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konstantin123 [22]
3 years ago
15

4x+1+8-x+5x-2=23 linear equations

Mathematics
1 answer:
DanielleElmas [232]3 years ago
5 0

Step-by-step explanation:

= 4x-x+5x+1+8-2

=8x+7

proved##

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The two-column proof below describes the statement and reason for proving that corresponding angles are congruent.
noname [10]
Step 6 wants us to show two angles which are also two interior angles that are located on the same side.

Interior angles are angles that are INSIDE the parallel lines.

On the diagram given, there are two pairs of interior angles that are on the same side:

Angle VQT and angle ZRS
Angle UQT and angle WRS

Two interior angles on the same sides add up to 180°

The missing statement that would fit statement in Step 6 is:
m∠VQT + m∠ZRS = 180°

Answer: Second option

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3 years ago
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A cleaning mixture requires 5 cups of water for every 2 cups of solution.
storchak [24]
I believe the correct awnser is c let me know !
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A sandwich shop offers 5 types of bread, 4 types of cheese, and 7 types of meat to choose from. Each sandwich will have 1 type o
katrin [286]

Answer:

I'm pretty sure the answer is B also known as 35

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3 years ago
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Solve using Fourier series.
Olin [163]
With 2L=\pi, the Fourier series expansion of f(x) is

\displaystyle f(x)\sim\frac{a_0}2+\sum_{n\ge1}a_n\cos\dfrac{n\pi x}L+\sum_{n\ge1}b_n\sin\dfrac{n\pi x}L
\displaystyle f(x)\sim\frac{a_0}2+\sum_{n\ge1}a_n\cos2nx+\sum_{n\ge1}b_n\sin2nx

where the coefficients are obtained by computing

\displaystyle a_0=\frac1L\int_0^{2L}f(x)\,\mathrm dx
\displaystyle a_0=\frac2\pi\int_0^\pi f(x)\,\mathrm dx

\displaystyle a_n=\frac1L\int_0^{2L}f(x)\cos\dfrac{n\pi x}L\,\mathrm dx
\displaystyle a_n=\frac2\pi\int_0^\pi f(x)\cos2nx\,\mathrm dx

\displaystyle b_n=\frac1L\int_0^{2L}f(x)\sin\dfrac{n\pi x}L\,\mathrm dx
\displaystyle b_n=\frac2\pi\int_0^\pi f(x)\sin2nx\,\mathrm dx

You should end up with

a_0=0
a_n=0
(both due to the fact that f(x) is odd)
b_n=\dfrac1{3n}\left(2-\cos\dfrac{2n\pi}3-\cos\dfrac{4n\pi}3\right)

Now the problem is that this expansion does not match the given one. As a matter of fact, since f(x) is odd, there is no cosine series. So I'm starting to think this question is missing some initial details.

One possibility is that you're actually supposed to use the even extension of f(x), which is to say we're actually considering the function

\varphi(x)=\begin{cases}\frac\pi3&\text{for }|x|\le\frac\pi3\\0&\text{for }\frac\pi3

and enforcing a period of 2L=2\pi. Now, you should find that

\varphi(x)\sim\dfrac2{\sqrt3}\left(\cos x-\dfrac{\cos5x}5+\dfrac{\cos7x}7-\dfrac{\cos11x}{11}+\cdots\right)

The value of the sum can then be verified by choosing x=0, which gives

\varphi(0)=\dfrac\pi3=\dfrac2{\sqrt3}\left(1-\dfrac15+\dfrac17-\dfrac1{11}+\cdots\right)
\implies\dfrac\pi{2\sqrt3}=1-\dfrac15+\dfrac17-\dfrac1{11}+\cdots

as required.
5 0
3 years ago
A box measures 1/6 ft. long, 1/4 ft. wide, and 1/3 ft. high. Find the volume of the box in inches. Do not include units in your
Viefleur [7K]

Answer:

24

Step-by-step explanation:

We know that the final answer has to be in inches.

To convert ft = in, multiply given ft. by 12.

1/6 = 1/6 * 12 = 2

1/4 = 0.25 * 12 = 3

1/3 = 0.3 * 12 = 4

2*3*4 = 23 cubic in.

6 0
1 year ago
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