50 points hlep Explain how to graph a polynomial function in factored form. What do the factors mean in terms of the polynomial? Graph f(x)=(x−2)^2 (x+1) (x−4)
Answers
Answer:
Given function: [tex]f(x)=(x-2)^2 (x+1) (x-4)[/tex]
The factors give us the zeros (x-intercepts) of the graph.
To find the zeros, set the function to zero and solve for x:
[tex](x-2)^2 (x+1) (x-4)=0[/tex]
Therefore,
[tex](x-2)^2=0\implies x-2=0 \implies x=2[/tex]
[tex](x+1)=0\implies x=-1[/tex]
[tex](x-4)=0 \implies x=4[/tex]
So the zeros are at (2, 0) (-1, 0) and (4, 0)
The multiplicity of a zero is the number of times the factor appears in the fully factored form of the polynomial, i.e. the exponent on the corresponding factor.
[tex]x = 2[/tex] has a multiplicity of 2[tex]x=-1[/tex] has a multiplicity of 1[tex]x=4[/tex] has a multiplicity of 1If the zero has an even multiplicity, the graph touches and bounces off the x-axis at that point.
If the zero has an odd multiplicity, the graph crosses the x-axis at that point.
To find the y-intercept, expand the function:
[tex]f(x)=x^4-7x^3+12x^2+4x-16[/tex]
Set [tex]x = 0[/tex] and solve:
[tex]f(0)=(0)^4-7(0)^3+12(0)^2+4(0)-16=-16[/tex]
Therefore, the y-intercept is at (0, -16)
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
As the leading degree is 4 (even) and the leading coefficient is positive, the end behavior of the function is:
[tex]f(x) \rightarrow + \infty \textsf{ as } x \rightarrow - \infty[/tex]
[tex]f(x) \rightarrow + \infty \textsf{ as } x \rightarrow + \infty[/tex]
Related Questions
2. Get the difference between 7 and the sum of 1.0006 and 4.06.
3
Answers
Given:
The difference between 7 and the sum of 1.0006 and 4.06.
To find:
The mathematical expression for given statement and it value.
Solution:
Sum of 1.0006 and 4.06 = [tex](1.0006+4.06)[/tex]
The expression for the difference between 7 and the sum of 1.0006 and 4.06 is
[tex]7-(1.0006+4.06)[/tex]
On simplification, we get
[tex]7-(1.0006+4.06)=7-5.0606[/tex]
[tex]7-(1.0006+4.06)=1.9394[/tex]
Therefore, the difference between 7 and the sum of 1.0006 and 4.06 is 1.9394.
In which number is the digit 5 one hundred times larger than it is in the number 253
Answers
Answer:
The 5 would be in the Thousands place
Step-by-step explanation:
Hope this helps any
The following histogram shows the relative frequencies of the hieight recorded to the nearest inch of population of women the mean of the population is 64.97 inches and the standard deviation is 2.66 inches
Answers
The following histogram shows the relative frequencies of the height recorded to the nearest inch of population of women the mean of the population is 64.97 inches and the standard deviation is 2.66 inches
(a) Based on the histogram, what is the probability that the selected woman will have a height of at least 67 inches? Show your work
Answer:
0.22268
Step-by-step explanation:
z-score is z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
(a) Based on the histogram, what is the probability that the selected woman will have a height of at least 67 inches? Show your work
At least means equal to or greater than 67 inches
z = 67 - 64.97/2.66
z = 0.76316
P-value from Z-Table:
P(x<67) = 0.77732
P(x>67) = 1 - P(x<67) = 0.22268
The probability that the selected woman will have a height of at least 67 inches is 0.22268
(5,-5) (6,-6) (7,-7) (8,-8) what is the slope
Answers
Answer:
i think its straight line
Which of the following is true?
A |−5| < 4
B |−4| < |−5|
C |−5| < |4|
D |−4| < −5
Answers
B is true
Step-by-step explanation:
because no number with them to lines can be a negative
Please help asap! I will gave brainlest!
Answers
Answer:
√2 + √6 / 4
Step-by-step explanation:
We know cos(-θ) = cosθ.
Therefore, cos(-15°) = cos15°.
cos15° = cos(45 - 30)
cos15° = cos45cos30 + sin45sin30cos15° = (1/√2)(1/2) + (1/√2)(√3/2)cos15° = 1/2√2 + √3/2√2cos15° = √3 + 1 / 2√2cos15° = (√3 + 1)(√2) / 4cos15° = √2 + √6 / 4Option 1For a project in his Geometry class, Elijah uses a mirror on the ground to measure the height of his school building. He walks a distance of 8.25 meters from the school, then places a mirror on flat on the ground, marked with an X at the center. He then steps 0.8 meters to the other side of the mirror, until he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.45 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.
Answers
The school is about 14.95 meters tall, and the mirror is 8.25 meters from the school.
What is trigonometric ratio?Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let Ф represent the angle Elijah makes with the ground, hence:
tanФ = 1.45/0.8
Ф = 61.11°
The angle of elevation to the building is 61.11°. Let h represent the height of the building.
tan(61.11°) = h/8.25
h = 14.95
The school is about 14.95 meters tall, and the mirror is 8.25 meters from the school.
Find out more on trigonometric ratio at: https://brainly.com/question/24349828
Let f(x) = logx
What is the average rate of change of f(x) from 4 to 6?
Round to the nearest hundredth.
(a.) 0.09
(b.) 0.18
(c.) 0.20
(d.) 0.41
Answers
(a.) 0.09
equation:
f(x) = log(x)
rate of change:
[tex]\sf \rightarrow \sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\sf \rightarrow \sf \dfrac{log(4) -log(6)}{4-6}[/tex]
[tex]\sf \rightarrow 0.088[/tex]
[tex]\sf \rightarrow 0.09[/tex]
Answer:
[tex]A.\: 0.09[/tex]
Step-by-step explanation:
Rate of Change is: [tex]\frac{y{_1-y{_2} } }{x_2-x_1}[/tex]
[tex]\frac{log(4)-log (6)}{4-6}[/tex]
[tex]0.088[/tex]
[tex]0.09[/tex]
Question: In the expression: 4x-5+6x-8
a: Identify the third term (options listed)
- (-6x)
- (-5)
- (6x)
- (-8)
b: is it a constant or a variable term?
c: what is the coefficient? (options listed)
- (6)
- (-6)
- (8)
d: simplified (options listed)
- (10x-3)
- (-1x-2)
- (10x-13)
Answers
Answer:
a -(-6x)
b variay term
c-(-6)
d no answer
You buy cheese in 1lb bags. Your receipt for burritos requires 0.7 ounces of cheese per serving. How many servings can you make
Answers
Answer:
Step-by-step explanation:
A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 29 feet more
than the length of the shortest side. Find the dimensions if the perimeter is 141 feet.
What is the length of the shortest side?
The length of the shortest side is
(1)
What is the length of the second side?
The length of the second side is
(2)
What is the length of the third side?
The length of the third side is
(3)
Answers
Answer:
Step-by-step explanation:
8y8yy89y99u98u89y7t8y7i6u7i9jo
A triangular pane of glass has a height of 44 inches and an area of 440 square inches. What is the length of the base of the pane?
Answers
Answer:
20 inches
Step-by-step explanation:
The base, height, and area of a triangle are related by the formula ...
A = 1/2bh
If you know two of these, you can use this formula to find the third.
440 in² = 1/2b(44 in)
(440 in²)/(22 in) = b = 20 in . . . . . . divide by the coefficient of b
The length of the base is 20 inches.
Find the value of xxx, yyy, and zzz in the parallelogram below.
Answers
Answer:
Step-by-step explanation:
Opposite angles of a parallelogram are congruent, so:
[tex]112=y-9 \longrightarrow y=121[/tex]
and adjacent angles are supplementary, so:
[tex]112+x+1=112+z+3=180 \longrightarrow x=67, z=65[/tex]
What is the value of the expression?
(7 2/3−4 8/9)+(5 2/3−2 1/2)
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answers
Answer:
5 17/18
Step-by-step explanation:
Your calculator can help with this.
__
The integer parts of the mixed numbers can be dealt with separately. The fractional parts are added and subtracted using a common denominator. Here, that denominator is the least common multiple (LCM) of 2, 3, and 9, so is 18.
((7 2/3) -(4 8/9)) +((5 2/3)) -(2 1/2))
= (7 2/3) +(5 2/3) -((4 8/9) +(2 1/2))
= 12 4/3 -(6 +8/9 +1/2)
= 13 6/18 -(6 +16/18 +9/18)
= 13 6/18 -(6 +25/18) = 13 6/18 -(7 7/18)
= (13 -7) +(6/18 -7/18)
= 6 -1/18
= 5 17/18
__
Additional comment
Doing the math in the manner shown above means you can mostly do it without a calculator. If you like, you can convert all of the numbers to improper fractions, then add those. This often requires a calculator.
= (138/18 -88/18) +(102/18 -45/18)
= 50/18 +57/18
= 107/18 = 5 17/18
Do you know the tricks to multiplying variables?
Answers
Answer:
yes I know how to to multiple variables.
The speed of a tidal wave, s, in hundreds of miles per hour can be modeled by the equation, [tex]s=\sqrt{t} -2t+6[/tex] , where t represents the time from its origin in hours. The graph of the tidal wave is shown.
Answers
Using it's concept, it is found that the domain of the function regarding the speed of the tidal wave is explained by:
[0, 4]: relating to the time of the tidal wave from it's origin in hours, restricted by the inability for the speed to be lees than zero.
What is the domain of a function?It is the set that contains all possible input values for the function. In a graph, it is given by the x-values, that is, the horizontal axis values.
In this graph, the horizontal axis assumes values between 0 and 4, which is the time after the wave, and considering that the wave cannot be less than zero. Hence, the correct option is:
[0, 4]: relating to the time of the tidal wave from it's origin in hours, restricted by the inability for the speed to be lees than zero.
More can be learned about the domain of a function at https://brainly.com/question/25897115
Two similar solid cones have their radii 15cm and 25cm respectively, if the volume of the bigger cone is 325cm³. Calculate (a) the linear scale factor (b) the volume scale factor (c) volume of the smaller cone
Answers
Answer:
The length scale factor = \(\frac{24}{6} = 4\)
The area scale factor = \(4^2 = 16\)
\[\text{Larger area} = 16 \times \text{smaller area}\]
\[50.3 \times 16 = 804.8\]
The area of the large clock face is approximately 804.8 cm2.
Step-by-step explanation:
The length scale factor = \(\frac{24}{6} = 4\)
The area scale factor = \(4^2 = 16\)
\[\text{Larger area} = 16 \times \text{smaller area}\]
\[50.3 \times 16 = 804.8\]
The area of the large clock face is approximately 804.8 cm2.
Answer:
a) the linear scale factor = 5/3
b) the volume scale factor = 125/27
c) 70.2 cm³
Step-by-step explanation:
r₁ = 15 cm, r₂ = 25 cm
r₂/r₁ = 25/15 = 5/3
They are similar, so h₂/h₁ = 5/3
a) the linear scale factor = 5/3
b) the volume scale factor = (5/3)³ = 125/27
c) V₂/V₁ = 125/27
Given V₂ = 325 cm³, V₁ = 325*27/125 = 70.2 cm³
QUESTION 1
The general term of the sequence is given by Tn= an + bn + c T2-T1 = 4; T3; -T2 = 6; T4-T3 = 8 and T2 = 6
1.1 Calculate a, b and c
Answers
Answer:
The general term of the sequence is given by
T
n
=
a
n
2
+
b
n
+
c
The general term of the sequence is given by
T
n
=
a
n
2
+
b
n
+
c
Calculate a,b and c
Determine the 12th term of the sequence.
grade12 general-term sequence series
Share your questions and answers with your friends.
answer comment
1 Answer
0
0
T3 - 6=6
T3=12
then T2-T1=4
6-T1=4
T1=2
T4-T3=8
T4-12=8
T4=20
Therefore terms= 2,6,12,20
1st difference= 4,6,8
2nd difference= 2,2,....
2a=2
a=1
3a+b=4
3(1) + b=4
b= 1
a+b+c= 2
c= 2-1- 1= 0
giving Tn= n^2 + n
T12 = 12^2 + 12 = 156
maths I need help asap it's about sequence and functions good rewards!
Answers
Answer:
a₄ = 50
Step-by-step explanation:
work back from the seventh term a₇ using the reverse of the term to term rule , that is
divide by 2 then subtract 3
a₇ = 442
a₆ = 442 ÷ 2 - 3 = 221 - 3 = 218
a₅ = 218 ÷ 2 - 3 = 109 - 3 = 106
a₄ = 106 ÷ 2 - 3 = 53 - 3 = 50
Answer:
[tex]a_{4}=50[/tex]
Step-by-step explanation:
[tex]a_{4} = 50[/tex]
a₇ = 442
a₆ = 442 ÷ 2 - 3 = 221 - 3 = 218
a₅ = 218 ÷ 2 - 3 = 109 - 3 = 106
a₄ = 106 ÷ 2 - 3 = 53 - 3 = 50
A hall is thrown straight up, from 3 m above the ground, with a velocity of 14m/s. When does it hit the ground? Use the vertical motion formula.
Answers
In this question, to find the total height first, we must also take into consideration the acceleration due to gravity as well. To find the distance by which acceleration due to gravity pulls the ball down must know the Initial velocity.
In the answer key, it says that gravity changes the ball's height by a distance of -5t^2
Is initial velocity in this question 0 or 14m/s? Because if it is 14, then gravity should change the balls position by -(14+5t^2), not -5t^2, because if I remember correctly, the formula for finding distance is vt(initial velocity)+(1/2)at^2 ,and not just (1/2)at^2
A triangular prism with 5 faces.
A triangular prism has faces.
Answers
Answer:
Pentahedron
Step-by-step explanation:
A triangular prism with 5 faces is called Pentahedron.
It has 5 faces, 6 vertices and 9 edges.
5 faces - Two are triangular faces and three are rectangular faces.
Answer:
its has 5 faces
Step-by-step explanation:
The mass of a carbon-12 atom is 1.99\times 10^{-23}1.99×10
−23
grams. The mass of a neutron is 1.68\times 10^{-24}1.68×10
−24
grams. How many times greater is the mass of a carbon-12 atom than the mass of a neutron? Write your answer in standard notation, rounding to the nearest tenth.
Answers
Answer:
If the mass of one electron is 9.11 x 10-28 g, and you are looking for the mass of a mole of electrons, you need to understand Avogadro's number. One mole is 6.02 x 1023 particles. So you will have to multiply (6.02 x 1023) x (9.11 x 10-28 g) to get your answer of 5.48 x 10-4 grams (answer rounded to significant figures)
Step-by-step explanation:
1.2 x 10¹ times greater is the mass of a carbon-12 atom than the mass of a neutron
What is Division?A division is a process of splitting a specific amount into equal parts.
To find the ratio of the mass of a carbon-12 atom to the mass of a neutron, we can divide the mass of carbon-12 by the mass of a neutron:
(1.99×10⁻²³ grams) / (1.68×10⁻²⁴ grams)
= 11.8 grams
This means the mass of a carbon-12 atom is 11.8 times greater than the mass of a neutron. Written in standard notation and rounded to the nearest tenth, the answer is 1.2 x 10¹
Hence, 1.2 x 10¹ times greater is the mass of a carbon-12 atom than the mass of a neutron
To learn more on Division click:
https://brainly.com/question/21416852
#SPJ2
Determine whether the pair of triangles is congruent.
Choose the correct answer below.
Congruent
Not congruent
Answers
Answer:
not congruent
Step-by-step explanation:
congruent is just a fancy way of saying the same in geometry. so to check if its congruent, see if all side lengths correspond to another side length on the other triangle. they do not, so they can't be congruent
hope this helped :)
Which of the following would be appropriate to measure in centimeters
Answers
Answer:
c
Step-by-step explanation:
Each batch of cookies is 8.9 oz. What is the weight of 2.5 batches of cookies
Answers
Answer:22.25 oz
Step-by-step explanation:
1 batch of cookies = 8.9 oz
2.5 batches of cookies = x oz
cross multiply
1x=8.9(2.5)
x=22.25 oz
the selling price of a product is $20 and the markup is $4 What percentage of the selling price does the markup represent
Answers
Answer:
20%
Step-by-step explanation:
The ratio of 20 to 4 can be simplified to 5:1, by switching it around, we get 1/5. 1/5 as a percentage can be expressed as 20%
Answer:
20%
Step-by-step explanation:
Given the following question:
20% of 20
To find the answer we will use the formula to calculate percentages.
[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{20\times20}{100}[/tex]
[tex]20\times20=400[/tex]
[tex]400\div100=4[/tex]
[tex]=4[/tex]
20% of 20 is 4, which means your answer is "20%."
Hope this helps.
Need help not sure if I got this right???????????
Answers
Use the volume formula to find the volume of the prism.
A. 21 cubic units B. 42 cubic units C. 27 cubic units D. 9 cubic units
Answers
Answer:
D Because
Step-by-step explanation:
1/2 +1/2 is 1 so 1+1+3+4 is 9
HOPE THIS HELP! :)
please help me with this
Answers
Answer:
y-5=3/4(x-6)
Step-by-step explanation:
The picture you posted is a bit unclear and difficult to look at, but that's alright.
This is a simple question if you understand that the point slope for equation is: y-y1 = m(x-x1).
m is the slope and (x1,y1) is a point on the graph.
So, if you input the point (6,5) on the graph, it works.
You can double check with the other equations to see that they are all wrong!
Factor 48e+180 using greatest common factor
Answers
48 = 24 × 31
180 = 22 × 32 × 51