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3 years ago

Solve for x in the equation 3x + 8 = x - 12.

Mathematics

2 answers:

Yuliya22 [10]3 years ago

5 0

Answer:

x = -10

Step-by-step explanation:

Combine like terms and solve for x

3x + 8 = x - 12

3x= x - 20

2x = -20

x = -10

Drupady [299]3 years ago

3 0

Answer:

The answer is x = -10

Step-by-step explanation:

3 x -10 + 8= -22

-10 - 12 = -22

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The population, P(t), of China, in billions, can be approximated by1 P(t)=1.394(1.006)t, where t is the number of years since th

vitfil [10]

Answer:

At the start of 2014, the population was growing at 8.34 million people per year.

At the start of 2015, the population was growing at 8.39 million people per year.

Step-by-step explanation:

To find how fast was the population growing at the start of 2014 and at the start of 2015 we need to take the derivative of the function with respect to t.

The derivative shows by how much the function (the population, in this case) is changing when the variable you're deriving with respect to (time) increases one unit (one year).

We know that the population, P(t), of China, in billions, can be approximated by $P(t)=1.394(1.006)^t$

To find the derivative you need to:

$\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=\\\\\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'\\\\1.394\frac{d}{dt}\left(1.006^t\right)\\\\\mathrm{Apply\:the\:derivative\:exponent\:rule}:\quad \frac{d}{dx}\left(a^x\right)=a^x\ln \left(a\right)\\\\1.394\cdot \:1.006^t\ln \left(1.006\right)\\\\\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=(1.394\cdot \ln \left(1.006\right))\cdot 1.006^t$

To find the population growing at the start of 2014 we say t = 0

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(0)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^0\\P(0)' = 0.00833901 \:Billion/year$

To find the population growing at the start of 2015 we say t = 1

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(1)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^1\\P(1)' = 0.00838904 \:Billion/year$

To convert billion to million you multiple by 1000

$P(0)' = 0.00833901 \:Billion/year \cdot 1000 = 8.34 \:Million/year \\P(1)' = 0.00838904 \:Billion/year \cdot 1000 = 8.39 \:Million/year$

6 0

3 years ago

Comppete the equation <br> X^2+y^2-10x+6y=15

mart [117]

I believe you meant: Use completing the square to determine the center and radius of the circle represented by this equation: <span>X^2+y^2-10x+6y=15

x^2 - 10x + 25 - 25 + y^2 + 6y + 9 - 9 = 15
Then:
(x-5)^2 + (y+3)^2 = 24 = 2sqrt(6)

This circle is centered at (5,-3) and has radius 2sqrt(6).</span>

8 0

4 years ago

Alex went to the grocery store and bought 5 avocados. He paid $10 and received $4.50 in change. How much did each avocado cost i

Delvig [45]

Answer:

$1.10

Step-by-step explanation:

We have been that Alex went to the grocery store and bought 5 avocados. He paid $10 and received $4.50 in change.

First of all, we will find amount paid for 5 avocados by subtracting $4.50 from $10.

$\text{Amount paid for 5 avocados}=\$10-\$4.50$