Given:
The leading coefficient of a polynomial is 8.
Polynomial roots are 1 and 2.
The graph passes through the point (4,5).
To find:
The 3rd root and the equation of the polynomial.
Solution:
The factor form of a polynomial is:
[tex]y=a(x-c_1)(x-c_2)...(x-c_n)[/tex]
Where, a is a constant and [tex]c_1,c_2,...,c_n[/tex] are the roots of the polynomial.
Polynomial roots are 1 and 2. So, [tex](x-1)[/tex] and [tex](x-2)[/tex] are the factors of the polynomial.
Let the third root of the polynomial by c, then [tex](x-c)[/tex] is a factor of the polynomial.
The leading coefficient of a polynomial is 8. So, a=8 and the equation of the polynomial is:
[tex]y=8(x-1)(x-2)(x-c)[/tex]
The graph passes through the point (4,5). Putting [tex]x=4,y=5[/tex], we get
[tex]5=8(4-1)(4-2)(4-c)[/tex]
[tex]5=8(3)(2)(4-c)[/tex]
[tex]5=48(4-c)[/tex]
Divide both sides by 48.
[tex]\dfrac{5}{48}=4-c[/tex]
[tex]c=4-\dfrac{5}{48}[/tex]
[tex]c=\dfrac{192-5}{48}[/tex]
[tex]c=\dfrac{187}{48}[/tex]
Therefore, the 3rd root on the polynomial is [tex]\dfrac{187}{48}[/tex].
How would I do this??
Part 1
[tex]\left(\frac{g}{h}\right)(x) = \frac{g(x)}{h(x)}\\\\\left(\frac{g}{h}\right)(x) = \frac{3x-5}{-2x^2+7}\\\\\left(\frac{g}{h}\right)(3) = \frac{3(3)-5}{-2(3)^2+7}\\\\\left(\frac{g}{h}\right)(3) = \frac{4}{-11}\\\\\left(\frac{g}{h}\right)(3) = -\frac{4}{11}\\\\[/tex]
Answer: -4/11
====================================================
Part 2
Set the denominator function equal to zero and solve for x to find which values to kick out of the domain.
[tex]h(x) = 0\\\\-2x^2+7 = 0\\\\7 = 2x^2\\\\2x^2 = 7\\\\x^2 = 7/2\\\\x^2 = 3.5\\\\x = \sqrt{3.5} \ \text{ or } x = -\sqrt{3.5}\\\\[/tex]
This shows that if x is equal to either of those values, then the denominator h(x) will be zero. These are the values to kick out of the domain to prevent a division by zero error. Any other value of x is valid in the domain.
Answer: [tex]x = \sqrt{3.5} \text{ and } x = -\sqrt{3.5}\\\\[/tex]
Use the box plots comparing the number of males and number of females attending the latest superhero movie each day for a month to answer the questions.
Two box plots shown. The top one is labeled Males. Minimum at 0, Q1 at 3, median at 10, Q3 at 15, maximum at 35. The bottom box plot is labeled Females. Minimum at 0, Q1 at 2, median at 6, Q3 at 9, maximum at 14, and a point at 31.
Part A: Estimate the IQR for the males' data. (2 points)
Part B: Estimate the difference between the median values of each data set. (2 points)
Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each. (4 points)
Part D: Provide a possible reason for the outlier in the data set. (2 points)
PLEASE HELP ME!!! IVE BEEN AVOIDING THIS FOR SO LONG
(a) The IQR for the males' data is 12, because Q3 is at 15 and Q1 is at 3.
(b) The difference between the median values of each data set is 4 because 10-6 = 4
(c) For the males' data, the median would be a better measure of center, since the data is skewed right. For the females' data, the mean would be a better measure of center, because the data is pretty balanced (except for the outlier).
(d) Maybe a superhero movie had their opening night one day of this month, which would explain the outlier.
First, find the length of each edge of the cube.
Then, find the volume.
since in a cube length, width and height are equal,
h = 6
w = 6
l = 6
and volume is 6³ = 216cm³
hope it helps :)
A square has an area of 49 cm squared what is the length of each side
Answer:
7
Step-by-step explanation:
[tex]s = {a}^{2} \: thus \: a = \sqrt{s } = \sqrt{49} = 7[/tex]
find cosØ if sinØ=-12/13 and tanØ>0.
A) -5/12
B) -5/13
C) 12/5
D) -13/12
Answer:
-5/13
Step-by-step explanation:
sin theta = opp / hyp
sin theta = -12 /13
we can find the adj side by using the pythagorean theorem
adj^2 + opp ^2 = hyp^2
adj^2 +(-12)^2 = 13^2
adj^2 +144 =169
adj^2 = 169-144
adj^2 = 25
Taking the square root of each side
adj = ±5
We know that it has to be negative since it is in the third quad
adj = -5
cos theta = adj / hyp
cos theta = -5/13
Answer:
B) -5/13
Step-by-step explanation:
i hope it will help
plzz mark as brainliest if you want
what is the sum of the square root of 63 and 144,divided by 5
Answer:
Step-by-step explanation:
(√63 + 144)/5 = (3√7 + 144)/5 = 0.6√7 + 28.8
Calculate the mean of the following list of numbers: 10, 12, 7, 9, 9, 11, 15, 9
PLEASE HELP!!!!
9
9.5
10.67
10.25
What is the range of the function?
Answer:
all real numbers greater than or equal to 11
2.1: Solve the one step equation
9. 70 = -5x
10. x4 = 36
11. 7x = -54
Answer:
-14, 9 and - 54/7
Step-by-step explanation:
70=-5x, x=-144x=36, x=97x=-54, x=-54/7Can someone help me I don't understand
Answer:
79.605
Step-by-step explanation:
sin 31° = 41/x
x = 41/sin 31°
x = 79.605
On a piece of paper graph
f(x) = {-1 if -1 <= x < 0}
{ -2 if 0 <= x < 0}
{ -3 if 1 <= x < 2
In this question, a piece-wise function is asked to be graphed.
Piece-wise function:
A piece-wise function is a function that has different definitions, depending on the input.
In this question, the function has three different definitions:
For x between -1(inclusive) and 0, y takes a constant value of -1.
For x between 0(inclusive) and 1, y takes a constant value of -2.
For x between 1(inclusive) and 2, y takes a constant value of -3.
Additionally:
At the inclusive points, the interval is circled, and thus, the graphic is given at the end of this answer.
For another example of the graphic of a piece-wise function, you can check https://brainly.com/question/16855064
Answer:
Step-by-step explanation:
1. (1, 3); (2, 3)
2. (0, 0) (1, 0)
3. (-1, 1) (0,0)
Please help me ill give brainliest!!
Answer:
3744.64
Step-by-step explanation:
To know the answer to this question you need to know the formulas to find the volume of the cylinder and the rectangular prism. The volume of a cylinder is pi*r^2*h while the volume of the rectangular prism is l*w*h. The cylinder is 1808.64 cubic in while the rectangular prism is 1936 cubic. Together, they are 3744.64 cubic in.
Answer:
cylinder= A=πr²h
=3.14×4²×9
=452.16
rectangle=A=l×w×h
=19×11×11
=2299
total area=452.16+2299
=2751.16
Step-by-step explanation:
In right triangle ABC, if AC = 5/13 and AB = 1, what is the length of BC?
Answer:
BC = [tex]\frac{12}{13}[/tex]
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
BC² + AC² = AB²
BC² + ([tex]\frac{5}{13}[/tex] )² = 1²
BC² + [tex]\frac{25}{169}[/tex] = 1 ( subtract [tex]\frac{25}{169}[/tex] from both sides )
BC² = [tex]\frac{169}{169}[/tex] - [tex]\frac{25}{169}[/tex] = [tex]\frac{144}{169}[/tex] ( take square root of both sides )
BC = [tex]\sqrt{\frac{144}{169} }[/tex] = [tex]\frac{12}{13}[/tex]
The circumference of a circle is 14 meters. Which of the following represents the area of the circle
Answer:
A = 49/pi
Step-by-step explanation:
C = 2 * pi *r
14 = 2 * pi *r
Divide each side by 2 pi
14/2pi = r
7/pi = r
The area is given by
A = pi r^2
A = pi ( 7/ pi)^2
A = pi * 49 / pi^2
A = 49/pi
Answer:
[tex]area = {15.61m}^{2} [/tex]
explanation is attached to the picture
Hope this helps you
What is the percent change from 75 to 14?
Answer:
the change is -81.33% (the 3 is repeating)
Rút gọn bthuc
7x(4y-x) + 4y(y-7x) - (4y^2 -7x)
¢✓¢==¢=
Step-by-step explanation:
==`==¢=¢✓%✓™€✓✓€=€✓€✓
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shhsshsh
please HELP ME!!! (16 POINTS) due today :)))
Answer:
Step-by-step explanation:
I'm not sure what the question is asking, but if you mean the angles in the blue lines
First one, we know that the full length is 90, and it has gacen us 80, so the angle would be 10
Second one, we see that the angle is still 90, and since the given degree is 30, the unkown angle would be 60
Third one, the given angle is 75 so 90-75=15.
The answers would be 10, 60, and 15.
Maya just bought a refrigerator for $642. She paid $160.40 in a down payment and will pay the rest in 4 equal installments. How much does she need to pay for each installment?
Answer:
120.40 per payment
Step-by-step explanation:
Subtract the down payment
642 - 160.40
481.60
Divide this by 4
481.60 / 4
120.40
how many line of symmetry is this figure
Answer:
There are sixteen lines.
8. The value of [3 - 4 * (3 - 4) ^ 4] ^ 3 is
a) 1
b) -1
c)0
d) 7
help me please
Answer:
-1
Step-by-step explanation:
[3-4(-1)^4]^3
=>(3-4)^3
=>(-1)^3
=>-1
Answer From Gauth Math
Answer:
-1
Step-by-step explanation:
[tex][3-4*(3-4)^4]^3[/tex]
[tex](3-4)^4= 1\\Therefore, [3-4*1]^3= -1^3\\So, -1^3= -1\\\\[/tex]
Cube of any negative integer will be negative, or, a negative integer raised to any odd number will be negative. Likewise, a negative integer raised to an even number will be positive.
A circle is represented by the equation below:
(x − 9)2 + (y + 8)2 = 16
Which statement is true?
a) The circle is centered at (−9, 8) and has a radius of 8.
b) The circle is centered at (9, −8) and has a diameter of 8.
c) The circle is centered at (9, −8) and has a radius of 8.
d) The circle is centered at (−9, 8) and has a diameter of 8.
Answer:
The center is (9,-8) and the diameter is 8
Step-by-step explanation:
(x − 9)^2 + (y + 8)^2 = 16
A circle is in the form
(x − h)^2 + (y -k)^2 = r^2 where (h,k) is the center and r is the radius
(x − 9)^2 + (y - -8)^2 = 4^2
The center is (9,-8) and the radius is 4
The diameter is 2 times the radius so the diameter is 8
The center is (9,-8) and the diameter is 8
help find the height
Answer:
A
Step-by-step explanation:
Heron's formula finds the area of any triangle.
Area = sqrt(s*(s - a)*(s-b)*(s-c) )
s = (a + b + c)/2
a = 8
b = 16
c = 12
s = 36/2 = 18
s-a = 18 - 8 = 10
s-b = 18 - 16 = 2
s-c = 18 - 12 = 6
Area = sqrt(18*10*2*6) = sqrt(2160)
Area = 12*sqrt(15)
Area = 46.4758
Now x is easily found. It is the altitude to 16
Area = 1/2 16 * h
46.4758 * 2 / 16 = h
h = 3*sqrt(15)/2
h= 5.81
what is the scale factor from figure A to figure B
Answer:
scale facor is 1/3
Step-by-step explanation:
g(x) = x3 + 2x2 - x - 2 to answer all the questions in Part II. 1. Use synthetic division to show that x = -2 is a zero of the polynomial.
Answer:[tex]x^{2} -1[/tex]
Step-by-step explanation:
Given :[tex]g(x)=x^{3} +2x^{2} -x-2[/tex]
Factor x+2,x=-2
Using synthesis division:
-2 ) 1 2 -1 -2
-2 0 2
1 0 -1 0
[tex]x^{2} +0x-1[/tex]
Yes, x = -2 is a zero of the polynomial.
Given that,
The function g(x) = x³ + 2x² - x - 2 is divided by (x + 2)
Now apply the synthetic division to show that x = -2 is a zero of the polynomial.
When we divide by using synthetic division as shown in the attached image.
Remainder = 0
Hence, this shows that x = -2 is a zero of the polynomial.
Therefore, x = -2 is a zero of the polynomial.
To learn more about the divide visit:
https://brainly.com/question/28119824
#SPJ4
Sweatshirts at the school store cost $30. They currently sell about 4 shirts per month. They have decided to decrease the price of the shirts. They found the for each each $1.50 decrease, they will sell 2 more shirts per month. How many decreases in prices will give the max value?
A. 30
B. 9
C. 363
D. 16.50
find the area of triangle
i. b=6cm ,h=4cm
ii. b=5cm ,h=7cm
iii. b=8.4 cm ,h=5cm
answer
[tex]i.12cm {}^{2} [/tex]
[tex]ii.17.5cm {}^{2} [/tex]
[tex]iii.21cm {}^{2} [/tex]
Answer:
Step-by-step explanation:
What are we supposed to do? You already have the answers and they’re all correct if that’s what you wanted to know
If a school camp has enough food for 150 students over 5 days
How long would the food last for is only 100 students are there
Answer:
It is over 7 days
hope it helps
[tex](32)^{1/5}[/tex]
Answer:
2Step-by-step explanation:
[tex] {32}^{ \frac{1}{5} } [/tex]
[tex] = \sqrt[5]{32} [/tex]
[tex] = \sqrt[5]{2 \times 2 \times 2 \times 2 \times 2} [/tex]
= 2 (Ans)
What is the difference between 15% of 7 and of 7?
2. find out the h.c.f
2a , 1st exp= a2 + ab
= a(a+b)
2nd exp = a2-b2
= (a+b) (a-b)
HCF = (a+b)
b, 1 st exp= (a+b)2
= (a+b)(a+)
2 nd exp = a2-b2
= (a+b) ( a-b)
HCF = (a+b)
c, 1 st exp= (a-1)2
= (a+1) (a-1)
2nd exp= a2-1
= (a+1)(a-1)
HCF = (a-1)
d, 1st exp= (x-2)(x-3)
= x(x-3)-2(x-3)
= x2 - 3x - 2x + 6
= x2- 5x+ 6
= x2 - (3+2)x + 6
=x2 -3x-2x+ 6
= x(x-3) -2(x-3)
=(x-3)(x-2)
2 nd exp = (x+2) (x-3)
= x( x-3) + 2 (x-3)
= x2 - 3 x+ 2x -6
= x(x-3) + 2(x-3)
=(x-3) ( x+ 2)
HCF = (x-3)
