Factor the polynomial and use the zeros to identify its graph. x4 − 5x3 − 20x2 + 60x + 144
Answers
The zeros of the polynomial are -3, -2, 4 and 6 and the graph of the polynomial is graph (a)
How to factor the polynomial?The polynomial is given as:
P(x) = x^4 - 5x^3 - 20x^2 + 60x + 144
Expand the polynomial function
P(x) = x^4 - 10x^3 + 5x^3 + 24x^2 - 50x^2 + 6x^2 + 120x - 60x + 144
Rewrite the function as:
P(x) = x^4 - 10x^3 + 24x^2 + 5x^3 - 50x^2 + 120x + 6x^2 - 60x + 144
Factorize the function
P(x) = x^2(x^2 - 10x + 24) + 5x(x^2 - 10x + 24) + 6(x^2 - 10x + 24)
Factor out x^2 - 10x + 24
P(x) = (x^2 + 5x + 6)(x^2 - 10x + 24)
Expand each bracket
P(x) = (x^2 + 3x + 2x + 6)(x^2 - 4x - 6x + 24)
Factorize each bracket
P(x) = [x(x + 3) + 2(x + 3)][x(x - 6) - 4(x - 6)]
Factor out x + 3 and x - 6
P(x) = (x + 3)(x + 2)(x - 4)(x - 6)
Set to 0
(x + 3)(x + 2)(x - 4)(x - 6) = 0
Solve for x
x =-3, -2, 4 and 6
Hence, the zeros of the polynomial are -3, -2, 4 and 6 and the graph of the polynomial is graph (a)
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Related Questions
Find the following given f(x) = - 9x - 2.
a. f(4)
b. f( - 3)
c. f(0)
D. F(1/7)
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Answer:
the answer for {a} is -38
Step-by-step explanation:
fill in the number for x then simplify
f(x)=-9x - 2
f(4) = -9 (4) - 2
= -36 - 2 = -38
Use the same process for the other questions.
Please help on the question as attached by providing detailed steps. Tq
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Answer:
Step-by-step explanation:
Use the picture attached.
How many lines of symmetry does the picture have?
A.
1
B.
3
C.
2
D.
0
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Answer: look honestly I am not sure but Probably it is choice c which is 2 lines of symmetry .
Step-by-step explanation: 2 lines of symmetry because one line is horizontal and the other is vertical . One line will be in the middle of the flower which is vertical and the other line is horizontal as they will make equivalent sides . HOPE IT HELPS BUDDY .
Look at the following ratio:
3:8
Write an equivalent ratio if it was three times greater:
Answers
multiple both sides by 3 to make it 3 times greater
the answer would be 9:24
hope this helps!!
-27 w3 + 125 factorize
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[tex]-1(3w-5)(9w^{2} +15w+25)[/tex]
NO LINKS!! Please help
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Answer:
FJ = 32
IJ = 24
FG = 48
Step-by-step explanation:
Getting Started with FG
[tex]\frac{IH}{AB} =\frac{FG}{ED}[/tex]
[tex]\frac{72}{36} =\frac{FG}{24}[/tex]
[tex]\frac{FG}{24} =2[/tex]
[tex]FG=24(2)=48[/tex]
The proportion between polygons is 2:1
[tex]IJ=2CB[/tex]
[tex]IJ=2(12)=24[/tex]
[tex]FJ=2BC=2(16)=32[/tex]
Hope this helps
Answer:
FJ = 32
IJ = 24
FG = 48
Step-by-step explanation:
Given: HGFJI ~ AEDCB
From inspection of the diagram, the corresponding sides are:
HG~AE
FG~DE
FJ~DC
IJ~CB
IH~BA
The only pair of sides that both have side lengths are IH and BA. Therefore, we can use these to figure out the scale factor of dilation.
IH = 72 and BA = 36
⇒ IH/BA= 72/36 = 2
Therefore, HGFJI is an enlargement of AEDCB by a scale factor of 2
If HG = 56
⇒ AE = 56 ÷ 2 = 28
If DE = 24
⇒ FG = 24 × 2 = 48
If DC = 16
⇒ FJ = 16 × 2 = 32
If CB = 12
⇒ IJ = 12 × 2 = 24
A stereo manufacturer determines that in order to sell x units of a new stereo, the price per unit , in dollars, must be p(x) = 100 - x. The manufacturer also determines that the total cost of producing x units is given by C(x) = 3000 + 2x. a. Express the total revenue function R as a function of x. b. Express the total profit P as a function of x. c. How many units must the company produce and sell in order to maximize profit d. What is the maximum profit? e. What price per unit must be charged in order to make this maximum profit .
Answers
Answer: See below
Step-by-step explanation:
a)
[tex]$$The total revenue R(x) is obtained as:\begin{align*} R\left( x \right) &= xp\left( x \right)\\ &= x\left( {100 - x} \right)\\ &= 100x - {x^2} &$$$ R(x) = 100x - {x^2} \end{align*}[/tex]
[tex]$$Thus, {R\left( x \right) = 100x - {x^2}[/tex]
b)
[tex]$$The total profit is obtained as: \begin{align*} P\left( x \right) &= R\left( x \right) - C\left( x \right)\\ &= 1000x - {x^2} - 3000 - 20x\\ &= - {x^2} + 980x - 3000 \end{align*}[/tex]
[tex]$$Hence, P\left( x \right) = - {x^2} + 980x - 3000[/tex]
c)
[tex]$$For maximum profit dP/dx should be equal to zero: \begin{align*} \dfrac{{dP}}{{dx}} &= 0\\ - 2x + 980 &= 0\\ x &= 490 \end{align*}[/tex]
[tex]$$So, the required units to maximize profit is 490[/tex]
d)
[tex]$$The maximum profit is calculated as: \begin{align*} P\left( x \right) &= - {x^2} + 980x - 3000\\ P\left( {490} \right) &= - {490^2} + 980 \times 490 - 3000\\ &= 237100 \end{align*}[/tex]
[tex]$$Accordingly, the maximum profit is \$237100.[/tex]
e)
[tex]$$Calculating the price at maximum profit as: \begin{align*} p\left( x \right) &= 1000 - x\\ p\left( {490} \right) &= 1000 - 490\\ &= 510 \end{align*}[/tex]
[tex]$$Consequently, the price at the maximum profit is \$510.[/tex]
What’s 1+2?
Answer fasttttt
I will mark you as branly
Answers
Answer:
3
Step-by-step explanation:
uhhhhhhhhhhhhh yeah
What is the measure of angle ACB? (geometry)
Answers
Answer:
30°Step-by-step explanation:
The angle between two secants is half the difference of intercepted arcs.
m∠ACB = 1/2(mAB - mDE)Substitute the arc values and calculate
m∠ACB =1/2(80° - 20°) = 1/2(60°) = 30°Answer:
∠ACB = 30°
Step-by-step explanation:
Finding ∠ACB :
∠ACB = 1/2 x (∡AB - ∡DE)∠ACB = 1/2 x (80° - 20°)∠ACB = 1/2 x 60°∠ACB = 30°Carter deposited $146.00 into a new savings account that earns 13% interest compounded
quarterly. How long will it take for the balance to grow to $239.00?
Round your answer to the nearest month.
___ years and ___ months
Answers
Answer:
it should be around 4 months I believe
Step-by-step explanation:
146.00(1+0.13/4)^(4×4)
How many hours would it take to watch 170 episodes of a show, each episode is about 23 minutes long.
Answers
Answer:
Around 65 hours(2 days and 17 hours)
Each episode is 23 minutes long, and there's 170 episodes, so multiply 23 by 170 being 23 minutes for each episode.
[tex]23 * 170 = 3,910[/tex]
Now, convert 3,910 minutes to hours by dividing for every 60 minutes.
[tex]3,910 / 60 = about~65[/tex]
Therefore, the answer is ≈65
the exact value is 65.16667
Which of the following will form the composite function G(F(x)) shown
below?
G(F(x)) = (x-7)2 + (x-7)-1
A. F(x)=(x-7)2 and G(x)=(x-7)-1
B. F(x)=x²+x-1 and G(x) = x-7
C. F(x)=(x-7)-1 and G(x)=(x-7)²
D. F(x)= x-7 and G(x)=x²+x-1
SUBMIT
Answers
Answer:
The answer is D.
Step-by-step explanation:
What is the value of n?
Answers
8n + 64 = 16n + 32
8n = 32
N = 4
I think that’s right.
in the table below x represents miles traveled and y represents the cost to travel by train what is the y intercept of this function?
Answers
Answer:
im pretty sure its 2.25...
Step-by-step explanation:
hope this helps:)
I need help ASAP!!!! Worth 20 points!
Answers
Answer:
x in (-oo:+oo)
(5/4)*x-(3/7) = 0
(5/4)*x-3/7 = 0
5/4*x-3/7 = 0 // + 3/7
5/4*x = 3/7 // : 5/4
x = 3/7/5/4
x = 12/35
x = 12/35
Step-by-step explanation:
I need to know how to solve this
Answers
Answer:
it would be 3(16-8x) also know as A
Step-by-step explanation:
Need help with math please
Answers
BG must equal AG = 9, because DG bisects AB at the midpoint of D.
AD must equal DB = 6, because DG bisects AB at the midpoint of D.
So, AB =6+6 =12
BG=9
AB=12
What is the slope and y-intercept of this line?
y=−12x+7
slope: 12, y-intercept: −7
slope: −7, y-intercept: −12
slope: −12, y-intercept: 7
slope: 7, y-intercept: −12
Answers
Answer:
(c) slope: -12, y-intercept: 7
Step-by-step explanation:
The given equation is in the slope-intercept form:
y = mx +b
In this form, m is the slope, and b is the y-intercept.
__
Comparing the given equation to the form, we see ...
y = mx +b
y = -12x +7 ⇒ m = -12, b = 7
The slope is -12; the y-intercept is 7.
y = −2x + 8
y = x − 1
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.
Answers
Answer:
(3, 2)
Explanation:
y = −2x + 8 ....equation 1y = x − 1 ....equation 2======================
substitute equation 2 into 1
x − 1 = −2x + 8x + 2x = 8 + 13x = 9x = 3find y
y = x − 1y = 3 − 1y = 2solution
(x, y) ⇒ (3, 2)Answer:
(3, 2)
Step-by-step explanation:
Given
Equation 1: y = -2x + 8
Equation 2: y = x - 1
Solving by Substitution
Substitute Equation 2 into Equation 1 and solve for x:
⇒ x - 1 = -2x + 8
Add 2x to both sides:
⇒ 3x - 1 = 8
Add 1 to both sides:
⇒ 3x = 9
Divide both sides by 3:
⇒ x = 3
Now substitute the found value of x into Equation 2 and solve for y:
⇒ y = 3 - 1
⇒ y = 2
Therefore, the solution is (3, 2)
If the area of a rectangle is x4 + 3x3 - 2x2 - 200 and the width is x + 5, find its length.
Answers
Answer:
Step-by-step explanation:
Area = 4x + 9 - 4 - 200
= 4x - 195
Since Area is lw, let the width be x + 5 and y be the unknown length.
Therefore (x + 5) (y) = 4x - 195
Answer:
x³ - 2x² + 8x - 40
Step-by-step explanation:
Area = length · width
(x⁴ + 3x³ - 2x² + 0x¹ - 200) = length · (x + 5)
length = (x⁴ + 3x³ - 2x² + 0x¹ - 200) ÷ (x + 5)
BRAINLIEST please if this helped!Calculate the percent
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519.6 x 10.86
by process.
Answers
Answer:
5642.856
Step-by-step explanation:
Multiply 5196 x 1086 without the decimal points
Then you will get the ans 5642856 then count how many decimal points are there altogether which is three points.
So go behind three numbers and put the point.
Final Answer - 5642.856
Pls help i need an A my mom is going to get mad at me pls help i will give 62 points
Answers
Answer:
orange one
Step-by-step explanation:
just the orange one since its 5 divided by 1 is 5
10 divided by 2 is 5
20 divided by 4 is 5
They answers are both correct
First you will look at the first pair of numbers then do some multiples of the numbers
Then compare them to the other points given and determine if you have a line from there
Write the inverse variation function given that y varies inversely with x, and y = 0.5 when x = 24.
Answers
[tex]\large{\text{Refer\:to\:explanation\:pls}}[/tex]
Calculation ↓If y varies inversely with x, we divide :
y = [tex]^k/_x[/tex]
Where
k = constant of proportionality
We are given that :
y = 0.5
x = 24
So we write :
0.5 = [tex]\Large\text{$^k/_{24}$}[/tex]
Multiply by 24 on [tex]\Large{\text{both\:sides\::}}[/tex]
12=k
[tex]\Large{\text{The\:constant\:of\:proportionality\:is\:12.}}[/tex]
So we havey = 12/x
[tex]\footnotesize{\text{hope\:helpful}}[/tex]
A self-serve car wash charges $5.52 to use its facilities, plus an additional $0.95 for each minute the customer is at the self-serve
car wash. If Tiffany was at the car wash for 5 minutes, how much was she charged?
A. $10.52
B. $6.47
C. $10.27
D. $4.75
Answers
How many kilograms are in 242,000 milligrams? The solution is
Answers
Answer:
i am from afghanistan and you
Answer:
.242 Kilograms
Step-by-step explanation:
To convert milligrams to kilograms multiply the value by .000001 or move the decimal mark 6 places to the left.
1. Based on the current market rates for bonds of Frenza, Nelo, and Lika, which of the following bonds do lenders believe has the highest risk level? 2. If Frenza decided to issue new bonds with a contract rate of 11%, would these new bonds be sold at a discount or premium based on the current market rate for Frenza bonds? 3. Frenza is planning an $160,000 expansion to launch a new product line. Frenza currently earns $100,000 in net income, and the new product line will yield $50,000 in additional income before any interest expense. Frenza has three options: (1) do not expand, (2) expand and issue $160,000 in debt that requires payments of 8% annual interest, or (3) expand and raise $160,000 from equity financing. For each option 1, 2, and 3, compute (a) net income and (b) return on equity (Net income ÷ Equity). Ignore any income tax effects.
Answers
The net income and return on equity for the first part for Frenzo will be $100000 and 25%.
How to calculate the net income?The net income and return on equity for the first part will be:
Net income = $100000 - 0 = $100000.
Return on equity = (100000/400000) × 100 = 25%
The net income and return on equity for the second part will be:
Net income = $150000 - $12800 = $137200
Return on equity will be:
= (137200/400000) × 100
= 34.3%
The net income and return on equity for the third part will be:
Net income = ($150000 - 0) = $150000
Return on equity will be:
= (150000/560000) × 100
= 26.8%
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what is 36x - 28 equal
Answers
Answer:
[tex]36x-28[/tex]
Rewrite 36 as 4*9 & Rewrite 28 as 4*7
[tex]4\cdot \:9x-4\cdot \:7[/tex]
Now, u can factor out the common term 4
[tex]4\left(9x-7\right)[/tex]
Let Vector a = LeftAngleBracket 3, 11, negative 8 RightAngleBracket. and Vector b = LeftAngleBracket 2, negative 3, c RightAngleBracket. . If Vector a minus vector b = LeftAngleBracket 1, 14, negative 3 RightAngleBracket., what is the value of c?
–11
–5
5
11
Answers
Answer:
c.5
Step-by-step explanation:
(3+2a)² alguien sabe la respuesta?
Answers
Answer:
3(3+2a)+2a(3+2a)
9+6a+6a+4a^2
9+12a+4a^2
ANS 4a^2+12a+9