3 years ago

Why does it work to break apart a number by place values to multiply

Mathematics

1 answer:

densk [106]3 years ago

5 0

Because you are still multiplying the same values of the number you are multiplying and it's standard form

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Tom's age is 5 more than twice Dic's age.

kvasek [131]

If we break the answer down, we can solve this pretty easily.
We can represent Dic's age with x.
Tom's age is 5 MORE (+5) than TWICE (2x) Dic's age (x)
Therefore, our answer is 5+2x (Five more than twice Dic's age)

The correct answer is C: 5+2x

4 0

4 years ago

If cos x=8/17, and 270° < x < 360°<br> what is cos(2x)?

svp [43]

Answer: $\bold{-\dfrac{161}{289}}$

<u>Step-by-step explanation:</u>

Given: cos x = $\dfrac{8}{17}$ , x is in Quadrant 4

Use Pythagorean Theorem to find sin x:

8² + y² = 17²

y² = 17² - 8²

y² = 289 - 64

y² = 225

y = 15

→ sin x = $-\dfrac{15}{17}$

Use the double angle formula to find cos (2x):

$cos (2x) = cos^2 x - sin^2 x\\\\.\qquad=\bigg(\dfrac{8}{17}\bigg)^2-\bigg(-\dfrac{15}{17}\bigg)^2\\\\\\.\qquad=\dfrac{64}{289}-\dfrac{225}{289}\\\\\\.\qquad=-\dfrac{161}{289}$