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3 years ago

Solve for x. Enter your answer below as an improper fraction in lowest terms,

Mathematics

1 answer:

ICE Princess25 [194]3 years ago

7 0

Answer:

x = $\frac{83}{36}$

Step-by-step explanation:

Given

x - 2 $\frac{1}{4}$ = $\frac{1}{18}$ ( change mixed number to improper fraction )

x - $\frac{9}{4}$ = $\frac{1}{18}$

Multiply through by 36 ( the LCM of 4 and 18 ) to clear the fractions

36x - 81 = 2 ( add 81 to both sides )

36x = 83 ( divide both sides by 36 )

x = $\frac{83}{36}$

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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

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3 years ago

Bonnie planted a garden in her backyard. Both the garden and the backyard are right triangles. The garden is proportional to the

Mandarinka [93]

You can find the area of Bonnue's backyard by comparing the hypotenuse of the garden to the hypotenuse of the back yard. If the hypotenuse of the garden is 10 (with the side lengths being 6, 8 and 10 - the longest is always the hypotenuse) and the hypotenuse of the back yard is 30, this is a scale factor of 3 (3 times longer).

This means the other two sides would also be 3 times longer.

6 yards x 3 = 18
8 yards x 3 = 24

To find the area using these dimensions, you will use the formula for finding the area of a triangle.

A = 1/2bh
A = 1/2 x 18 x 24
A = 216 square yards

The area of the backyard is 216 square yards.

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4 years ago

The cost of 6 pounds of oranges is $12.06. What is the constant of proportionality that relates the cost and dollars, y, to the

iren2701 [21]

Answer:

I'm not 100% correct but this is what I believe proportionality is where k=y/x and k is proportionality constant

$6.57: 3 pounds of orange

y dollar: x pounds of orange

so the proportion

$6.57 y

_____ = _____

3 x

6.57×

_____ = y

2.19x = y

so k = 2.19

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3 years ago

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ira [324]

I dont know what youre really asking for but i believe the answer is 5 = C because that is all youre really giving

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4 years ago

Jasmine surveyed the people at a local playground. She found that 33 out of 55 people brought water bottles. On Wednesday, Jasmi

zepelin [54]

Answer:

2,020 people were at the park.

Step-by-step explanation:

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(1212 * 55)/33 = 2,020

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3 years ago