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3 years ago

2(x + 4) = 3(2x - 2) HELP!!!

Mathematics

2 answers:

olga2289 [7]3 years ago

7 0

Answer:

7/2 = x

Step-by-step explanation:

2(x + 4) = 3(2x - 2)

Distribute

2x+8 = 6x -6

Subtract 2x from each side

2x-2x+8 = 6x-2x -6

8 = 4x -6

Add 6 to each side

8+6 = 4x-6+6

14 = 4x

14/4 = 4x/4

7/2 = x

Galina-37 [17]3 years ago

4 0

Answer:

x= 7/2

Step-by-step explanation:

2x + 8 = 6x - 6

2x - 6x = -6 - 8

- 4x = -14

x = 7/2

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1+1+8 what's the best answer to this question

grandymaker [24]

10 because 1 +1= 2 and 2 + 8 = 10

3 0

3 years ago

What is the antiderivative of sin^2(x)cos^2(x)?

marin [14]

Answer:

$\frac{x}{8}-\frac{\sin(4x)}{32}+C$

Step-by-step explanation:

[Most of the work here comes from manipulating the trig to make the term (integrand) integrable.]

Recall that we can express the squared trig functions in terms of cos(2x). That is,

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

And so inverting these,

$\cos^2x=\frac{1}{2} (1+\cos2x) \\ \sin^2x=\frac{1}{2} (1-\cos2x)$ .

Multiply them together to obtain an equivalent expression for sin^2(x)cos^2(x) in terms of cos(2x).

$\sin^2x \cdot \cos^2x =\frac{1}{2} (1-\cos2x) \cdot \frac{1}{2} (1+\cos2x) = \frac{1}{4}(1-\cos^2(2x)).$

Notice we have cos^2(2x) in the integrand now. We've made it worse! Let's try plugging back in to the first identity for cos^2(2x).

$\cos(2x)=2\cos^2x-1 \Rightarrow \cos(4x)=2\cos^2(2x)-1 \Rightarrow \cos^2(2x) = \frac{1}{2}(1+\cos(4x))$

So then,

$\sin^2x \cdot \cos^2x = \frac{1}{4}(1-\cos^2(2x)) = \frac{1}{4}(1-\frac{1}{2}(1+\cos(4x))) = \frac{1}{4}(1-\frac{1}{2}-\frac{1}{2}\cos(4x))=\frac{1}{8}(1-\cos(4x)).$

This is now integrable (phew),

$\int \sin^2x\cos^2x \ dx = \int \frac{1}{8}(1-\cos(4x)) \ dx = \frac{1}{8} \int (1-\cos(4x)) \ dx = \frac{1}{8}(x-\frac{1}{4}\sin(4x))+C.$

7 0

3 years ago

Please answer the question

Jlenok [28]

Triangles: 2(1/2)*8*6=
Left side: 6*10 =
Right side: 8*10 =
Back side: 10*10 =
48 + 60 + 80 + 100 = 288cm^2

8 0

4 years ago

Help asappppp? i’m having trouble on wat the 1/4 point is

blagie [28]

Answer:

(-14, 5.5)

Step-by-step explanation:

Perhaps the easiest way to find the 1/4 point is to find (x, y), then find the midpoint between that and M.

(x, y) = 2M -(13, 25) = 2(-5, 12) -(13, 25) = (-23, -1)

Then the 1/4 point is ...

((-23, -1) +M)/2 = ((-23, -1) +(-5, 12))/2 = (-28, 11)/2 = (-14, 5.5)

_____

If we call the end points A(x, y) and B(13, 25), then we know ...

M = (A+B)/2

A = 2M -B . . . . we'll need this in a bit

and the 1/4 point Q is such that ...

(Q -A)/(B -A) = 1/4

4Q -4A = B -A . . . . cross multipliy

Q = (B +3A)/4 = (B +3(2M -B))/4 = (6M -2B)/4 . . . . solve for Q

Q = (3M -B)/2 . . . . reduce the fractions

Q = (3(-5, 12) -(13, 25))/2 = (-28, 11)/2 = (-14, 5.5) . . . as above

6 0

3 years ago

Can someone help me with this pls. I’ll give brainliest

nasty-shy [4]

Answer:

Step-by-step explanation:

a triangle is 180 degrees add 120 + 34 to get 154

180 -154 = 26

3 0

3 years ago