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Alex17521 [72]
3 years ago
5

Solve for x -2^2(-5x+10)=100

Mathematics
1 answer:
masha68 [24]3 years ago
3 0

Answer:

x=7

Step-by-step explanation:

Hi there!

-2^2(-5x+10)=100

Solve -2^2:

-4(-5x+10)=100

Divide both sides by -4:

\displaystyle \frac{ -4(-5x+10)}{-4}=\frac{100}{-4} \\\\-5x+10=-25

Subtract 10 from both sides:

-5x+10-10=-25-10\\-5x=-35

Divide both sides by -5:

\displaystyle \frac{-5x}{-5} = \frac{-35}{-5} \\\\x=7

Therefore, x = 7.

I hope this helps!

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Please help me in this questions....​
Ivahew [28]

Part (i)

I'm going to use the notation T(n) instead of T_n

To find the first term, we plug in n = 1

T(n) = 2 - 3n

T(1) = 2 - 3(1)

T(1) = -1

The first term is -1

Repeat for n = 2 to find the second term

T(n) = 2 - 3n

T(2) = 2 - 3(2)

T(2) = -4

The second term is -4

<h3>Answers: -1, -4</h3>

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

Part (ii)

Plug in T(n) = -61 and solve for n

T(n) = 2 - 3n

-61 = 2 - 3n

-61-2 = -3n

-63 = -3n

-3n = -63

n = -63/(-3)

n = 21

Note that plugging in n = 21 leads to T(21) = -61, similar to how we computed the items back in part (i).

<h3>Answer:  21st term</h3>

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

Part (iii)

We're given that T(n) = 2 - 3n

Let's compute T(2n). We do so by replacing every copy of n with 2n like so

T(n) = 2 - 3n

T(2n) = 2 - 3(2n)

T(2n) = 2 - 6n

Now subtract T(2n) from T(n)

T(n) - T(2n) = (2-3n) - (2-6n)

T(n) - T(2n) = 2-3n - 2+6n

T(n) - T(2n) = 3n

Then set this equal to 24 and solve for n

T(n) - T(2n) = 24

3n = 24

n = 24/3

n = 8

This means 2n = 2*8 = 16. So subtracting T(8) - T(16) will get us 24.

<h3>Answer: 8</h3>
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