Answers
Answer:
The vertex is at [tex](0, -9)[/tex]
The axis of symmetry [tex]x = 0[/tex]
Step-by-step explanation:
Note: You can answer all the questions looking at the graph
We have the function [tex]f: \mathbb{R} \rightarrow\mathbb{R}[/tex](I am assuming this) such that [tex]f(x) = y = (x-3)(x+3)[/tex]
We note that
[tex](x-3)(x+3) = x^2-9[/tex] once we have a difference of squares
Therefore, we have a quadratic function.
So
[tex]y = x^2-9[/tex]
The vertex [tex](h, k)[/tex] is
[tex]h = \dfrac{-b}{2a} = \dfrac{-0}{2 \cdot 1} = 0[/tex]
[tex]k= h^2 - 9 = 0^2 - 9 =-9[/tex]
Therefore, the vertex is at [tex](0, -9)[/tex]
As we know the vertex, we conclude that the axis of symmetry [tex]x = 0[/tex]
The x-intercepts occur at [tex]y = 0[/tex]
[tex]y = (x-3)(x+3) \implies x = -3, x=3[/tex]
So, the left x-intercept is [tex](-3, 0)[/tex] and the right x-intercept is [tex](3, 0)[/tex]
As I stated in the beginning, the domain is the set of all real numbers. Precisely,
[tex]Dom(f) = \mathbb{R} = (-\infty, \infty)[/tex]
Once, we know the vertex, we also conclude that the Range is
[tex]Ran(f)= [-9,\infty)[/tex]
Greater than or equal to -9
Related Questions
Solve the equation using the method of factorisation-
x2 - 4x - 45 = 0
x² + 4x -9= (x + a)^2 + b
Find the value of a and the value of b.
Answers
Answer:
X = 9,X= -5, a = 2, b = -13
Step-by-step explanation:
For (1),
Using Cross-factorization,
it can be reduced to (X - 9)(X + 5) = 0
Equate each factor to 0:
we have X = 9 and X = -5
For (2),
It is the case of completing the Square,
add 4 so we get the completed square ( we want the form X^2 + 2a + a^2)
(X^2 + 4X + 4) - 9
can be simplified to (X+2)^2 -9
However since we added 4 it means we have to subtract 4
So it becomes (X+2)^2 -9 -4
= (X+2)^2 -13
A recipe requires 1 cup of flour for every batch of cookies. How many full batches of cookies can be
made with 52 cups of flour?
Answers
giving 100 pts after its answered correctly
Answers
Answer:
I think he just wanted the answer so there isnt free 100 pts :/
Step-by-step explanation:
Answer:
just got robed out of 10 pts tho
Step-by-step explanation:
Find the mean of the
data set:
14, 19, 13, 22,7
Answers
Answer:
Add up all the numbers and divide it by how many numbers there are.
14+19+13+22+7=75
75÷5 =15
Caroline is making cookies for a large fundraiser taking place in two days. Her recipe says it
makes 24 cookies, but she needs to make 60 cookies. The recipe consists of the following
ingredients: 1 cup flour; 2/3 cup powdered sugar; 1/2 cup cornstarch; and 3/4 cup butter. How
should she go about increasing the recipe to make 60 cookies? What is the measurements
needed to make 60 cookies?
Answers
Step-by-step explanation:
you need to double the recipe and add 1/2, because doubling gets you 48 and adding 1/2 gets you to 60 cookies.
rather than the given recipe, multiply the numbers by 2.5 (double and a half): 2.5c flour
1 2/3 c powdered sugar
1 1/2 c cornstarch
1 7/8 c butter
hope this helps!
2 × 3² - 5² = ???????????????????????????????????????????????????????????????????????????????
Answers
Answer:
I think its -7
Step-by-step explanation:
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Answer:
-7 is your answer
Step-by-step explanation:
2 × 3² - 5²=18-25=-7
Charles invested $15,000 in stocks and bonds. He made a 12% profit on his stock investments and a 5% profit on his bond investments. If Charles's combined profits on both types of investments were $1,450, how much did he invest in stocks?
Answers
Answer:When you leave the interest in your
account or reinvest the money you earn on your
investments, the money you earn starts to earn
money too. Over time, the magic of
compounding works, allowing your money to
grow with dramatic results. The more time you
have to save, the less money you need to save
because of compounding. And the longer you
wait to start saving, the more you have to spend
to reach your goal. For example, let’s assume
that Maria’s savings grow by 5% a year. If she
starts to save $243 a month now, it will cost her
$58,320 to have $100,000 in twenty years. If
she waits 10 years to start saving, she will have to
save $644 a month for 10 years, and it will cost
her $77,280 to reach $100,000 in twenty years.
Step-by-step explanation:Hope this helps!!!!
Answer:
$10,000 invested into stocks
Step-by-step explanation:
a right retangular prism is 10 1/2 m wide 15 1/2 m long and 3 m tall what is the volume of the prism
Answers
Answer:
V = 488.25
Step-by-step explanation:
Formula:
V = whl
V = 10.5(15.5)(3)
V = 162.75(3)
V = 488.25
jane saved $20 from her $60 allowance. june saved $15 from her $50 allowance. who saved a greater proportion of her allowance
Answers
Answer:
Jane
Step-by-step explanation:
Jane saved 33.333%
While
june saved 30%
Solve for a: a + 6 - 2 x 6 + 4 – 8 + 3 x 2 = 0
Answers
Step-by-step explanation:
[tex]a + 6 - 12 + 4 - 8 + 6 = 0 \\ a - 4 = 0 \\ a = 4[/tex]
Find the surface area of the figure
Answers
Answer:
2400 square feet
Step-by-step explanation:
20 x 20 = 400
400 x 6 = 2400
Hope that helps!
Write an expression that is equivalent to -0.5(14a-22)
-0.5(14a-22) = _?_a+_?_
Answers
Answer:
- 7a + 11Step-by-step explanation:
-0.5(14a - 22) = -0.5(14a) + (-0.5)(-22) = - 7a + 11The blanks are -7 and 11
Answer:
-7 and 11
Step-by-step explanation:
The local park has a circular pond with a radius of 9 feet. What is the pond's circumference?
Answers
Answer:
Using 3.14 as pi, the answer would be 56.52, and using just pi (as in the input on a calculator) would be 56.54867.
Step-by-step explanation:
The equation for circumference of a circle is C = πd, C representing the circumference and d representing the diameter. Since the equation shows the radius, the equation can also be C = 2πr, since the radius is half of the diameter. Multiply nine by two to get eighteen. 18 times 3.14 = 56.52.
Help me please (NO LINKS )
Answers
Answer:
Hey! Finally found a question of yours!
Step-by-step explanation:
1. A=9
2. A=12
3. A=21
4. A=15
5. A=7
6. A=5
7. A=20.8
8. A=48
9. A=0.25
Two investments totaling $37,500 produce an annual income of $2210. One investment yields 6% per year, while the other yields 5% per year. How much is invested at each rate?
Answers
Answer:
a = $33,500 at 6%
b = $4,000 at 5%
Detailed Answer:
37,500 = a + b
b = 37,500 - a
a = 37,500 - b
2,210 = a*6% + b*5%
2,210 = a*6% + 5%*(37,500 - a)
2,210 = a*6% - a*5% + 37,500*5%
2,210 = a*(6% - 5%) + 1,875
335 = a*( 6/100 - 5/100)
335 = a*( 1/100)
a = (335*100)/1
a = $33,500
b = 37500 - a
b = 37500 - 33500
b = 4000
Plug back in to check if the amounts invested at each rate equal $2210:
$2210 = a*6% + b*5%
$2210 = 33500*6% + 4000*5%
$2210 = $2010 + $200
$2210 = $2210
Molly emailed her clients offering a free 30-minute massage for referrals. In the following validation set of 100, class 1 reflects the clients predicted to provide referrals and class 0 reflects the clients predicted to not provide referrals. Based on the confusion matrix, what was the False Negative (FN) of current clients who provided referrals for a free message?Actual Class Predicted Class 1 Predicted Class 0Class 1 18 11Class 0 11 60a. 29b. 18c. 11d. 60
Answers
Answer:
b 18
Step-by-step explanation:
From the given data: the right table arrangement is:
[tex]Actual \ Class[/tex] [tex]\text{ Predicted Class 1}[/tex] [tex]\text{Predicted Class 0}[/tex]
[tex]Class \ 1[/tex] 18 11
[tex]Class \ 0[/tex] 11 60
The True Positive is the number of current customers who were predicted to give references to a free back rub and who actually gave references to a free back rub.
This number is given by the section in the segment relating to Predicted Class 1 and the line comparing to A[tex]Class \ 1[/tex]tual Class 1 which is 18.
Ten years ago, the average amount of time a family spent eating supper together was 27.8 minutes. A sociologist believes this average has decreased. She randomly selects a sample of 12 families and finds the sample average to be 24.307 minutes. The sample data look about bell-shaped. She calculated a test statistic of t
Answers
Mr. Tough can grade the final exams in 12 hours. His assistant, Ms. Nice, can grade the same exams in 15 hours. What fraction of the exams can Mr. Tough grade in 1 hour, without any help? This is impossible. Please help me. I spent sooo loong on this and got it wrong. I don't have many points. Sorry about the 20 points. IT IS VERY URGENT!!!!!!!!!!!!!!!!!
Answers
Answer:
1/12
Step-by-step explanation:
if Mr.Tough can grade 1 in 12 hours he can do 1/12
The fraction of the exams that Mr Tough and Mrs Nice grade in 1 hour if they work together is 3/20
What are fractions?A fraction is used to denote a portion or component of a whole. Numerator and denominator are the two components that make up a fraction. There are three types of fractions: proper, incorrect, and mixed.
Using, rate × time = work done
So, Mr Tough's rate:
Mr Tough's rate × 12 hours = final exam
Mr Tough's rate = 1/12
and, Mrs. Nice's' rate:
Mrs .Nice's' rate × 15 hours = final exam
Mrs .Nice's' rate = 1/15
So, Total time:
T(1/12 hours + 1/15 hours) = final exam
T = final exam / (1/12 + 1/15)
T = final exam / (0.15)
Now, 1 hour = final exam / (0.15)
final exam = 1 × 0.15
= 0.15
= 15/ 100
= 3/20
Therefore, 3/20 fraction of the final exam.
Learn more about work, time and rate here:
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Find y if the line through (5, 2) and (7, y) has a slope of 4.
Y=___
Answers
Y=(4*2)+2=10
Ans.10
Can someone give me the answers I will mark u brilliant
Answers
Answer: 4+x=11
Step-by-step explanation:
4+7=11
Answer:
b
Step-by-step explanation:
Apples cost $2 each, while bananas cost $3 each. Maria purchased 10 fruits in total and spent $22. How many apples did she buy?
Answers
You are sending a package in the mail. The box is a cube
measuring 14 inches on all sides. How many cubic inches
is the package?
Answers
Answer: 2744
:)
Hope it’s right
The volume of a cube with a side length of 14 inches is 2744 cubic inches.
Side of the cube = 14 inches
What is the volume of a cube?The volume of a cube with side length a is a³.
So, the volume of a cube with a side length of 14=14³
The volume of a cube with a side length of 14=2744 cubic inches.
Hence, the volume of a cube with a side length of 14 inches is 2744 cubic inches.
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pls help mee help help help help
Answers
r = 4.8
4.8^2 * 3.14 = 23.04 * 3.14
= 72.3456
Which is the quotient of 15 divided 4? 4/15, 2 2/3, 3 3/4, 4 4/15
Answers
Answer:
its 3 3/4 or in decimal form 3.75
Step-by-step explanation:
15 divided by 4 gives you that answer
Help! for brainiest and thanks! + 5 stars VOLUME
please respond with the solution and reasoning if possible!
Answers
Answer:
the volume of the rectangular prism is 448.5 in^3
Step-by-step explanation:
The computation of the volume of the rectangular prism is shown below:
As we know that
The volume of the rectangular prism is
= 7.8 × 11.5 × 5
= 448.5 in^3
It is basically multiplied with the height, width and the length
Hence, the volume of the rectangular prism is 448.5 in^3
Baka borrows $3,000 to buy a piano. The simple
interest owed at the end of 2 years is $540. what is the annual interest rate on Bakas loan for the piano?
a. 4.5%
b. 9%
c. 11.11%
d. 18%
please answer asap!
Answers
3,000x9%=270.
Altogether would be 18%. But, if we’re solving it for each separate year, then it would be 9%.
The required interest rate on the Bakas loan for the piano is 9%.
Given that,
Baka borrows $3,000 to buy a piano. The simple interest owed at the end of 2 years is $540. what is the annual interest rate on Baka loan for the piano is to be determined.
When some apply for their money on something so that they can get higher value in returns of their money.
Here,
Simple interest = principal × rate × time / 100
Substitute value in the above equation,
540 = 3000 × rate × 2 / 100
Rate = 540 × 100 / 3000 × 2
Rate = 9%.
Thus, the required interest rate on the Bakas loan for the piano is 9%.
Learn more about investment here:
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What is the equation of the line that passes through (4, -1) and (-2, 3)?
Answers
Answer:
-2/3
Step-by-step explanation:
(4, -1) and (-2, 3)
-1 +4 =3
4 - 6 = -2
-4/6 divided by 2/2 equals -2/3
A box contains 2 3/4
pounds of apples. Sage uses 1/5
of the box of apples.
How many pounds of apples does Sage use?
Answers
Answer:
.55 or 11/20
Step-by-step explanation:
multiply 2 3/4 by 1/5 to get the pounds of apples Sage uses.
Sage uses 11/20 of a pound of apples or approximately 0.55 pounds of apples.
What is a mixed expression?A fraction with a mixed expression, also known as a complex fraction, has a fraction in either the numerator, the denominator, or both.
The box contains 2³/₄ pounds of apples, which can be written as a mixed number or an improper fraction:
2³/₄ = (2 × 4 + 3)/4 = 11/4
To find out how many pounds of apples Sage uses, we need to multiply the amount in the box by the fraction that represents the proportion of the box that Sage uses, which is 1/5:
(1/5) × (11/4) = (1 × 11)/(5 × 4) = 11/20
Therefore, Sage uses 11/20 of a pound of apples or approximately 0.55 pounds of apples.
To know more about mixed expressions follow
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May I please get help on this
Answers
Do not click on his link it is a virus
Can someone help me on this one
Answers
Answer:
same as last because it is a circle
Step-by-step explanation:
Answer: diameter = 16 area = 201.06
Step-by-step explanation: