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3 years ago

What is the slope of the line passing through (16, -2) and (-30, 6)?

Mathematics

2 answers:

Travka [436]3 years ago

7 0

- 4/23 is what i got

Novay_Z [31]3 years ago

5 0

$m=\frac{\Delta y}{\Delta x}=\frac{-2-6}{16-(-30)}=\frac{-8}{46}=\boxed{-\frac{4}{23}}$ .

Hope this helps.

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What is the coefficient of x2y3 in the expansion of (2x + y)5?

Zigmanuir [339]

Option C:

The coefficient of $x^{2} y^{3}$ is 40.

Solution:

Given expression:

$(2 x+y)^{5}$

Using binomial theorem:

$(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}$

Here $a=2 x, b=y$

Substitute in the binomial formula, we get

$(2x+y)^5=\sum_{i=0}^{5}\left(\begin{array}{l}5 \\i\end{array}\right)(2 x)^{(5-i)} y^{i}$

Now to expand the summation, substitute i = 0, 1, 2, 3, 4 and 5.

$$=\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}+\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1}+\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}+\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}$

$$+\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}+\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}$

Let us solve the term one by one.

$$\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}=32 x^{5}$

$$\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1} = 80 x^{4} y$

$$\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}= 80 x^{3} y^{2}$

$$\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}= 40 x^{2} y^{3}$

$$\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}= 10 x y^{4}$

$$\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}=y^{5}$

Substitute these into the above expansion.

$(2x+y)^5=32 x^{5}+80 x^{4} y+80 x^{3} y^{2}+40 x^{2} y^{3}+10 x y^{4}+y^{5}$

The coefficient of $x^{2} y^{3}$ is 40.

Option C is the correct answer.

5 0

3 years ago

What are the coordinates of pont P on the coordinate grid below?

Shalnov [3]

Answer:

It would be (-5,3). Hope this helps!

Step-by-step explanation:

Start from zero on the x line and count until you get to the where the P is, then start from zero and count on the Y line till you get to the P.

5 0

2 years ago

T: 3(t + 3) + 5(3 + 2t) – 76 = 0

Setler [38]

Answer:

$\huge\boxed{\sf t = 4}$

Step-by-step explanation:

$\sf 3(t+3)+5(3+2t)-76 = 0\\\\Expanding \ Parenthesis\\\\3t + 9 + 15 + 10t -76 = 0\\\\13t + 24 -76 = 0\\\\13t - 52 = 0\\\\Add \ 52 \ to \ both \ sides\\\\13t = 52\\\\Dividing\ both\ sides\ by\ 13\\\\t = 52/13\\\\t = 4\\\\\rule[225]{225}{2}$

Hope this helped!

6 0

3 years ago

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Marta_Voda [28]

Answer:

Step-by-step explanation:

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work

6 0

3 years ago

A town's population is 38,200. About 100 people move out of the town each month. Each month, 150

Svetach [21]

Answer:

in 11 months

Step-by-step explanation:

y=50x+38,200

y=-150x + 40,400

6 0

2 years ago

Read 2 more answers