Ask question

Ask question

All categories

AleksAgata [21]

4 years ago

11

Question 2(Multiple Choice Worth 5 points)

1 answer:

Zina [86]4 years ago

3 0

Answer:

14 over 12

Step-by-step explanation:

You might be interested in

Factor f(x)=x4-x3-7x2+13x-6 completely. Then Sketch the graph

Dennis_Churaev [7]

ANSWER TO QUESTION 1

$f(x)=(x-2)(x+3)(x-1)^2$ .

EXPLANATION

The function given to us is,

$f(x)=x^4-x^3-7x^2+13x-6$

According to rational roots theorem,

$\pm1,\pm2,\pm3,\pm6$ are possible rational zeros of

$f(x)=x^4-x^3-7x^2+13x-6$ .

We find out that,

$f(-3)=(-3)^4-(-3)^3-7(-3)^2+13(-3)-6$

$f(-3)=81+27-63-39-6$

$f(-3)=6-6$

$f(-3)=0$

Also

$f(2)=(2)^4-(2)^3-7(2)^2+13(2)-6$

$f(2)=16-8-28+26-6$

$f(2)=6-6$

$f(2)=0$

This implies that

$x-2 and x+3$ are factors of

$f(x)=x^4-x^3-7x^2+13x-6$ and hence $(x-2)(x+3)=x^2+x-6$ is also a factor.

We perform the long division as shown in the diagram.

Hence,

$f(x)=(x-2)(x+3)(x-1)^2$ .

ANSWER TO QUESTION 2

Sketching the graph

We can see from the factorization that the roots

$x=2$ and $x=-3$ have a multiplicity of 1, which is odd. This means that the graph crosses the x-axis at this intercepts.

Also the root $x=1$ has a multiplicity of 2, which is even. This means the graph does not cross the x-axis at this intercept.

Now we determine the position of the graph on the following intervals,

$x\le -3$

$f(-4)=(-4)^4-(-4)^3-7(-4)^2+13(-4)-6$

$f(-4)=150\:>0$

$-3\le x \le 1$

$f(0)=-6\:$

$1\le x\le 2$

$f(1.5)=-0.56\:$

$x \ge 2$

$f(3)=24\:>0$

We can now use these information to sketch the function as shown in diagram

4 0

3 years ago

Of all rectangles with a perimeter of 7, which one has the maximum area? (give the dimensions.)

Elena L [17]

The rectangle with maximum area will actually be a square.

Each side will be of length 7/4 = 1 3/4.

3 0

3 years ago

A tank can contain 40 gallons of gas, but it is not completely full. How much gas is in the tank if 6.5% of the tank is empty?

alukav5142 [94]

The amount of gas in the tank would be 93.5%, which is .935 in decimal form. Multiply that by 40 and the answer is 37.4 gallons.

6 0

3 years ago

Who was the proprietor of the colony of Pennsylvania?

Alex787 [66]

Answer:A William Penn

Step-by-step explanation:

Given to him in 1681 for a debt

4 0

4 years ago

Read 2 more answers

The product of 13 and the sum of a number an 15

FrozenT [24]

Answer:

(15+x) · 13

Step-by-step explanation:

plz mark brainliest!

7 0

4 years ago