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Mrrafil [7]
1 year ago
9

I just need the answers for questions 9 and 10

Mathematics
1 answer:
OverLord2011 [107]1 year ago
6 0

Hello. To answer this questions, we need to remember some properties about fractions and equivalences.

Starting by the question 9:

Call the population 5 years ago by P. If the population has decreased 12000 in these 5 years and this represents a decrease of 3%, so it means the new population is 0.97P.

With this, we can make the following equation:

P - 12000 = 0.97P

Subtract 0.97P and sum 12000 in both sides of the equation

0.03P = 12000

Divide both sides of the equation by a factor of 0.03

P = 3600000

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Masja [62]

Answer:

A^{-1}=\begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}

Step-by-step explanation:

A=\begin{bmatrix}-7 & -2\\ 4 & 1\end{bmatrix}

det\ A=-7\times 1-(-2)\times 4\\\Rightarrow det\ A=1

A^{-1}=\frac{1}{det\ A}\begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}\\\Rightarrow A^{-1}=\frac{1}{1}\begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}\\\Rightarrow A^{-1}=\begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}

\therefore A^{-1}=\begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}

A.A^{-1}=\begin{bmatrix}-7 & -2\\ 4 & 1\end{bmatrix}\times \begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}\\\Rightarrow A.A^{-1}=\begin{pmatrix}\left(-7\right)\cdot \:1+\left(-2\right)\left(-4\right)&\left(-7\right)\cdot \:2+\left(-2\right)\left(-7\right)\\ 4\cdot \:1+1\cdot \left(-4\right)&4\cdot \:2+1\cdot \left(-7\right)\end{pmatrix}\\\Rightarrow A.A^{-1}=\begin{pmatrix}1&0\\ 0&1\end{pmatrix}

Hence, confirmed

6 0
3 years ago
A bus covers a distance of 90km at a uniform speed. Had the speed been 15km/hour it would have taken 30 minutes less for the jou
Brrunno [24]

Answer:

Step-by-step explanation

Let's say d = distance, r = speed and t = time

We know the distance formula is :

distance = speed x time

d = r multiplied by t

d = rt

If the speed is 15km/hr, the time would be 30 minutes shorter.

Since d = rt,

90 = 15t

t = 6,

This means the time taken for the bus to complete the journey at 15km/hr would be 6hrs.

Originally though, the journey takes 30 minutes longer.

So we can say t = 6.5 hrs , and we know d = 90

Now we use the distance formula:

d = rt, since we want to find the original speed, we want to find r.

Speed = distance/time

r = d/t

r = 90/6.5

r = 180/13

Therefore the original speed is 180/13 km/hr

4 0
3 years ago
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2 years ago
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3 years ago
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masha68 [24]

The answers are 3.19 or -2.19.

In order to complete the square, you must first get the constant to the other side of the equation. WE do that by adding 7 to both sides.

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Now we must take half of the x coefficient (-1), which would be -.5. Then we square it and add it to both sides. This is the second step to any completing the square problem.

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Now that we have done that, the left side will be a perfect square so that, we can factor it.

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After having done that, we can take the square root of both sides

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Now we can take the value of that square root and solve.

x - .5 = +/-\sqrt{7.25}

x - .5 = +/-2.69

x = .5 +/- 2.69

And with the + and - both there, we need to do both to get the two answers.

.5 + 2.69 = 3.19

.5 - 2.69 = -2.19

4 0
3 years ago
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