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2 years ago

What is the function f(x) = 2(x + 6), find x if f(x) = 22

Mathematics

1 answer:

lord [1]2 years ago

3 0

Answer:

Step-by-step explanation:

f(x) = 2(x + 6)

f(x) = 22

thereofre we have the equation:

2(x + 6) = 22 <em>use distributive property</em>

2x + 12 = 22 <em>subtract 12 from both sides</em>

2x = 10 <em>divide both sides by 2</em>

x = 5

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Find all solutions of the equation: 2cos^2x-cosx=1

Art [367]

If you're using the app, try seeing this answer through your browser: brainly.com/question/3166243

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Solve the trigonometric equation:

$\mathsf{2\,cos^2\,x-cos\,x=1}\\\\ \mathsf{2\,cos^2\,x-cos\,x-1=0}$

Make a substitution:

$\mathsf{cos\,x=t\qquad (-1\le t\le 1)}$

and the equation becomes

$\mathsf{2t^2-t-1=0}$

Rewrite conveniently – t as + t – 2t, and then factor the left-hand side by grouping:

$\mathsf{2t^2+t-2t-1=0}\\\\ \mathsf{t\cdot (2t+1)-1\cdot (2t+1)=0}$

Factor out 2t + 1:

$\mathsf{(2t+1)\cdot (t-1)=0}\\\\ \begin{array}{rcl} \mathsf{2t+1=0}&~\textsf{ or }~&\mathsf{t-1=0}\\\\ \mathsf{2t=1}&~\textsf{ or }~&\mathsf{t=1}\\\\ \mathsf{t=\dfrac{\,1\,}{2}}&~\textsf{ or }~&\mathsf{t=1} \end{array}$

Substitute back for t = cos x:

$\begin{array}{rcl}\mathsf{cos\,x=\dfrac{\,1\,}{2}}&~\textsf{ or }~&\mathsf{cos\,x=1}\\\\ \mathsf{cos\,x=cos\,60^\circ}&~\textsf{ or }~&\mathsf{cos\,x=cos\,0} \end{array}$

Therefore,

$\begin{array}{rcl} \mathsf{x=\pm\,60^\circ+k\cdot 360^\circ}&~\textsf{ or }~&\mathsf{cos\,x=0+k\cdot 360^\circ} \end{array}$

where k is an integer.

Solution set:

$\mathsf{S=\left\{x\in\mathbb{R}:~~x=-\,60^\circ+k\cdot 360^\circ~~or~~x=60^\circ+k\cdot 360^\circ~~or~~x=k\cdot 360^\circ,~~k\in\mathbb{Z}\right\}}$

I hope this helps. =)

3 0

2 years ago

A ski slope drops 30 feet for every horizontal 70 feet

ASHA 777 [7]

The angle of depression is

tan^-1 3/7 = 23.2 deg

8 0

2 years ago

Please this is urgent

joja [24]

4 & 9 LCM - 36
8 & 10 LCM - 40
12 & 5 LCM - 60
3 & 6 LCM - 6
3 & 5 LCM - 15
4 & 11 LCM - 44

4 0

1 year ago

Sales for a company were 3 million dollars more the second year than the first, and sales for the third year were doubled the sa

Sati [7]

Year 3 = 2s

Year 2 = 3 + x

Year 1 = x

s = second year

x = first year

2s = 26

s = 13

The second year they made 13 million

13 - 3 = 10

x = 10

They made 10 million the first year.

6 0

2 years ago

Read 2 more answers

Expand and simplify 2(a + 3) + 3(2a - 1)

Svetlanka [38]

2(a+3) + 3(2a-1)
First, let's use the distributive property to expand 2(a+3):
2(a+3) = 2*a + 2*3 = 2a + 6
Let's use the distributive property now to expand 3(2a-1):
3(2a - 1) = 3*2a - 3*1 = 6a - 3

So 2(a+3) + 3(2a-1) = 2a + 6 + 6a - 3
Now you calculate variables between each others, and numbers between each others:
2a + 6 + 6a - 3 = 2a + 6a + 6 - 3 = 8a + 3

So the simplified form of 2(a+3) + 3(2a-1) is 8a + 3.

Hope this Helps! :)

4 0

2 years ago