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2 years ago

I WILL AWARD BRAINLIEST!! PLEASE HELP!!!! SOLVE EACH!!!

Mathematics

1 answer:

Jlenok [28]2 years ago

4 0

Answer:

A. $-\frac{9}{4}\le \:m\le \frac{9}{4}$

B. $-\frac{58}{5}$

C. $k$ or $k>7$

Step-by-step explanation:

$\left|\frac{m+3m}{3}\right|-1\le \:2$

$\left|\frac{m+3m}{3}\right|\le \:3$

$-3\le \frac{m+3m}{3}\le \:3$

$m\ge \:-\frac{9}{4}$

$m\le \frac{9}{4}$

$-\frac{9}{4}\le \:m\le \frac{9}{4}$

____________________

$\left|\frac{5z-6}{8}\right|$

$-8$

$z>-\frac{58}{5}$

$z$

$-\frac{58}{5}$

____________________

$5$

$\left|\frac{3k-1}{4}\right|>5$

$k$

$k>7$

$k$

$k>7$

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Barack walks 2 kilometers south and then x kilometers east. He ends 5 kilometers away from his starting position. Find x

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Answer:

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Step-by-step explanation:

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2 years ago

A triangular flag has an area of 187.5 square inches. The base of the flag measures 25 inch How tall is the triangular flag?

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2 years ago

What is the coefficient of the x^5y^5- term in the biomial expansion of (2x-3y)^10

jasenka [17]

<u>Answer:</u>

The coefficient of $x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552$

<u>Solution: </u>

The given expression is $(2 x-3 y)^{10}$

As per binomial theorem, we know,

$(x+y)^{n}=\sum n C_{k} x^{n-k} y^{k}$

Now here a = 2x, b = (- 3y) and n = 10 and k = 0,1,2,….10

Now $x^{5}\times y^5$ will be the 6 term where k =5

Now, $\mathrm{T}_{6}=10 \mathrm{C}_{5} \times(2 \mathrm{x})^{(10-5)} \times(-3 \mathrm{y})^{5}=10 \mathrm{C}_{5} 2^{5} \times \mathrm{x}^{5} \times(-3)^{5} \times \mathrm{y}^{5}$

So, the coefficient of $x^{5} \times y^{5} \text { is }=10\left(5 \times 2^{5} \times(-3)^{5}\right$ .

$10 \mathrm{C}_{5}=\frac{10 !}{5 ! \times(10-5) !}=\frac{10 !}{5 !+5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 !}{5 ! \times 5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1}=\left(\frac{30240}{120}\right)=252$