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3 years ago

Solve each system by substitution. y = -4x - 18 y = -3x - 13

Mathematics

1 answer:

evablogger [386]3 years ago

7 0

Answer:

x=5 and y=2

Step-by-step explanation:

hope it will enough to explain u .... if anything extra needed then ask me in comment section

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Trig proofs with Pythagorean Identities.

lorasvet [3.4K]

To prove:

$$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1$

Solution:

$$LHS = \frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}$

Multiply first term by $\frac{1+cos x}{1+cos x}$ and second term by $\frac{1-cos x}{1-cos x}$ .

$$= \frac{1(1+\cos x)}{(1-\cos x)(1+\cos x)}-\frac{\cos x(1-\cos x)}{(1+\cos x)(1-\cos x)}$

Using the identity: $(a-b)(a+b)=(a^2-b^2)$

$$= \frac{1+\cos x}{(1^2-\cos^2 x)}-\frac{\cos x-\cos^2 x}{(1^2-\cos^2 x)}$

Denominators are same, you can subtract the fractions.

$$= \frac{1+\cos x-\cos x+\cos^2 x}{(1^2-\cos^2 x)}$

Using the identity: $1-\cos ^{2}(x)=\sin ^{2}(x)$

$$= \frac{1+\cos^2 x}{\sin^2x}$

Using the identity: $1=\cos ^{2}(x)+\sin ^{2}(x)$

$$=\frac{\cos ^{2}x+\cos ^{2}x+\sin ^{2}x}{\sin ^{2}x}$

$$=\frac{\sin ^{2}x+2 \cos ^{2}x}{\sin ^{2}x}$ ------------ (1)

$RHS=2 \cot ^{2} x+1$

Using the identity: $\cot (x)=\frac{\cos (x)}{\sin (x)}$

$$=1+2\left(\frac{\cos x}{\sin x}\right)^{2}$

$$=1+2\frac{\cos^{2} x}{\sin^{2} x}$

$$=\frac{\sin^2 x + 2\cos^{2} x}{\sin^2 x}$ ------------ (2)

Equation (1) = Equation (2)

LHS = RHS

$$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1$

Hence proved.

5 0

4 years ago

6x + 7 = -5<br> How to solve

SCORPION-xisa [38]

Answer:
x= -2

explanation:

5 0

3 years ago

Read 2 more answers

The slope of the line below is to use the corners of the labeled point to find a point slope equation of the line.

dexar [7]

Answer: Choice A) y - 10 = 2(x - 3)

============================================================

Explanation:

We can rule out choices C and D because this diagonal line has a positive slope (as it moves uphill when moving to the right).

So m = 2 must be the slope.

---------

Recall that

y - y1 = m(x - x1)

represents the point slope form of a linear equation.

The point shown on this graph is (3,10) meaning that x1 = 3 and y1 = 10 pair up together.

So,

y - y1 = m(x - x1)

y - 10 = 2(x - 3)

which points to <u>choice A</u> as the final answer

4 0

3 years ago

Find the value of c that completes the square.

lesya [120]

Answer:

C. 400

Step-by-step explanation:

${v}^{2} - 40v + c \\ = {v}^{2} - 2.20.v + {20}^{2} \\ = {v}^{2} - 2.20.v + 400 \\ c = 400$

4 0

3 years ago

Determine the sum of the first 20 terms of an arithmetic series with an initial term of 3 and a common difference of 2.

olasank [31]

Answer:

440

Step-by-step explanation:

3 0

4 years ago

Solve each system by substitution. y = -4x - 18 y = -3x - 13​

Solve each system by substitution. y = -4x - 18 y = -3x - 13