Two times what equals twenty-two

Which of the following represents the zeros of f(x) = 2x3 − 5x2 − 28x + 15?

likoan [24]

$\mathrm{Use\:the\:rational\:root\:theorem}$

$a_0=15,\:\quad a_n=2$

$\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:3,\:5,\:15,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1,\:2$

$\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:3,\:5,\:15}{1,\:2}$

$-\frac{3}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+3$

$\mathrm{Compute\:}\frac{2x^3-5x^2-28x+15}{x+3}\mathrm{\:to\:get\:the\:rest\:of\:the\:eqution:\quad }2x^2-11x+5$

$=\left(x+3\right)\left(2x^2-11x+5\right)$

$Factor: 2x^2-11x+5$

$2x^2-11x+5=\left(2x^2-x\right)+\left(-10x+5\right)$

$=x\left(2x-1\right)-5\left(2x-1\right)$

$2x^3-5x^2-28x+15=\left(x+3\right)\left(x-5\right)\left(2x-1\right)$

$\left(x+3\right)\left(x-5\right)\left(2x-1\right)=0$

$\mathrm{Using\:the\:Zero\:Factor\:Principle:}$

thus zeros of f(x) is

$x=-3,\:x=5,\:x=\frac{1}{2}$

5 0

3 years ago

Read 2 more answers

Solve the equation 0.2(d-6)=0.3d+5-3+0.1d for d

WINSTONCH [101]

Answer:

d= -16

Step-by-step explanation:

To answer this question you'll have to first simplify the equation to

0.2d+-1.2=0.3d+5-3+0.1d

then combining like terms you get

0.2d-1.2=(0.3d+0.1d)+(5+-3)

0.2d-1.2=0.4d+2

then subtract 0.4d from both sides leaving you with

-0.2d-1.2=2

then add 1.2 to both sides

-0.2d=3.2

after you divide both sides by -0.2

leaving you with the answer

D= -16

7 0

2 years ago

Read 2 more answers

In the figure below, BD and AC are diameters of circle P.

elena-14-01-66 [18.8K]

Answer:

$arc\ DC=30^o$

Step-by-step explanation:

The picture of the question in the attached figure

The point P is the center of the circle (the drawing is not a scale )

step 1

Find the measure of angle ∠CPD

we know that

$m\angle CPD+150^o=180^o$ ---> by supplementary angles (form a linear pair)

$m\angle CPD=180^o-150^o=30^o$

step 2

Find the measure of arc DC

we know that

Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it

so

$arc\ DC=m\angle CPD$ ----> by central angle

therefore

$arc\ DC=30^o$

5 0

3 years ago

The equation of a line is given below. 6x -4y = 24. Find the x-intercept and the Y-intercept then use them to graph the line

ipn [44]

Answer:

x intercept is 4 and the y intercept is -6

Step-by-step explanation:

x-int:

6x=24

x=4

y-int:

-4y=24

y=-6

5 0

3 years ago

A container of club soda has a volume of 3200 cubic meter. How many liters of soda does the container hold

svetoff [14.1K]

Answer:

3200000

Step-by-step explanation:

multiply the volume value by 1000

7 0

3 years ago