Answer:
f(x) = 2x³ - 12x² - 2x + 60
Step-by-step explanation:
Given that the zeros are x = - 2, x = 3, x = 5 , then the factors are
(x + 2), (x - 3), (x - 5)
The polynomial is then the product of the factors, that is
f(x) = a(x + 2)(x - 3)(x - 5) ← a is a multiplier
To find a substitute (6, 48) into the polynomial
48 = a(8)(3)(1) = 24a ( divide both sides by 24 )
a = 2 , thus
f(x) = 2(x + 2)(x - 3)(x - 5) ← expand the last 2 factors using FOIL
= 2(x + 2)(x² - 8x + 15) ← distribute the parenthesis
= 2(x³ - 8x² + 15x + 2x² - 16x + 30)
= 2(x³ - 6x² - x + 30) ← distribute by 2
= 2x³ - 12x² - 2x + 60
Using the factor theorem, it is found that the polynomial function is given by:
[tex]p(x) = 2(x^3 - 6x^2 - x + 30)[/tex]
-----------------------------
Factor theorem:
Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.
-----------------------------
Zeros of -2, 3 and 5 mean that [tex]x_1 = -2, x_2 = 3, x_3 = 5[/tex]The polynomial is given by:
[tex]p(x) = a(x - x_1)(x - x_2)(x-x_3)[/tex]
[tex]p(x) = a(x - (-2))(x - 3)(x - 5)[/tex]
[tex]p(x) = a(x + 2)(x - 3)(x - 5)[/tex]
[tex]p(x) = a(x^2 - x - 6)(x - 5)[/tex]
[tex]p(x) = a(x^3 - 6x^2 - x + 30)[/tex]
-----------------------------
It passes through the point (6,48), thus when [tex]x = 6, p(x) = 48[/tex].This is used to find the leading coefficient.[tex]p(x) = a(x^3 - 6x^2 - x + 30)[/tex]
[tex]48 = a(6^3 - 6(6)^2 - (6) + 30)[/tex]
[tex]24a = 48[/tex]
[tex]a = \frac{48}{24}[/tex]
[tex]a = 2[/tex]
Thus, the polynomial is given by:
[tex]p(x) = 2(x^3 - 6x^2 - x + 30)[/tex]
A similar question is given at https://brainly.com/question/24380382
can some one help me i'm im elementary and i do not know wut to do
Answer:
4,950
Step-by-step explanation:
5 or up rounds up 4 or down rounds down therefore 4,952 rounds to 4,950
Answer:
4,950
Step-by-step explanation:
Evaluate the given expression.
5P2
a.
40
b.
32
C.
25
D.
20
Hey!!!!
Your question is not clear..
So,I looked the options and I thought the question is like this:
(5)^2
=5*5
=25
So the answer is 25.
Hope it helps...
Good luck on your assignment
8. Reasoning Matt's family is thinking
about buying a family pass to the city
pool. The pass is $80 for a family of 4.
Individual passes are $25 each. How
much money can Matt's family save by
purchasing a family pass instead of
4 individual passes?
Answer:
They would be able to save 20$
Step-by-step explanation:
To find how much 4 individual passes are, you do 25 times 4. 25 times 4 equals 100. So, you would have to pay 100$. So, the family pass is a better deal. They can save 25$.
Pls help I would give who ever brainlessly
Answer:
64
Step-by-step explanation:
step one would be to divide 140 by 56 and once you do that you would get 2.5 so then you would divide 160 by 2.5 to get 64.
Answer:
Step-by-step explanation:
NEED HELP ASP WITHE CORRECT ANSWER AND WILL GIVE YOU 14 POINTS !!!!!
Using rigid motion, which
statement is true about the
triangles?
Answer:
Step-by-step explanation:
Answer:
its c
Step-by-step explanation:
i just got it right
pls help me out i need it
Answer:
answer is number 3.
Step-by-step explanation:
The sum of the squares of two consecutive positive odd integers is 202. Find the numbers. Let statement and algebraic solution please. Thanks!
Answer:
ysbbs
Step-by-step explanation:
gebsjsjsisisuisiddd
Val asked a random sample of 50 students at her school
if they brought lunch from home today. If 30 answered
"yes," about what percent of students at Val's school
brought lunch from home today?
ano
A 15%
B50%
C 30%
D 60%
Trey chose B as the correct answer. How did he get that
answer?
Answer:
Trey is incorrect. D is the correct answer
Step-by-step explanation:
30/50= 3/5=60%
Which of the following numbers is closest to zero?
a. 2.3 x 10^-2
b. -1/15
c. -0.01
d. 0.4%
Answer:
C
Step-by-step explanation:
The pre image point B(-4,3) is translated to B 1.1) What was the translation used?
Given the general form: ax + by = c How can we rewrite this general for the equation of a line, so that it is in slope intercept form? (a, b, and c are real numbers other than 0.) Hint: Substitute in values for a,b,c if you are confused) YOUR FINAL ANSWER SHOULD HAVE a,b,c in it. *
Answer:
[tex]y = \frac{c}{b} - \frac{ax}{b}[/tex] or [tex]y = \frac{c-ax}{b}[/tex]
Step-by-step explanation:
Slope intercept form is y = mx + b, so you rewrite it to equal y.
ax + by = c
by = c - ax
y = (c - ax) / b
[tex]y = \frac{c}{b} - \frac{ax}{b}[/tex]
In the image, all the lines overlap. This proves that all the equations are equal to each other.
Find the volume of the prism.
The volume is
cubic centimeters.
So the right answer is 21/16 cubic centimetres
Look at the attached picture
Hope it will help you
good luck on your assignment
I would like some help
There are 5 cities listed. The mean is 273, so the total calls should be 5 x 273 = 1,365.
Find the total of know calls: 244 + 353 + 235 + 311 = 1143.
The calls in Thornbury are: 1365 - 1143 = 222
Answer:
I cant view the image??
Step-by-step explanation:
Select the double number line that correctly labels.
Choose 1 answer.
hi got a question!
convert 20 m\s into km\hr ?
HELPPP!! PLEASEEE!
AND THANK YOUUUU
Answer: 72 km / hour
Step-by-step explanation:
Answer:
72 km/hr
Step-by-step explanation:
First, convert from meters to kilometers. 20 meters is 0.02 kilometers.
Now that you have km/s, convert 0.02 km/s into km/h by multiplying it by the number of seconds in an hour. There are 3,600 seconds in an hour. Multiply 0.02 km/s by 3,600 secs/h to get 72km/h!
Please help!
In the figure, b and c are parallel lines. Which of the following statements are true?
1.Joe claims the measure of angle 3 is equal to 90 degrees. Is he correct, why or why not?
2.state the measure of angle 5 and how you know!
Here is the figure thank you for any help!! :)
What is the measure of an angle, in degrees, if its supplement is six times its complement?
Answer:
72 degrees.
Step-by-step explanation:
We can name the measure of the angle x.
We can name the measure of the complement of it y.
Note that complementary angles add up to 90 degrees and supplementary angles add up to 180 degrees.
Using this info, we can set up two equations.
x+y=90
x+6y=180
Subtract the first equation from the second to eliminate x. You can do both ways, but I prefer to keep the equation positive.
x+6y=180
-x -y -90
5y=90
Divide both sides by 5.
y=18
The complement is 18, now we can plug that in to find x.
x+18=90
Subtract 18 from both sides.
x=72
The measure of the angle is 72 degrees.
What is the first step in solving the quadratic equation x² - 40 = 0?
Answer:
Step-by-step explanation:
40
Answer: x^2 = 40 Is the first step
which graph and solution?
20 POINTS ASAP 16 = 2^x − 2
a)2
b)4
c)6
d)8
Answer:
4
Step-by-step explanation:
Exact Form:
x
=
ln( 18)
---------
ln (2)
Decimal Form:
x=4.16992500
…
Factor this polynomial completely.
x2-X-20
A. (x - 5)(x + 4)
B. (X - 5)(x – 4)
C. (x – 4)(x + 5)
D. (x + 10)(x - 2)
Answer:
a
Step-by-step explanation:
Jose ran13
1
3
mile in 3 minutes and 15 seconds. Calculate Jose's rate in minutes per mile; in other words, the time that it would take for him to run 1 mile.
Answer:
you have to find the unit rate first then try to solve
Step-by-step explanation:
Answer:
1/4 minutes
Step-by-step explanation:
1 minute = 60 seconds
3 minutes = 180 seconds
3 minutes and 15 seconds = 195 seconds
13 miles/195 seconds
195/13 = 15
His speed --> 1 mile/15 seconds
1/4 minutes = 15 seconds
Pls mark me as brainliest ;)
Help plz
1/2 (3)(4 + 2) =
The Answer Is 9
Step-by-step explanation:
0.5(3)(6)
1.5(6)
9
Answer:
9
Step-by-step explanation:
I chose 9 because first you have to add 4+2 because it's in parenthesis and the other with parenthesis has no other numbers so 4+2 first then 4+2 is 6 then you multiply 6 by the 3 in the parenthesis because it is in the parenthesis then divide by 2 because 1/2 is basically dividing by 2
50 POINTS PLZ. HELP PLZ HELP PLZ
Answer:
no 6^2 + 8^2 ≠ 12^2 so this is not a right triangle
Step-by-step explanation:
The Pythagorean theorem tells you if you have a right triangle
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
6^2 + 8^2 = 12^2
36+64 = 144
100 = 144
This is not true so this is not a right triangle
3a + b to the second power
Answer:
9a^2 + b^2
Step-by-step explanation:
(3a + b)^2
9a^2 + b^2
what is the measure of one interior angle of the regular 32 gon?
Answer:
180°
Step-by-step explanation:
A polygon that has 32 sides is called a triacontadigon or a triacontakaidigon.
The angles of a triacontadigon add up to 5760°.
5760÷32=180°
For what values of b will F(x) = logo x be an increasing function?
A. b< 1
B. b> 1
C. b>0
D. b< 0
Answer:
A b(1
Step-by-step explanation:
Using logarithmic function concepts, it is found that for values of b > 1, [tex]f(x)=log_{b}x[/tex] will be an increasing function.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
A logarithmic function is modeled by:
[tex]f(x)=log_{b}x[/tex]
The coefficient b determines the behavior of the function, as follows:
b > 1: The function is increasing.
b < 1: The function is decreasing.
Using logarithmic function concepts, it is found that for values of b > 1, [tex]f(x)=log_{b}x[/tex] will be an increasing function.
Hence, for values of b > 1, [tex]f(x)=log_{b}x[/tex]will be an increasing function.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ7
Find the mean absolute deviation for the set below:
62, 71, 83, 110, 501, 94, 227
Answer:
(MAD) mean absolute deviation: 114.2
Step-by-step explanation:
Mean: 62 + 71 + 83 + 110 + 501 + 94 + 227 = 1,148/7 = 164
164 - 62 = 102
164 - 71 = 93
164 - 83 = 81
164 - 110 = 54
164 - 501 = 337
164 - 94 = 70
164 - 227 = 63
Mean Absolute Deviation: 102 + 93 + 81 + 54 + 337 + 70 + 63 = 800/7 = 114.2
Answer:
Step-by-step explanation:
First, add all the numbers and count the total amount of numbers.
Once you've done that find the mean by dividing the total of the numbers by how many numbers you have.
Next make a chart, have 2 parts in the chart. Make boxes for however many numbers you have. Make another row in the chart for the distance from the mean ( how many numbers is it from the mean.)
Add all the "distance from mean" numbers and divide by total numbers, If a decimal, round up or down.
Then, you have the M.A,D ( Mean Absolute Deviation )
Robert wants to put lights around the edge of his deck the deck is 46 feet long and 26 feet wide how many yards of lights dose he need
Answer:
24 yards
Step-by-step explanation:
46+26=72
72/3=24
Identify the graph of y=3x^-2x+5 for T (2,-3) and write and equation of the translated or rotated graph in general form
Answer:
0=3x^2-14x-y+18
Step-by-step explanation:
Video showed me on Edge
Answer:
A
Step-by-step explanation:
edge