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3 years ago

Use the graph of △GHI and its image to answer the question.

Mathematics

1 answer:

Tresset [83]3 years ago

8 0

Answer:

D. Rotate △GHI 90∘ clockwise about the origin and dilate it by a factor of 2/3 through the origin

Step-by-step explanation:

Segment HI points south, and segment H'I' points west, so a rotation of 90° clockwise is involved. (This eliminates choices A and C.)

The image is smaller than the original by a factor of 2/3, eliminating choice B and confirming choice D.

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Write an equation of the parabola that opens up whose vertex (−1, 2) is 3 units from the focus. (Vertex form or Parabola Form is

TEA [102]

Answer:

y2 = 4ax (opens right, a > 0)

y2 = -4ax (opens right, a > 0)

x2 = 4ay (opens up, a > 0)

x2 = -4ay (opens down, a > 0)

Vertex at (h, k) :

(y - k)2 = 4a(x - h) (opens right, a > 0)

(y - k)2 = -4a(x - h) (opens right, a > 0)

(x - h)2 = 4a(y - k) (opens up, a > 0)

(x - h)2 = -4a(y - k) (opens down, a > 0)

Equation of a Parabola in Vertex form

Vertex at Origin :

y = ax2 (opens up, a > 0)

y = -ax2 (opens down, a > 0)

x = ay2 (opens right, a > 0)

x = -ay2 (opens left, a > 0)

Vertex at (h, k) :

y = a(x - h)2 + k (opens up, a > 0)

y = -a(x - h)2 + k (opens down, a > 0)

x = a(y - k)2 + h (opens right, a > 0)

y = -a(y - k)2 + h (opens left, a > 0)

Step-by-step explanation:

7 0

2 years ago

Is three and five a factor pair of 15

Pie

Yes because 3*5 = 15

Factors multiply to get the product.

6 0

3 years ago

Read 2 more answers

PLS HELP ME!! this test will bring my grade up ahhh (question in picture(

weqwewe [10]

Answer:

A or D

Step-by-step explanation:

You know that triangles are Similar if they have like same angles. If too triangles are the same the 3rd one has to be too!

Hope this helped and I hope you do well on your test!! Good Luck!

*Sends good vibes* :)) <33

"You were born to be real, Not perfect.."

-SUGA-

4 0

3 years ago

Could someone help me and explain?

ExtremeBDS [4]

Answer:

length 3 in
width 2 in

Step-by-step explanation:

Since none of the answer choices match the drawing of the gardener, we assume the question is referring to the drawing of the partner.

The gardener's drawing is 1/4 of actual size. So, in terms of the gardener's drawing, actual size is ...

gardener's drawing = (1/4)actual size

actual size = 4(gardener's drawing)

The partner's drawing is 1/20 of actual size, so is ...

partner's drawing = actual size/20 = (4(gardener's drawing))/20

partner's drawing = (4/20)(gardener's drawing)

partner's drawing = (gardener's drawing)/5

Then the {length, width} of the partner's drawing are ...

partner's drawing {length, width} = {15 in, 10 in}/5 = {3 in, 2 in}

The partner's drawing has a length of 3 inches and a width of 2 inches.

6 0

3 years ago

Find all roots: x^3 + 7x^2 + 12x = 0 Show all work and check your answer.

Aliun [14]

The three roots of x^3 + 7x^2 + 12x = 0 is 0,-3 and -4

Solution:

We have been given a cubic polynomial.

$x^{3}+7 x^{2}+12 x=0$

We need to find the three roots of the given polynomial.

Since it is a cubic polynomial, we can start by taking ‘x’ common from the equation.

This gives us:

$x^{3}+7 x^{2}+12 x=0$

$x\left(x^{2}+7 x+12\right)=0$ ----- eqn 1

So, from the above eq1 we can find the first root of the polynomial, which will be:

x = 0

Now, we need to find the remaining two roots which are taken from the remaining part of the equation which is:

$x^{2}+7 x+12=0$

we have to use the quadratic equation to solve this polynomial. The quadratic formula is:

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Now, a = 1, b = 7 and c = 12

By substituting the values of a,b and c in the quadratic equation we get;

$\begin{array}{l}{x=\frac{-7 \pm \sqrt{7^{2}-4 \times 1 \times 12}}{2 \times 1}} \\\\{x=\frac{-7 \pm \sqrt{1}}{2}}\end{array}$

Therefore, the two roots are:

$\begin{array}{l}{x=\frac{-7+\sqrt{1}}{2}=\frac{-7+1}{2}=\frac{-6}{2}} \\\\ {x=-3}\end{array}$

And,

$\begin{array}{c}{x=\frac{-7-\sqrt{1}}{2}} \\\\ {x=-4}\end{array}$

Hence, the three roots of the given cubic polynomial is 0, -3 and -4

4 0

3 years ago