Answer:
The equation of the polynomial in vertex form is [tex]y +8= (-2)\cdot (x-3)^{2}[/tex], its vertex is [tex](h,k) = (3, -8)[/tex].
The expression of the axis of symmetry is [tex]x = 3[/tex].
The y-intercept of the function is -26.
Step-by-step explanation:
The vertex form of the second order polynomial is defined by the following expression:
[tex]y-k = C\cdot (x-h)^{2}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]h,k[/tex] - Coordinates of the vertex, dimensionless.
[tex]C[/tex] - Vertex constant, dimensionless.
Let [tex]y = -2\cdot x^{2}+12\cdot x - 26[/tex], then we proceed to present the produre for the determination of the vertex form:
1) [tex]y = -2\cdot x^{2}+12\cdot x - 26[/tex] Given
2) [tex]y = (-1)\cdot (2\cdot x^{2})+(-1)\cdot (-12\cdot x) + (-1)\cdot (26)[/tex] [tex](-a)\cdot (-b) = a\cdot b[/tex]/[tex](-a)\cdot b = -a\cdot b[/tex]
3) [tex]y = (-1)\cdot (2\cdot x^{2}-12\cdot x +26)[/tex] Distributive property
4) [tex]y = [(-1)\cdot (2)]\cdot (x^{2}-6\cdot x +13)[/tex] Associative and distributive properties
5) [tex]y = (-2)\cdot [(x^{2}-6\cdot x+9)+4][/tex] [tex](-a)\cdot b = -a\cdot b[/tex]
6) [tex]y = (-2) \cdot [(x-3)^{2}+4][/tex] Perfect square trinomial
7) [tex]y = (-2)\cdot (x-3)^{2}+4\cdot (-2)[/tex] Distributive property
8) [tex]y = (-2)\cdot (x-3)^{2}+(-8)[/tex] [tex](-a)\cdot b = -a\cdot b[/tex]
9) [tex]y +8= (-2)\cdot (x-3)^{2}[/tex] Compatibility of addition/Existence of the additive inverse/Modulative property/Result.
The equation of the polynomial in vertex form is [tex]y +8= (-2)\cdot (x-3)^{2}[/tex], its vertex is [tex](h,k) = (3, -8)[/tex].
The axis of symmetry is a line perpendicular to axis in which the square component of the vertex form is set. The expression of the axis of symmetry is [tex]x = 3[/tex].
The y-intercept is the value of the polynomial when [tex]x = 0[/tex], then, the value is:
[tex]y = -2\cdot (0)^{2}+12\cdot (0) -26[/tex]
[tex]y = -26[/tex]
The y-intercept of the function is -26.
Choose the diagram that correctly represents the ordered pairs below.
(1,4), (4, -1), (2,3), (-3, 1), (0,-5)
Answer:
Step-by-step explanation:
Is there a picture
What is the length of the unknown leg in the right triangle
Answer:
i think it might be 15m
Step-by-step explanation:
How are the angles of an equilateral triangle related?
Please explain so a smol brained person can understand
pamela ran 7/10 miles on tuesday and 3/8 mile on thursday. How much farther did she sun on tuesday ?
Answer:
she ran 0.325 more on tuesday then tursday
Step-by-step explanation:
because i know
g(x) = x3 - 4
h(x) = x2 + 2
Find h(-2) - g(-1)
Answer:
11
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
g(x) = x³ - 4
h(x) = x² + 2
h(-2) is x = -2
g(-1) is x = -1
Step 2: Find h(-2) - g(-1)
Substitute: ((-2)² + 2) - ((-1)³ - 4)Exponents: (4 + 2) - (-1 - 4)Add/Subtract: 6 - (-5)Subtract: 11I will GIVE BRAILYEST
Mario has 20 yards to mow this week. By Wednesday, he had mowed 50%or the yards. How many yards had he mowed by Wednesday?
2
5
10
15
Answer: 10 yards
Step-by-step explanation: 50% = 1/2
1/2 x 20 = 10
15 yeards mowed by Wednesday
how to solve this? im not sure if i get the correct answer
Answer:
k = 3.5
Step-by-step explanation:
Area of a rectangle = length × width
Area of the bigger triangle - Area of the smaller triangle = 35 cm²
Thus:
(2k + 6)(k) - (3)(k) = 35 cm²
2k² + 6k - 3k = 35
2k² + 3k - 35 = 0
Factorise
2k² + 10k - 7k - 35 = 0
2k(k + 5) -7(k + 5) = 0
(2k - 7)(k + 5) = 0
2k - 7 = 0
2k = 7
k = 3.5
Or
k + 5 = 0
k = -5
The value of k would be the positive number which is 3.5.
Constructing a frequency distribution for grouped data
Ten cyclists were each asked the distance in miles they biked last week.
Their responses are given below.
Complete the grouped frequency distribution for the data.
In the distribution, the frequency of a class is the number of distances in that class.
(Note that we are using a class width of 5.)
Distance in miles
Distance in miles
Frequency
3
20
6
3
7
8
13
10
18
12
6 to 10
11 to 15
16 to 20 and 1 to 5
The grouped frequency distribution for the data with the given intervals is 2, 4, 2 and 2 respectively.
Given that, ten cyclists were each asked the distance in miles they biked last week. The distance travelled by 10 cyclists is 3, 20, 6, 3, 7, 8, 13, 10, 18 and 12.
We need to complete the grouped frequency distribution for the data.
What is the grouped frequency distribution?In this type, the data is arranged and separated into groups called class intervals. The frequency of data belonging to each class interval is noted in a frequency distribution table. The grouped frequency table shows the distribution of frequencies in class intervals.
Now, the frequency distribution for the given intervals is as follows:
That is, for intervals 1 to 5 the frequency is 2.
For intervals 5 to 10 the frequency is 4.
For intervals 11 to 15 the frequency is 2.
For intervals 16 to 20 the frequency is 2.
Therefore, the grouped frequency distribution for the data with the given intervals is 2, 4, 2 and 2 respectively.
To learn more about the grouped frequency distribution visit:
brainly.com/question/4679134.
#SPJ2
Which equation is represented by the graph below
a bowling alley charges $4.00 per game and will rent a pair of shoes for $2.00 for any number of games. The bowling alley has an earnings goal of $400 for the day. write the linear equation.
Answer:
We need 130 games to reach the goal
Step-by-step explanation:
A cell phone manufacturer samples cell phones from the assembly to test. She noticed that the number of faulty cell phones in a production run is usually small and that the quality of one day’s run seems to have no bearing on the next day.
a) What model might you use to model the number of faulty cell phones produced in one day?
(write a name of this probability model)
An analysts estimates the mean number of defective cell phones to be 2 per day.
b) What is the probability of having a day with no faulty cell phone in a production run?
(write to 3 decimal places)
c) What is the probability of having a day with more then 3 faulty cell phones in a production run?
probability:
Answer:
b
Step-by-step explanation:
probability can't be defined
say a number between 1 and 10 if u guss right u get brainlist
29. Which of the following expressions will result in a real answer after being simplified? Select all that apply.
A. (4+5i)(4-5i)
B. (4+91)(41-9)
C. (3+2i)(3-2i)
D. (2i+5i) (21-3)
E. (312+7i) (312-7i)
F. (3i2+7i)(312+7i)
Answer: A, B, C, and E
Step-by-step explanation:
If both sides are real numbers, then the product will be a real number.
If in at least one of the sides we have a complex number, then the product will be real if:
The other number is zero.
The other number is the conjugate of the first.
This is when:
Suppose we have a number:
z = a + b*i
The conjugate will be:
w = a - b*i
And the product between them is:
(a + b*i)*(a - b*i) = a^2 + a*b*i - a*b*i + b^2 = a^2 + b^2
Then the options that will have a real answer are:
A. (4+5i)(4-5i) = 4^2 + 5^2 = 16 + 25 = 41
B. (4 + 91)*(41 - 9) = 3040
C. (3 + 2*i)*(3 -2*i) = 3^2 + 2^2 = 9 + 4 = 13
E. (312 + 7i)*(312 - 7i) = 312^2 + 7^2 = 97,393
What the equivalent (2×)(5y)(5y)
Answer:
50xy
Step-by-step explanation:
(2x)(5y)(5y)
~Simplify
(2x)(25y)
~Multiply
50xy
Best of Luck!
Whats the answer to part b and above?
Answer:
4/5 would be at the 8th line, and 3/10 would be on the 3rd
Step-by-step explanation:
Kim performed a transformation on rectangle ABCD to create rectangle A'B'C'D', as shown in the figure below: A(-1,2) B(-1,5) C(-3,5) D(-3,2) A'(-1,-2) B'(-1,-5) C'(-3,-5) D'(-3,-2)
What transformation did Kim perform to create rectangle A'B'C'D? (5 points)
A)Reflection across the y-axis
B)Rotation of 270 degrees counterclockwise about the origin
C)Reflection across the x-axis
D)Rotation of 90 degrees counterclockwise about the origin
Answer:
C) Reflection across the x-axis.
Step-by-step explanation:
From Linear Algebra we define the reflection across the x-axis is for [tex]P(x,y) =(x,y)[/tex]:
[tex]P'(x,y) = (x, -y)[/tex] (1)
If we know that [tex]A(x,y) = (-1, 2)[/tex], [tex]B(x,y) =(-1,5)[/tex], [tex]C(x,y) = (-3, 5)[/tex] and [tex]D(x,y) =(-3, 2)[/tex], then the reflected points are, respectively:
[tex]A'(x,y) = (-1, -2)[/tex]
[tex]B'(x,y) = (-1,-5)[/tex]
[tex]C'(x,y) = (-3,-5)[/tex]
[tex]D'(x,y) = (-3,-2)[/tex]
In consequence, Kim performed a reflection across the x-axis to create triangle A'B'C'D'. The correct answer is C.
This question is based on the reflection of x- axis. Hence the correct answer is C, reflection across the x-axis.
Given:
Transform rectangle ABCD to rectangle A'B'C'D',
The vertices of rectangle ABCD is A(-1,2) B(-1,5) C(-3,5) D(-3,2).
The vertices of rectangle A'B'C'D is A'(-1,-2) B'(-1,-5) C'(-3,-5) D'(-3,-2).
We need to determined the transformation that Kim perform to create rectangle A'B'C'D.
From Linear Algebra we define the reflection across the x-axis is for,
P(x,y) = (x,y)
P(x,y) = (x,-y) .....(1)
It is given that A(-1,2), B(-1,5), C(-3,5) and D(-3,2).
Therefore from equation (1) above point becomes,
A'(x,y) = (-1,-2)
B'(x,y) =(-1,-5)
C'(x,y) =(-3,-5)
D'(x,y) =(-3,-2)
Therefore, It is observe that Kim performed a reflection across the x-axis to create triangle A'B'C'D'. Hence the correct answer is C, reflection across the x-axis.
For further details, please refer this link:
https://brainly.com/question/25095797
what fraction is equal to 5%
Answer:
5/100
1/20
Step-by-step explanation:
Answer: 5/100
Step-by-step explanation:
I need this fast please
Answer: It is B/Spinner 2
There are 2400 students in a school 45% of them are boys how many boys are in the school
Show your work in the answer
Answer:
1080 boys
Step-by-step explanation:
2400 x 0.45 = 1080
i need some help here
Answer:
the answer above is correct
Answer:
boxes
7
8
58.1
119.7
Step-by-step explanation:
look when u solve this it equals
8.3(7)+7.7(8)=119.7 but it tells u to add 61.6 so u go backwards subtract
119.7-61.6
58.1
just plug in
8.3(7)+7.7(8)=____+61.6
plug in
58.1+61.6
119.7
Question #5
Consider the equation.
72 +48 = 8
1+6)
Enter the unknown number that makes the equation true.
Your answer
Σ
Definition of dilation in geometry
Answer:
Geometry
Step-by-step explanation:
A table of values of a linear function is shown below.
Answer:
Slope is -2
y intercept is -3
Equation :y=-2x-3
Step-by-step explanation:
а) 6x = 7y
Can someone help
Answer:
36 x 2 - 49 y 2
Step-by-step explanation:
6 x (6x) +6 x ( - 7 y ) + 7 y (6x) +7 y ( - 7 y)
Tell whether the relation is a function. Explain.
Given: f(x) = x - 7 and h(x) = 2x + 3
Write the rule for f(h(x))
Answer:
2x - 4
Step-by-step explanation:
f(x) = x - 7
= 2x + 3 - 7
= 2x - 4
A baker had additional flour at the end of the day. He uses 1/8 of a bucket of flour to bake two cakes. How much flour did he use to make one cake?
Answer:
0.0625
Step-by-step explanation:
You can convert this into a fraction by entering this into a calc
Please give me the correct answer
Answer: Many people assume that because DNA is so small, we can't see it without powerful microscopes. But in fact, DNA can be easily seen with the naked eye when collected from thousands of cells.
Twelve of the 28 students in the 6th grade class have a dog. What is the ratio of students who have a dog to the students who do not have a dog? Write this ration in 3 different ways. Then, explain which ratio is greater. Please help
Answer:
1:4
Step-by-step explanation:
As, number of students have 12
Which don't, are 28 - 12 = 16
So ratio = 12:16
1:4
3) Luan is borrowing $5000 to buy Sacramento Kings season tickets
for her family. She is planning to pay it back over three years.
She can borrow the money from a finance company at a 6.5% add-on
interest rate for three years or she can borrow it instead from
her credit union, making 36 monthly payments of $164.50. Find the
total amount Luan will have to pay back with each option and the
APR (to the nearest half percent) of each loan.
Answer:
16000
Step-by-step explanation:
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