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3 years ago

What is the equation of the directrix of the parabola given by the equation (y − 3)2 = 8(x − 5)?

1 answer:

8 0

The vertex of the parabola is at (5,3) and its focal length is 8/4 = 2.
Since it opens to the right, the directrix will be a vertical line 2 units to the left of the vertex, so its equation will be x=(5-2), or x=3

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If the points A(x,2), B(-3, -4) and C(7, -5) are collinear, then find the value of x

DochEvi [55]

Answer:

x = -63

Step-by-step explanation:

If the points A(x,2), B(-3, -4), and C(7, -5) are collinear, the line that passes B and C, also passes A.

The line passes B and C has the form of y = ax + b

=> -4 = a(-3) + b

-5 = a(7) + b

=> Subtraction 1st equation from 2nd equation, we have:

-1 = 10a

=> a = -1/10

=> b = -4 + 3(-1/0) = -43/10

=> This line has form of y = (-1/10)x -43/10

This line passes A(x, 2)

=> 2 = (-1/10)x - 43/10

=> 2 + 43/10 = (-1/10)x

=> 63/10 = (-1/10)x

=> x = -63

Hope this helps!

3 0

3 years ago

Find the value of x and HI. H and J are the endpoints

a_sh-v [17]

Answer:

x = 6

HI = 29

Step-by-step explanation:

✔️HI = ½(AB) => Triangle Mid-segment Theorem

HI = 5x - 1

AB = 58

Plug in the values and solve for x

5x - 1 = ½(58)

5x - 1 = 29

Add 1 to both sides

5x - 1 + 1 = 29 + 1

5x = 30

Divide both sides by 5

5x/5 = 30/5

x = 6

✔️HI = 5x - 1

Plug in the value of x

HI = 5(6) - 1

HI = 30 - 1

HI = 29

5 0

2 years ago

Solve the following system in three variables using linear combinations. 3x−2y+z=0 4x+y−3z=−9 9x−2y+2z=20

goblinko [34]

Answer:

The solution of the system of equations is

x=2,y=7,z=8

Step-by-step explanation:

we have

3x-2y+z=0

isolate the variable z

z=2y-3x ------> equation A

4x+y-3z=-9 ----> equation B

9x-2y+2z=20 ----> equation C

substitute equation A in equation B and equation C

4x+y-3(2y-3x)=-9

4x+y-6y+9x=-9

13x-5y=-9 -------> equation D

9x-2y+2(2y-3x)=20

9x-2y+4y-6x=20

3x+2y=20 ----> equation E

Solve the system

13x-5y=-9 -------> equation D

3x+2y=20 ----> equation E

Multiply equation E by 2.5 both sides

2.5*(3x+2y)=20*2.5

7.5x+5y=50 -----> equation F

Adds equation D and equation F

13x-5y=-9

7.5x+5y=50

------------------

13x+7.5x=-9+50

20.5x=41

x=41/20.5

x=2

Find the value of y

substitute the value of x in the equation E

3(2)+2y=20

6+2y=20

2y=20-6

2y=14

y=7

Find the value of z

Substitute the value of x and the value of y in equation A

z=2y-3x

z=2(7)-3(2)

z=14-6

z=8

therefore

The solution of the system of equations is

x=2,y=7,z=8

5 0

3 years ago

1. Find the number of real number solutions for the equation.

exis [7]

Answer:

b. 2

Step-by-step explanation:

3 0

2 years ago

Tania believes that if she increases the price of an item (mark up) by 10% and then decrease it (mark down) by 10%,she will have

dezoksy [38]

She is incorrect as 10% of the higher marked up price is larger than 10% of the original price.

For example: If you mark up $100 by 10% you get $110.

If you mark down $110 by 10%, you will get $99, as 10% of $110 ($11) is larger than 10% of $100 ($10).

5 0

3 years ago