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3 years ago

One number is 3 more than another. Their sum is -13. Find the numbers

1 answer:

4 0

According to the question if we take one number as a M and 3 more than other represent m+3
so the equation will be : m+(m+3)=-13
2m+3=-13
2m=-16
m=-8(one number)
to get another number plug in -8 for m and that gives us -8+3=-5
prove if we pluged in all than we get the same result,-8-5=-13
that was the prove of that math hopefully you get it

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Find the first three terms in the expansion , in ascending power of x , of (2+x)^6 and obtain the coefficient of x^2 in the expa

Nataly_w [17]

Answer:

The first 3 terms in the expansion of $(2 + x)^{6}$ , in ascending power of x are,

$64 , 192 \times x^{1} {\textrm{ and }}240 \times x^{2}$

coefficient of $x^{2}$ in the expansion of $(2+x - x^{2})^{6}$ = (240 - 192) = 48

Step-by-step explanation:

$(2+x)^{6}$

= $\sum_{k=0}^{6}(6_{C_{k}} \times x^{k} \times 2^{6 - k})$

= $6_{C_{0}} \times x^{0} \times 2^{6} + 6_{C_{1}} \times x^{1} \times 2^{5} + 6_{C_{2}} \times x^{2} \times 2^{4}$ + terms involving higher powers of x

= $64 + 192 \times x^{1} + 240 \times x^{2}$ + terms involving higher powers of x

so, the first 3 terms in the expansion of $(2 + x)^{6}$ , in ascending power of x are,

$64 , 192 \times x^{1} {\textrm{ and }}240 \times x^{2}$

Again,

$(2+x - x^{2})^{6}$

= $\sum_{k=0}^{6}(6_{C_{k}} \times (2 + x)^{k} \times (-x^{2})^{6 - k})$

Now, by inspection,

the term $x^{2}$ comes from k =5 and k = 6

for k = 5, the coefficient of $x^{2}$ is , $(-32) \times 6$ = -192

for k = 6 , the coefficient of $x^{2}$ is, $6_{C_{2}} \times 2^{4}$ = 240

so, coefficient of $x^{2}$ in the final expression = (240 - 192) = 48

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3 years ago

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Effectus [21]

The answer is 17 you are correct

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If a convex polyhedron has 12 edges and 8 faces, then how many vertices does it have?

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Hi

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3 years ago

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svetoff [14.1K]

THE CORRECT ANSWER IS:

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3 years ago

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MAVERICK [17]

Answer:

10, 22, 48.4, 106.48, 234.256

Step-by-step explanation:

The first term is already given it is 10.

The second term is the first term times 2.2.

10×2.2=22

The second term is 22.

The third term is the second term times 2.2.

22×2.2=48.4

The third term is 48.4.

The fourth term is the third term times 2.2.

48.4×2.2=106.48

The fourth term is 106.48.

The fifth term is the fourth term times 2.2.

106.48×2.2=234.256

The fifth term is 234.256.

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