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3 years ago

8

DEF rotates 90 degrees clockwise about point A to create D’E’F. Therefore, which equation must be true

1 answer:

Rom4ik [11]3 years ago

5 0

Answer:

m∠EAE ' = m∠FAF '

Step-by-step explanation:

Rotation is a type of transformation referred to a in which the shape of the original object is preserved and the angle of rotation is constant for all the parts of the body.

Thus, when ΔDEF rotates 90° clockwise about point A to create ΔD 'E 'F.

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Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

5 0

2 years ago

Read 2 more answers

Triangle ABC is an equilateral triangle. Segment AD measures 18 inches.Which statements about the diagram are correct? Check all

Margaret [11]

Answer:

The correct answer is option C and D.

C). DC = 6√3

D). AC = 12√3

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

It Says Least To Greatest With These Numbers 7/12 0.75 5/6

Umnica [9.8K]

If you mean what I think you mean then I think it is
7/12, 5/6, and then 0.75
I could be wrong though but I hope I am right good luck

5 0

3 years ago

What is the solution of |x- 5|-2=10?

Lelu [443]

Answer:

x=17, x=-7

Step-by-step explanation:

Step 1 :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered

|x-5|-2 = 10

Another term is moved / added to the right hand side.

|x-5| = 12

Step 2 :

Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |x-5|

For the Negative case we'll use -(x-5)

For the Positive case we'll use (x-5)

Step 3 :

Solve the Negative Case

-(x-5) = 12

Multiply

-x+5 = 12

Rearrange and Add up

-x = 7

Multiply both sides by (-1)

x = -7

Which is the solution for the Negative Case

Step 4 :

Solve the Positive Case

(x-5) = 12

Rearrange and Add up

x = 17

Which is the solution for the Positive Case

Step 5 :

Wrap up the solution

x=-7

x=17

8 0

3 years ago

Read 2 more answers

Help me guys. plz no Decimal please. Thank you!

Scrat [10]

Answer: 1,145,375cm^3

Step-by-step explanation:

8 0

3 years ago