Answer:
[tex]\displaystyle f(x)=\frac{5}{24}(x+2)^2(x-6)(x-2)[/tex]
Step-by-step explanation:
The standard, factored polynomial function is given by:
[tex]f(x)=a(x-p)^n(x-q)^m...[/tex]
Where a is the leading coefficient,
p and q are factors,
And n and m are the powers or multiplicity they are being raised to.
We know that our polynomial function is of degree 4.
We have a root of multiplicity of 2 at x=-2.
So, our factor is:
[tex](x-(-2))=(x+2)\\[/tex]
It is has a multiplicity of 2, it is squared. So:
[tex](x+2)^2[/tex]
We have another root with multiplicity of 1 at x=6.
So, our factor is:
[tex](x-6)[/tex]
And since it is to the first power, we can write it as is.
Finally, we have another root of multiplicity of 1 at x=2.
So, our factor is:
[tex](x-2)[/tex]
Therefore, our entire function is:
[tex]f(x)=a(x+2)^2(x-6)(x-2)[/tex]
We still have to determine our leading coefficient, a.
We can use that y-intercept. The y-intercept is at (0, 10). So, when x=0, y=10. By substitution:
[tex]10=a(0+2)^2(0-6)(0-2)[/tex]
Evaluate:
[tex]10=a(4)(-6)(-2)[/tex]
Multiply:
[tex]10=48a[/tex]
Therefore:
[tex]\displaystyle a=\frac{10}{48}=\frac{5}{24}[/tex]
Therefore, our final function is:
[tex]\displaystyle f(x)=\frac{5}{24}(x+2)^2(x-6)(x-2)[/tex]
What is the answer? I need help quick!
Answer:
Point BStep-by-step explanation:
-6 is to the left from origin and π/12 is in between 0 and π/6 above the x-axis. So the point (-6, π/12) is in the second quadrant.
Other points represent coordinates of:
A=(6, π/12), C=(-6, -π/12), D=(6, -π/12)This is point B and correct choice is option B.
9514 1404 393
Answer:
point C
Step-by-step explanation:
The given coordinates (-6, π/12) are equivalent to (6, 13π/12). That is, the negative radius is equivalent to a positive radius in the opposite direction (angle different by π radians).
The point on the diagram with coordinates (6, 13π/12) is point C.
Alice purchased a cell phone for 30% ff the original price. The sales price was $84 . What was the original price of the cell
Answer: $120
Step-by-step explanation:Quick maths.
help with geometry pleasee
Answer:
Angle E
Step-by-step explanation:
Use the scale drawing and the scale factor to enlarge a square that has a side length of 12 in. Scale factor= 3 in:2m.
Which proportion could you use to solve the side length, x, of the enlarged square?
Given:
The side of square = 12 in.
Scale factor of enlargement = 3 in : 2 m
To find:
The proportion that is use to solve the side length, x, of the enlarged square.
Solution:
Let, the side of length of enlarged square = x m
In case of enlargement the corresponding sides are proportional.
[tex]\dfrac{3}{12}=\dfrac{2}{x}[/tex]
[tex]3x=2\times 12[/tex]
[tex]3x=24[/tex]
Divide both sides by 3.
[tex]x=\dfrac{24}{3}[/tex]
[tex]x=8[/tex]
Therefore, the required proportion is [tex]\dfrac{3}{12}=\dfrac{2}{x}[/tex] and the side length of the square after enlargement is 8 m.
HELP PLZZZ ASAP THNAKS
Answer:
x = 40
Step-by-step explanation:
x + 2x + 6 = 126
3x + 6 = 126
3x = 120
x = 40
The following data represent the number of grams of fat in breakfast meals offered at a local fast food restaurant. (a) Construct an ordered stem-and-leaf plot and (b) describe the shape of the distribution.
37
43
18
27
20
16
35
23
12
5
17
23
2
12
18
17
39
25
3
4
19
6
easy question????????????/
Answer:
The answer to this is...........
Step-by-step explanation:
unknown
or 95
Answer:
95
Step-by-step explanation:
help pleaseee! with geometry
Answer:
2x(x+6)(x-6)
Step-by-step explanation:
2x³-72
2x(x²-36)
2x(x+6)(x-6)
What is the value of - |-60|?
Answer:
-60
Step-by-step explanation:
because the abousulte value at first is 60 and then you multiple it by the negative that's there
Answer:
-60
Step-by-step explanation:
first you do inside the absolute it has to be positive
so it`s 60
but the outside is negative
so the answer must be -60
Don't steal points
its not cool
i WILL report
and also
answer this and u could have a chance to get brainliest
ill be asking 10 questions
whoever has the best answer in any of these ill give brainliest :D
Answer:
179
Step-by-step explanation:
5x^2 + x - 7
5(6)^2 + 6 - 7
5(36) + 6 - 7
180 +6 -7
180 - 1
179
Answer:
179 is the correct answer.
Step-by-step explanation:
x = 6
5x^2 + x - 7
Now, replace both x's with 6 and solve,
5(6)^2 + 6 - 7
(6 x 6 = 36)
5 x 36 + 6 - 7
(5 x 36 = 180)
180 + 6 - 7 = 179
square?
i neeed 200000000 charaters reeeeeeeee
Answer:
31
Step-by-step explanation:
you do 6×3=18 then you do 18+7=25 last 25+17=42 then you add 2
Answer:
i dont know what ur saying but square would me x2 or somthing like that.
DA−2qA=B^3
Solve for A
Answer:
[tex]a=\frac{b^{3} }{d-2q}[/tex]
Step-by-step explanation:
i think
The value of A from the given equation is A=B³/(D-2q).
The given equation is DA-2qA=B³.
We need to solve the given equation for A.
What is an equation?
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, DA-2qA=B³ can be solved for A as follows:
A(D-2q)=B³
⇒A=B³/(D-2q)
Therefore, the value of A from the given equation is A=B³/(D-2q).
To learn more about an equation visit:
brainly.com/question/14686792.
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I really think it’s a good question and my homework
Answer:
77.245 i used me brane and paper and give brainliest and your in shcool why why why cheat
Step-by-step explanation:
Answer:
680.745
Step-by-step explanation:
hope this helps.
Which points are on the graph of g(x) = (1/5)^x
Choose all answers that are correct.
A.(-1,5)
B.(3,1/125)
C.(1,0)
D.(-2,1/25 )
Answer:
A) The point( -1 , 5) is satisfies the given graph [tex]g(x) = (\frac{1}{5} )^{x}[/tex]
B) The point( 3 , 1/125) is satisfies the given graph [tex]g(x) = (\frac{1}{5} )^{x}[/tex]
Step-by-step explanation:
Explanation:-
Given graph
y = [tex]g(x) = (\frac{1}{5} )^{x}[/tex]
Put the point ( -1 , 5)
Put y =5 and x =-1
[tex]5 = (\frac{1}{5} )^{-1} = 5[/tex]
The point( -1 , 5) is satisfies the given graph
ii)
Given graph
y = [tex]g(x) = (\frac{1}{5} )^{x}[/tex]
[tex]\frac{1}{125} = (\frac{1}{5} )^{3} = \frac{1}{125}[/tex]
The point( 3 , 1/125) is satisfies the given graph [tex]g(x) = (\frac{1}{5} )^{x}[/tex]
Which expression is equivalent to 33.63. 23 without exponents?
A. 3+3+3+6+6+6+2+2+2
B. 3x3x3x6x6x6x2x2x2
C. 9+18+6
D. 9x18x6
An armount of nitrogen undergoes a physical change and increases its volurme, What can be knoW) about this
physical change?
O The boiling point of the nitrogen increased.
O The mass of nitrogen increased.
O The color changed.
O The density changed.
Answer:
d
Step-by-step explanation:
Graph y= 3x+4 Please help! 8th grade math
A trombone acts like an open pipe of length 2.96 m .On a cold day it plays,its 4th harmonic at 221 hz what is the speed of the sound waves in the horn that day?
Answer:
327.08 m/s
Step-by-step explanation:
Given that:
Length of pipe = 2.96m
4th harmonic frequency = 221 Hz
Speed of wave in the horn :
Speed of wave (v) = fλ
For 4th harmonic :
Wavelength, λ = (2/4)L
λ = L/2 ; 2λ = L
2λ = 2.96
λ = 2.96 / 2
λ = 1.48 m
Hence, speed of wave in the horn = 221 * 1.48 = 327.08 m/s
Which Inequality is shown on the accompanying graph (image included)
If you can, pls explain :’)
Answer:
4. x ≥ -1
Step-by-step explanation:
The graph shows a directed line that starts at -1 towards the your right. The full circle indicates that -1 is included among the possible values of x. This means that all possible values of x include -1 and above.
Therefore, we can say x is greater than or equal to -1.
This is represented as:
x ≥ -1
In the figure shown below, lines j and k are parallel. Which equation can be used to find the value of x in the figure?
Answer:
Step-by-step explanation:
D b/c you know that the two angles add to 180°
The solution is Option D.
The value of x can be calculated from the equation
( x + 40 ) + ( 2x + 20 ) = 180
What are Parallel Lines Cut by Transversal?
Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles
Given data ,
Let the parallel lines be j and k
The transversal line is m
Now , the value ( 2x + 20 )° lies on one side of the transversal line
And the value ( x + 40 )° lies on one side of the transversal line
The total angle of a line is 180°
So ,
The sum of ( 2x + 20 )° and ( x + 40 )° will be 180°
Therefore , The solution is ( x + 40 ) + ( 2x + 20 ) = 180
Hence , The value of x can be calculated from the equation
( x + 40 ) + ( 2x + 20 ) = 180
To learn more about angles in parallel lines click :
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1. Yejin plans to retire at age 60. She wants to create an annuity fund, which will pay her a monthly allowance of $4000 during her retirement. She wants to save enough money so that the payments lasts for 30 years. A financial advisor has told her the she can expect to earn 5% interest on her funds, compounded annually.
2. Yejin has just turned 28 years old. She currently has no retirement savings. She wants to save part of her salary each month into her annuity fund. Calculate the amount Yejin needs to save each month, to meet her retirement goal.
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Answer:
$3891.10
Step-by-step explanation:
This question is a bit unusual in that the interest is compounded annually, but payments and withdrawals are made monthly. The effective monthly rate is ...
1.05^(1/12) -1 = 0.407412378% = i
We assume that payments to the annuity are made at the end of the month, and that withdrawals are made at the beginning of the month. (The last payment and the first withdrawal are made on the same day.)
The amount of money required in the fund is ...
A = $4000(1 -(1.00407^-360))/(1 -1.00407^-1) = $757,712.88
The amount of money needed each month to be put into the fund is P, where ...
$757,712.88 = P(1 -1.00407)^(-12(60-28))/(1 -1.00407^-1) = 194.7297P
P = $757,712.88/194.7297 = $3891.10
Yejin needs to save $3891.10 each month to meet her retirement goal.
_____
Sanity check
Yejin wants payments for 30 years from the fund to which she has contributed for 32 years. The similarity of the time periods means that Yejin's monthly contribution will need to be very similar to the amount she plans to withdraw.
The only ways to reduce the required contribution are to earn a higher interest on deposits, or to adjust the relative time periods (retire later).
the grade point average for 10 students are listed below. find the range of the data set.
0.8, 0.9 1.8, 2.0, 2.9, 3.2, 3.3 ,3.6, 4.0
Answer:
might be 22.5 i think but i'm not sure correct me if i'm wrong
Step-by-step explanation:
Answer:
Step-by-step explanation:
the range is the difference between the largest and the smallest value
4.0-0.8=3.2
Find the result when 5m+2 is subtracted from 9m
Answer:
6m
Step-by-step explanation:
9m - (5m-2) =
5m-2= 3m
9m - 3m= 6m
Please give Brainliest if it helped.
HELP ME PLZ
Two parallel lines are cut by a transversal as shown below.
Suppose mZ1 = 121°. Find m2 6 and m2 7.
m26 = Me
HL7 =
Step-by-step explanation:
hope this will help you.....
Answer:
m angle 6 = (180°-121°) =59°m angle 7 = 121°prove tha "an empty set is a subset of any set"
Answ
yes it is
Step-by-step explanation:
What is the difference in height between the shortest and longest candy bars?
Answer:
1.5 inches
Step-by-step explanation:
The number of points scored by a basketball player in the first eight games of a season are shown below. 15, 35, 18, 30, 25, 21, 32, 16 What would happen to the data distribution if she scored 24, 22, 27, and 28 points in her next four games?
Answer:
im not sure how the data should be interpreted but here is the distribution. It goes up by .416
Step-by-step explanation:
the average of the first 8 games is 24
the average of the 12 games is 24.416
can someone explain how 1/4 × 900/1 is equal to 225, my mom is asking for an explanation and I used a calculator help me
Answer:
See below
Step-by-step explanation:
[tex] \frac{1}{4} \times \frac{900}{1} \\ \\ = \frac{1 \times 900}{4 \times 1} \\ \\ = \frac{900}{4} \\ \\ = \frac{9 \times \cancel {100} }{\cancel4} \\ \\ = 9 \times 25 \\ \\ = 225[/tex]
Answer:
four of 225 makes 900/1, or 900. So, one 225 should be one of the four 225s that equal 900. 1/4 × 1/900, or 1/4 of 900, should be 225.
If the balance at the end of eight years on an investment of $196 that has been invested at a rate of 9% is $337.12, how much was the interest
Answer:
$141.12
Step-by-step explanation:
Initial investment = $196
After 8 years with 9% interest rate it becomes: $337.12
The amount of interest will be:
= $337.12 - $196
= $141.12
Kyle was asked to make a model to solve the following problem.
Mr. Bloom is creating a garden. 4/10 of his garden will be roses and 2/10 will be made up of sunflowers. How much room does Mr. Bloom have left after planting the roses and sunflowers?
Kyle said the answer was 2/5. Do you agree? Justify your reasoning in the post below.
Answer:
yes, kyle is right.
Step-by-step explanation:
4/10 + 2/10 = 6/10
there are 4/10 left after planting which can be reduced by 2 = 2/5
Answer:
No, it is 3/5
Step-by-step explanation:
Because you divide by 2 for both bottom and top of the fractions and you will get 1/5, and 2/5 and you add them together and you get 3/5.