Given:
Degree of a polynomial = 3
Zeros of the polynomial = 0,5,8
f(10)=17
To find:
The polynomial function.
Solution:
The general form of a polynomial is
[tex]P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}[/tex]
Where, a is a constant, [tex]c_1,c_2,...,c_n[/tex] are zeros with multiplicity [tex]m_1,m_2,...,m_n[/tex] respectively.
Since, 0,5,8 are zeros of the polynomial, therefore, (x-0),(x-5), (x-8) are the factors of required polynomial.
[tex]f(x)=a(x)(x-5)(x-8)[/tex] ...(i)
Putting x=10, we get
[tex]f(10)=a(10)(10-5)(10-8)[/tex]
We have f(10)=17.
[tex]17=a(10)(5)(2)[/tex]
[tex]17=a(100)[/tex]
[tex]\dfrac{17}{100}=a[/tex]
[tex]0.17=a[/tex]
Putting a=0.17 in (i).
[tex]f(x)=0.17(x)(x-5)(x-8)[/tex]
Therefore, the required polynomial is [tex]f(x)=0.17(x)(x-5)(x-8)[/tex].
5x to the second power-13x +6
guys answer only
Answer:
-138
Step-by-step explanation:
There is a sample of 500 and the population proportion is 0.47. What is the probability that the proportion is greater then 0.50
Answer: 0.0895
Step-by-step explanation:
Let p= population proportion.
Given : Sample size : n= 500
p= 0.47
Required probability = [tex]P(\ha{p}>0.50)[/tex]
[tex]=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.50-0.47}{\sqrt{\dfrac{0.47(1-0.47)}{500}}}) \\\\=P(z>1.344)\ \ \ [z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}]\\\\=1-P(z<1.344)\\\\=1-0.9105\approx0.0895[/tex]
Hence, required probability = 0.0895
Lucy paid $45 for a new sweater that was on sale. It was on sale for 25% off the original price. How much was the original price of the sweater?
Please give an explanation please please please
Answer:
it was 33.75
Step-by-step explanation:
Please answer this question
Answer:
3/100
Step-by-step explanation:
1 m = 100 cm
Scale factor = 3/100
Hope it helps you
Answer:
the answer would be 3/100
Determine the domain on which the following function is decreasing.
(Please include an explanation)
If a line has a slope of 9/5. If one of the points on the line is (-10, -16), which could be another point?
Answer:
(–5, –7)
Step-by-step explanation:
From the question given above, the following data were obtained:
Slope = 9/5
Coordinate 1 = (–10, –16)
x₁ = –10
y₁ = –16
Coordinate 2 = (x₂, y₂)
Next, we shall determine the change in x and y coordinate. This can be obtained as follow:
Slope = change in y–coordinate / change in x–coordinate
Slope = Δy / Δx
Slope = 9/5
9/5 = Δy / Δx
Thus,
Δy = 9
Δx = 5
Next, we shall determine the second coordinates as follow:
Δy = y₂ – y₁
Δx = x₂ – x₁
For x–coordinate:
x₁ = –10
Δx = 5
Δx = x₂ – x₁
5 = x₂ – (–10)
5 = x₂ + 10
Collect like terms
x₂ = 5 – 10
x₂ = – 5
For y–coordinate:
y₁ = –16
Δy = 9
Δy = y₂ – y₁
9 = y₂ – (–16)
9 = y₂ + 16
Collect like terms
y₂ = 9 – 16
y₂ = – 7
Coordinate 2 = (x₂, y₂)
Coordinate 2 = (–5, –7)
Safe wheelchair ramp specifications require about 4.75° maximum angle to be constructed with the ground. At a particular building, the owner is installing a wheelchair ramp that needs to rise 1 feet off the ground. The owner insists on constructing the angle with the ground at 3°. How much horizontal distance will the ramp cover with these specifications?
Answer:
The ramp must cover a horizontal distance of approximately 19.081 feet.
Step-by-step explanation:
Given the vertical distance ([tex]y[/tex]), measured in feet, and the angle of the wheelchair ramp ([tex]\theta[/tex]), measured in sexagesimal degrees. The horizontal distance needed for the ramp ([tex]x[/tex]), measured in feet, is estimated by the following trigonometrical expression:
[tex]x = \frac{y}{\tan \theta}[/tex] (1)
If we know that [tex]y = 1\,ft[/tex] and [tex]\theta = 3^{\circ}[/tex], then the horizontal distance covered by this ramp is:
[tex]x = \frac{1\,ft}{\tan 3^{\circ}}[/tex]
[tex]x \approx 19.081\,ft[/tex]
The ramp must cover a horizontal distance of approximately 19.081 feet.
Solve the system of equations by first multiplying.
ſ 3x +y = -5
1 2x + 5y = 27
Write the solution as an ordered pair.
3x+y=-5
12x+5y=27
Let y =-5-3x
Insert y into equ.2
12x+5(-5-3x)=27
12x-25-15x=27 den rearrange
-3x=2 den x =-2/3
Den put xinto equ 1
3(-2/3)+y=5
-2+y=5(collect like terms)
Y =7
a + 3 + 2a = - 1 + 3a + 4 solve for A
Answer:
A=0
Step-by-step explanation:
a + 3 + 2a = - 1 + 3a + 4
a+2a-3a=-1+4-3
3a-3a=0.
0=0
please answer the question :(
Answer:
y = (- 4/3) x + 2
Step-by-step explanation:
Remark
The y intercept is (0,2)
The other point is you could use is (3,-2)
First find the slope
The two given points are (0,2) and (3,-2)
Givens
y2 = - 2
y1 = 2
x2 = 3
x1 = 0
Formula
m = (y2 - y1)/(x2 - x1)
Solution for m
m = (-2 - 2)/(3-0)
m = -4/3
Solution for the line
m = - 4/3
y intercept = 0,2
y = mx + b
y = (- 4/3) x + 2
What is the difference between (-10)² & -10²? What are the values for each expression?
Answer:
(-10)² = 100
-10² = -100
Difference = 200
Step-by-step explanation:
For the individual expressions;
(-10)² = -10 * -10
(-10)² = +100
For -10²
-10² = -(10*10)
-10² = -100
Taking the difference;
(-10)² - (-10²) = 100 - (-100)
(-10)² - (-10²) = 100 + 100
(-10)² - (-10²) = 200
Hence the difference is 200
HELPPP it’s a test quest.. 20pts
Answer:
I think that the answer is A
Answer:
and because it was a test.
Step-by-step explanation:
that was the answer ok so for the mathematical errors. okay? undostands?
what is the reciprocal of 3 3/5
Answer:
5/18
Step-by-step explanation:
Can someone help. Will award if correct.
Answer:
Shari is correct
Step-by-step explanation:
Here, we want to select the correct translation of the graphed function
9 spaces down (vertically on y-axis) and 4 spaces right, to the positive x axis
What we have here means we go 9 units down, subtracting 9 from the y-value(f (x)) and adding 4 to x
The correct answer is;
f(x) = -2(7/10)^(x + 4) - 9
(x-5)(x+1)
O x= -1 and x = 5
O x= -1 and x = 14
O x= 1 and x = -5
O x = 14 and x = 5
Function: Yes or no
{(-3,4),(-2,5),(0,0),(-2,5),(4,8)}
Answer:
Yes.
Step-by-step explanation:
Every input has a specific output.
ima say yes but I may not be correct if somebody else answers chose them and let me be your last chose ;-;
1/2(7x- 6) = 6x – 10.
Answer:
Hopes this answer your question :)
Step-by-step explanation:
NEED HELP ASAP PLZZZZZZZZZZ!!!!!!!!!!!!!!!!!!!!!
A conference is expecting between 640 and 1,088 attendees. The conference is serving pizza for lunch. If the conference must order 8 pizzas per 32 attendees, approximately how many pizzas should the conference order?
A.
27 pizzas
B.
13,824 pizzas
C.
56 pizzas
D.
216 pizzas
Answer:
D 216 pizzas
Step-by-step explanation:
if there expecting 1,088 I would say that's 56 pizzas
HELP ME W THIS PROBLEM PLEASE!!!!!
Answer:
d
Step-by-step explanation:
(4x + 5x) + 6x = 4x + (5x + 6x)
Answer:
9x=15x
Step-by-step explanation:
This is not correct
Answer:
it's correct
Step-by-step explanation:
(4x + 5x) + 6x = 4x + (5x + 6x)
9x+6x = 4x+ 11x
15x=15x
proved ✓✓
In a pack of pretzel sticks , 1/4 number of the total number pretzel sticks is 14. Write and solve an equation to find the total number of pretzel sticks in the pack "x"
Zachary and his children went into a grocery store and will buy bananas and peaches.
Each banana costs $0.50 and each peach costs $1.50. Zachary has a total of $8 to
spend on bananas and peaches. Write an inequality that would represent the possible
values for the number of bananas purchased, b, and the number of peaches
purchased, p.
Answer:
0.5b + 1.5p ≤ 8
Step-by-step explanation:
The inequality function is as follows:
Let us assume the number of bananas acquired be b
And, the number of peaches acquired be p
Cost of each banana be $0.50
ANd, the cost of each peach be $1.50
Also the total would be $8
The possible values of banana is 0.5b
And, for peaches it would be 1.5p
So, the inequality function is
0.5b + 1.5p ≤ 8
Answer:
0.5b + 1.5p ≤ 8
Step-by-step explanation:
3 type of different triangles
Answer:
read below
Step-by-step explanation:
equilateral
isosceles
scalene
Please help its my last question
Answer:
Step-by-step explanation:
Acute as it is less than 90 degrees
Answer:
acute
Step-by-step explanation:
its less than 90 see the image
An elevator in a mine shaft is stopped at a .25 feet below ground level. And then travels 28 feet downward. What equation can be written to find the final position in feet of the elevator in relations to ground level?
Correct question:
An elevator in a mine shaft is stopped at 25 feet below ground level. And then travels 28 feet downward. What equation can be written to find the final position in feet of the elevator in relations to ground level?
Answer:
-53 feets
Step-by-step explanation:
Initial stop point = 25 feets below ground level
Further distance traveled = 28 feets below ground level
Final position in feet = Initial stop point + further distance traveled
Note : distances or point traveled below ground level or downward is represented as negative.
Final position in feets = (-25)feets + (-28)feets
Final position in feets = - 53 feets
Someone please help me ?:)
9514 1404 393
Answer:
(c) 6 inches
Step-by-step explanation:
The ratio ...
1 in : 2 ft
can be multiplied by 6 to find the length corresponding to 12 ft:
6×1 in : 6×2 ft
6 in : 12 ft
The ceiling height in the model is 6 inches.
If x(x - 3) = 0, what are the two values of x that would make the statement 10 points
true?
Answer:
0 & 3
Step-by-step explanation:
First x is by itself so the root is 0
Second is 3 because you set x-3=0 and add 3 to the other side so x=3
Answer:
0 and 3
Step-by-step explanation:
You need to find the root of the equation, which would be 0, and 3.
To find the root, all you do is solve for x.
Two students flipped a coin 100 times and recorded the results. Find the experimental probability of flipping the coin and getting tails.
Answer:
I'm not too sure about this one, but I think it's 36% since that's
how many they got when they flipped the coin. In reality, it's 50% for both sides.
find unit rate for me pls ? which check marks which box
Answer:
the answers are
60
90
30
30
60
Please help please....
Answer:
Step 3
Step-by-step explanation:
They didn't subtract the 1 on the right side making it equivalent
