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3 years ago

Which product is modeled by the number line below?

Mathematics

1 answer:

Ede4ka [16]3 years ago

4 0

Answer:

(-2)(4)

Step-by-step explanation:

(-2)(4) because we made four ”steps” of the lenght of two on the left

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5a - 3a + 2a simplify expression

zalisa [80]

4a is the answer I believe you’re looking for

5 0

3 years ago

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Hello! Verify the identity. Please show your work! Use trigonometric identities to verify each expression is equal.

RSB [31]

Answer:

See Below.

Step-by-step explanation:

We want to verify the identity:

$\displaystyle \csc^2 x -2\csc x \cot x +\cot ^2 x = \tan^2\left(\frac{x}{2}\right)$

Note that the left-hand side is a perfect square trinomial pattern. Namely:

$a^2-2ab+b^2=(a-b)^2$

If we let a = csc(x) and b = cot(x), we can factor it as such:

$\displaystyle (\csc x - \cot x)^2 = \tan^2\left(\frac{x}{2}\right)$

Let csc(x) = 1 / sin(x) and cot(x) = cos(x) / sin(x):

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

Combine fractions:

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

Square (but do not simplify yet):

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

Now, we can make a substitution. Let u = x / 2. So, x = 2u. Substitute:

$\displaystyle \frac{(1-\cos 2u)^2}{\sin ^22u}=\tan^2u$

Recall that cos(2u) = 1 - sin²(u). Hence:

$\displaystyle \frac{(1-(1-2\sin^2u))^2}{\sin ^2 2u}=\tan^2u$

Simplify:

$\displaystyle \frac{4\sin^4 u}{\sin ^2 2u}=\tan^2 u$

Recall that sin(2u) = 2sin(u)cos(u). Hence:

$\displaystyle \frac{4\sin^4 u}{(2\sin u\cos u)^2}=\tan^2 u$

Square:

$\displaystyle \frac{4\sin^4 u}{4\sin^2 u\cos ^2u}=\tan^2 u$

Cancel:

$\displaystyle \frac{\sin ^2 u}{\cos ^2 u}=\tan ^2 u$

Since sin(u) / cos(u) = tan(u):

$\displaystyle \left(\frac{\sin u}{\cos u}\right)^2=\tan^2u=\tan^2u$

We can substitute u back for x / 2:

$\displaystyle \tan^2\left(\frac{x}{2}\right)= \tan^2\left(\frac{x}{2}\right)$

Hence proven.

3 0

3 years ago

PLEASE HELP!!!!!!!!!!!!! Select the equation in which you use the inverse property of multiplication to find the solution.

Musya8 [376]

Answer:

First one

(12/12) +7=8

1+7=8

8=8

7 0

3 years ago

Solve the equation 2cos^2x = sin2x , giving your answer in terms of π. 0

Sveta_85 [38]

2cos^2x = sin2x 2cos^2x = 2sin x cos x (2sin x cos x) / (2cos^2x) = 1 sin x / cos x = 1 tan x = 1 x = π/4

8 0

3 years ago

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Please help ill give you 20 points :c

posledela

Answer: D+Q= 30

0.10 d+ 0.25 q= 4.80

Step-by-step explanation:

A dime is worth 10 cents and a quarter is worth 25 cents.

7 0

4 years ago

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