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3 years ago

Which expressions are equal to 10 to the 5th power?

1 answer:

4 0

Hey there!

10 to the fifth power is equivalent to the expression:

10 x 10 x 10 x 10 x 10 because you are multiplying 10 by 10 5 times.

Hope this helps you.
Have a great day!

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A number between 10 and 20 is both a foctor of 60 and<br>a multiple of 6.<br>What is the number?

Kisachek [45]

Answer:

Step-by-step explanation:

List out factors of 60 =

1 x 60 = 60

2 x 30 = 60

3 x 20 = 60

4 x 15 = 60

5 x 12 = 60

6 x 10 = 60

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 are factors of 60.

List out multiples of 6 from 10 to 20.

12 and 18.

Since 12 is seen on one of the factors of 60 and a multiple of 6 between 10 and 20, the answer is 12.

6 0

3 years ago

baherus [9]

Answer: see proof below

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

Given: cos 330 = $\frac{\sqrt3}{2}$

Use the Double-Angle Identity: cos 2A = 2 cos² A - 1

$\text{Scratchwork:}\quad \bigg(\dfrac{\sqrt3 + 2}{2\sqrt2}\bigg)^2 = \dfrac{2\sqrt3 + 4}{8}$

Proof LHS → RHS:

LHS cos 165

Double-Angle: cos (2 · 165) = 2 cos² 165 - 1

⇒ cos 330 = 2 cos² 165 - 1

⇒ 2 cos² 165 = cos 330 + 1

Given: $2 \cos^2 165 = \dfrac{\sqrt3}{2} + 1$

$\rightarrow 2 \cos^2 165 = \dfrac{\sqrt3}{2} + \dfrac{2}{2}$

Divide by 2: $\cos^2 165 = \dfrac{\sqrt3+2}{4}$

$\rightarrow \cos^2 165 = \bigg(\dfrac{2}{2}\bigg)\dfrac{\sqrt3+2}{4}$

$\rightarrow \cos^2 165 = \dfrac{2\sqrt3+4}{8}$

Square root: $\sqrt{\cos^2 165} = \sqrt{\dfrac{4+2\sqrt3}{8}}$

Scratchwork: $\cos^2 165 = \bigg(\dfrac{\sqrt3+1}{2\sqrt2}\bigg)^2$

$\rightarrow \cos 165 = \pm \dfrac{\sqrt3+1}{2\sqrt2}$

Since cos 165 is in the 2nd Quadrant, the sign is NEGATIVE

$\rightarrow \cos 165 = - \dfrac{\sqrt3+1}{2\sqrt2}$

LHS = RHS $\checkmark$

4 0

3 years ago

Find the perimeter of each polygon. Assume that lines which appear to be tangent are tangent.

ratelena [41]

9514 1404 393

Answer:

34.8

Step-by-step explanation:

The only polygon in the figure is the triangle outlined in red. Its perimeter is the sum of its side lengths: 15 +6.1 +13.7 = 34.8 units.

The two halves of the chord are the same length.

4 0

2 years ago

What is the mixed number and improper fraction for 4.8

Gelneren [198K]

Mixed number=4 8/10=4 4/5

improper fraction=48/10=24/5

3 0

3 years ago

Why does3,600 dived by 6 have the same quotient as 1,800 divided by three

sp2606 [1]

Both of the problems equal 600

5 0

3 years ago