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anyanavicka [17]
3 years ago
12

SSSSSSSSSSSSSSSSSSSSSSSSSSss Which of the following equations is graphed as a vertical line?

Mathematics
1 answer:
Marysya12 [62]3 years ago
8 0
Vertical line is x=0
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The population of a city grows exponentially at rate of 8% per year.Find the number of years it takes for the population to be d
Ilya [14]

Answer:

<em>It will take 9 years for the population to double</em>

Step-by-step explanation:

<u>Exponential Growth </u>

The natural growth of some magnitudes can be modeled by the equation:

P=P_o(1+r)^t

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

The population of a city grows at a rate of r=8% = 0.08 per year. We are required to find when (t) the population will double, or P=2Po.

Substituting in the equation:

2P_o=P_o(1+0.08)^t

Simplifying:

2=(1.08)^t

Taking logarithms:

\log 2=\log (1.08)^t

Applying the exponent property of logs:

\log 2=t\log (1.08)

Solving for t:

\displaystyle t=\frac{\log 2}{\log (1.08)}

Calculating:

t\approx 9

It will take 9 years for the population to double

8 0
3 years ago
Which expression is equivalent to 1/4 -3/4 x?
Dmitriy789 [7]

Answer:

factor out 1/4 from the expression

1/4x(1-3x)

5 0
3 years ago
Read 2 more answers
Find the inverse of the function y = 3x - 4
irina1246 [14]
4/3 or 1.3. hope this helps.
4 0
3 years ago
4 times as much money as $5
lesantik [10]
The answer is 4x5=20
4 0
3 years ago
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Which triangle drfined by the given points on the coordinate plane is similar to the triangle illustrated? ​
Harrizon [31]

Answer:D.) (-1, 1), (-1, 5), (-7, 1)

Step-by-step explanation:The length of the horizontal segment of the triangle graphed is 3.  The length of the vertical segment of the triangle graphed is 2.  Using the Pythagorean theorem, this makes the length of the missing side

2²+3²=c²

4+9 = c²

13=c²

√13 = c

This makes our side lengths 2, 3, and √13.

For choice A our vertices are (-1, 1), (-1, 4), (-6, 1).

This makes the length of the horizontal segment 5 and the length of the vertical segment 3.  This makes the missing side length

5²+3²=c²

25+9=c²

34=c²

√34 = c

This is not proportional to the triangle drawn, so it is not similar.

The vertices of the triangle in option B are (-1, 1), (-1, 5), and (-6, 1).  This makes the horizontal segment 5 units long and the vertical segment 4 units long.  This makes the missing side length

4²+5²=c²

16+25=c²

41=c²

√41=c

These are not proportional to the triangle drawn, so the triangles are not similar.

The vertices of the triangle in choice C are (-1, 1), (-1, 4) and (-7, 1).  This makes the length of the horizontal segment 6 and the length of the vertical segment 3.  This makes the missing side length

3²+6²=c²

9+36=c²

45=c²

√45=c

3√5=c

These sides are not proportional to the sides of the triangle drawn, so the triangles are not similar.

The vertices of the triangle in choice D are (-1, 1), (-1, 5) and (-7, 1).  This makes the length of the horizontal segment 6 and the length of the vertical segment 4.  This makes the missing side length

6²+4²=c²

36+16=c²

52=c²

√52=c²

2√13=c

These sides are all twice as long as the sides of the triangle drawn; this means the triangles are similar.

4 0
3 years ago
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