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3 years ago

Simplify the following expression by combining like terms. Select the most simplified expression 31y + 10 + 11

Mathematics

1 answer:

Bad White [126]3 years ago

4 0

Answer: 31y+21

Step-by-step explanation:

10 and 11 are the only like terms, so combine them.

10+11=21

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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

-125>-135 divide each side by -5 what is the resulting true inequality

Reptile [31]

Answer: 25<27

Step-by-step explanation:

-125/-5=25

-135/-5=27

25<27

5 0

3 years ago

Read 2 more answers

Find the inverse function. f (x)=1/2x+6

Lana71 [14]

The inverse of this function is f(x) = 2x - 12.

You can find the inverse of any function by switching the f(x) and x values in the equation. Then you can solve for the new f(x) value. The result is your inverse function. The work for this one is below.

f(x) = 1/2x + 6 ----> switch f(x) and x

x = 1/2f(x) + 6 ----> subtract 6

x - 6 = 1/2f(x) ----> multiply by 2

2x - 12 = f(x) ----> change the order for consistency.

f(x) = 2x - 12

7 0

3 years ago

at a ice cream shop the ratio of sugar cones sold to waffle cones sold is 10:7. if there are 40 sugar cones sold. how many waffl

Korvikt [17]

40/10=4
4*7=28
so answer is 28

8 0

3 years ago

What is a scale factor?

Blababa [14]

Answer:

Here is some helpful information from my mini lessons.

Step-by-step explanation:

If two objects have the same shape, they are called "similar." When two figures are similar, the ratios of the lengths of their corresponding sides are equal. To determine if the triangles shown are similar, compare their corresponding sides. Here you'll learn that the ratio of the perimeters of similar figures is equal to their scale factor and that the ratio of their areas is equal to the square of their scale factor. If two polygons are similar, then the ratio of the lengths of any two corresponding sides is called the scale factor. This means that the ratio of all parts of a polygon is the same as the ratio of the sides.

3 0

3 years ago