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4 years ago

Use the reverse tabular method to determine the quotient (2x^3+ 11x^2+ 7x+10)/(x+5)

Mathematics

1 answer:

dusya [7]4 years ago

5 0

Answer:

2x^2 + x +2

Step-by-step explanation:

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Use substitution to solve the linear system of equations. 2y = x-6 x= 9

xxTIMURxx [149]

2y = x-6, x=9
2y = 9-6; plug 9 in for x
2y = 3; evaluate 9-6
y = 3/2; divide each side by 2

x = 9
y = 3/2

Hope this helps!

6 0

4 years ago

Task 2 a. Do some research and find a city that has experienced population growth. Determine its population on January 1st of a

Galina-37 [17]

Exponential functions are functions defined by y = ab^x, where a represents the initial value, and b represents the rate

<h3>The equation of a city that has experienced a population growth</h3>

The initial population of the city is 10000, and the growth rate of the population is 4%.

So, the exponential equation is:

$y = 10000 * 1.04^x$

<h3>The equation of a city that has experienced a population decline</h3>

The initial population of the city is 12000, and the decay rate of the population is 3%.

So, the exponential equation is:

$y = 12000* 0.97^x$

<h3>The similarities in the equations</h3>

The similarity in both equations is that, they both represent exponential function.

<h3>The year the population of city A exceeds B</h3>

In (a) and (b), we have:

$y = 10000 * 1.04^x$ ---- city A

$y = 12000* 0.97^x$ --- city B

When city A exceeds city B, we have the following inequality

$10000 * 1.04^x > 12000 * 0.97^x$

Divide both sides by 10000

$1.04^x > 1.2 * 0.97^x$

Divide both sides by 0.97^x

$(\frac{1.04}{0.97})^x > 1.2$

$1.07^x > 1.2$

Take the natural logarithm of both sides

$\ln(1.07)^x > \ln(1.2)$

This gives

$x\ln(1.07) > \ln(1.2)$

Solve for x

$x > \frac{\ln(1.2)}{\ln(1.07)}$

$x > 2.69$

This means that, the population of city A will exceed city B after 3 years

<h3>The year the population of city A will be at least twice of city B</h3>

In (a) and (b), we have:

$y = 10000 * 1.04^x$ ---- city A

$y = 12000* 0.97^x$ --- city B

When city A is at least twice city B, we have the following inequality

$10000 * 1.04^x \ge 2 * 12000 * 0.97^x$

$10000 * 1.04^x \ge 24000 * 0.97^x$

Divide both sides by 10000

$1.04^x \ge 2.4 * 0.97^x$

Divide both sides by 0.97^x

$(\frac{1.04}{ 0.97})^x \ge 2.4$

$1.07^x \ge 2.4$

Take the natural logarithm of both sides

$\ln(1.07)^x \ge \ln(2.4)$

This gives

$x\ln(1.07) \ge \ln(2.4)$

Solve for x

$x\ge \frac{\ln(2.4)}{\ln(1.07) }$

$x\ge 12.9$

This means that, the population of city A will be at least twice city B after 13 years

Read more about exponential functions at:

brainly.com/question/11464095

3 0

3 years ago

Find the limit of the function by using direct substitution. limit as x approaches zero of quantity x squared minus five.

blondinia [14]

Simply plug in x = 0

f(x) = x^2 - 5
f(0) = 0^2 - 5
f(0) = -5

Answer: -5

3 0

4 years ago

Read 2 more answers

The sum of twice a number n and 8 is less than 25

Irina18 [472]

Answer:

2n+8=25

Equation

Step-by-step explanation:

n=8.5

This is the answer

5 0

4 years ago

Nine squared plus a number (<br> b. is 89.

Andrei [34K]

The number is 8 since 9 squared is 81

4 0

3 years ago