write a quadratic equation for the points (2,0) and (12,5). make sure to include the axis and five points used to graph the parabola
Answers
Using the Factor Theorem, the parabola is given by: [tex]f(x) = 0.05(x^2 - 4x + 4)[/tex]
The graph is sketched at the end of this answer.
The Factor Theorem states that a polynomial function with roots is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
In this problem:
The graph is a parabola, which means that the function is of the 2nd degree.One zero, with multiplicity 2, at [tex]x = 2[/tex], hence, [tex]x_1 = x_2 = 2[/tex].Then:
[tex]f(x) = a(x - 2)(x - 2)[/tex]
[tex]f(x) = a(x^2 - 4x + 4)[/tex]
Point (12,5) means that when [tex]x = 12, y = 5[/tex], and this is used to find a.
[tex]f(x) = a(x^2 - 4x + 4)[/tex]
[tex]5 = a(12^2 - 4(12) + 4)[/tex]
[tex]100a = 5[/tex]
[tex]a = \frac{5}{100}[/tex]
[tex]a = 0.05[/tex]
Hence, the parabola is:
[tex]f(x) = 0.05(x^2 - 4x + 4)[/tex]
At the end of this answer, the graph with five points is sketched.
A similar problem is given at https://brainly.com/question/24380382
Related Questions
**PLEASE HELP ME**
its pre calc !
Answers
Answer:
a32 = -80
Step-by-step explanation:
The generic term of an arithmetic sequence is ...
an = a1 +d(n -1)
Using the supplied values for an and n, we can write two equations that can be solved for a1 and d.
-221 = a1 +d(79 -1)
-14 = a1 +d(10 -1)
Subtracting the second equation from the first, we have ...
-221 -(-14) = (a1 +78d) -(a1 +9d)
-207 = 69d . . . . . simplify
-3 = d . . . . . . . . . . divide by the coefficient of d
Then the value of a1 can be found as ...
-14 = a1 +(-3)(9) . . . . substitute for d in the second equation
13 = a1 . . . . . . . . . . . add 27
__
Using our formula to find the 32nd term, we have ...
an = 13 -3(n -1)
a32 = 13 -3(32 -1)
a32 = -80
The 32nd term of the sequence is -80.
. A rectangular trunk has a volume of 28,600 cubic inches. The trunk is 50 inches long by 22 inches wide. What is the trunk’s height
Answers
If 12 inches = 1 foot, and 3 feet = 1 yard, how many inches are there in 2.5 yards? step by step
Answers
Answer:
There are 90 inches in 2.5 yards.
Step-by-step explanation:
12 inches per foot and 3 feet per yard means 36 inches per yard.
[tex]12*3=36[/tex]
Now, just multiply 2.5 yards by 36 inches/yard.
[tex]2.5*36=90[/tex]
There are 90 inches in 2.5 yards.
Does the following relationship represent a function?
Answers
What is the image of the point. (6, – 7) after a rotation of 180° counterclockwise
about the origin?
Answers
Answer:
(-6,7)
Step-by-step explanation:
The rotation is 180 degrees, so its means that the direction (clockwise vs counterclockwise) doesn't actually matter. With a rotation of 180 degrees, the preimage is switched to the opposite side of both the y and x-axis. This means that the rule for rotation around 180 is (-h,-k). Therefore, the answer will have the opposite signs. Thus. the image of (6,-7) is (-6,7).
Answer:
(-6, 7)
Step-by-step explanation:
the original and new points are both six units above/below the x-axis and 7 units to the right/left of the y-axis
y = x square - 4x + 6
Answers
In order to solve this we also need your question!! Are we putting this in slope intercept, solving for y, or solving for X, and if so, what is one of the variables? What is the question asking?
how long will it take the wave to reach the shore?
Answers
Each side of an equilateral triangle has length x+3 and each side of a square has length 4x-2. Write an expression for the sum of their perimeters.
Please help me!!
Answers
Answer:
square: 16x-8
triangle: 3x+9
Step-by-step explanation:
Squares have 4 equal sides. Equilateral triangles have 3 equal sides.
Multiply the length of one side by the total number of sides for each shape to find the perimeter. Then combine like terms.
Answer:
square: 16x-8
triangle: 3x+9
Step-by-step explanation:
15 divided by 1/5 as quotient
Answers
Answer:
15/1/5=15*5=75.
Step-by-step explanation:
Gina places biscuits in a circular pan in the fashion shown below. What is the area of the pan not covered by a
biscuit if the diameter of each biscuit is 2 cm? Use 3.14 for pi.
A. 6.28 cm2
B. 113.04 cm2
C. 3.14 cm2
D. 21.98 cm2
E. 28.26 cm2
Answers
Answer:
that isnt the full question like what is the area of the pan and stuff
Step-by-step explanation:
solve pls brainliest
Answers
Answer:
95%
Step-by-step explanation:
19/20=0.95
0.95x100=95%
hope this helps ^^
Please help me I don’t know how to solve this
|-4-r|=4
Answers
Answer:
r = 0 and r = -8
Step-by-step explanation:
|-4-r|=4
-4 = -4-r = 4
0 = - r = 8
0 = r = -8
When you have absolute value signs, to get rid of the absolute value signs and find the value of the term, you simply add another eqaul sign (=), and add a negative in front (- =). If it is already set to equal a negative, there isn't any solution.
|x| = 4
-4 = x = 4
So x would equal 4 and -4 for this example.
Another example:
|x|=-5
Because it's equal to a negative, the solution is automatically no solution.
The actual answer is r = 0 and r = -8
can i have help with geometry??????
Answers
Answer:
Yeah sure, but I cant guarantee i will answer all the questions. What grade level?
Round the quantity to th given place value 13.989 to the nearest tenth
Answers
Answer:
13.989 rounded to nearest tenth is 14.0.
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
round
You are buying carpet to cover a room that measures 38 ft by 40 ft. The carpet
cost $18 per square yard. How much will the carpet cost?
Answers
Answer:
27360
Step-by-step explanation:
38x40=1520
1520*18=27360
Can someone please help me
Answers
Answer:
Step-by-step explanation:
1) Statements Reasons
ABCD is a trapezoid Given
AD ║ BC bases of trapezoid are parallel
∠AED = ∠CEB vertically opposite angles are equal
∠EBC = ∠ADE alternate interior angles are equal and BD is transversal
∠ECB = ∠EAD alternate interior angles are equal and AC is transversal
ΔAED ~ ΔCEB ∠ECB = ∠EAD & ∠AED = ∠BEC & ∠EBC = ∠ADE
all angles are same and their shape is same, so similar
2) hope you can write 2nd one as above two column proof
T is the mid point of QR
U is the mid point of QS
V is the mid point of RS
Definition: The segment of line joining the middle points of two sides of a triangle is called middle segment.
Inference: A middle segment of a triangle is parallel to the third side and its lengths is half the third side's.
so here TU ║ RV and TU = RV
UV ║ TR and UV = TR
so TUVR becomes a parallelogram
∠TUV = ∠TRV --------> condition 1
same goes with parallelogram TQUV
∠TQU = ∠UVT ----------> condition 2
same goes with parallelogram TUSV
∠UTV = ∠USV ------------> condition 3
from the above 3 conditions we can say
ΔQRS ~ ΔVUT
3) see the below figure for graph
in both triangles ∠B is common
AC and TS are parallel lines
BC and BA are transversals
∠C ∠S are equal --> corresponding angles
∠A ∠T are equal ---> corresponding angles
so ΔABC & ΔTBS are similar
What is the slope of the graph shown below?
Answers
Answer:
A -2
Step-by-step explanation:
the line meets up there and it would be rise divided by run and it would get you -2
Answer:
Step-by-step explanation:
You look at where the lines cross a point, which could be (-1,3) and (0,-2). By looking at the graph and using rise over run, your slope would be -5.
what kind of cup that doesn't hold water
Answers
Step-by-step explanation:
cupcake that doesn't hold the water.
Pls help me
Question 8 (5 points)
(03.05 LC)
What is the volume of a cylinder (in cubic inches) with a radius of 6 inches and a height of 3 inches?
Use 3.14 for n. Round your answer to the nearest hundredth. (5 points)
a
339.12 cubic inches
b
56.52 cubic inches
с
100.48 cubic inches
d
113.04 cubic inches
Question 9 (5 points)
Answers
The correct answer according to a cylinder calculator would be 339.29 cubic inches but the closest answer you have would be 339.12 cubic inches
Tucker rings up an item that costs $35. After sales tax, the total is $37.80. What is the sales tax percentage?
Answers
Answer:
3 PERCENT
Step-by-step explanation:
I DID THE QUIZ
Write 1 over 9 as a decimal and round it to 2 decimal places
Answers
Answer:
0.111
Step-by-step explanation:
1/9 as a decimal is 0.11111111 but rounded to 2 decimal places is 0.111.
Hope this helps :)
Have a good day / night
Step-by-step explanation:
1/9 converted to a decimal is 0.11111111111 to round it to any place if it is 5 or greater like this 0.55 rounded would be 0.6 because the second five is greater than four if not greater than four like this: 0.44 the rounded form will be 0.4 then get your answer!
If the point (2K-3, K+2) lies on the graph of the equation 2x+y+14=0, find the value of k.?
Answers
Answer:
k = -2
Step-by-step explanation:
Substitute 2k-3 for x and k+2 for 2
2x + y + 14 =0
2(2k-3) + (k + 2) + 14 = 0
4k - 6 + k + 2 + 14 = 0
4k + k - 6 + 2 + 14 = 0
5k + 10 = 0
5k + 10 - 10 = 0 - 10
5k = -10
[tex]\frac{5k}{5} = \frac{-10}{5}[/tex]
k = -2
103.8 is what percent of 64? Round to the nearest thousandth
Answers
Answer: 162.1875%. Based on the given conditions, formulate: 103.8 / 64 Convert decimal to fraction:dfrac 1038/10 64Div
Step-by-step explanation:
The bakery decides to
make only 100 corn muffins on Tuesday. How many
kilograms of sugar will be needed?
Answers
Answer:
we need to know how many kilograms are in each corn muffin to answer that queastion
Step-by-step explanation:
we need to know how many kilograms are in each corn muffin to answer that queastion
Write 9 2/3 as a inpropper fraction
Answers
9/1 x3/3 = 27/3
27/3 + 2/3 = 29/3
Answer:
29/3
Step-by-step explanation:
hopes this helps :)
can some one help me pleaseeee :(
Answers
a) 5/8
b) 3/5
Hope this helps
How many minutes is 6:45 to 9:25 ?
Answers
Answer:
It is 15 minutes from 6:45 to 7:00. From 7:00 to 9:25 it is 2 hours and 25 minutes. Note: one hour is 60 minutes.
15 + 60(2) + 25
15 + 120 + 25
160 minutes
:)
Complete the equation line through (1,4) and (2,2) use exact numbers
Answers
(Graphed in the image below, green dots are the points given)
The transformation shown is a rotation.
true or false
Answers
Answer:
True
Step-by-step explanation:
Actually, I'm pretty sure it can also be a reflection! :) Have a good day!!!
A cloth bag contains a mix of black, white and red balls. Selecting one ball at random, the probability of getting a black ball is 0.2 , while the probability of getting a white ball is 0.5 . (a) Selecting one ball at random, what is the probability of getting a red ball ? (b) If in total there are 5 white balls in the bag, how many black balls are there ? (c) If there are in total 3 red balls in the bag, how many balls are there altogether ?
pls give the way
Answers
Answer:
a) 0.3
Step-by-step explanation:
The probability of getting a red ball, the number of black balls and total balls are 0.3, 2 and 10 respectively.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
Given that,
The probability of getting a black ball is 0.2.
The probability of getting a white ball is 0.5.
(a) As the bag contains only black, white and red balls, the probability of getting a red ball is,
1 - (0.2 + 0.5)
= 0.3
(a) The probability of getting white balls can be written as,
P (white ball) = Number of white balls ÷ Total number of balls
Substitute all the given values to get,
Total number of balls = 5 ÷ 0.5
= 10
Similarly, for black balls it can be written that,
P (black ball) = Number of black balls ÷ Total number of balls
Substitute all the given values to get,
Number of black balls = 10 × 0.2
= 2
(c) When number of red balls are three then,
P (red ball) = Number of red balls ÷ Total number of balls
Substitute all the given values to get,
Total number of balls = 3 ÷ 0.3
= 10.
Hence, the answers for all the parts are 0.3, 2 and 10 respectively.
To know more about probability click on,
https://brainly.com/question/11234923
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