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3 years ago

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Select all the factors of: 7x2 − 28 options: 7 7x (x + 2) (x − 2) (x2 + 4)

1 answer:

Salsk061 [2.6K]3 years ago

8 0

Answer:

7(x-2)(x+2)

Step-by-step explanation:

7x^2 -28

Factor out a 7

7(x^2 -4)

The terms inside the parentheses is the difference of squares, so it is factorable (a^2-b^2) = (a-b)(a+b)

7(x-2)(x+2)

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For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va

Black_prince [1.1K]

Answer:

3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

$cos(\frac{\theta}{2})\neq0$

so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

or

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so:

$\theta\neq \pi$

having said this, we can now start solving the equation:

$tan(\frac{\theta}{2})=sin(\theta)$

we can start solving this equation by using the half angle formula, such a formula tells us the following:

$tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}$

so we can substitute it into our equation:

$\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)$

we can now multiply both sides of the equation by $sin(\theta)$

so we get:

$1-cos(\theta)=sin^{2}(\theta)$

we can use the pythagorean identity to rewrite $sin^{2}(\theta)$ in terms of cos:

$sin^{2}(\theta)=1-cos^{2}(\theta)$

so we get:

$1-cos(\theta)=1-cos^{2}(\theta)$

we can subtract a 1 from both sides of the equation so we end up with:

$-cos(\theta)=-cos^{2}(\theta)$

and we can now add $cos^{2}(\theta)$

to both sides of the equation so we get:

$cos^{2}(\theta)-cos(\theta)=0$

and we can solve this equation by factoring. We can factor $cos(\theta)$ to get:

$cos(\theta)(cos(\theta)-1)=0$

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

$cos(\theta)=0$

$\theta=cos^{-1}(0)$

$\theta={\frac{\pi}{2}, \frac{3\pi}{2}}$

Equation 2:

$cos(\theta)-1=0$

we add a 1 to both sides of the equation so we get:

$cos(\theta)=1$

$\theta=cos^{-1}(1)$

$\theta=0$

so we end up with three answers to this equation:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

7 0

2 years ago

What is the domain of f(x)=<br> 10x1-(4)<br> ?

MakcuM [25]

Answer:

Domain:(−∞,∞),{x|x∈R}

Step-by-step explanation:

5 0

2 years ago

15(x-3) over 5 = 3(2x-3) <br> What is X?

fgiga [73]

Answer:

x=0

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

You must get a 90 or higher to pass the course

pentagon [3]

Hi!! Okay thanks! And yes I think that’s correct.

6 0

2 years ago

plez help me it comes with 98 points ill even mark your answer as the brainliest plzz i really need the answer

Keith_Richards [23]

Answer:

a = 100

b = 5

Step-by-step explanation:

Just plug this into the equation it shows:

R(1) = (500 + (100)(1)) (50 - (5)(1))

4 0

2 years ago

Read 2 more answers