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4 years ago

(80 POINTS) What rule describes a dilation with a scale factor of ½ and the center of dilation at the origin?

Mathematics

2 answers:

coldgirl [10]4 years ago

8 0

Answer:

C. (x,y) → (1/2x,1/2y)

Step-by-step explanation:

Dialation means to multiply each coordinate by scale factor and in this case it's 1/2

lesya [120]4 years ago

6 0

Answer:

Step-by-step explanation:

(x, y) -> (1/2x, 1/2y)

When you dilate a side, point, etc, you are multiplying the original dimension by the scale factor. That is represented in option C: the original x and y are multiplied by the scale factor, 1/2! Hope that helps! :)

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3 years ago

Simplify completely quantity 4 x squared minus 32 x plus 48 all over quantity 3 x squared minus 17 x minus 6.

Yuki888 [10]

For this case we must simplify the following expression:

$\frac {4x ^ 2-32x + 48} {3x ^ 2-17x-6}$

Simplifying the numerator, dividing all the terms by 4, we have:

$x ^ 2-8x + 12$

We factor by looking for two numbers that when added together give -8 and when multiplied by 12. These are: -6 and -2

$-6-2 = -8\\-6 * -2 = 12$

So, we have to:

$x ^ 2-8x + 12 = (x-6) (x-2)$

Simplifying the denominator:

We rewrite -17x as -18x + x:

$3x ^ 2-18x + x-6$

We factor the highest common denominator of each group:

$3x (x-6) +1 (x-6)$

We factor the polynomial by factoring the highest common denominator (x-6):

$(x-6) (3x + 1)$

So, we have to:

$3x ^ 2-17x-6 = (x-6) (3x + 1)$

Substituting in the original expression we have:

$\frac {(x-6) (x-2)} {(x-6) (3x + 1)} = \frac {x-2} {3x + 1}$

ANswer:

$\frac {4x ^ 2-32x + 48} {3x ^ 2-17x-6} = \frac {x-2} {3x + 1}$

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3 years ago

Can you help me solve systems of equations by elimination step by step 6x+y=15 -7x-2y=-10

Anna71 [15]

Answer: (4, -9)

Step-by-step explanation:

Use elimination method. Manipulate one (or both) equations to eliminate one of the variables and solve for the remaining variable. I will be eliminating y

6x + y = 15 → 2(6x + y = 15) → 12x + 2y = 30

-7x - 2y = -10 → 1(-7x + 2y = -10) → -7x - 2y = -10

5x = 20

x = 4

Next, replace "x" with "4" into either equation and solve for y.

6(4) + y = 15

24 + y = 15

y = -9

Check:

Plug in x = 4 and y = -9 into the other equation to verify it makes a true statement.

-7x - 2y = -10

-7(4) - 2(-9) = -10

-28 - -18 = -10

-28 + 18 = -10

-10 = -10 $\checkmark$

6 0

4 years ago