MATHEMATICS MIDDLE SCHOOL

PLEASEE HURRY!!!!!!!! Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola.
Equation 1: (x – 3)2 = y – 4
Equation 2: y = -x + b
In order for Tom’s thinking to be correct, which qualifications must be met?
A: b must equal 7 and a second solution to the system must be located at the point (2, 5).
B: b must equal 1 and a second solution to the system must be located at the point (4, 5).
C: b must equal 7 and a second solution to the system must be located at the point (1, 8).
D: b must equal 1 and a second solution to the system must be located at the point (3, 4).

Answers

Answer 1

Answer:

Answer:

Option A: b must equal 7 and a second solution to the system must be located at the point (2, 5)

Step-by-step explanation:

step 1

Find the vertex of the quadratic equation

The general equation of a vertical parabola in vertex form is

$y=a(x-h)^2+k$

where

(h,k) is the vertex

we have

$(x-3)^(2)=y-4$

$y=(x-3)^(2)+4$

The vertex is the point (3,4)

step 2

Find out the value of b in the linear equation

we know that

If the vertex is a solution of the system of equations, then the vertex must satisfy both equations

substitute the value of x and the value of y of the vertex in the linear equation

$y=-x+b$

For x=3, y=4

$4=-3+b$

$b=7$

$y=-x+7$

step 3

Find out the second solution of the system of equations

we have

$y=(x-3)^(2)+4$ -----> equation A

$y=-x+7$ ----> equation B

solve the system of equations by graphing

Remember that the solutions are the intersection points both graphs

The second solution of the system of equations is (2,5)

see the attached figure

therefore

b must equal 7 and a second solution to the system must be located at the point (2, 5)

Answer 2

Answer:

Answer:

Step-by-step explanation:

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Donna charges $25.75 for a haircut and $40.50 for a color treatment. Donna did 5 haircuts and 3 color treatment each day for 6 days. How much money did Donna earn altogether?

Answers

The answer is 1501.5

First, do 25.75 and multiply it times 5.
Second, do 40.50 and multiply it by 3.
Third, add your answers together
Fourth, multiply your answer by 6. Tada!

What is the distance between the points (–3, 4) and (–7, 4)?

Answers

Okay. This is going to be a very long one.

$\sqrt{(x_(2)-{x_1)}^(2)+(y_2-y_1)^2} = distance\n-3--7 = 4, 4^2 = 16\n4-4 = 0, 0^2 = 0\n\sqrt {16} = 4\n\boxed 4$

Answer:

11 units

Step-by-step explanation:

A pound of beans costs $4.70. Mrs. Patel buys 6.5 pounds of beans. How much dose she pay for the beans ?

Answers

$30.55
-----------------------------------------
4.70
x 6.5
_____
2350
28200
_______
30.550

4.70
x 6 ( lbs)
28.20

4.70 divided by 2 is 2.35

28.20 +2.35 = 30.55

The pyramid shown has a square base that is 32 32 centimeters on each side. The slant height is 24 24 centimeters. What is the lateral surface area?

Answers

The answer is 3072 cm².

Lateral surface area of a pyramid can be expressed as:
L = P × l
where:
L - Lateral surface area
P - Perimeter of a base
l - slant height

We have:
L = ?
P = ?
l = 24 cm
a = 32 cm

Perimeter of a base which is a square is:
P = 4 × a
P = 4 × 32 cm
P = 128 cm

Thus,
L = P × l
L = 128 cm × 24 cm
L = 3072 cm²

Therefore, the lateral surface area is 3072 cm².

Answer:

1536

Step-by-step explanation:

A strong man takes 2 minutes to make one cut through a log. How long will he need to cut a ten-foot log into into 4 equal pieces?