The temperature startedat 10 degrees F. The temperature dropped 5

What is the quotient x-3/4x^2+3x+2

Elena L [17]

Answer:

STEP

1

:

Equation at the end of step 1

(((x3) - 22x2) - 3x) + 2 = 0

STEP

2

:

Checking for a perfect cube

2.1 x3-4x2-3x+2 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3-4x2-3x+2

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -3x+2

Group 2: x3-4x2

Pull out from each group separately :

Group 1: (-3x+2) • (1) = (3x-2) • (-1)

Group 2: (x-4) • (x2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

2.3 Find roots (zeroes) of : F(x) = x3-4x2-3x+2

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 1 and the Trailing Constant is 2.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,2

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 0.00 x+1

-2 1 -2.00 -16.00

1 1 1.00 -4.00

2 1 2.00 -12.00

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that

x3-4x2-3x+2

can be divided with x+1

Polynomial Long Division :

2.4 Polynomial Long Division

Dividing : x3-4x2-3x+2

("Dividend")

By : x+1 ("Divisor")

dividend x3 - 4x2 - 3x + 2

- divisor * x2 x3 + x2

remainder - 5x2 - 3x + 2

- divisor * -5x1 - 5x2 - 5x

remainder 2x + 2

- divisor * 2x0 2x + 2

remainder 0

Quotient : x2-5x+2 Remainder: 0

Trying to factor by splitting the middle term

2.5 Factoring x2-5x+2

The first term is, x2 its coefficient is 1 .

The middle term is, -5x its coefficient is -5 .

The last term, "the constant", is +2

Step-1 : Multiply the coefficient of the first term by the constant 1 • 2 = 2

Step-2 : Find two factors of 2 whose sum equals the coefficient of the middle term, which is -5 .

-2 + -1 = -3

-1 + -2 = -3

1 + 2 = 3

2 + 1 = 3

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

2

:

(x2 - 5x + 2) • (x + 1) = 0

STEP

3

:

Theory - Roots of a product

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Parabola, Finding the Vertex:

3.2 Find the Vertex of y = x2-5x+2

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 2.5000

Plugging into the parabola formula 2.5000 for x we can calculate the y -coordinate :

y = 1.0 * 2.50 * 2.50 - 5.0 * 2.50 + 2.0

or y = -4.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2-5x+2

Axis of Symmetry (dashed) {x}={ 2.50}

Vertex at {x,y} = { 2.50,-4.25}

x -Intercepts (Roots) :

Root 1 at {x,y} = { 0.44, 0.00}

Root 2 at {x,y} = { 4.56, 0.00}

Solve Quadratic Equation by Completing The Square

Step-by-step explanation:

5 0

4 years ago

3 x 7/18 as a fraction in simplest form

vazorg [7]

7/6 is the answer. If you divide the denominator by 3, you would get it

6 0

3 years ago

Which is the best estimate of the time Laura spent riding her bike on Saturday and Sunday? Look at the picture ^-^ Thank you!

anzhelika [568]

Answer B Because the total comes out as 7 7/8

8 0

4 years ago

Read 2 more answers

Suppose a lawn and garden company wants to determine the current percentage of customers who use fertilizer on their lawns. How

marishachu [46]

Answer:

n=601

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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 population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.04$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Since we don't have a prior estimation for the proportion we can use 0.5 as estimation. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.96})^2}=600.25$

And rounded up we have that n=601

3 0

3 years ago

Talia is buying beads to make bracelets. She makes a bracelet with 7 plastic beads and 5 metal beads for $7.25. She makes anothe

SVETLANKA909090 [29]

<h2>Plastic Beads = $0.50</h2><h2>Metal Beads = $0.75</h2><h2 />

p = Plastic Beads

m = Metal Beads

Equations:

7p + 5m = 7.25

9p + 3m = 6.75

Make one pair of coefficients the same:

3 * (7p + 5m = 7.25) = 21p + 15m = 21.75

5 * (9p + 3m = 6.75) = 45p + 15m = 33.75

Remove that coefficient;

(45p + 15m) - (21p + 15m) = 33.75 - 21.75

(45p - 21p ) + ( 15m - 15m) = 33.75 - 21.75

24p = 12

24p / 24 = 12 / 24

Substitute the result into one of the original equations.

(7 * 0.5) + 5m = 7.25

Rearrange to find the missing value:

7.25 - (7 * 0.5) = 5m

7.25 - 3.5 = 3.75

5m = 3.75

5m / 5 = 3.75 / 5

3 0

3 years ago