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4 years ago

How do I solve this?

Mathematics

1 answer:

lakkis [162]4 years ago

3 0

Answer:

$\large\boxed{4\sqrt{-81}+\sqrt{-25}=41i}$

Step-by-step explanation:

$i=\sqrt{-1}\\\\\sqrt{-81}=\sqrt{(81)(-1)}=\sqrt{81}\cdot\sqrt{-1}=9i\\\\\sqrt{-25}=\sqrt{(25)(-1)}=\sqrt{25}\cdot\sqrt{-1}=5i\\\\4\sqrt{-81}+\sqrt{-25}=4(9i)+5i=36i+5i=41i$

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Finding the coefficient a of the term in the expansion of the binomial.<img src="https://tex.z-dn.net/?f=%28x%5E%7B2%7D%20%2B%20

Tomtit [17]

Answer:

3,247,695

Step-by-step explanation:

We want the coefficient of the term with x^8

So Use Newton's Binomial Expansion formula

Formula is (x + y) ^n = Sum for i=0 to n (n choose i) x^(n-i)*y^i

here (x^2 + 3) ^ 12

( 12 choose i) * (x^2)^(12-i) * (3)^i

i needs to equal 8 for us to get x^8

(12 choose 8) * (x^2)^(12-8) * (3^8)

= (12 choose 8) * x^8 * (3^8)

so a = (12 choose 8) * $3^{8}$

a = (12! /(8! * 4!) ) * $3^{8}$

a = ( 12*11*10*9/ 4*3*2*1) * $3^{8}$

a = (11*5*9) * $3^{8}$

a = 11*5*9 * 6561

a = 3,247,695

4 0

3 years ago

Consider the graph shown.

Butoxors [25]

Answer:

$Slope=\frac{3}{4}$

The equation of line is $y=\frac{3}{4}x+1$ .

Step-by-step explanation:

If a line passes through two points $(x_1,y_1)$ and $(x_2,y_2)$ , then the slope of the line is

$m=\frac{y_2-y_1}{x_2-x_1}$

From the given graph it is clear that the line is passes through the points (0,1) and (4,4).

$Slope=\frac{4-1}{4-0}$

$Slope=\frac{3}{4}$

The

The slope intercept form of a line is

$y=mx+b$

where, m is slope and b is y-intercept

The slope of the line is $\frac{3}{4}$ and y-intercept is 1, so the equation of line is

$y=\frac{3}{4}x+1$

Therefore, the equation of line is $y=\frac{3}{4}x+1$ .

4 0

3 years ago

Note: You may use a calculator to solve the following problems. If 1 kilogram = 2.206 pounds, how many pounds are in a gram?

Semenov [28]

0.0022 pound.... is not 0.002206

5 0

4 years ago

Katryn owes her father $25.write this number as an integer.

Romashka-Z-Leto [24]

Answer:

-25

Step-by-step explanation:

When you owe someone something, in integers, your answer is in the negative.

3 0

3 years ago

Can you help me it’s algebra 2 and I need the answers for like 5 more questions, it’s urgent like really urgent!!!!

nikitadnepr [17]

Answer: B) as x → -5 from the left, y → -∞

as x → -5 from the right, y → +∞

<u>Step-by-step explanation:</u>

$g(x) =\dfrac{x^2+15x+56}{x+5}\quad =\dfrac{(x+7)(x+8)}{x+5}\\\\\\\text{Evaluate from the left. Let x = -6}\rightarrow \dfrac{(-)(-)}{(-)}=-\\\\\\\text{Evaluate from the right. Let x = -4}\rightarrow \dfrac{(-)(-)}{(+)}=+$

Refer to the graph which confirms that

from the left, y tends toward -∞

from the right, y tends toward + ∞

3 0

3 years ago

How do I solve this?​

How do I solve this?