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3 years ago

The table below represents a linear function f(x) and the equation represents a function g(x):

Mathematics

1 answer:

Novosadov [1.4K]3 years ago

7 0

Part A: The slope of f(x) is three times as great as the slope of g(x).

Part B: The y-intercept of g(x) is 12 larger than the y-intercept of f(x).

In order to find these two answers, you need to find a model for f(x). You can do that by first finding the slope. The formula is below.

slope (m) = (y2 - y1)/(x2 - x1)

In this equation (x1, y1) is the first point and (x2, y2) is a second point. For this purpose, we'll pick (1, 0) and (0, -6)

slope (m) = (-6 - 0)/(0 - 1)

m = -6/-1

m = 6

Now we know that the slope is 6, which is 3 times as great as the first slope. Now to find the y-intercept, we can use either point and the slope in slope intercept form.

y = mx + b

0 = 6(1) + b

0 = 6 + b

-6 = b

So we know the y-intercept is -6, which is 12 less than the y-intercept of g(x).

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In 2010, the population of Kingsford was 8000. By 2014 the population had increased by 15% and 2/5 of the population was age 12

Anastasy [175]

<h2>Hello!</h2>

The answer is: The population age 12 or under was 3680.

If in 2010 the population of Kignsford was 8000, and by 2014 the population had increased by 15% we need to calculate the total population and then, calculate how many people was age 12 or under.

We must remember that we cannot work with percentage values, so, to make 15% a real number, we need to divide it by 100:

$15(Percentage)=\frac{15}{100}=0.15$

So,

Calculating the population by 2014, we have:

$Population_{2014}=Population_{2010}+ Population_{2010}*0.15$

Then, substituting we have:

$Population_{2014}=8000+ 8000*0.15=9200$

Now, calculating the population that was age 12 or under, knowing that it was 2/5 of the total population, we have:

$Population=TotalPopulation*\frac{2}{5}\\\\Population=9200*\frac{2}{5}=3680$

So, the population age 12 or under was 3680.

Have a nice day!

6 0

3 years ago

Find all roots: x^3 + 7x^2 + 12x = 0 <br> Show all work and check your answer.

Aliun [14]

The three roots of x^3 + 7x^2 + 12x = 0 is 0,-3 and -4

<u>Solution:</u>

We have been given a cubic polynomial.

$x^{3}+7 x^{2}+12 x=0$

We need to find the three roots of the given polynomial.

Since it is a cubic polynomial, we can start by taking ‘x’ common from the equation.

This gives us:

$x^{3}+7 x^{2}+12 x=0$

$x\left(x^{2}+7 x+12\right)=0$ ----- eqn 1

So, from the above eq1 we can find the first root of the polynomial, which will be:

x = 0

Now, we need to find the remaining two roots which are taken from the remaining part of the equation which is:

$x^{2}+7 x+12=0$

we have to use the quadratic equation to solve this polynomial. The quadratic formula is:

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Now, a = 1, b = 7 and c = 12

By substituting the values of a,b and c in the quadratic equation we get;

$\begin{array}{l}{x=\frac{-7 \pm \sqrt{7^{2}-4 \times 1 \times 12}}{2 \times 1}} \\\\{x=\frac{-7 \pm \sqrt{1}}{2}}\end{array}$

<em><u>Therefore, the two roots are:</u></em>

$\begin{array}{l}{x=\frac{-7+\sqrt{1}}{2}=\frac{-7+1}{2}=\frac{-6}{2}} \\\\ {x=-3}\end{array}$

And,

$\begin{array}{c}{x=\frac{-7-\sqrt{1}}{2}} \\\\ {x=-4}\end{array}$

Hence, the three roots of the given cubic polynomial is 0, -3 and -4

4 0

3 years ago

Write the equation and identify the slope, y-intercept, an

Deffense [45]

Equation: y=-2x-4
slope: -2
y-int: -4
x-int: -2

3 0

3 years ago

A store had 300 empty shelves. Each shelf could hold 20 cans. What is the total number of cans the shelves could hold?

Debora [2.8K]

Answer:

it can hold 6000 cans

Step-by-step explanation:

brainliest plz

3 0

3 years ago

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Which equation represents a linear function that has a slope of 4/5<br> and a y-intercept of –6?

vredina [299]

Answer:

$\large\boxed{y=\dfrac{4}{5}x-6}$

Step-by-step explanation:

The slope-intercept form of equation of a linear function:

$y=mx+b$

m - slope

b - y-intercept

We have the slope m = 4/5 and the y-intercept b = -6. Substitute:

$y=\dfrac{4}{5}x-6$

3 0

3 years ago

Read 2 more answers