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3 years ago

Expand and simplify (x+2)(x+4)(x+6)

Mathematics

1 answer:

Deffense [45]3 years ago

5 0

Answer:

Multiply the first two binomials: (x+2) & (x+4) using the FOIL method (First, Outer, Inner & Last).

(x+2)(x+4) = x^² + 4x + 2x + 8 = x^² + 6x + 8

Then we multiply the trinomial that we got from the first stage and multiply that by the remaining binomial:

(x^² + 6x + 8) (x + 4)

= x^³ + 4x^² + 6x^² + 24x + 8x + 32

Collect the like terms together to give you:

x^³ + 10x^² + 32x + 32

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Which triangle defined by three points on the coordinate plane is congruent with the triangle illustrated, and why?

jekas [21]

Check the picture below.

the "red" pair of sides are congruent, notice, both are 3 and 5 units in length respectively.

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3 years ago

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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

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3 years ago

If a lb of beef cost $4.25, how much would 1 1/4 lb cost?

AlladinOne [14]

Step-by-step explanation:

$4.25×1 1/4=$4.25/1×5/4=$21.25/4=$5.25

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3 years ago

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La suma de dos polinomios de grado 4 siempre da, como resultado, un polinomio de 4

julsineya [31]

<span>No entiendo esto, esta no es una pregunta. Más que un hecho realmente.</span>

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4 years ago

Given that f(x) = x^2? + 9x + 18 and g(x) = x + 3, find (f ÷ g) (x) and express the result in standard form.

lawyer [7]

Answer:

x + 6

Step-by-step explanation:

(f ÷ g)(x)

= $\frac{x^2+9x+18}{x+3}$ factorise the numerator

= $\frac{(x+3)(x+6)}{x+3}$ ← cancel the factor (x + 3) on numerator/ denominator

= x + 6

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3 years ago