Answer:
[tex]f(x)=-\frac{1}{12}(x-3)^2(x+2)^2(x-4)[/tex]
Step-by-step explanation:
The standard form for a polynomial equation in its factored form is:
[tex]f(x)=a(x-p)(x-q)...[/tex]
Where p and q are the zeros and a is the leading coefficient.
We know that the degree of the polynomial is 5.
We are also given roots at x=3 and x=-2. Hence, our factors are (x-3) and (x+2).
These have a multiplicity of two, so we will square them.
We also know that there is a root at x=4. Hence, the factor is (x-4). This has a multiplicity of 1.
Therefore, our polynomial is now:
[tex]f(x)=a(x-3)^2(x+2)^2(x-4)[/tex]
We know that the y-intercept is 12. Therefore, if we substitute in 0 for x, we should get 12 for y. Here, we are solving for our a. Therefore:
[tex]12=a(0-3)^2(0+2)^2(0-4)[/tex]
Evaluate:
[tex]12=a(9)(4)(-4)[/tex]
Evaluate:
[tex]-144a=12[/tex]
Divide both sides by -144:
[tex]a=-1/12[/tex]
Hence, our entire polynomial is:
[tex]f(x)=-\frac{1}{12}(x-3)^2(x+2)^2(x-4)[/tex]
Given the sequence, 26, 13, 6.5, ..... find a) the 10th term and b) the sum of the first 18 terms X Clear * Undo Redo
Answer:
[tex]T_{10} = 0.05078125[/tex]
[tex]S_{18} = 51.9998016358[/tex]
Step-by-step explanation:
Given:
Sequence = 26, 13, 6.5 ....
Solving (a): The 10th term
The sequence is a geometric progression and the nth term will be solved using:
[tex]T_n = ar^{n-1}[/tex]
In this case:
[tex]n = 10[/tex]
[tex]r = \frac{T_2}{T_1}[/tex] --- Common Ratio
[tex]r = \frac{13}{26}[/tex]
[tex]r = 0.5[/tex]
[tex]a = 26[/tex] --- First term
So, [tex]T_n = ar^{n-1}[/tex] becomes
[tex]T_{10} = 26 * 0.5^{10-1}[/tex]
[tex]T_{10} = 26 * 0.5^{9}[/tex]
[tex]T_{10} = 26 * 0.001953125[/tex]
[tex]T_{10} = 0.05078125[/tex]
Solving (b): The sum of first 18 terms
This will be calculated using:
[tex]S_n = \frac{a(1 - r^n)}{1 - r}[/tex]
Substitute values for n, a and r
[tex]S_{18} = \frac{26 * (1 - 0.5^{18})}{1 - 0.5}[/tex]
[tex]S_{18} = \frac{25.9999008179}{0.5}[/tex]
[tex]S_{18} = 51.9998016358[/tex]
Hence, the sum of first 18 terms is 51.9998016358
Let C(t) be the amount of U.S. cash per capita in circulation at time 1. The table, supplied by the Treasury Department, gives values of C(t) as of June 30 of the specificd year. Interpret and estimate the value of C'(1980).
Answer:
Following are the solution to this question:
Step-by-step explanation:
C'(t) was its time, in years, or t shift of cash per unit. That C'(1980) meaning, therefore, becomes the change of cashier's population to t = 1980.
They could either use t = 1970 or t = 1990 to approximate the C'(1980) price. When using t = 1970:
[tex]C'(1980) = \frac{[C(1980) - C(1970)]}{[1980 - 1970]}\\\\[/tex]
[tex]= \frac{(571 - 265)}{10}\\\\ = \$ \ 30.6 \\[/tex]
t = 1990:
[tex]C'(1980) = \frac{[C(1980) - C(1990)]}{[1980 - 1990]}[/tex]
[tex]= \frac{(571 - 1063)}{ -10} \\\\= \$ \ 49.2[/tex]
What is the range of the function represented by the table?
A 2-column table with 5 rows. Column 1 is labeled x with entries 2, 4, 6, 8, 10. Column 2 is labeled y with entries 2.5, 5.0, 7.5, 10.0, 12.5.
{2, 4, 6, 8, 10}
{2.5, 5.0, 7.5, 10.0, 12.5}
{2, 2.5, 4, 5.0, 6, 7.5, 8, 10, 12.5}
{0.0, 0.5}
Answer:
{2.3, 5.0, 7.5, 10.0, 12.5} Option b
Step-by-step explanation:
Domain is the input values and the range is the output values. The y values.
Answer:
b
Step-by-step explanation:
Avni designs a game in which a player either wins or loses 4 points during each turn. Which equation represents all numbers of points, p, a player may have after his or her first turn of the game? A. p = 4 B. p = –4 C. |p| = 4 D. |p| = –4
Answer:
C |p| = 4
Step-by-step explanation:
If a player wins 4points during each turn, then, the total points will be +4points
If the player looses 4points, total points lost will be -4points
The total number of point p the player can have will be represented as;
|p| = 4 (since is both positive and negative 4 )
Note that the nodulus of a variable will return both positive and negative value of that variable
At Green Island Farms the annual Turkey Trot is being held. This year’s contestants are Tom Turkey, Gary Gobbler and Donny Drumstick. The turkeys chase little RC cars loaded with feed. The buzzer sounds and the turkeys are off. Gary Gobbler chases his RC car trying to eat that sweet turkey feed for 15 feet before he manages to side swipe the RC car and knock it on its side. All the feed spills out and Gary Gobbler gobbles it down. That silly turkey happily eats his food for 1.75 seconds. A mouse comes out of the hay bale and tries to join Gary Gobbler in his feasting. But Gary Gobbler is scared of mice so when he sees the mouse he freaks out and tears down the racetrack.
Write a similar story for Tom Turkey making sure to include the different segments of the graph.
Answer:
The company is expected the company will receive
Armon has a prepaid cell phone. This month he will like to purchase a $9 message package. The rate plan for the talk time is $0.10 per minute. Write an inequality for the maximum amount of talk time that Armon can purchase for his bill to stay under $45.
Pls show step-by-step! :)
The sum of 4 thirteens and 16 thirteens, need answer ASAP :(
Answer:
260?
Step-by-step explanation:
I used the equation (4)13+(16)13 and plugged it into my calculator and got 260.
The sum of 4 thirteens and 16 thirteens is 260.
What is the meaning of sum?
You add up all the numbers to arrive at the sum. When you summarise something, you pay attention to all of its crucial components. A specific sum of money can also be referred to using the word sum. You might have to spend a sizable sum of money on a new car. However, you might be able to justify spending so much if you add up or total all of its advantages. When you add up the costs of everything you ordered, the total on a restaurant bill is determined. Sum need not be restricted to numbers. When you summarise something, you're providing a summary or overarching statement about it.
Here, 4 thirteens = 4 × 13 = 52
16 thirteens = 16 × 13 = 208
Sum of 4 thirteens and 16 thirteens = 52 + 208 = 260
Hence, 260 is the correct answer.
Learn more about sum from the link.
https://brainly.com/question/24205483
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Fill in the blank to find the y-intercept.
(0,_____)
Answer:
-2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
the y intercept is the point on the graph where the line crosses the x axis
Find the percent increase from the first number to the second in the following pairs.
A. 100, 140
B. 80, 125
C. 60, 80
D. 9,1
What is i2=-1 math test
Answer:
Your answer is: ↓
If your converting in Logarithmic Form then your answer is: [tex]log_{i}(-1)=2[/tex]
If you are trying to figure if that equation is determined T/F: The answer is T.
If you are trying to evaluate (expand) the question your answer is:[tex]-1=-1[/tex]
Step-by-step explanation:
Hope this helped : )
Division expression
The following is a conversion table for hours and minutes. Which numbers belong in the hours column?
1, 2, 3
1, 2, 4
2, 3, 4
2, 5, 6
Answer:
Lesson 2 and metric conversions from Module 2. ... Problem 2: Convert hours to minutes. ... of minutes in one hour. How many minutes are in an hour? 0. 1. 2. 3. 4. 5. 6. 7. 8.
The complete table is given below. Then the correct option is C.
Hours Minutes
2 120 3 180 4 240What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The following is a conversion table for hours and minutes.
We know that in one hour, there are 60 minutes.
In two hours, there are 120 minutes.
In three hours, there are 180 minutes.
Similarly, in four hours, there are 240 minutes.
Then the complete table is given below.
Hours Minutes
2 120
3 180
4 240
Then the correct option is C.
The complete question is given below.
The following is a conversion table for hours and minutes. Which numbers belong in the hour's column?
Hours Minutes
120
180
240
More about the Algebra link is given below.
https://brainly.com/question/953809
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let f(x) = x^4 -4x^2 +3x find f(-3) a.-54 b.36 c.-126 d.108
Answer:
b. 36
Step-by-step explanation:
Evaluate x^4 - 4 x^2 + 3 x where x = -3:
x^4 - 4 x^2 + 3 x = (-3)^4 - 4×(-3)^2 - 3×3
Hint: | Evaluate (-3)^2.
(-3)^2 = 9:
(-3)^4 - 49 - 3×3
Hint: | Determine the sign of (-3)^4.
(-3)^4 = (-1)^4×3^4 = 1×3^4:
3^4 - 4×9 - 3×3
Hint: | Compute 3^4 by repeated squaring.
3^4 = (3^2)^2:
(3^2)^2 - 4×9 - 3×3
Hint: | Evaluate 3^2.
3^2 = 9:
9^2 - 4×9 - 3×3
Hint: | Evaluate 9^2.
9^2 = 81:
81 - 4×9 - 3×3
Hint: | Multiply -4 and 9 together.
-4×9 = -36:
81 + -36 - 3×3
Hint: | Multiply 3 and -3 together.
3 (-3) = -9:
81 - 36 + -9
Hint: | Group the negative terms in 81 - 36 - 9 together and factor out the minus sign.
81 - 36 - 9 = 81 - (36 + 9):
81 - (36 + 9)
Hint: | Evaluate 36 + 9 using long addition.
| 1 |
| 3 | 6
+ | | 9
| 4 | 5:
81 - 45
Hint: | Subtract 45 from 81.
| 7 | 11
| 8 | 1
- | 4 | 5
| 3 | 6:
Answer: 36
what is the remainder of 58,511 divided by 21, the quotient is 2,786 R
Answer:
the remainder is 5. 2,786 R 5
Help ASAP WILL NSRK BRAINLIST IF CORRECT
Answer:
(1,1)
Step-by-step explanation:
Find the simplified product 5/n+1 x n+1/n+3
Answer: C) 5/n+3
Step-by-step explanation:
A sales manager analyzed the sales, in dollars, y, of beach products compared to the outside temperature, in Fahrenheit, x. The manager calculated the correlation coefficient of r = 0.75.
Which conclusion is most appropriate based on the correlation coefficient of the data?
There is a strong positive relationship, therefore as x increases, y increases.
There is a strong positive relationship, therefore as x increases, y decreases.
There is a weak positive relationship, therefore as x increases, y increases.
There is a weak positive relationship, therefore as x increases, y decreases.
Answer:
There is a strong positive relationship, therefore as x increases, y increases
Step-by-step explanation:
7. In the drawing below, identify the following. (This is NOT multiple choice!)
A) Alternate Interior Angles
B) Alternate Exterior Angles
C) Consecutive Interior Angles
D) Corresponding Angles
Which of the following graphs shows the set of points that represents the number of hours that Leah
can work in order to earn at least $120 and not work more than 20 hours per month?
Answer:
I think it’s A,C, and E
Step-by-step explanation:
I’m not for sure but if you plot those points in the shaded region for graph C, those should be correct .
factor 2x^2-9x+9=0 and please show ur steps
Answer:
♡ hi there, madi here! ♡
hope your having a great day.
I did the math so here's your answer.
2x−3)(x−3)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
2x-3=0. x-3=0
Set the first factor equal to 0 and solve.
x=3/2
Set the next factor equal to 0 and solve.
x=3
Therefore, the final solution is all the values that make (2x-3) (x-3)=0 true. x=3/2,3♡
✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧
Which expression is equivalent to sqrt(80)?
Answer:
b on edg
Step-by-step explanation:
second part
a=4
b=5
help! open the attachment below!
Answer:
yes it is
Step-by-step explanation:X=side lenghths 2/3
Y=perimeter 12/18
2 time 6=12 and 3 times 6=18 and it is paraticly telling you
2/6 and 3/6 i beleve i need a lil more info
find the smallest number by which the number108 must be multiplied to obtain a perfect cube
Answer:
2
Step-by-step explanation:
108*2
=216
216
=6^3
PLS GIVE BRAINLIEST
MADKING BRAINIEST!!Complete the following ratio table so that each pair represents the same rate.
Answer:
3=15
4=20
5=25
Step-by-step explanation:
bold are the answers
Find log1/4 rounded to the nearest hundredth.
Answer:
-log_4
Step-by-step explanation:
The value of log1/4 rounded to the nearest hundredth is -0.60
Given the parameter which is needed for our Calculation:
log1/4Using a calculator, the value of log1/4 is -0.602059
Rounding to the nearest hundredth, is two digits after the decimal point.
Hence, we have ;
-0.60 (since the value after 0 is less than 5)Therefore, log1/4 is -0.60
Learn more on logarithm :https://brainly.com/question/30226560
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Please answer fast !!!!!!
Look at the picture
Answer:
< EAC = 31 (small angle of blue triangle)
< BCA = 31 (small angle of green triangle)
< ABC = 104 (big angle of green triangle)
< BDC = 45 (yellow triangle)
< BDF = 135 (outside yellow triangle)
< AEG = 76 (outside blue triangle)
Miguel has $25. He spends $6.75 on a movie ticket, $3.70 for snacks, and $2.00 for bus fare each way.
How much money does Miguel have left?
Miguel has $_____
left.
Answer:
$12.55
Step-by-step explanation:
25-6.75=18.25
18.25-3.70=14.55
14.55-2=12.55
Miguel has $12.55 left
PLEASE HELP!! GEOMETRY!!
=685.67Step-by-step explanation:
A class has 48 minutes available to hear reports from 15 students. if the time is to be divided equally, how long may each student have?
Answer:
No, every student will have 3.2 minutes
Answer:
Each student has approximately 3 minutes and 12 seconds.
Step-by-step explanation:
You divide the total amount of minutes by the total amount of students. 48/15=3.2
After you get your answer, you convert to minutes. There are 3 minutes and the .2 converts to 12 seconds
Kennedy draws 12 circles she shades 3/4 how many circles does jennedy shade
Answer:
9
Step-by-step explanation:
12 / 4 = 3
3 x 3 = 9