

216 = 8 * 27

8 = 2³; 27 = 3³

18 = 9 * 2 or 3² * 2

∛(8 * 27 * 18)

Simplifying:

∛(2³ * 3³ * 3² * 2)

2 * 3 ∛(3² * 2

6 * 2.62 = 15.72 or 6 ∛18

Miguel has already put 36 sports cards in 5 folders. He buys 372 more cards. He puts the same number of cards into the 5 folders with any extra cards going into the green folder. How many cards are now in the green folder?

Answers

I think the answer is 75.6 because i divided 36 cards by 5 folders and i got 1.2. And then i divided 372 extra cards by 5 folders am got 74.4. I add the two total and have 75.6 5/36 = 1.2 5/372 = 74.4 1.2+74.4= 75.6 srry if I'm wrong

Can someone help me please thank u