Simplify the following expression.<br><br> 9 1/2 r 5/2 t<br> _________

Which rule yields the dilation of the figure QRST centered at the origin?

denis-greek [22]

A) (x, y) → (3x, 3y)

<h2>Explanation:</h2>

When you dilate an object, you enlarge or reduce the size of it. To do this, we need a scale factor which allows us to make the object larger or smaller depending on the value of that factor. Let's call this factor as k, then it is true that:

If k > 1, the object will be larger than the original one.
If k < 1, the object will be smaller than the original one.

If the dilation is performed centered at the origin, then corresponding points of the original and dilated figures will be connected by straight lines, being the center of dilation the point where all the lines meet.

The only option that meets this requirement is:

A) (x, y) → (3x, 3y)

Whose scale factor is k = 3 making the dilated figure larger than the original one.

<h2>Learn more:</h2>

Dilation: brainly.com/question/10946046

#LearnWithBrainly

5 0

2 years ago

Find the measure of HG¯¯¯¯¯¯¯¯.<br> A. 12<br> B. 16<br> C. 14<br> D. 7

Paraphin [41]

HG^2 = FG * (FG + EF)

Fill in the values:

(x+3)^2 = x * (7+x)

Simplify the right side:

(x+3)^2 = 7x +x^2

Rewrite the left side using the FOIL method

x^2 + 6x + 9 = 7x +x^2

Subtract x^2 from both sides:

6x +9 = 7x

Subtract 6x from both sides:

x = 9

Now you have x solve for HG

HG = x +3 = 9+3 = 12

The answer is A.

3 0

3 years ago

1. Simplify. 5–1(3–2)

konstantin123 [22]

Answer with explanation:

Using following law of indices

$1.x^a \times x^b=x^{a+b}\\\\2. (x^m)^n=x^{mn}\\\\ 3. x^{-n}=\frac{1}{x^n}\\\\4. \frac{x^m}{x^n}=x^{m-n}$

$1.5^{-1}\times 3^{-2}=\frac{1}{5}\times\frac{1}{3^2}\\\\=\frac{1}{5\times9}\\\\=\frac{1}{45}\\\\2. \frac{mn^{-4}}{p^0*q^{-2}}=\frac{mq^2}{n^4}\\\\ 3.0.0042=4.2\times 10^3\\\\4.6.12 \times 10^3=6.12 \times 1000=6120\\\\ 5.0.5 \times(8\times10^5})=\frac{1}{2}\times8 \times 10^5=4\times 10^5\\\\6. (9 \times 10^3)^2=9^2 \times (10^3)^2=81 \times 10^6\\\\7.( \frac{1}{2}a^{-4}\times b^2 )_{a=-2,b=4}{\text{or}}( \frac{1}{2}a^{4}\times b^{-2} )_{a=-2,b=4}=\frac{1}{2}\times (-2)^{-4}\times(4)^2{\text{or}}=\frac{1}{2}\times (-2)^{4}\times(4)^{-2}=\frac{16}{2\times16}=\frac{1}{2}$

$9. (4\times x\times y^2)^3\times (xy)^5=4^3\times x^3\times (y^2)^3\times x^5 \times y^5\\\\=64\times x^{3+5}\times y^{5+6}\\\\=64x^8y^{11}\\\\10.(2\times t^3)^3(0.4\times r)^2=2^3 \times (t^3)^3\times (0.4)^2 \times r^2=8\times t^9 \times 0.16 \times r^2=1.28r^2t^9$

8. A number raised to a negative exponent is negative.

Explaining with the help of few examples

$1.2^{-3}=\frac{1}{2^3}=\frac{1}{8}\\\\ 2.(-3)^{-3}=\frac{1}{(-3)^{3}}=\frac{-1}{27}$

Option C: Sometimes

1.Option B

2.Option A

3.Option C

4.Option A

5.Option D

6. $81 \times 10^6$

7.Option B

8.Option C

9.Option A

10.Option $1.28 r^2 \times t^9$

4 0

3 years ago

Read 2 more answers

Write the word sentence as an equation. 12 less than a number m equals 20.

PolarNik [594]

Answer

Equation: m - 12 = 20

5 0

2 years ago

Which vector best describes the translation below?

Nimfa-mama [501]

<h3>Answer: Choice A) <9,0></h3>

Explanation:

Focus on one of the points in the figure on the left. Let's say we go for the upper left corner point (-7, 4)

Notice it moves to the corresponding image point (2,4). It has shifted 9 units to the right to follow the translation rule $(x,y) \to (x+9, y)$ . We've added 9 to the x coordinate, and the y coordinate stays the same.

This notation can be shortened to <9, 0>

In general, the notation $(x,y) \to (x+a, y+b)$ is shortened to the translation vector notation $< a, b >$ . In this case, a = 9 and b = 0.

8 0

2 years ago

Simplify the following expression. 9 1/2 r 5/2 t __________ rt 1/2