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3 years ago

4a + (–6b) – 3a + 2b factor the expression

Mathematics

1 answer:

Gemiola [76]3 years ago

5 0

Answer:

a−4b

Step-by-step explanation:

Combine Like Terms:

=4a+−6b+−3a+2b

=(4a+−3a)+(−6b+2b)

=a+−4b

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Solve questions 15,16,17, and 18. Will give Brainliest!! Please!!! Show minimal work!

SVEN [57.7K]

15. The terminal side of $\frac{3\pi}{2}$ intercepted the unit circle at:

(0,-1).

This implies that:

$(\cos \frac{3\pi}{2}, \sin \frac{3\pi}{2}=(0,-1)$

This implies that:

$\cos \frac{3\pi}{2}=0,\:and\: \sin \frac{3\pi}{2}=-1$

16) We have that: $\cot \theta =-\frac{6}{7}$ .

We illustrate this on the right triangle and apply the Pythagoras Theorem as follows:

$h^2=6^2+7^2$

$h^2=36+49$

$h^2=85$

$h=\sqrt{85}$

Using the mnemonics SOH-CAH-TOAH, we have:

$\sin \theta=-\frac{Opp}{Hyp}=-\frac{7}{\sqrt{85} }=-\frac{7\sqrt{85} }{85}$

$\cos \theta=\frac{Adj}{Hyp}=\frac{6}{\sqrt{85} }=\frac{6\sqrt{85} }{85}$

$\tan \theta=-\frac{Opp}{Adj}=-\frac{7}{6}}$

$\csc \theta=-\frac{Hyp}{Opp}=-\frac{\sqrt{85} }{7}$

$\sec \theta=\frac{Hyp}{Adj}=\frac{\sqrt{85} }{6}$

17. We want to verify that: $sin^4x-sin^2x=cos^4x-cos^2x$

Verifying from the LHS

$\sin^4x-sin^2x=(sin^2x)^2-sin^2x$

Recall that from the Pythagorean identity: $\sin^2x=1-\cos^2x$

$\sin^4x-sin^2x=(1-cos^2x)^2-(1-\cos^2x)$

$\sin^4x-sin^2x=1-2cos^2x+\cos^4x-1+\cos^2x$

$\sin^4x-sin^2x=\cos^4x-\cos^2x$

18. We have:

$\tan^2x\sec^2x+2\sec^2x-\tan^2x=2$

$\tan^2x\sec^2x+2\sec^2x-\tan^2x-2=0$

$\sec^2x(\tan^2x+2)-1(\tan^2x+2)=0$

$(\sec^2x-1)(\tan^2x+2)=0$

When $(\sec^2x-1)=0$ , we have

$x=0,\pi$

When $\tan^2x+2=0$ , $\tan^2x=-2$

We can see this is not defined for all real values of x.

6 0

3 years ago

4x + 5 = x + 26 need help

motikmotik

Answer:

x = 7

Step-by-step explanation:

4x + 5 = x + 26

4x - x = 26 - 5

3x = 21

x = 21/3

x = 7

Check:

4*7 + 5 = 7 + 26

28 + 5 = 33

7 0

3 years ago

Write an equation to represent the following statement. j is 14 less than 22.

solniwko [45]

Answer:

22-14=8

J=8

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

A club raised 175% of its goal for a charity. The club raises $875. What was the goal?

charle [14.2K]

Answer: The goal was $500

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

Work Shown:

x% = x/100

175% = 175/100 = 1.75

Let g be the goal, which is the amount of money the club wanted to raise

175% of goal = 175% of g = 1.75g

The expression 1.75g represents how much money was actually raised, which was $875. Set the two expressions equal to each other. Solve for g

1.75g = 875

g = 875/1.75 ....... divide both sides by 1.75

g = 500

The club's goal was to raise $500

Note how 75% of $500 is 0.75*500 = 375

When they raised 175% of the goal, this means they went 75% overboard and added on 375 additional dollars (on top of the 500 they wanted). So they got to 500+375 = 875 which lines up with the instructions. This helps verify the answer.

Or we can see that 1.75*g = 1.75*500 = 875 which helps confirm the answer as well.

3 0

3 years ago

If 60% of A is 20% of B, then B is what percent of A? a. 3% b. 30% c. 200% d. 300%

aleksley [76]

Answer:

d. 300%

Step-by-step explanation:

The given relation is ...

60%·A = 20%·B

Dividing by 20%, we see that ...

3·A = B

Of course, 3 = 3×100% = 300%, so B is 300% of A.

7 0

3 years ago