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3 years ago

Identify the numerator and denominator of the following number. 1/6

1 answer:

8 0

The numerator is the top number while the denominator is the bottom number. So 1 is the numerator and 6 is the denominator.

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Triangle ABC is being dilated with the center of dilation at the origin. The image of C, point C' has coordinates of (7.2, 3.6).

MAXImum [283]

General Idea:

When we are given a point P(x, y) centered at origin with a scale factor of k, then the dilated point will be given by P' (kx, ky)

Applying the concept:

In the diagram given, the coordinate of C is (6, 3). Triangle ABC is being dilated with the center of dilation at the origin. The image of C, point C' has coordinates of (7.2, 3.6).

If C (x, y) centered at origin with a scale factor of k, then the dilated point will be given by C' (kx, ky)

We know $x = 6$ & $kx = 7.2$

Substituting 6 for x in the equation $kx = 7.2$ , we get $6k = 7.2$ .

Dividing 6 on both sides $\frac{6k}{6}=\frac{7.2}{6}$

Simplifying fractions on both sides $k=1.2$

Point A from the diagram is (-3, 3)

x-coordinate of A' = $kx=1.2 * -3 = -3.6$

y-coordinate of A' = $ky =1.2*3=3.6$

Point A' is given by (-3.6, 3.6)

Conclusion:

Scale factor of dilation is 1.2

The coordinates of point A' is (-3.6, 3.6)

6 0

4 years ago

Read 2 more answers

Simplify the expression. 2³ times 2^5 A. 4^15 B. 4^8 C. 2^15 D. 2^8

Luden [163]

$(x^m)(x^n)=x^{m+n}$
so
$(2^3)(2^5)=2^{3+5}=2^{8}$
D is answer

7 0

3 years ago

Read 2 more answers

Answer with the explanation step by step

andrey2020 [161]

Answer:

The answer is A. $\frac{3(x-21)}{(x+7)(x-7)}$ .

Step-by-step explanation:

To find the difference of this problem, start by simplifying the denominator, which will look like $\frac{3}{x+7}-\frac{42}{(x+7)(x-7)}$ . Next, multiply $\frac{3}{x+7}$ by $\frac{x-7}{x-7}$ to create a fraction with a common denominator in order to subtract from $\frac{42}{(x+7)(x-7)}$ . The problem will now look like $\frac{3}{x+7}*\frac{x-7}{x-7}-\frac{42}{(x+7)(x-7)}$ .

Then, simplify the terms in the problem by first multiplying $\frac{3}{x+7}$ and $\frac{x-7}{x-7}$ , which will look like $\frac{3(x-7)}{(x+7)(x-7)}-\frac{42}{(x+7)(x-7)}$ . The next step is to combine the numerators over the common denominator, which will look like $\frac{3(x-7)-42}{(x+7)(x-7)}$ .

Next, simplify the numerator, and to simplify the numerator start by factoring 3 out of $3(x-7)-42$ , which will look like $\frac{3(x-7-14)}{(x+7)(x-7)}$ . Then, subtract 14 from -7, which will look like $\frac{3(x-21)}{(x+7)(x-7)}$ . The final answer will be $\frac{3(x-21)}{(x+7)(x-7)}$ .