Angie divides the polynomial function f(x)=x3+3x2−7x−21 by (x + 3). What can she conclude from the fact that the remainder is equal to 0?

Answers

Answer 1

Answer:

See below

Step-by-step explanation:

Given function

f(x)=x³ + 3x²- 7x - 21

We can find its factors:

x³ + 3x² - 7x - 21 =x²(x + 3) - 7(x + 3) =(x² - 7)(x + 3)

We can conclude that the given polynomial function is fully divisible by (x + 3) and the quotient is (x² - 7)

Also one of zeros of the function is -3


Related Questions

PLEASE I NEED HELP!! LOOK AT THE PHOTO!!
ILL GIVE POINTS!!

Answers

Answer:

The system of inequalities representing the situation above is given as:

Number of ink drawings x ≥ 0

Number of water colors ≥ 0

Number of preparation time: 0.3x + 0.5y ≤ 120

Number of packaging time: 0.2x + 0.2y ≤ 60

Step-by-step explanation:

They volunteered to spend:

Number of hours for preparation = 120

Number of hours for packaging = 60

Number of hours to prepare ink drawing = 0.3

Number of hours to prepare water colour = 0.5

Number of hours it takes to package each card = 0.2

x = number of ink drawings

y = number rod water colour

The system of inequalities representing the situation above is given as:

Number of ink drawings x ≥ 0

Number of water colors ≥ 0

Number of preparation time: 0.3x + 0.5y ≤ 120

Number of packaging time: 0.2x + 0.2y ≤ 60

Option d is the correct option

Y=log base(rootx) x find dy/dx

Answers

Given:

[tex]y=\log_{\sqrt{x}}x[/tex]

To find:

The value of [tex]\dfrac{dy}{dx}[/tex].

Solution:

We have,

[tex]y=\log_{\sqrt{x}}x[/tex]

It can be written as

[tex]y=\log_{\sqrt{x}}(\sqrt{x})^2[/tex]

Using property of log, we get

[tex]y=2[/tex]          [tex][\because \log_aa^x=x][/tex]

Now, differentiate both sides with respect to x.

[tex]\dfrac{dy}{dx}=\dfrac{d}{dx}(2)[/tex]

[tex]\dfrac{dy}{dx}=0[/tex]          [tex][\because \dfrac{d}{dx}(Constant)=0][/tex]

Therefore, the value of [tex]\dfrac{dy}{dx}[/tex] is 0.

The graph of the equation x = 8 is what type of line
line.

Answers

Answer: Vertical Line

Step-by-step explanation:

Dwayne is going on a hike to the top of a mountain. It will take 3 hours and 40 minutes to hike up the mountain and 1 hour and 50 minutes to hike back down. If Dwayne wants to finish the hike by 1:45 P.M., what is the latest time he can start the hike up the mountain?

Include A.M. or P.M. in your answer. Please help me fast !!!

Answers

Answer: 8:15Am

Step-by-step explanation:

Answer: 8:15 am
Explanation: I added together the 3 hours and 40 minutes with 1 hour and 50 minutes. I got a total of five hours and thirty minutes
I then subtracted five hours and thirty minutes from 1:45 pm and I got 8:15 am.

You are Christmas shopping and your bill at the register is $130. You have two coupons, but you are only allowed to use one. Coupon 1 is for 10% off. Coupon 2 is for $10 off. Answer the following question 7a-7b-7c

Answers

Answer:

the answer is 10 percent off because that is 13 dollars

Step-by-step explanation:

if you do 130 times 10 it is 1300, then divide by 100 it equals 13 dollars off. if you did the other coupon it would only be 10 dollars off

I WILL MARK BRAINLIEST IN 5 MINUTES!
solve this and explain

Answers

Answer:

no, it's not.

Step-by-step explanation:

300- 284 = 16

284 - 236 = 48

236 - 156 = 80

156 - 44 = 112

for every one the top line goes up, the bottom line changes too, but it's not at a constant rate. it's not constant, therefore it cannot be linear.

the rate of change formula (or slope formula, they're the same thing) is :

y2- y1/ x2 -x1 and to solve it you plug in the points. x is the same a t and y is h

284-300/ 1-0

-16 /1

-16 (this is the rate of change between the first two points)

236- 284/ 2-1

-48/ 1

-48 (rate of change between the second and third points)

since the rate of change isn't constant, it's not possible for it to be a linear relationship.

Answer:

I  D  K

Step-by-step explanation:

my brains not working right now

can someone help please​

Answers

I’d say the letter b

Nine children on the swim team dont like ice cream if this represents 18% of children on the swim team how many children are on the swim team

Answers

Answer:

Um.. Im not sure about this one.. you're in college?

Step-by-step explanation:

Answer:

50 children in total

Step-by-step explanation:

question is really asking this:  9 is 18% of what number

9 = .18x

9/.18 = 50

which equation is equivalent to the formula below?
Y = A ( X - H) ^2 + K

Answers

Answer:

B. a = y - k/(x-h)²

Step-by-step explanation:

Given the expression y = a (x-h)² + k

First make  a the subject of the formula

Subtract k from both sides

y = a (x-h)² + k

y- k = a (x-h)² + k - k

y - k = a (x-h)²

Divide through by (x-h)²

y - k/(x-h)²  = a

a = y - k/(x-h)²

Hence option B is correct

Answer:

a=y-k/(x-h)^2

Please help me slove this problem
7 = 4x - 5

Answers

Answer:

x = 3

Step-by-step explanation:

7 = 4x - 5

7 - 4x = -5

-4x = -5 - 7

-4x = -12

x = 12 ÷ 4

x = 3

Answer:

×=3

Step-by-step explanation:

7=4×-5

7-4×=5

-4×=-5-7

-4×=-12

×=12÷4

×=3

Anthony is 154 cm tall, his brother Gerry is 5/7 as tall as him. How tall is Gerry?

:D can someone please help me with these problems please

Answers

The correct answer is 110 cm

Explanation:

Fractions always include two values (one at the top and the other at the bottom) and they represent the proportion of something, for example, 1/2 of an apple means there is only half apple. Now, to calculate how much is 5/7 of 154 centimeters, simply divide the total number into the denominator (bottom number) and then multiply the result by the numerator (top number). This process is shown in detail below:

[tex]\frac{5}{7}[/tex]  -  5 is the numerator and 7 is the denominator

5/7 of 154 cm

154 cm / 7 = 22

22 x 5 = 110 cm

The diagram below shows the start and finish diagrams of a construction using a compass and straightedge.
Start
Finish
G
Which of the following statements are true about this construction? Select all that apply.
G
O
O
O
O
O
The construction is of a line perpendicular to FG from a point not on FG
The first step of the construction is to draw a circle with center X.
The first step of the construction is to draw the perpendicular bisector of wY
The second step of the construction is to draw the perpendicular bisector of FG.
The second step of the construction is to draw the perpendicular bisector of VwY.q

Answers

Answer:

Choices 1, 2, 4

Step-by-step explanation:

i took the test

Solve the following equations all of six

Answers

Answer:

First one x=2 y=7 (2,7)

second one top right x=-2

Mid left: x=-5 and y=9 (-5,9)

mid right: x=4 and y=−1 (4,-1)

Bottom left: x=6 and y=−2 (6,-2)

Bottom Right: x=−4 and y=−5 (-4,-5)

Step-by-step explanation:

IM GOING LEFT TO RIGHT FROM UP TO DOWN

1. 2x+y=11

7x=14

rewrite them like this

7x=14;2x+y=11

solve for 7x=14

7x=14

x=2

Substitute 2 for x in 2x+y=11

(2)(2)+y=11

y+4=11

y=7

2. −7x=14;9x+8y=6

9x+8y=6

-7x=14

fist solve for x

x=-2

Then substitute in first equation

y=3

3. 6x+4y=6;3x=−15

6x+4y=6

3x=-15

solve for x

x=-5

Then plug in and solve

(6)(−5)+4y=6

4y=36

y=9

4. 7x+4y=24;4x=16

same process solve for x and plug in

x=4 and y=−1

5.  5x+8y=14;4x=24

same process

x=6 and y=−2

6. x-5y=21;-6x=24

same process solve for x and plug it in

x=−4 and y=−5

Hope this helps

Please help me slove this problem
-6x + 4 = -20

Answers

Answer:

x = 4

Step-by-step explanation:

-6x + 4 = -20, Subtract 4 on both sides

-6x = -24, Divide -6 on both sides

x = 4

pt.2 for find tge unknown

Answers

Answer:

[tex]c = 65[/tex]

[tex]x = 158[/tex]

Step-by-step explanation:

In the first triangle, one of the angles are already given to us, the 25. But the other angle is 90 degrees because it's a right angle. A right angle measures 90 degrees. We now add both the numbers together and subtract it from 180 to find the answer. We are subtracting it from 180 because a triangle equals 180 degrees.

[tex]90 + 25 = 115 \\ 180 - 115 = 65[/tex]

In the second triangle, one of the angles are already given to us, the 68. But the other angle is 90 degrees because it's a right angle. A right angle measures 90 degrees. We now add both the numbers together and subtract it from 180 to find the answer. We are subtracting it from 180 because a triangle equals 180 degrees.

[tex]68 + 90 = 158 \\ 180 - 158 = 22[/tex]

We figured out all the angles inside the triangle.

68, 90, and 22. We need to find the exterior angle. Remmeber that Consecutive angles are supplementary. The 22 and the x are one a straight line. A straight line equals 180 degrees. You are going to subtract 22 from 180 to get your answer.

[tex]180 - 22 = 158[/tex]

If you wanted to write it as an equation and solve it, it would be:

[tex]22 + x = 180[/tex]

Indicate the answer choice that best completes the statement or answers the question.
✓ The table shows the cost of long distance calls as a function of the number of minutes used. Is the cost a linear or nonlinear function of the
number of minutes used? Explain.
Number of Minutes 40 180 120 160 1200
Cost (S)
14.00 8.00
16.00 20.00
12.00

Answers

Answer:

The correct answer is:

Option C: Linear; as x increases by 40 minutes and y increases by $4 each time. The rate of change is constant, so this function is linear.

Step-by-step explanation:

Given is the table,

The input is x and output is y.

We can see from the table that the x-values are increasing 40 minutes after each input and the output is increasing by equal amount i.e. $4.

The rate of change remains the same.

Hence,

The correct answer is:

Option C: Linear; as x increases by 40 minutes and y increases by $4 each time. The rate of change is constant, so this function is linear.

Simplify this problem :

2 5/8 - 1 1/3

Answers

Answer:

-1 1/24

Step-by-step explanation:

Answer:

31/24 is the simplified answer

Step-by-step explanation:

PLEASE HELP ITS DUE IN 10 MINUTES

write a linear function f with the values f(1)=4 and f0=3

Answers

Answer:

Write a linear function f with the values f(2)=−2 and f(1)=1.

So, this is just a different way to say two different coordinates (x, y) and (x1, y1). f(x)=y and f(x1) = y1

We have: (2,-2) and (1,1) and we want to know the equation of the line that goes through those two points.

Find the : M = (y-y1)/(x - x1) = (-2 - 1) / (2 - 1) = -3/1 = 3; M = 3

Find the Y intercept by in one of the points for x and y and solving for B

Y = 3(X) + B

I'll choose the (1,1) to plug in: 1 = 3(1) + B; so B = -2

Put them together in intercept form: Y = 3(X) -2

Step-by-step explanation:

Does this help you understand the steps to take to solve this type of problem? please mark me as brainlest answer hope this helps

at a deli counter, someone bought 1.6 pounds of ham for 14.50. How much will it cost per one pound

Answers

Answer:

approx. 9.06 for one pound

Step-by-step explanation:

In great detail, with full work done out, please find x
1 + x = 2

Answers

Answer:

x = 1

Step-by-step explanation:

1 + x = 2

Subtract 1 form both sides,

1 + x - 1 = 2 - 1

       x  = 1

what is 1% of 73023.60

Answers

Answer:

730.236

the answer

730.236!! I’m pretty sure

I don’t know what to do?!? Help please

Answers

Answer:

Option A

Step-by-step explanation:

[tex]\frac{5-i}{4+3i} *\frac{4-3i}{4-3i} =\frac{20-15i-4i+3i^{2} }{16-9i^{2} }=\frac{20-19i+3(-1)}{16-9(-1)} =\frac{17-19i}{25}=\frac{17}{25}- \frac{19}{25} i[/tex]

Its A I think hopwd this helped

in eleven years ted will be 22 years old how old is he now?

Answers

Answer:

11

Step-by-step explanation:

22-11=11

Which number, when placed in the box, will make the equation true?
_^2 =square root of 64

Answers

Answer:

2.828 (the square root of 8)

Step-by-step explanation:

2.828 squared is 8, which is also the square root of 64

The value in the missing is x = 2√2 or x = -2√2 or x = ±√8 if the expression is _² = √64.

What is an expression?

It is defined as the combination of constants and variables with mathematical operators.

We have a mathematical expression:

_² = √64

Let the missing number be x:

Then, the equation becomes:

x² = √64

√64 = √(8x8) = 8

x² = 8

The above equation represents a quadratic equation, Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

x = ±√8

x = ±2√2

Thus, the value in the missing is x = 2√2 or x = -2√2 or x = ±√8 if the expression is _² = √64.

Learn more about the expression here:

brainly.com/question/14083225

#SPJ5

Alexandra has 4 bags of beads. Some of the bags contain 3 purple beads and the rest contain 6 indigo beads. If Alexandra has 21 beads in all, how many bags of each color bead does Alexandra have?
Please help me fast !!

Answers

Answer:

1 bag of 3 purple beads and 3 bags of 6 indigo beads

Step-by-step explanation:

3 + 18 = 21

A scientist add drops of liquid to a test tube. Each drop contains o.14mL. After 6 drops how much liquid has the scientist added?​

Answers

Answer:

We conclude that after 6 drops how much liquid the scientist has added 0.84 mL.

Step-by-step explanation:

Given that the scientist adds drops of liquid to a test tube.

The amount of liquid in 1 drop = 0.14 mL

In order to determine the amount of liquid after 6 drops, all we need is to multiply 0.14 mL by 6.

i.e.

The amount of liquid in 6 drops = 0.14 × 6

                                                     = 0.84 mL

Therefore, we conclude that after 6 drops how much liquid the scientist has added 0.84 mL.


Marbleslides: Lines

Answers

Answer:

ok

Step-by-step explanation:

calculate the slope of the line​

Answers

THE CALCULATED SLOPE IS -1

HELP ME PLEASEEEEEEEEEEEE !!!!!

Answers

he got 4 percent right. 16 percent of 15 is 4 :)

What is the digit to the right of the decimal point in the decimal form of 4/37
?

Answers

Answer:

2/15

Step-by-step explanation:

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