Carla is wrapping a present in the box shown. How much wrapping paper does she need, not including overlap?

Answer:  see proof below

Step-by-step explanation:

Use the following Double Angle identity: cos 2A = 2cos²A - 1

We are going to find one factor at a time:

2 cos16A + 1 = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1)

                              ↓                 ↓                  ↓                 ↓

                                factor last              factor 2nd    factor 1st

Proof LHS → RHS:

Given:        2 cos16A + 1

                  let α = 8A, then 2·cos2α + 1

Identity:     2(2cos²α - 1) + 1

Distribute:  4cos²α - 2 + 1

Simplify:    4cos²α - 1

Factor:     (2cosα - 1)(2cosα + 1)

Substitute: (2cos8A - 1)(2cos8A + 1)

                                       let β = 4A, then 2·cos2β + 1

Identity:                           2(2cos²β - 1) + 1

Distribute:                      4cos²β - 2 + 1

Simplify:                         4cos²β - 1

Factor:                           (2cosβ - 1)(2cosβ + 1)

Substitute:                     (2cos4A - 1)(2cos4A + 1)

                                                           let Ф = 4A, then 2·cos2Ф + 1  

Identity:                                               2(2cos²Ф - 1) + 1

Distribute:                                          4cos²Ф - 2 + 1

Simplify:                                             4cos²Ф - 1

Factor:                                               (2cosФ - 1)(2cosФ + 1)

Substitute:                                        (2cos2A - 1)(2cos2A + 1)      

(2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1) = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1)   \(\checkmark\)

Answer:Use the following Double Angle identity: cos 2A = 2cos²A - 1

We are going to find one factor at a time:

2 cos16A + 1 = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1)

Step-by-step explanation:

Answer:

a) 90°

b) 56°

Step-by-step explanation:

If we connect O with B to get two isosceles triangles: ΔAOB and ΔBOC

∠BOC= is central angle ans is twice as ∠BAC, so equals to 2*34°= 68°

Then ∠BCA= (180°- 68°)/2= 56°

∠ABC= ∠ABO+∠CBO= 34°+56°= 90°

Answer:

40 ÷ 1

Step-by-step explanation:

Speed = Distance : Time

Speed = 40 ÷ 1

Answer:

9 on a number line

Step-by-step explanation:

-3(-2-1)

-3(-3)

9

Answer:

Step-by-step explanation:

-

-3(-3) = 9

let's draw a number line from 1 to 9 by taking a scale of 1

1_2_3_4_5_6_ 7 _8_ 9__

The volume of the original box is given as

V = lwh

V = 10(6)(3)

V = 180 in³

Answer:

4+2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sally's Bakery has 45 1/3 cups of flour. To make one cake, she needs 1/6 cups of flour. How many cakes can Sally make?   =272

135/3 x 6/1= 272

they all relate by making 816

The answer to this is 3

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PEMDAS=  Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction

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9/12 - 1/4 = 0.5  

0.5 x 5 = 2.5

2.5 + 0.5 =3

Answer:

6km/h

Step-by-step explanation:

\(speed \: = \frac{distance}{time} \\ 50m \: = 0.5km \\ 30s \: = 0.0833333 \: hours\)

\(speed \: = \frac{0.5}{0.0833333} \\ speed \: = 6.0\)

Answer:

Step-by-step explanation:

Solution,

Distance travelled = 50 m

Time taken = 30 second

Let's find the speed in meter/ second

Speed = \( \frac{distance \: travelled \: }{time \: taken} \)

plug the values

\( = \frac{50}{30} \)

\( = \frac{5}{3 \: } \: meter \: per \: second\)

Now,Let's find the speed in km/ hour

\( \frac{5}{3} \times \frac{3600}{1000} \)

Reduce the numbers with G.C.F 3

\(5 \times \frac{1200}{1000} \)

Reduce the numbers with GCF 5

\( \frac{1200}{200} \)

Reduce the fraction with 200

\(6 \: kilometer \: per \: hour\)

Hope this helps..

Best regards!

It's about C. 333cm using the equation \(V=\frac{4}{3}\pi r^3\)

Step-by-step explanation:

The difference beteen 9.2 ounces and 8.1 ounces is  1.1 ounces

   and the difference in price is   .49

       so 1.1 ounces cost .49

           $ .49 / 1.1 oz = $  .445  per ounce

Then Reid's bowl should cost   7.8 oz  * $ .445 / oz = $3.47

Answer:

you are correct please give me brainliest

Step-by-step explanation:

Answer

to solve, plug the value of the variables in each equation in the system

(1,2) means x = 1 and y = 2

y = -2x + 4

2 = -2(1) + 4

2 = -2 + 4

2 = 2

the ordered pair is a solution to the first equation

7x - 2y = 3

7(1) - 2(2) = 3

7 - 4 = 3

3 = 3

the ordered pair is a solution for the second equation

Because the ordered pair is a solution for BOTH equations in the system, it is a solution to the system. Therefore, the correct answers are:

"When (1,2) is substituted into the first equation, the equation is true."

"The ordered pair (1,2) is a solution to the system of linear equations."

"When (1,2) is substituted into the second equation, the equation is true."

Hope this helps!

Answer:

3

Step-by-step explanation:  9

can be expressed in three such ways, 2+3+4

, 4+5

or simply 9

Answer: The next number in the quotient is  2

Step-by-step explanation:  Sorry for the messy handwriting

Here are the pairs matched with their products:

- (-5)(4.2) matches with -21

- (-7)(-3) matches with 21

- (2.5)(-9) matches with -22.5

Pairs (4) and (5) do not have corresponding products in the given options.

1. Atoms 2. electrons, 3. protons and neutrons 4. Static, 5. Gains.

Answer:

30

Step-by-step explanation:

just trust me A+ here you come

Answer:

D) 30

Step-by-step explanation:

see attachment for step-by-step explanation

Answer:

100$

Step-by-step explanation:

painter and the new place to go is to the best and I would love for a couple days of work and

Answer:

Choice A. \(\frac{2}{3}\)

Step-by-step explanation:

Turn the mixed numbers into improper fractions:

Flip the second term and multiply:

Simplify:

Answer:

A

Step-by-step explanation: