12. Find all x- and y-intercepts, state the multiplicity of each zero and tell if the graph crosses or
bounces, and state the end behavior Then graph each polynomial by hand,
P(x)=x^2(x-3)^2(x+2)
P(x)=x^4-4x^2
Answers
Step-by-step explanation:
12a. To
find x intercepts, set each factor equal to zero
[tex] {x}^{2} = 0[/tex]
[tex]x = 0[/tex]
[tex](x - 3) {}^{2} = 0[/tex]
[tex]x = 3[/tex]
[tex]x + 2 = 0[/tex]
[tex]x = - 2[/tex]
So the x intercepts are( 0,-2,3.)
The multiplicity of 0 and 3 is 2,
The multiplicity of -2 is 1.
The y intercepts are
[tex]0 {}^{2} (0 - 3) {}^{2} (0 + 2) = 0[/tex]
The y intercept is 0.
End Behavior: Since this is a positve 5th root function, as x increases, f(x) increases while as x decreases, f(x) decreases.
The First picture shows the graph of the function. Notice ried the zeroes that have a multiplicity of 2 have a parabolic reflection after thre function reaches their zero.
The zero that have a multiplicity of 1 have just passes through the graph.
12b. We have
[tex] {x}^{4} - 4 {x}^{2} [/tex]
We can easily find y intercept, which is 0.
To find x intercept,
Factor
[tex] {x}^{2} ( {x}^{2} - 4)[/tex]
[tex] {x}^{2} (x + 2)(x - 2) = 0[/tex]
[tex]x = 0[/tex]
[tex]x = 2[/tex]
[tex]x = - 2[/tex]
So the x intercepts are (0,2,-2).
The multiplicity of 0 is 2 while 2 and -2 is 1.
End Behavior: Since this is a positve quartic function, as x increases or decreases , f(x) increases
Look at the second graph,
Answer:
[tex]P(x)=x^2(x-3)^2(x+2)[/tex]
y-intercept is when x = 0:
[tex]\implies P(0)=0^2(0-3)^2(0+2)=0[/tex]
Therefore, y-intercept is at (0, 0)
x-intercept(s) is when P(x) = 0
[tex]\implies x^2(x-3)^2(x+2)=0[/tex]
[tex]\implies x^2=0\implies x=0[/tex]
[tex]\implies (x-3)^2=0\implies x=3[/tex]
[tex]\implies (x+2)=0\implies x=-2[/tex]
Therefore, x-intercepts are:
(0, 0) with multiplicity 2 → bounces(3, 0) with multiplicity 2 → bounces(-2, 0) with multiplicity 1 → crosses x-axisEnd-behavior:
As the lead coefficient is positive and the lead degree is odd,
[tex]P(x) \rightarrow - \infty \textsf{ as }x\rightarrow - \infty[/tex]
[tex]P(x) \rightarrow + \infty \textsf{ as }x\rightarrow +\infty[/tex]
-------------------------------------------------------------------------------
[tex]P(x)=x^4-4x^2[/tex]
y-intercept is when x = 0:
[tex]\implies P(0)=(0)^4-4(0)^2=0[/tex]
Therefore, y-intercept is at (0, 0)
x-intercept(s) is when P(x) = 0
[tex]\implies x^4-4x^2=0[/tex]
[tex]\implies x^2(x^2-4)=0[/tex]
[tex]\implies x^2(x-2)(x+2)=0[/tex]
[tex]\implies x^2=0 \implies x=0[/tex]
[tex]\implies (x-2)=0 \implies x=2[/tex]
[tex]\implies (x+2)=0 \implies x=-2[/tex]
Therefore, x-intercepts are:
(0, 0) with multiplicity 1 → crosses x-axis(2, 0) with multiplicity 1 → crosses x-axis(-2, 0) with multiplicity 1 → crosses x-axisEnd-behavior:
As the lead coefficient is positive and the lead degree is even,
[tex]P(x) \rightarrow + \infty \textsf{ as }x\rightarrow - \infty[/tex]
[tex]P(x) \rightarrow + \infty \textsf{ as }x\rightarrow +\infty[/tex]
Related Questions
Complete this word
[tex] _ r _ch_i_ [\tex]
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Answer:
Arachnid is my guess.
Please helppppppppppppp
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The line DB is 8cm which is made up of DE and EB which are equal to each other, thus DE and DB are both 4 cm.
Secondly, since AC and DB are perpendicular, that means angle DEC and angle DEA are ninety degrees.
Thus using the Pythagorean theorem, we can find the length of AE and EC which we can add up to find the length of AC.
[tex]AE = \sqrt{AD^2-DE^2} =\sqrt{5^2-4^2} =\sqrt{25-16} =\sqrt{9}=3\\ \\EC=\sqrt{DC^2-DE^2}=\sqrt{6^2-4^2}=\sqrt{36-16} =\sqrt{20} =2\sqrt{5} =4.47[/tex]
By adding AE and EC, we get that the length of AE and EC is 7.47 or as approximated to the nearest tenth 7.5.
Hope that helps!
Let A = {O, 2, 4, 6, 8, 10}, B = {O, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8,9, 10}. Find
Answers
Answer:
Ans= {0,1,2,3,4,5,6,7,8,9,10}
Step-by-step explanation:
Union of set A, B, C
A={0,2,4,6,8,10}
B={0,1,2,3,4,5,6}
C={4,5,6,7,8,9,10}
Union={0,1,2,3,4,5,6,7,8,9,10}
NEED HELP QUICK WILL GIVE OUT 30 POINTS
Answers
4
1-
6
Step-by-step explanation:
its because i cant understand
Answer:
[tex]\Large \displaystyle \frac{7}{8}[/tex]
Step-by-step explanation:
Volume = area of cross-section × height
Mixed to improper fraction
7/4 × 1/2 = 7/8
Findthe y -intercept oftheparabolay = x2 + 5x + 9.
Answers
Answer:
x = 5 ± i√11 / 2
Step-by-step explanation:
At the y-intercept the value of y is equal to 0.
=> 0 = x² + 5x + 9
=> x = -5 ± √25 - 4(9) / 2
=> x = 5 ± √-11 / 2
=> x = 5 ± i√11 / 2
James Marbury is the payroll accountant at All's Fair Gifts The employees of All's Fair Gifts are paid semimonthly. Lauren Stenn comes to him on April 2 and requests a pay advance of $1000, which Lauren will pay back in equal parts on the April 15 and May 15 paychecks Lauren is single with one dependent under 17 and is paid $51,680 per year Lauren contributes 3 percent of gross pay to a 401(k) and has $139 per paycheck deducted for a Section 125 plan.
Answers
Based on Lauren's income and the various deductions, the net pay for April is $1,151.44.
What is the taxable income?Taxable income:
= Semimonthly income - 401k - Section 125 plan
= (51,680 / 24 pay periods) - (0.03 x 51,680/24 periods) - 139
= 2,153.33 - 64.6 - 139
= $1,949.73
What is Lauren's April net pay?= Taxable income - federal income tax - state income tax - social security - Medicare - advance repayment
= 1,949.73 - (1.6% x 1,949.73) - (5.25% x 1,949.73) - (6.2% x 2,153.33 gross income) - (1.45% x 2,153.33) - 500
= $1,151.44
Find out more on taxable income at https://brainly.com/question/10137785.
A flower pot has a circumference of 47 inches. What is the approximate length of the radius of the flower pot? Use 3.14 for .
please answer
Answers
Answer:
7.48
Step-by-step explanation:
C=2πr
Solving for
r=C
2π=47
2·π≈7.48028
Answer:
Step-by-step explanation:
Circumference = 47 inches
[tex]2\pi r = 47\\\\2*3.14*r = 47\\\\6.28*r = 47\\\\r = \dfrac{47}{6.28}\\\\[/tex]
r = 7.48 in
The Jurassic Zoo charges $8 for each adult admission and $6 for each child. The total bill for the 119 people from a school trip was $754. How many adults and how many children went to the zoo?
PLEASE HELP!!! I cant figure this out!!!
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Sean baked 5 batches of cookies. Each batch contained between 3 dozen and 5 dozen cookies. Which is a reasonable estimate of the
total number of cookies Sean baked?
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Answer:
96 or 2,160
Step-by-step explanation:
raise v to the 8th power, triple the result, then subtract w from what you have
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Answer:
Step-by-step explanation:
[tex]3(v^{8}) -w\\ 3v^{8}-w[/tex]
Find the value of 2/5 -3/5
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What is the circumference of a pizza that has the area of 50.3 inches?
Answers
Answer:
C = 25.1
Step-by-step explanation:
Use the formulas:
A = π r ²C = 2 π rSolving for C:
C = 2√πA = 2 · √π ·50.3 ≈ 25.14137Round to the nearest tenth:
Result = 25.1Write a mixed number to describe the length of the ribbon shown in the figure below.
Answers
Step-by-step explanation:
what did we learn in the other question ?
there are 8 equal sub-segments of 1/8 length between neighboring whole numbers.
so, each little line is 1/8.
the marker goes first to 1, and then one little line towards 2.
therefore, that number is 1 1/8.
There are 5 subjects each school day. Each subject is 45 minutes long. Lunch and recess are 35 minutes long. How long is the school day?
Answers
Answer:
4 hours and 33 minutes
Step-by-step explanation:
Before I answer, I was confused if recess and lunch are 35 minutes in total or 35 minutes each. My answer is if they are 35 minutes combined. If that's wrong, you can just add 35 minutes to my answer.
5*45 = 225
225+35 = 260 minutes or 4 hours and 33 minutes
Round 58.5 to the nearest whole number
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This is because we would round the decimal up to a whole number. The decimal .5 would round up, since numbers 5 and greater round up.
12.5 is 8% of what number?
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8 percent of the number 156.25 is 12.5.
Let the unknown number be x.
Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Here, 8% of x is 12.5
8% of x= 12.5
8/100 ×x= 12.5
0.08x=12.5
x=12.5/0.08
x= 156.25
Therefore, 8 percent of the number 156.25 is 12.5.
To learn more about the percentage visit:
brainly.com/question/24159063.
#SPJ6
Two stores are having sales on cameras. • At Store X all cameras are on sale for 15% off the original price.
• At Store Y all cameras are on sale for off the original price. Which store would have the better sale price for a camera with an original price of $80?
Answers
Answer:
Store X, because the sale price would be $68
Step-by-step explanation:
vStore X, because the sale price would be $68
Assuming at Store Y all cameras are on sale for off the original price. The store with the better sale price is: Store y, because the sales price is $64.
Store x and yStore x
x=80×(1-0.15)
x=80×0.85
x=68
Store y
y=80×(-1/5+1)
y=80×4/5
y=64
y=64≤68
Based on the above calculation store y is the best.
Inconclusion the store that would have the better sale price is: Store y, because the sales price is $64.
Learn more about store x and y here:https://brainly.com/question/20455611
eight multiply by 5 over 12 equals
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Hi! I hope you're enjoying your day!
First, 8 multiplied by 5 is equal to 40.
Then, 40 over 12 is the same as 40 divided by 12.
But hey! 40 isn't divisible by 12.
So we write this as a fraction:
[tex]\bold{\displaystyle\frac{40}{12} }[/tex]
Surprise! This fraction can be reduced.
Divide both the numerator (40) and the denominator (12) by 4:[tex]\bold{\displaystyle\frac{10}{3} }[/tex]
Hence, the answer is:
[tex]\boxed{\boxed{\bold{\displaystyle\frac{10}{3} }}}[/tex] <-- the answer written as an improper fraction
[tex]\boxed{\boxed{\bold{3\displaystyle\frac{1}{3}}}}[/tex] <-- the answer written as a mixed number
Hope everything is clear.
If you have any questions, please comment.
#LearningIsFun
[tex]\rule{250}{2}[/tex]
i dont understand this
Answers
The circumference of a roll of party streamers is 11 inches. The circumference decreases by 3 inches after you use the streamers to decorate for a birthday party. Find the diameter of the roll after the decrease. Round your answer to the nearest hundredth.
Answers
Answer:
2.55
Step-by-step explanation:
First take 11 and subtract it by 3 to get 8.
Then divide it by 3.14 and get 2.547770701...
After that round it to 2.55
Which relationships describe angles 1 and 2?
Select each correct answer.
O supplementary angles
O complementary angles
O vertical angles
O adjacent angles
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good estimate of the length of a standard bed pillow
Answers
Answer:
I would say 2 ft
Step-by-step explanation:
Have amazing day!
Please rate!
(Algebra 2)
Find the inverse of f(x) and its domain.
Answers
f^-1(x)=x
y=1/(x+5) - 1
y+1=1/(x+5)
(x+5)=1/(y+1)
x=1/(y+1)-5
f^-1(x)=1/(x+1) -5
denominator cannot equals to zero
x+1≠0
x≠-1
answer
B
explain turning point in graphs
Answers
A turning point is a point at which the derivative changes sign. A turning point may be either a relative maximum or a relative minimum (also known as local minimum and maximum).
Analyze the diagram below and complete the instructions that follow.
Find the value of x and the value of y.
Answers
Answer:
B
Step-by-step explanation:
This is an isosceles triangle. So, the sides opposite to equal angles are equal.
y = 5
To find x, use Pythagorean theorem,
x² = 5² + 5²
= 25 + 25
= 50
[tex]x =\sqrt{50}\\\\x=\sqrt{2*5*5}\\\\x=5\sqrt{2}[/tex]
Zoe invested $16,000 in an account paying an interest rate of 3.6% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 20 years?
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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$16000\\ r=rate\to 3.6\%\to \frac{3.6}{100}\dotfill &0.036\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &20 \end{cases} \\\\\\ A=16000\left(1+\frac{0.036}{4}\right)^{4\cdot 20}\implies A=16000(1.009)^{20}\implies A\approx 19100[/tex]
solve the inequality |x+6-|3x+6||+|x+2|-x-4 less then or equal to 0
Answers
It looks like the inequality is
[tex]\bigg|x + 6 - |3x + 6|\bigg| + |x + 2| - x - 4 \le 0[/tex]
or equivalently,
[tex]\bigg|x + 6 - 3 |x + 2|\bigg| + |x + 2| - x - 4 \le 0[/tex]
Recall the definition of absolute value:
[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]
By this definition, we have
[tex]|x + 2| = \begin{cases} x + 2 & \text{if } x + 2 \ge 0 \\ -(x + 2) & \text{if } x + 2 < 0 \end{cases} = \begin{cases} x + 2 & \text{if } x \ge -2 \\ -x - 2 & \text{if } x < -2 \end{cases}[/tex]
Suppose [tex]x < -2[/tex]. Then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = |x + 6 - 3 (-x - 2)| + (-x - 2) - x - 4 \\\\ = |4x + 12| - 2x - 6[/tex]
By definition of absolute value,
[tex]|4x + 12| = 4 |x + 3| = \begin{cases} 4x + 12 & \text{if } x \ge -3 \\ -4x - 12 & \text{if } x < -3 \end{cases}[/tex]
so we further suppose that [tex]x < -3[/tex]. Then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = |4x + 12| - 2x - 6 \\\\ = (-4x - 12) - 2x - 6 \\\\ = -6x - 18 \le 0 \\\\ \implies x \ge -3[/tex]
but this is a contradiction, so this case gives no solution.
If instead we have [tex]-3 \le x < -2[/tex], then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = |4x + 12| - 2x - 6 \\\\ = (4x + 12) - 2x - 6 \\\\ = 2x + 6 \le 0 \\\\ \implies x \le -3[/tex]
and [tex]-3 \le x[/tex] and [tex]x \le -3[/tex] means that [tex]\boxed{x = -3}[/tex].
Now suppose [tex]x \ge -2[/tex]. Then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = |x + 6 - 3 (x + 2)| + (x + 2) - x - 4 \\\\ = |-2x| - 2 \\\\ = 2 |x| - 2[/tex]
If we further suppose that [tex]-2 \le x < 0[/tex], then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = 2 |x| - 2 \\\\ = -2x - 2 \le 0 \\\\ \implies x \ge -1[/tex]
Otherwise, if [tex]x \ge 0[/tex], then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = 2 |x| - 2 \\\\ = 2x - 2 \le 0 \\\\ \implies x \le 1[/tex]
Taken together, this case gives the solution [tex]\boxed{-1 \le x \le 1}[/tex]
So, the overall solution to the inequality is the set
[tex]\boxed{\left\{ x \in \mathbb R : x = -3 \text{ or } -1 \le x \le -1 \right\}}[/tex]
In the formula l2 = h2 +r2, l=25 and r=7, then the value of h is
Answers
Answer:
18
Step-by-step explanation:
I2=h2+r2
25(2)=h2+7(2)
50=h2+14
-14 -14
36=h2
÷2 ÷2
18=h
Please please can someone help me !!! math question !!!!
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Using the graph, it is found that:
a) The local minimum value of the function is of y = 0.
b) The values are x = -3, x = 3.
How to find the local minimums of a function is a graph?The local minimum of a function in a graph is the point at which the function changes from decreasing to increasing. In this problem, they are given by y = 0.
The values at which this happen is the values of x, that is, the horizontal axis. In this problem, they are at x = -3 and x = 3.
More can be learned about functions at https://brainly.com/question/25537936
Help please. Very easy
Which description can be written as the expression 6b+5?
the difference of six times a number and five
the sum of six times a number and five
the quotient of six times a number and five
the product of six times a number and five
Thanks.
Answers
explanation: b is your variable which is going to by multiplied by 6, since there is no other symbol next to it. afterwards, you would add 5 to get your final answer.