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2. Consider the function, f(x)=x^3+x^2-9x-9

Sedaia [141]

The intercepts of the graph are:

x-axis interception: $\left(-1,\:0\right),\:\left(-3,\:0\right),\:\left(3,\:0\right)$ .

y-axis interception: $\left(0,\:-9\right)$ .

See the graph of the function $f(x)=x^3+x^2-9x-9$ in the attached image.

<h3>Constructing a graph</h3>

For constructing a graph we have the following steps:

Determine the range of values for x of your graph.

For this exercise, for example, we can define a range -4<x<4. In others words, the values of x will be in this interval.

Determine the points

Replace these x-values in the given equation. For example:

When x=-4, we will have: $\left(-4\right)^3+\left(-4\right)^2-9\left(-4\right)-9=-21$ . Do this for the all x-values of your ranges.

See the results for this step in the attached table.

Draw the graph

Mark the points <u>x</u> and<u> y</u> that you found in the last step. After that, connect the dots to draw the graph.

The attached image shows the graph for the given function.

<h3>Find the x- and y-intercepts</h3>

The intercepts are points that crosses the axes of your plot. From your graph is possible to see:

x-axis interception points (y=f(x)=0) are: $\left(-1,\:0\right),\:\left(-3,\:0\right),\:\left(3,\:0\right)$ .

y-axis interception point (x=0) is: $\left(0,\:-9\right)$ .

Learn more about intercepts of the graph here:

brainly.com/question/4504979

5 0

2 years ago

Consider the following equation.

EastWind [94]

The approximate solution of the above equation is: 55/15 (Option A). This is solved using the quartic formula, not quadratic equation.

<h3>What is the Quartic Formula?</h3>

The quartic formula has up to four various solutions including real and imaginary numbers. Read on for more explanation.

<h3>What is the solution to the above question?</h3>

First we restate the above equation:

x²-3x+2= √(x-2) + 2

Next we remove square roots

$x^{4}$ - 6x³ + 9x² = x - 2

Add two to both sides

→ $x^{4}$ - 6x³ + 9x²+2 = x - 2 +2

→ $x^{4}$ - 6x³ + 9x²+2 = x

Subtract X from both sides

→ $x^{4}$ - 6x³ + 9x²+2 -x = x -x

→ $x^{4}$ - 6x³ + 9x²+2 - x= 0

Using the Quartic formula to solve the fourth order equation:
a $x^{4}$ + bx³ + cx² + dx + e

The resolution of x is given as:

x = 2.691085, 3.346753

Because the fraction nearest to 3.4 is 55/16

hence, the correct answer is Option A.

Learn more about quadratic equations at;
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6 0

1 year ago

Write a function rule that gives the total cost c(p) of p pounds of sugar if each pound costs $0.42.

julia-pushkina [17]

Since a pound of sugar increases proportionally to the total cost of sugar bought, then the function can be written as:

c(p) = 0.42p

Where: c(p) = total cost of sugar bought
p = pounds of sugar

c(p) is a function of p, because c(p) depends on p.

5 0

3 years ago

Read 2 more answers

Making handcrafted pottery usually takes two major steps:wheel throwing and firing. The time of wheel throwing and thetime of fi

levacccp [35]

Answer:

a) $P(R$

And we can find this probability using the normal standard table or excel and we got:

$P(z$

b) $P(R>110)=P(\frac{R-\mu}{\sigma}>\frac{110-\mu}{\sigma})=P(Z>\frac{110-100}{3.606})=P(Z>2.774)$

And we can find this probability using the complement rule and the normal standard table or excel and we got:

$P(z>2.774)=1-P(Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the time for the step 1 and Y the time for the step 2, we define the random variable R= X+Y for the total time and the distribution for R assuming independence between X and Y is:

$R \sim N(40+60 = 100,\sqrt{2^2 +3^2}= 3.606 s)$