How many points was each multiple choice question worth?

Polygon ABCD is reflected and dilated to give polygon PQRS. The coordinates of the preimage are (2, 2), (6, 8), (12, 8), and (16

HACTEHA [7]

Answer: The scale factor of the dilation is 0.5.

Explanation:

It is given that ABCD is polygon which is reflected and dilated , then we get PQRS.

The vertices of ABCD are (2, 2), (6, 8), (12, 8), and (16, 2) respectively. The vertices of image PQRS are (11, 15),(9, 12), (6, 12), and (4, 15) respectively.

The reflection affects the coordinates but does not affect the length of the sides.

But when we talk about dilation it affects the length of sides according to the scale factor or a constant factor.

If a line segment AB is dilated by scale factor k then length of A'B' is k times length of AB.

$|A'B'|=k\times |AB|$ .... (1)

So we have to find any side length of preimage and the side length of that side in image. it means we have to find AB and PQ.

Use distance formula to find the side length.

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$AB=\sqrt{(8-2)^2+(6-2)^2}=\sqrt{36+16}=2\sqrt{13}$

$PQ=\sqrt{(9-11)^2+(12-15)^2}=\sqrt{4+9}=\sqrt{13}$

It is noticed that the size of side in preimage is $2\sqrt{13}$ and the size of same side in image is $\sqrt{13}$ .

Using equation (1), we get

$\sqrt{13}=k \times 2\sqrt{13}$

$k=\frac{1}{2}$

$k=0.5$

Hence, the value of scale factor is 0.5.

7 0

2 years ago

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How many repeating digits are in the smallest group of repeating digits in the decimal equivalent of 2/9

AVprozaik [17]

Answer:

The answer is A.

Step-by-step explanation:

First, divide two by nine. The result is the decimal zero point two repeating.

Second, the digit that repeats is two. So, since two is one digit, the answer is A.

8 0

3 years ago

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Which statement describes the translation of y = −one half (x − 2)2 − 2 from standard position?

kaheart [24]

A quadratic in vertex form can be represented as

$y = a(x-h)^{2} +k$

a represents reflection over the x-axis, and a vertical stretch or compress
- is reflection and a fraction (1/2) represents a compression.

-h represents a shift of that many units to the right (-2 shifts to the right two units)

k represents a shift up or down (-2 is shifting down 2 units_

Reflected over the x-axis, Vertically compressed by a factor of 1/2, shifted 2 units to the right, and shifted 2 units down

5 0

2 years ago

A specimen of charcoal found at Stonehenge contains 63% as much Carbon-14 as a sample of present-day charcoal. What is the age o

seraphim [82]

Since we are given with the identity of the chemical as Carbon-14, we obtain the half-life of the chemical from a reliable source and get a value of 5730 years. The equation that we are going to use for this item is,
A(t)/A(0) = (0.50)^(n/5730)
where A(t) is the current amount, A(0) is the initial amount and n is the number of years. We know from the given that the ratio of A(t) and A(0) is equal to 0.63. Substituting this to the given,
0.63 = 0.50^(n/5730)
n = 3819.48
Thus, the sample is approximately 3819.5 years old.

5 0

2 years ago

What is a way to write 11 more than twice x is less than 44

madam [21]

(2x) + 11 < 44

x is multiplied by two because we are looking for twice of x. 11 is added to the 2x because we are looking for eleven more than the sum of twice of x. Since 2x + 11 is less than 44, we use the lesser than ( < ) symbol.

4 0

2 years ago

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