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2 years ago

Prove algebraically that n^2-2-(n-2)^2 is always even

Mathematics

2 answers:

Juliette [100K]2 years ago

6 0

Answer:

It is even because it is equal to 2(2n-3) so you can divide it by two and get (2n-3)

Step-by-step explanation:

${n}^{2} - 2 - ( {n}^{2} + 4 - 4n) = \\ {n}^{2} - 2 - {n}^{2} - 4 + 4n = \\ 4n - 6 = 2(2n - 3)$

tresset_1 [31]2 years ago

3 0

Step-by-step explanation:

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a business owner pays $500 a week for rent.He also pays an employee $16 an hour.If his total weekly expenses are $1,172 ,how man

Ganezh [65]

42 hours

EXPLANATION:

To find the answer, we should start with the total and get rid of the amounts that we know.

So we know the total is 1,172 in a week, and that 500 dollars of it is for rent.

1,172 - 500 =672.

Now we have 672 left.

We know that it was all spent on employees.

we know it is $16 for each hour.

672 divided by 16 is 42 total hours.

Hope this helps!

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3 years ago

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yarga [219]

C

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3 years ago

The tree diagram shows the possible win/loss paths for a basketball team playing in a tournament. Harris High School loses 1 gam

ladessa [460]

There are three ways it can happen: WWL, WLW, LWW.

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3 years ago

Evaluate the integral x^2(x^3+9)^1/2

CaHeK987 [17]

$\bf \displaystyle \int x^2(x^3+9)^{\frac{1}{2}}\cdot dx\\\\
-------------------------------\\\\
u=x^3+9\implies \cfrac{du}{dx}=3x^2\implies \cfrac{du}{3x^2}=dx\\\\
-------------------------------\\\\$

$\bf \displaystyle \int \underline{x^2}(u)^{\frac{1}{2}}\cdot \cfrac{du}{3\underline{x^2}}\implies \int \cfrac{u^{\frac{1}{2}}}{3}\cdot du\implies \cfrac{1}{3}\int u^{\frac{1}{2}}\cdot du
\\\\\\
\cfrac{1}{3}\cdot \cfrac{u^{\frac{3}{2}}}{\frac{3}{2}}\implies \cfrac{1}{3}\cdot \cfrac{2\sqrt{u^3}}{3}\implies \cfrac{2\sqrt{u^3}}{9}\implies \cfrac{2\sqrt{(x^3+9)^3}}{9}+C$

5 0

3 years ago

Please I need help! I will mark you as brainliest!

Alex_Xolod [135]

Answer:

33%

Step-by-step explanation:

The area of a circle is $\pi r^{2}$ , where r is the radius. In this case, the area of the second largest circle is $\pi (3+4)^{2}$ (because the radius is 3 + 4 = 7) = 49 $\pi$ .

The area of the smallest circle is $\pi 4^{2}$ = 16 $\pi$ .

Now, the area of the shaded region is just the smallest circle's area subtracted from the second-largest circle's area:

49 $\pi$ - 16 $\pi$ = 33 $\pi$

To find the percentage of the logo that is shaded, we need to find the total area, which is just the area of the largest circle: $\pi *(4 + 3 + 3)^{2} = \pi *10^{2} = 100\pi$

Now, we just divide 33 $\pi$ by 100 $\pi$ to get:

33 $\pi$ /100 $\pi$ = 33/100 = 33%, which is our answer.

5 0

3 years ago

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