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3 years ago

What is 32.03 in expanded form

1 answer:

5 0

When you write a number in expanded form, you separate the digits based on their place value and turn it into an addition expression. The answer is 30+2+0.0+0.03, or if your teacher doesn't require the extra 0.0, just remove it.
Hope that helped.

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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

Mr. Smith donated $378 to 2 charities. Charity A received 5 times as much as Charity B. How much did Charity B received from Mr

MariettaO [177]

Answer:

$63

Step-by-step explanation:

let x represent Charity B then Charity A = 5x

Sum the two and equate to 378, that is

x + 5x = 378

6x = 378 ( divide both sides by 6 )

x = 63

Thus Charity B received $63

5 0

3 years ago

1) a yogurt shop has vanilla chocolate and strawberry blueberry and raspberry flavors served in small medium or large cups. How

sergey [27]

1 a 2c 3b 4a 5d hoooooooooppppppppeeeee thiiss hellps

3 0

3 years ago

The sum of two numbers is 51. The smaller number is 17 less than the larger number. What are the numbers?

djverab [1.8K]

Answer:

smaller number = 17, larger number = 34

Step-by-step explanation:

Let x be the smaller number and y be the larger nuber

x + y = 51 --(1)

y - 17 = x --(2)

Sub (2) into (1)

y - 17 + y = 51

y = 34

Put y = 34 into (2)

34 - 17 = x

x = 17

Ans: smaller number = 17, larger number = 34

3 0

3 years ago

Read 2 more answers

HELP!!!! In Ottawa you can ride on a tour bus for a fixed price plus a variable amount that depends on the length of the trip. t

german

Answer:

C = 2d + 15

Step-by-step explanation:

$2 per km, so $40 for 20km.

55-40 is 15 so $15 is a fixed price.

Hence, C = 2d + 15

5 0

3 years ago