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3 years ago

Help ASAP!!! Read the question and answer please!!! First answer and correct answer gets the brain-

Mathematics

1 answer:

Oksi-84 [34.3K]3 years ago

7 0

Answer:

First blank is 15.

Second blank is 60.

Third blank is 8.

$15x-60=8$

Step-by-step explanation:

To clear the fractions, multiply both side by the least common multiple (or a common multiple) of the denominators you see.

The least common multiply of 4 and 5 is 4(5)=20.

So multiply both sides by 20:

$20(\frac{3}{4}x-3)=20(\frac{2}{5})$

$\frac{3(20)}{4}x-3(20)=\frac{2(20)}{5}$

Simplify:

$3(5)x-60=2(4)$

$15x-60=8$

First blank is 15.

Second blank is 60.

Third blank is 8.

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Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola.

xxTIMURxx [149]

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:

The complete question is

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).

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)

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3 years ago

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Given H(6,7) and I (-7,-6) if point G lies 1/2 of the way long line segment HI, Santiago argues that point G is located at the o

amid [387]

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3 years ago