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4 years ago

If you have 24 square pieces of wood, describe all the different ways you could make a rectangle by placing them side by side.

Mathematics

1 answer:

Vilka [71]4 years ago

6 0

Think of all pairs of numbers that multiply to give 24

1 × 24
2 × 12
3 × 8
4 × 6

We can have four different rectangles by placing the square side by side

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Can someone answer number 5 plz

Georgia [21]

Answer:

C) 113 m^2

Step-by-step explanation:

diameter/2 =radius = 12/2 = 6

area = 6^2(3.14) = 6x6x3.14 = 113 m^2

5 0

3 years ago

A board 91 cm long is to be cut into two parts so that the longer part is 10 cm more than twice as long as the shorter part. Fin

mojhsa [17]

Answer:

The parts are 27 cm and 64 cm long.

Step-by-step explanation:

Let the shorter part be x.

"The longer part is 10 cm more than twice as long as the shorter part."

shorter part: x

longer part: 2x + 10

total length: x + 2x + 10

total length: 91

x + 2x + 10 = 91

3x + 10 = 91

3x = 81

x = 27

2x + 10 = 2(27) + 10 = 54 + 10 = 64

Answer: The parts are 27 cm and 64 cm long.

7 0

3 years ago

Sin(4x) in the term of just x<br> Please help!!

Nina [5.8K]

I think you mean in terms of $\sin(x)$ ?

Recall Euler's identity

$e^{ix} = \cos(x) + i \sin(x)$

and de Moivre's theorem

$\left(e^{ix}\right)^n = \left(\cos(x) + i \sin(x)\right)^n = \cos(nx) + i \sin(nx) = e^{inx}$

where $i=\sqrt{-1}$ .

It follows that

$\sin(4x) = \mathrm{Im}\left(\cos(x) + i \sin(x)\right)^4$

By the binomial theorem, expanding the right side gives

$\cos^4(x) + 4i \cos^3(x) \sin(x) - 6\cos^2(x) \sin^2(x) - 4i \cos(x) \sin^3(x) + \sin^4(x)$

and so

$\sin(4x) = 4\cos^3(x) \sin(x) - 4 \cos(x) \sin^3(x)$

We can factorize this as

$\sin(4x) = 4 \cos(x) \sin(x) \left(\cos^2(x) - \sin^2(x)\right)$

and using the Pythagorean identity

$\cos^2(x)+\sin^2(x) = 1 \implies \cos(x) = \pm \sqrt{1-\sin^2(x)}$

this reduces to

$\sin(4x) = \pm 4 \sqrt{1-\sin^2(x)} \sin(x) (1 - 2 \sin^2(x))$

8 0

2 years ago

Help!!!!!!!!!!!!!!!!!

azamat

Answer:

1. D 2. B 3. C

Step-by-step explanation:

WARNING: I am not 100% sure about 2.

1. If you simplify the first part of the equation for letter D, you'll realise it is the same equation.

2. It is either B or D. I believe it is B because you would not have to multiply 4 again.

3. The square root of 121 is eleven, the square root of x^2 is x. x=11.

4 0

4 years ago

3x+3y=12 x-5y=10 3(x-5y=10) Janiah is solving the system using elimination. Her first step is shown (The one in parenthesis) Wha

vesna_86 [32]

Equation 1) 3x + 3y = 12
Equation 2) x - 5y = 10

First step : 3(x - 5y = 10)

Well, we have to simplify this equation first. *Remember, this is the second equation.

Equation 1) 3x + 3y = 12
Equation 2) 3x - 14y = 30

Well, because both equation 1 & 2 have positive 3x in their equations, we must subtract the equations from one another in order to find the y value.

So, your answer is : C) Subtract the equations.

~Hope I helped!~

5 0

4 years ago

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