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3 years ago

-FAST PLEASE- How do I simplify expressions with 2 or more variables?

Mathematics

1 answer:

meriva3 years ago

3 0

Answer:

10+2x=4x

-2x -2x

10=2x

10/2 2/2

5=x

Step-by-step explanation:

So when you simplify an expression with two or more variables you always go for the lowest variable first. Then you can do your normal inverse steps.

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In 2000 the population of a country reached 1 billion, and in 2025 it is projected to be 1.2 billion. (a) Find values for C an

Mice21 [21]

Answer:

(a) The value of C is 1.

(b) In 2010, the population would be 1.07555 billions.

(c) In 2047, the population would be 1.4 billions.

Step-by-step explanation:

(a) Here, the given function that shows the population(in billions) of the country in year x,

$P(x)=Ca^{x-2000}$

So, the population in 2000,

$P(2000)=Ca^{2000-2000}$

$=Ca^{0}$

$=C$

According to the question,

$P(2000)=1$

$\implies C=1$

(b) Similarly,

The population in 2025,

$P(2025)=Ca^{2025-2000}$

$=Ca^{25}$

$=a^{25}$ (∵ C = 1)

Again according to the question,

$P(2025)=1.2$

$a^{25}=1.2$

Taking ln both sides,

$\ln a^{25}=\ln 1.2$

$25\ln a = \ln 1.2$

$\ln a = \frac{\ln 1.2}{25}\approx 0.00729$

$a=e^{0.00729}=1.00731$

Thus, the function that shows the population in year x,

$P(x)=(1.00731)^{x-2000}$ ...... (1)

The population in 2010,

$P(2010)=(1.00731)^{2010-2000}=(1.00731)^{10}=1.07555$

Hence, the population in 2010 would be 1.07555 billions.

(c) If population P(x) = 1.4 billion,

Then, from equation (1),

$1.4=(1.00731)^{x-2000}$

$\ln 1.4=(x-2000)\ln 1.00731$

$0.33647 = (x-2000)0.00728$

$0.33647 = 0.00728x-14.56682$

$0.33647 + 14.56682 = 0.00728x$

$14.90329 = 0.00728x$

$\implies x=\frac{14.90329}{0.00728}\approx 2047$

Therefore, the country's population might reach 1.4 billion in 2047.

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3 years ago

When the town of Manning first started its voluntary recycling program, 2500 of the town's residence participated. The town pred

Paraphin [41]

Answer: The correct answer is Choice D.

This is an example of an exponential equation. They are in the form of y=ab^x, where a is the starting value, b is the rate and x is the number of years.

Our data starts at 2500 and increases by 5%, or 100% + 5% = 1.05.

If you put them together, you have the equation y = 2500(1.05)^x, Choice D.

3 0

3 years ago

Boyd’s dartboard is octagonal. Each side measures 9 in. He drew a copy of the board that was smaller by a scale factor 0.25.

Basile [38]

<span>The question is about the side length of a copy of the dartboard. We know that the original dartboard has sides that measure 9 inches. We also have the scale factor 0.25. The ratio of the corresponding sides is called the scale factor. If we have the scale factor 0.25 it means that for 1 unit of the original figure there are 0.25 units of length of a copy. Therefore: x = 9 * 0.25; x = 2.25 in. Answer: The side length of the dartboard Boyd drew is 2.25 inches.</span>

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3 years ago

Which of the following sequences is not arithmetic?

Yanka [14]

Answer:

option c

Step-by-step explanation:

c doesnt follow a pattern

3 0

3 years ago

Read 2 more answers

Factor the expression completely over the complex numbers. <br><br> x^3-4x^2+4x-16

Orlov [11]

First you must know that is i∧2= -1

x∧3-4x∧2+4x-16 = x∧2 (x-4) + 4 (x-4) = (x-4) (x∧2+4) = (x-4) (x∧2-(-4)) =

= (x-4) (x∧2-(-1) *4) = (x-4) (x∧2- i∧2*2∧2) = (x-4) (x∧2-(2i)∧2) = (x-4) (x-2i) (x+2i)

Good luck!!!

5 0

3 years ago