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
Identifica el cuadrante en el cual se encuentra el ángulo 2.200
Answers
Answer:your
Step-by-step explanation:
mom
a farmer sells 7.6 kg of apples and pears at the Farmers Market. Two-fifths of this weight is Apple's, and the rest is pairs. How many kilograms of pears does she sell at the Farmers Market?
Answers
40% of 7.6 is 3.04
Subtract 3.04 from 7.6, you get 4.56
The farmer sells 4.56 kilograms of pears at the Farmers Market.
What is the equation of the line that is perpendicular to y=-3x+1 that passes through the point (9,0)?
y=1/3x-3
y=-1/3x+3
y=3x+9
y=-3x+3
Answers
Answer:
Step-by-step explanation:
the correct answer of the question is y=x/3-3 b.c
m1.m2 = -1 But m1=-3
so -3.m2=-1
-3.m2/-3=-1/-3
m2=1/3 therefore
Y=1/3x-3
Triangle XYZ has vertices X(1, –1), Y(3, 4), and Z(5, –1). Nikko rotated the triangle 90° counterclockwise about the origin. What is the correct set of image points for triangle X’Y’Z’?
X’(1, 1), Y’(-4, 3), Z’(1, 5)
X’(1, 1), Y’(–3, –4), Z’(–1, –5)
X’(–1, 1), Y’(–3, –4), Z’(–5, 1)
X’(–1, –1),Y’(4, –3), Z’(–1, –5)
Answers
Answer:
When a figure is rotated counterclockwise about the origin, its original coordinates of point P (x,y) will now be positioned as P' (-y,x).
X (1,-1) --> X' (1,1)
Y (3,4) --> Y' (-4,3)
Z (5,-1) --> Z' (1,5)
The correct set of image points for triangle X'Y'Z' is X'(1,1), Y'(-4,3), and Z'(1,5).
Step-by-step explanation:
Triangle XYZ is rotated 90° counterclockwise, the new coordinate is X'(1, 1), Y'(-4, 4) and Z'(1, -5)
TransformationTransformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.
If a point A(x, y) is rotated 90° counterclockwise the new point is A'(-y, x).
Triangle XYZ is rotated 90° counterclockwise, the new coordinate is X'(1, 1), Y'(-4, 4) and Z'(1, -5)
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Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
A and B
Step-by-step explanation:
Can somebody help me? I need help ;-;...
Answers
Answer:
Bottom left
Step-by-step explanation:
Dots are on the inside and outside of the line as well as being on the line
PLS ANSWER 10 POINTS!!
Answers
Answer:
the answer is 58°
Step-by-step explanation:
90 - 32 = 58
If another sample of size 100 is taken, what is the probability that its sample mean will
be greater than 2.56 in?
Answers
Answer:
I don't know the answer to this but
Suppose we draw a sample of size n=16 from this population and want to know how likely we are to see a sample average greater than 22, that is P( > 22)? So the probability that the sample mean will be >22 is the probability that Z is > 1.6 We use the Z table to determine this: P( > 22) = P(Z > 1.6) = 0.0548.
Step-by-step explanation:
Which of the following best describes the difference between simple and compound interest?
Simple interest is easier to calculate than compound interest.
Simple interest earns interest on the previous interest earned only.
Compound interest earns interest on the principal plus any previous interest earned.
Compound interest earns interest on the principal only.
Answers
Answer:
Compound interest earns interest on the principal plus any previous interest earned.
Step-by-step explanation:
compound interest gets its name because the interest keeps on 'compounding' which means earning interest on interest
The correct best describes the difference between simple and compound interest is,
⇒ Compound interest earns interest on the principal plus any previous interest earned.
Option 3 is true.
What is Simple interest?A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
We have to given that;
To defined best describes the difference between simple and compound interest.
Now, We know that;
Compound interest pays interest on your previous balance plus your previous earned interest; simple interest pays interest only on your original balance.
Hence, The correct best describes the difference between simple and compound interest is,
⇒ Compound interest earns interest on the principal plus any previous interest earned.
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Plz help! Pretty easy problems!
Answers
Answer:
The first is 9 sq.units
The second is 8 sq units
The third is 180mm squared
Step-by-step explanation:
Calculate: Find the perimeter of a triangle with sides 11 inches, 5 inches, and 13 inches. Show your work.
Answers
Answer:
29
Step-by-step explanation:
P=a+b+c=11+5+13=29
How do you find out if a number is an integer or not?
Answers
Answer:
Integers are any whole number negative or positive
Step-by-step explanation:
What is the resulting integral?
Answers
Answer:
[tex]\displaystyle \int {\frac{2}{(1 + \sqrt{x})^5}} \, dx = \frac{-(4\sqrt{x} + 1)}{3(\sqrt{x} + 1)^4} + C[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Calculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Antiderivatives - Integrals
Integration Constant C
U-Substitution
U-SolveIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int {\frac{2}{(1 + \sqrt{x})^5}} \, dx[/tex]
Step 2: Identify Variables
Find the variables u-solve using u-substitution.
U-Substitution
[tex]\displaystyle u = 1 + \sqrt{x}[/tex]
[tex]\displaystyle du = \frac{1}{2\sqrt{x}}dx[/tex]
U-Solve
[tex]\displaystyle x = (u - 1)^2[/tex]
[tex]\displaystyle dx = 2\sqrt{x}du[/tex]
Step 3: Integration
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle 2\int {\frac{1}{(1 + \sqrt{x})^5}} \, dx[/tex][Integral] U-Solve: [tex]\displaystyle 2\int {\frac{1}{(1 + \sqrt{(u - 1)^2})^5}} \, 2\sqrt{x}du[/tex][Integral] Simplify: [tex]\displaystyle 2\int {\frac{2\sqrt{x}}{u^5}} \, du[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle 4\int {\frac{\sqrt{x}}{u^5}} \, du[/tex][Integral] U-Solve: [tex]\displaystyle 4\int {\frac{\sqrt{(u - 1)^2}}{u^5}} \, du[/tex][Integral] Simplify: [tex]\displaystyle 4\int {\frac{u - 1}{u^5}} \, du[/tex][Integral] Rewrite [Integration Property - Subtraction]: [tex]\displaystyle 4[\int {\frac{u}{u^5}} \, du - \int {\frac{1}{u^5}} \, du][/tex][Integrals] Simplify: [tex]\displaystyle 4[\int {\frac{1}{u^4}} \, du - \int {\frac{1}{u^5}} \, du][/tex][Integrals] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle 4[\int {u^{-4}} \, du - \int {u^{-5}} \, du][/tex][Integrals] Reverse Power Rule: [tex]\displaystyle 4[\frac{u^{-3}}{-3} - \frac{u^{-4}}{-4}] + C[/tex]Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle 4[\frac{-1}{3u^3} + \frac{1}{4u^4}] + C[/tex][Brackets] Multiply: [tex]\displaystyle \frac{-4}{3u^3} + \frac{4}{4u^4} + C[/tex]Back-Substitute: [tex]\displaystyle \frac{-4}{3(1 + \sqrt{x})^3} + \frac{4}{4(1 + \sqrt{x})^4} + C[/tex]Combine: [tex]\displaystyle \frac{-(4\sqrt{x} + 1)}{3(\sqrt{x} + 1)^4} + C[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration
Book: College Calculus 10e
someone plz help no links stg
Answers
axis of symmetry: x=0
i don’t have the graph but
left x-intercept: (-3,0)
right x intercept: (3,0) (there’s two x intercepts)
the domain is the set of all real numbers
the range is -9, so i think it’s greater than?
help with math pretty easy will give 5 star and brainlyist
Answers
Answer:
area = 96 units²
Step-by-step explanation:
area = 16 x 12 x 0.5 = 96 units²
what is the answer to 1\2÷3
Answers
Answer:
1/6
Step-by-step explanation:
1/2÷3
1/2×1/3
1×1/2×3
1/2×3
1/6
(d) Chris chooses a card at random, replaces it, then chooses a
cards she chooses has the letter M printed on it.
(e) Graham chooses a card at random and does not replace it. He continues until he chooses a card with the letter M
printed on it. Find the probability that this happens when he chooses the 3rd card.
Question 2
Percy throws a fair dice until he gets a five.
...
:
20
(a) Work out the probability that Percy gets the five on his first throw.
(b) Find the probability that he has to throw the dice exactly twice to get the five.
(c) Calculate the probability that he will have the throw the dice more than twice to get a five.
Answers
Answer:
Step-by-step explanation:
I'm assuming you have 26 cards each with a different letter on it.
(d) Prob(Not M, Not M , M)
= 25/26 * 25*26 * 1/26
= 625/17576
or 0.036 to nearest thousand
(e) Prob(Not M, Not M, M) without replacement
= 25/26*24/25*/1/24
= 1/26
or 0.038 to nearest thousandth.
2(a)
1/6.
(b)
5/6 * 1/6
= 5/36.
(c)
5/6 * 5/6
= 25/36
can you help me pls it's only 3 question's
Answers
Answer:
1. 0.8 2. 1.25 3. 27.5
Step-by-step explanation:
Number 1 is 4/5
Number 2 is just 5/4
And I think number 3 is 22/4 which is 5.5 then times 5 which is 27.5.
One year a surf board maker had $3.5 million in sales. In later year,
sales y (in millions) increased by about 15% each year. Which function
models the amount of money the maker will have after t years?
Answers
Answer:
I need help with this one
Step-by-step explanation:
Thomas lives more than 0.55 km and less than 0.75 km from his school.
Thomas lives from his school?
A. 0.06 km
B 0.50 km
c. 0.60 km
D. 1.30 km
Which choice could be the distance Thomas lives from his school?
Answers
Which equation describes the function in the table below?
Answers
Answer:
A
Step-by-step explanation:
So, first we have to eliminate answers, let us check A first. If we simplify this equation, it's basically saying Y is equal to 1.3 times X plus 10. So, 0 x 1.3 = 0 plus 10 = 10. Now we check the rest of the table. 5 x 1.3 = 6.5 + 10 = 16.5. 10 x 1.3 + 10 = 23. 15 x 1.3 + 10 = 29.5, and 20 x 1.3 = 26 + 10= 36. The math matches with the table so we're done.
You have 12 gallons of punch. You estimate that each guest will drink 3 cups. Do you have enough punch for 60 guests?
Answers
Answer:i got 1 2 3 4 5 6 7 8 shooters ready to gun you down
Step-by-step explanation:
i will give a crown if you are the first one to answer and if you get it right and if you just get it right then i will i give you a full star rating and a thanks
Answers
Question
( 10 + 5x )7
Lets solve this easily.
So, basically, 10 + 5x is 15 but we still didn't
get rid of the x so therefore it's still 15x and then there's 7 so we multiply 15 x 7 giving us 105x.
Hence, the answer is.
(C), 70 + 35x is the answer.
plz help. I Need help with it
Answers
Answer:
O that easy just flip the sign for example - becomes + becomes-
this is an is simple trick I learn hope it helps you.
Step-by-step explanation:
so k goes to -3 j goes to -2
What is 70000% + 8100000
Answers
Answer:
8100700
Step-by-step explanation:
I used a calculator
Could you pls mark me brainliest I only need one more
Answer:
8100700
hop i helped look at my drawing
Step-by-step explanation:
(this is a practice question)
Answers
Answer:
<GHI = 135 degrees
Step-by-step explanation:
(3x + 12) + (x + 4) = 180
4x + 16 = 180
4x + 16 - 16 = 4x
180 - 16 = 164
4x = 164
4x / 4 = x
164 / 4 = 41
x = 41
3 * 41 + 12
3 * 41 = 123
123 + 12 = 135
What is 6 less than a number t is 7?
Answers
Answer:
t-6=7
Step-by-step explanation:
Answer:
6-t=7
Step-by-step explanation:
Cherry Hill Orchards produced 500 tons of cherries during their first year of business, 2012. Since then, the cherry harvest continues to increase in production by 5.7% over the previous year. Write an exponential function f(x) that models the tons of cherries produced by cherry hill orchards x years after 2012
A. f(x) = 500(1.057)^x
B. f(x) = 50(1.057)^x
C. f(x) = 500(0.057)^x
D. f(x) = 500(1.57)^x
Answers
Answer: A, f(x) = 500(1.057)^x
What is the probability that a data value in a normal distribution is between a
z-score of -0.37 and a z-score of 1.22? Round your answer to the nearest
tenth of a percent.
A. 54.3%
B. 52.3%
C. 51.3%
D. 53.3%
Answers
Answer:
53.3%
Step-by-step explanation:
It's the correct answer that's why
In ΔVWX, w = 680 cm, ∠X=80° and ∠V=32°. Find the area of ΔVWX, to the nearest 10th of a square centimeter
Answers
Answer:
56
Step-by-step explanation:
Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
The area of the triangle.
= 1/2 x base x height
The area of the triangle is 105760 cm².
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
In ΔVWX.
w = 680 cm
∠X=80°
∠V=32°
This means,
∠W + ∠X + ∠V = 180
∠W = 180 - 112
∠W = 68°
This means,
68° = 680
1° = 10
Now,
∠X=80°
x = 800 cm
∠V=32°
v = 320 cm
Now,
V
/ | \
(x) / | \ (w)
/ | \
W M X
(v)
680² = VM² + (320/2)²
462400 = VM² + 25600
VM² = 436800
VM = 661 cm
Thus,
The area of the triangle.
= 1/2 x base x height
= 1/2 x 320 x 661
= 160 x 661
= 105760 cm²
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