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2 years ago

The area of a rectangular cocktail table is x²-18x +32. If the width is x-16, what is it's length?

Mathematics

1 answer:

Ad libitum [116K]2 years ago

5 0

Answer:

x-2

Step-by-step explanation:

The formula for area of rectangle is length x width
And we know that width is x-16
And we know that the area is $x^{2} -18x +32$

So we know that when x-2 is multiplied with x-16, it gives off $x^{2} -18x +32$

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Simplify the expression

Stolb23 [73]

Answer:

A. ${x}^{3} - x - \frac{6}{2x + 3}$

Step-by-step explanation:

$\frac{2 {x}^{4} + 3 {x}^{3} - 2 {x}^{2} - 3x - 6}{2x + 3} \\ \\ = \frac{(2 {x}^{4} + 3 {x}^{3} ) - (2 {x}^{2} + 3x) - 6}{2x + 3} \\ \\ = \frac{ {x}^{3} (2 {x} + 3 ) - x(2 {x} + 3) - 6}{2x + 3} \\ \\ = \frac{ {x}^{3} (2x + 3)}{2x + 3} - \frac{x(2x + 3)}{2x + 3} - \frac{6}{2x + 3} \\ \\ \purple { \bold{= {x}^{3} - x - \frac{6}{2x + 3} }}$

8 0

3 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

6x9x0x7x6x5x7x8x9=?

sergiy2304 [10]

Answer:

Step-by-step explanation: the answer is zero because when you multiply anything by zero itll always be zero

6 0

3 years ago

Read 2 more answers

How do you solve this for h?

pshichka [43]

Answer:

-multiply both sides by 2, so you will have 2A= h(b+c)

- divide both sides by (b+c), so you will have 2A/(b+c)=h and this is your final answer

7 0

3 years ago

At the air show 1/3 of the airplanes were gliders. which fraction is an equivalent fractions for 1/3?

Neko [114]

2/6 because 1×2=2 and 3×2=6 ...but whatever you multiply to one side you have to multiply to the other side

8 0

3 years ago