Answers
Answer:
[tex]P(x) -0.1(x+1)(x-3)^2[/tex]
Step-by-step explanation:
So you can express a polynomial in factored form, where each factor of the polynomial is being multiplied by each other to get the original polynomial as such: [tex]p(x) = a(x+a)(x+b)(x+c)...[/tex] notice the a in front? Sometimes the value is 1, sometimes it's not, and I'm assuming it's not 1, since the y-intercept is given.
Anyways, when we express a polynomial in factored form: [tex]p(x) = a(x+a)(x+b)(x+c)...[/tex], it's pretty easy to see that -a, -b, and -c are roots, since if we plug in -a, the factor (x+a) becomes (-a + a) = 0, and since the factors are being multiplied by each other, the value p(-a) will be 0, since 0 * some value = 0.
The next thing to know is what multiplicity means. It essentially means when you have the same root "multiple times", or in other words it's the degree of the factor. For example: [tex]f(x) = (x+a)^3(x+b)^2(x+c) = (x+a)(x+a)(x+a)(x+b)(x+b)(x+c)[/tex], if you took each factor, you would see that the root -a shows up 3 times, thus the multiplicity is 3, which can also be determined by just looking at the initial degree... 3. The same thing goes for b and c, except for c, the degree isn't explicitly said, it's just 1.
Since we have a zero at x=3 one of the factors will be (x-3) since plugging in 3 to this makes it 0. But this has a multiplicity of 2, so the degree of the this factor is 2. So for we have the polynomial: [tex]p(x) = (x-3)^2[/tex]
Since we have a zero at x=-1, one of the factors will be at (x+1), since plugging in 1 into this makes the value 0. This has a multiplicity of 1, and you can write the degree 1, but if you don't explicitly write it, it can just be assumed to be 1, since a^1=a
So now we have the polynomial: [tex]p(x) = (x+1)(x-3)^2[/tex]
So let's just assume we have an "a" value in front as mentioned in the very beginning, we have the polynomial: [tex]p(x) = a(x+1)(x-3)^2[/tex] and we can solve for this value, using any point except for the zeroes. We can use the y-intercept given to solve for a
Plug in 0 as x (by definition of y-intercept) and set p(x) = -0.9
[tex]-0.9 = a(0+1)(0-3)^2[/tex]
Subtract/add values
[tex]-0.9 = a(1)(-3)^2[/tex]
Simplify
[tex]-0.9 = 9a[/tex]
Divide both sides by 9
-0.1 = a
So now let's plug this into our polynomial to get the final result!
[tex]P(x) -0.1(x+1)(x-3)^2[/tex]
Related Questions
For the equation:
y=−x^2+10x−24, the x-intercepts are already given on the graph. Now, using the parabola tool, graph rest of the equation.
Answers
The graph of the parabola can be seen in the image below.
How to graph the parabola?
We need to find some points on the parabola, and then draw a curve that connects them.
On the graph you already have the x-intercepts, so you already have two points.
Now let's get another point which is the vertex.
For our parabola:
[tex]y = -x^2 + 10x - 24[/tex]
The vertex is at:
[tex]x = -10/(2*-1) = 5[/tex]
Evaluating in x = 5 we get:
[tex]y = -5^2 + 10*5 - 24 = 1[/tex]
So we also have the point (5, 1), now we can just connect the points and get the parabola:
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A rectangular tank 60cm long, 50cm wide and 24cm height was 1/3 filled with water at first. A tap was turned on to completely fill the tank. The rate of water flowing from the tap into the tank was 3 litre per minute. How long did it take to fill the tank completely? Give your answers in minutes.
Answers
=72000
volume that is needed to fill it up
(72000/3) x 2 = 48000
3 litre per minute
48000cm^3 = 48litre
48/3=16 minutes
Let f(r) = 6,
find f-¹(r)
Answers
There is no answer because there cannot be one to one function inverse.
In a recent year, 28.7% of all registered doctors were female. If there were 52,900 female registered doctors that year, what was the total number of registered doctors?
Answers
Step-by-step explanation:
(52900 ÷ 28.7) × 100 = 184320 ( rounded to nearest whole number, since you cannot have half humans)
. Last weekend, Michael
drove to his friend's house.
When he left, he noticed
that the fuel gauge in his
car indicated that his gas
tank was 4 full. When he
returned home, the fuel
gauge in his car indicated
that his gas tank was ½ full.
If the gas tank holds 24
gallons, how many gallons
did Michael use on his
drive?
Answers
It can be said that the total amount of fuel that was used by Michael when he was away to his friends was 12 gallons.
How to solve for the quantity.The question said that the tank was full before he left to his friends. This was after he checked the gauge of the gas tank.
The question says that the required quantity needed to fill up this tank is 24 gallon. Hence if it is full, then the total gallon it had before he made this trip was 24 gallon.
Then we are told that he went ahead to check the gauge when he finished and was at home. The quantity of fuel he had at this time was 1/2 of what was there.
This would be 1/2 * 24
12
Hence he made use of 12 gallons when he was away.
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
Answers
The options Patel has to solve the quadratic equation 8x² + 16x + 3 = 0 is x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot.
Quadratic equation8x² + 16x + 3 = 0
8x² + 16x = -3
8(x² + 2x) = -3
Using completing the square8(x² + 2x + 1) = -3 + 8
factorization8(x² + 1) = 5
(x² + 1) = 5/8
Taking the square root of both sides(x + 1) = ± √5/8
x = -1 ± √5/8
Therefore,
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
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PLS ANSWER BOTH PARTS I WILL GIVE BRAINLIEST PLSSS HURRRYYYY
Answers
Answer: slope is 1/3
Step-by-step explanation: make a graph of y=1/3x+9
So I need to know what company changes more or less
Answers
Because for 10miles it would be the same as Moussa’s taxicab. However, for 20 miles for Anand’s taxicab its shown as $48 but Moussa’s is shown as the equation 20•$2.20=$44+$3(pickup fee)=$47
$47(Moussa)<$48(Anand)
Anand’s charges more
Moussa’s charges less
Craig has a watch that is losing time. For every minute that passes, his watch loses 10 seconds. If Craig set his watch correctly at 9am, what time whould it show when it is 10am on the house clock?
Answers
Answer:
9:50 am
Step-by-step explanation:
because 10 x 60 is equal to 1 hour, so you get 600 seconds subtracted from 10am. 600 seconds is equal to 10 minutes. so 10 am - 10 minutes = 9:50am
Which of the following options have the same value as 5\%5%5, percent of 353535?
Answers
Answer:
[tex]\frac{5}{100}\times35[/tex]
[tex]0.05\times35[/tex]
Step-by-step explanation:
Given:
Which of the following options have the same value as 5% 35, percent of 35?
Following Options:
[tex]5 \times 35[/tex]
[tex]\frac{5}{100}\times35[/tex]
[tex]0.5\times0.35[/tex]
[tex]0.05\times35[/tex]
[tex]\frac{5}{10}\times35[/tex]
Solve:
[tex]5[/tex] % [tex]= 0.05=\frac{5}{100}[/tex]
Thus the following options:
[tex]5 \times 35[/tex] [ False x ]
5 does not equal 5%
[tex]\frac{5}{100}\times35[/tex] [True √ ]
[tex]5[/tex]% [tex]=\frac{5}{100}[/tex]
[tex]0.5\times0.35[/tex] [ False x ]
[tex]0.5 = 0.50[/tex]
[tex]0.05\times35[/tex] [True √ ]
[tex]5[/tex]% [tex]= 0.05=\frac{5}{100}[/tex]
[tex]\frac{5}{10}\times35[/tex] [ False x ]
[tex]\frac{5}{10}=0.50[/tex]
Therefore, the options [B] [tex]\frac{5}{100}\times35[/tex] and [D] [tex]0.05\times35[/tex] is True.
Kavinsky
help me find the answer that bests best
represents this relationship
Answers
Answer:
c
Step-by-step explanation:
consider points (0,2) and (-4,0)
slope=(0-2)/(-4-0)=-2/-4=1/2
y-intercept=2
y=mx+c
y=1/2 x+2
Answer:
y=1/2x+2
Step-by-step explanation:
Solve the following equation for W.
P=2L+2W
Answers
**Disclaimer** Hi there! I assumed the question is to represent W in terms of all other variables (P, L). The following answer corresponds to this understanding. If it is incorrect, please let me know and I will modify my answer.
Answer: W = (P/2) - L
Step-by-step explanation:
Given equation
P = 2L + 2W
Factorize 2 out
P = 2 (L + W)
Divide 2 on both sides
P / 2 = 2 (L + W) / 2
P / 2 = L + W
Subtract L on both sides
(P / 2) - L = L + W - L
[tex]\Large\boxed{W=\frac{P}{2} -L}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
[tex]\displaystyle{W = \dfrac{P}{2} - L}[/tex]
Step-by-step explanation:
To solve for W, we have to isolate the W-variable. First, we can factor the expression 2L + 2W to 2(L+W):
[tex]\displaystyle{P = 2(L+W)}[/tex]
Next, we'll be dividing both sides by 2:
[tex]\displaystyle{\dfrac{P}{2} = \dfrac{2(L+W)}{2}}\\\\\displaystyle{\dfrac{P}{2} = L+W}[/tex]
Then subtract both sides by L:
[tex]\displaystyle{\dfrac{P}{2} - L= L+W-L}\\\\\displaystyle{\dfrac{P}{2} - L= W}[/tex]
Therefore, we'll obtain W = P/2 - L.
Note that the given formula is perimeter formula of a rectangle where Perimeter = 2 * Length + 2 * Width.
So if we solve for W (Width) then we'll get Width = Perimeter / 2 - Length which can be useful to find width with given perimeter and length.
If you chose an angle, how are the construction steps you completed similar to the steps you would have taken to construct and bisect a line segment? How are they different?
Answers
There are different ways to construct an angle. The steps used in making a line segment are; First, you have to put the compass at one specific end of the line segment. Then you shift the compass slowly a little bit so it will be longer than half the length of the line segment. Then you have to draw arcs up and down the line. while using the same compass width, you then draw arcs from one specific end of the line. and thereafter you put your ruler at the point where the arcs cross, and you then draw the line segment. The difference is that to bisect an angle, one has to divide the shape or angle into two congruent parts while in the construction of a line segment, there are differences in length. What is the construction process of Angles? This entails a good construction process in making angles. They are step-by-step processes used to produce detailed and exact geometric figures.
Please help pls help mEE THIS IS REALLY CONFUSING MARKING BRAINlIST AND GIvinG 50 POINTS IF CORRECT!!
The ratio of the number of cupcakes to the number of pastries in a box is 7:2. Which table shows the possible amounts of cupcakes and pastries in a box, given the ratio?
Answers
Last box
If you found this useful, please mark it as the BRAINLIEST.XDHave a nice day ツAs it's 7:2
The variation is directDifference between x and y must increase in big number as x and y increases
Option D is correct in that manner
Let's double check
7:214:428:856:16PLS HELP plsssssssssssssss
Answers
Answer:
a. 33
Step-by-step explanation:
a straight line is 180° so
3x = 180 - 81
3x = 99
to find x divide by 3
x = 99/3
x = 33
A tumor is injected with 0.9 grams of Iodine-125, which has a decay rate of 1.15% per day. Write an exponential model representing the amount of Iodine-125 remaining in the tumor after t days. Then use the formula to find the amount of Iodine-125 that would remain in the tumor after 60 days.
Answers
With the use of formula, the amount of Iodine-125 that would remain in the tumor after 60 days is 0.45 grams
Word Problem Leading to Exponential FunctionFirst analyze the problem and represent them in exponential function. The decay rate is different from increase rate with minus and plus sign.
Given that a tumor is injected with 0.9 grams of Iodine-125, which has a decay rate of 1.15% per day. Let
I = initial amount injected = 0.9 gramsR = decay rate = 1.15%t = number of days = 60 daysA = the remaining amount of Iodine - 125An exponential model representing the amount of Iodine-125 remaining in the tumor after t days will be
A = I( 1 - R%)^t
Let us use the formula to find the amount of Iodine-125 that would remain in the tumor after 60 days by substituting all the given parameters into the formula
A = 0.9 ( 1 - 1.15/100)^60
A = 0.9 ( 1 - 0.0115)^60
A = 0.9 ( 0.9885)^60
A = 0.9 x 0.4995
A = 0.45 grams
Therefore, the amount of Iodine-125 that would remain in the tumor after 60 days is 0.45 grams
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Which value of w makes 14 = 11 + w/8 x 6 a true statemen?
choose 1 answer:
w = 1
w = 4
w = 16
w = 24
Answers
answer
is true statement w= 4
9) If m/1 = 45° and 21 and 22 are complementary angles. Find m22.
Answers
❄ Hi there,
keeping in mind that the sum of complementary angles is 90°,
set up an equation, letting [tex]\angle2[/tex] be x –
[tex]\triangleright \ \sf{\angle1+x=90}[/tex] {and we know that [tex]\boxed{\angle1=45}[/tex]}
[tex]\triangleright \ \sf{45+x=90}[/tex]
[tex]\triangleright \ \sf{x=90-45}[/tex]
[tex]\triangleright \ \sf{x=45}[/tex]
[tex]\triangleright \ \sf{\angle2=45\textdegree}[/tex]
__________
Keeping in mind that a right angle is 90°,
set up an equation, letting [tex]\angle1[/tex] be x:
[tex]\triangleright \ \sf{x+\angle2=90}[/tex] {and we know that [tex]\boxed{\angle2=63}[/tex]}
[tex]\triangleright \ \sf{x+63=90}[/tex]
[tex]\triangleright \ \sf{x=27}[/tex]
[tex]\triangleright \ \sf{\angle1=47\textdegree}[/tex]
❄
A coordinate grid with 2 lines. One line, labeled f(x) passing through (negative 2, 4), (0, 2), and the point (1, 1). The other line is labeled g(x) and passes through (negative 3, negative 3), (0, 0) and the point (1, 1). Which input value produces the same output value for the two functions on the graph? x = −1 x = 0 x = 1 x = 2 Mark this and return
Answers
Answer:
Step-by-step explanation:
why is it so hard omg
Using the principle of
mathematical induction show that 10^(2n-1 ) + 1 is divisible by 11 for all z
Answers
When [tex]n=1[/tex],
[tex]10^{2\cdot1 - 1} + 1 = 10^1 + 1 = 11[/tex]
which is of course divisible by 11.
Assume this holds for [tex]n=k[/tex], that
[tex]11 \mid 10^{2k - 1} + 1[/tex]
In other words,
[tex]10^{2k - 1} + 1 = 11\ell[/tex]
for some integer [tex]\ell[/tex].
Use this to show the claim is true for [tex]n=k+1[/tex].
[tex]10^{2(k+1) - 1} + 1 = 10^{2k + 1} + 1 \\\\ ~~~~~~~~~~~~~~~~~~~~ = 10^{2k+1} + \left(10^{2k-1} + 10^{2k-1}\right) + 1 \\\\ ~~~~~~~~~~~~~~~~~~~~ = \left(10^{2k+1} - 10^{2k-1}\right) + \left(10^{2k-1} + 1\right) \\\\ ~~~~~~~~~~~~~~~~~~~~ = 10^{2k-1} \left(10^2 - 1\right) + 11\ell \\\\ ~~~~~~~~~~~~~~~~~~~~ = 99\times10^{2k-1} + 11\ell \\\\ ~~~~~~~~~~~~~~~~~~~~ = 11\left(9\times10^{2k-1} + \ell\right)[/tex]
which is indeed divisible by 11. QED
On the off-chance you meant [tex]10^{2^n-1}+1[/tex], notice that [tex]2n-1[/tex] is odd for any integer [tex]n[/tex]. Similarly [tex]2^n-1[/tex] is odd for all [tex]n[/tex], so the above proof actually proves this automatically.
Which table represents exponential growth? A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 6, 8. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 7, 11. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 6, 10.'
Answers
The table that represents exponential growth is the second table.
What is exponential growth?Exponential growth simply means a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself.
Exponential growth is the pattern of data which shows sharper increases over time. In finance, compounding creates exponential returns and the savings accounts with a compounding interest rate can show exponential growth.
In this case, the second table described represents an exponential function. It has a common ratio of 4, meaning that each y-value is multiplied by 4 to get to the next value. Here, every time the Xs increase by 1, the Ys increase by a multiple of 4.
One of the best examples of exponential growth is observed in bacteria. Here, it takes bacteria roughly an hour to reproduce through prokaryotic fission. This illustrates exponential growth.
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Answer: B
Step-by-step explanation:
You are volunteering to help with the soccer team's Valentine's Day fundraiser. Each 16-ounce bag of nuts the team sold must include at least 60% chocolate-covered nuts inside.
However, instead of receiving a shipment of separated plain nuts and chocolate nuts, they delivered two large containers of mixed nuts. The first says it is 50/50 plain and chocolate covered. The second contains 80% chocolate-covered nuts.
The team is dismayed, but you come up with a solution. You suggest combining
ounces* of the 50/50 nuts with
ounces* of the 80% chocolate-covered nuts, to create the 60% mixture required for each bag.
*estimate
Then Bob, another student on the team says, "Wait, we promised at least 60%. So if we just do half and half, won't we be giving them at least 60%?"
Bob
correct.
Answers
Proportionately, if they do half and half of 50% and 80% of the two bags, Bob is correct.
What is a proportion?A proportion is a mathematical measure that compares two variables or numbers.
Proportions can be stated in percentages or ratios, as decimals or fractions.
Data and Calculations:Content of 16-ounce bag of nuts = 60% chocolate-covered nuts
Content of first bag = 50/50 plain and chocolate-covered nuts
Content of second bag = 80% chocolate-covered nuts
A mixture of half of 50% bag with half of 80% bag will result in 65% (50% + 80%)/2.
Thus, since the promise for each 16-ounce bag is for at least 60% chocolate-covered nuts, Bob is correct.
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Question Completion:Is Bob correct?
What is the equation of the line described below in slope-intercept form?
The line passing through point (-1, 5) and parallel to the line whose equation is x + y = 10
Answers
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]x + y = 10\implies y = -x+10\implies y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+10 \leftarrow \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so, we're really looking for the equation of al ine whose slope is -1 and that passes through (-1 , 5)
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{-1}( ~~ x-\stackrel{x_1}{(-1) ~~ }) \\\\\\ y-5 = -(x+1)\implies y-5=-x-1\implies y=-x+4[/tex]
Evaluate the expression
for (2^2x2/xy^2) for x=3 and y=2
Answers
Step-by-step explanation:
(2^2x²/xy²) for x=3 and y=2
we have
2^2(3)²/((3)(2²))
2^2(9)/((3)(4))
2^18/12
262144/12
21845.3
The value of expression [tex]2^{2} x^{2}/xy^{2}[/tex] for x=3 and y=2 is, 3
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
The expression, [tex]2^{2} x^{2}/xy^{2}[/tex]
The value of expression when, x = 3 & y = 2
⇒ 2²×3²/3×2²
⇒ 3
Hence, The value is 3
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Vanessa knows that about 20% of the students in her school are bilingual. She wants to estimate the probability that if 3 students were randomly selected, all 3 of them would be bilingual. To do so, she will use a spinner with 5 equally sized sections labeled as either "bilingual" or "monolingual". She will spin the spinner 3 times, record the results, and repeat the process 50 times.
How many of the 5 sections should she label "bilingual"?
How many of the 5 sections should she label "monolingual"?
Answers
Answer:
1 section should be labelled "bilingual".
4 sections should be labelled "monolingual".
Step-by-step explanation:
If 20% of students in the school are bilingual, then 80% of students in the school are monolingual, since 100% - 20% = 80%.
If the spinner is to be divided into 5 equally sized sections, with each section labeled as "bilingual" or "monolingual" to represent the corresponding proportion of students in the school, then:
Bilingual
20% of 5
= 20/100 × 5
= 100/100
= 1 section
Monolingual
80% of 5
= 80/100 × 5
= 400/100
= 4 sections
Therefore:
1 section should be labelled "bilingual".4 sections should be labelled "monolingual".Cos(11*)cos(19*) - sin(11*) sin(19*)
Write the expression as a function of one number then find it’s exact value.
Answers
Answer:
√3/2
Step-by-step explanation:
This is compound angle of cosine
cos(11+19)
=cos(30)
=√3/2
urgently need help please help
Answers
Answer: 40
Step-by-step explanation:
Sub x=4 into 3x²-2x+1
∴ 3(4)²-2(4)+1
=3(16)-8+1
=48-8+1
=40
Answer:
41
Step-by-step explanation:
substitute the x to 4
so 3(4)² - 2(4) + 1 = 41
What is the solution to this equation?
9x - 4(x - 2) = x + 20
Answers
9x - 4(x - 2) =x + 20
We move all terms to the left:
9x -4(x - 2) - (x + 20) = 0Multiply
9x - 4x -(x + 20) + 8 = 0We get rid of the parentheses.
9x - 4x - x - 20 + 8 = 0We add all the numbers and all the variables.
4x - 12 = 0We move all terms containing x to the left hand side, all other terms to the right hand side
4x=12x = 12/4x = 3HELPPPP PLSSSSSss!!!!!!!
Answers
Answer:(5-1)(7-1)
Step-by-step explanation:
We have give 4 numbers that are 1,1,5,7. we have to apply operations on it to make it 24.
Solution :» ( 7 - 1) × (5 - 1)
» (6) × (4)
» 24
Here's our answer..!!
An account begins the year with a
$4000.00 balance. If the account
earns 3% simple interest, what is the
balance at the end of one year?
A. $4,120.00
C. $4,300.00
B. $4,003.00
D. $4,012.00
Answers
[tex]s = c(1 + in) \\ s = 4000(1 + 0.03 \times 1) [/tex]
[tex]s = 4120.00[/tex]
Option: A