Answers
Remember the shortcut way for graphing quadratic equations
A quadratic function has graph as parabolaHence on both sides of vertex the parabola is symmetric and axis of symmetry is vertex x values .y on both sides for -x and +x is same#1
y=2(x-3)²-1Vertex
(h,k)=(3,-1)As a is positive parabola facing upwards
Find y for same x distance from vertex
I took 3-1=2 and 3+1=4
f(2)=2(2-3)²-1=2(-1)²-1=2-1=1f(4)=2(4-3)²-1=1Now plot vertex and these two points (2,1) and (4,1) on graph then draw a parabola by freehand
#2
y=(x-2)(x+4)y=x²+4x-2x-8y=x²+2x-8Convert to vertex form
y=x²+2x+1-9y=(x+1)²-9Vertex at (-1,-9)
Same take two equidistant x values
Let's take -1-1=-2 and -1+1 =0
f(-2)=(-2+1)²-9=1-9=-8f(0)=(1)²-9=-8Put (-1,-9),(-2,-8),(0,-8) on graph and draw a freehand parabola
#3.
Yes it can be verified by finding the coordinate theoretically on putting them on function then can be verified through putting them on graph whether they matches or not
Related Questions
Please help will give brainlist and 30 points
Answers
Answer:
1156
Area = base times height
Area = (36-1-1) times (45-10-1)
=1156
How do I solve and find x?
Answers
Answer:
x = 76.5
Step-by-step explanation:
[tex]\frac{x}{4.5}[/tex] = 22 - 5
[tex]\frac{x}{4.5}[/tex] = 17
x = 17 x 4.5
x = 76.5
what is the equation of the function y=3/x translated 4 units up and three units to the left
Answers
Using translation concepts, it is found that the equation of the function after the changes is given by:
[tex]y = \frac{3}{x + 3} + 4[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent function is given by:
[tex]y = \frac{3}{x}[/tex]
Then, these following changes happened:
Shift left of 3 units, which means that x -> x + 3.Shift up of 4 units, which means that y -> y + 4.Hence, the equation of the function after the changes is given by:
[tex]y = \frac{3}{x + 3} + 4[/tex]
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HELP PLEASE HURRY!!
g(x)
3
f(x) = 4x + 5
-32
#12
Which function has the greatest y-intercept?
3/
h(x)=3 sin(2x + 1)-2
Answers
I’m pretty sure
Write a quadratic function with zeroes 6 and 7
Answers
Answer:
f(x) = x² - 13x + 42
Step-by-step explanation:
given zeros are x = 6 and x = 7 then the corresponding factors are
(x - 6) and (x - 7)
the quadratic function is then the product of the factors , that is
f(x) = (x - 6)(x - 7) ← expand using FOIL
= x² - 13x + 42
Identify the errors made in finding the inverse of
y = x2 + 12x.
An image shows a student's work. Line 1 is x = y squared + 12 x. Line 2 is y squared = x minus 12 x. Line 3 is y squared = negative 11 x. Line 4 is y = StartRoot negative 11 x EndRoot, for x greater-than-or-equal 0.
Describe the three errors.
Answers
The errors made by the student are:
The variables y and x are not properly swappedThe square root should include the ± signThe domain of the function is incorrectHow to identify the errors?The equation is given as:
[tex]y = x^2 + 12x[/tex]
The first step of the student is given as:
[tex]x = y^2 + 12x[/tex]
This is incorrect because the variables x and y must be completely swapped.
So, the actual step is [tex]x = y^2 + 12y[/tex]
The second step is given as:
[tex]y^2 = x - 12x[/tex]
The third step is given as:
[tex]y^2 = - 11x[/tex]
The last step is given as:
[tex]y = \sqrt{-11x}[/tex] for [tex]x \ge 0[/tex]
This is incorrect because [tex]y = \sqrt{-11x}[/tex] would have complex solution for [tex]x \ge 0[/tex] and the square root needs to have a ±
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C. If f(4x+5)=12x+18 then find f¹(x).
Answers
If f¹ is supposed to say f⁻¹ : rewrite f(4x + 5) as an "obvious" function of 4x + 5, then replace 4x + 5 with x. By "obvious", I mean make it clear how 4x + 5 is the argument to f.
[tex]f(4x+5) = 12x+18 = 3 (4x + 6) = 3 (4x + 5 + 1) = 3 (4x + 5) + 3[/tex]
Then swapping out 4x + 5 for x gives
[tex]f(x) = 3x + 3[/tex]
The inverse of f(x), if it exists, is a function f⁻¹(x) such that
[tex]f\left(f^{-1}(x)\right) = x[/tex]
Evaluate f at f⁻¹ and solve for f⁻¹ :
[tex]f\left(f^{-1}(x)\right) = 3 f^{-1}(x) + 3 = x \implies \boxed{f^{-1}(x) = \dfrac{x-3}3}[/tex]
If f¹ instead means f' (as in the first derivative of f) : earlier we found f(x) = 3x + 3, and differentiating this is trivial.
[tex]f(x) = 3x+3 \implies f'(x) = 3[/tex]
Daniel used the formula to find the area of the following special trapezoid. His work is shown. Identify his error and correct it to find the area of the special trapezoid.
Answers
Daniel made an error in line 3. He wrongly divided the sum of sides and height. The area of the trapezoid is 42 cm².
What is the area of the trapezoid?A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides.
Area of a trapezoid = 1/2 x (sum of the lengths of the parallel sides) x height
Line 1: A = 1/2 x (6) + (7 + 7) Line 2: A = 1/2 (6) (14) Line 3 : 3 x 14 Line 4 : A = 42 cm²To learn more about trapezoids, please check: https://brainly.com/question/25748893
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the ratio of the measures of the three angles in a triangle is 9:3:6.
find the measures of the largest angle.
Answers
Step-by-step explanation:
this is how you solve it :)
The thousand islands are located along the border between new york and canada. the adventure club wants to place a stone marker on 684 of the islands. the club has 36 members. if every club member goes to the same number of islands, how many islands will each member have to visit? a. 720 islands b. 648 islands c. 19 islands d. 24,624 islands
Answers
Using proportions, it is found that the number of islands that each member will have to visit is given by:
c. 19 islands.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, there are 684 islands, and 36 members, hence the number of islands per member is given by:
n = 684/36 = 19.
Which means that option c is correct.
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John and Elijah are both driving from New York City to Richmond. John leaves
at 7:20 and averages 60 mph (miles per hour) on the way. Elijah leaves at 7:30
and averages 62 mph on the way. The situation is modeled by this system,
where x is the number of hours after Elijah leaves and y is the distance each
will travel.
y = 60x+10
y = 62x
How long after Elijah leaves will he pass John, and how far will they each
have traveled?
OA. Elijah will pass John after 4 hours, and they each will have traveled
248 miles.
OB. Elijah will not pass John, because he will never catch up with him.
C. Elijah will pass John after 5 hours, and they each will have traveled
310 miles.
D. Elijah will pass John after 2 hours, and they each will have traveled
128 miles.
2
5-
Answers
Elijah will pass John after 5 hours, and they each will have traveled 310 miles. Then the correct option is C.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
John and Elijah are both driving from New York City to Richmond.
John leaves at 7:20 and averages 60 mph (miles per hour) on the way.
Elijah leaves at 7:30 and averages 62 mph on the way.
The situation is modeled by this system, where x is the number of hours after Elijah leaves and y is the distance each will travel.
y = 60x + 10 ...1
y = 62x ...2
The time is taken by Elijah to cross John will be
62x = 60x + 10
2x = 10
x = 5 hours
The distance traveled in 5 hours will be
y = 62 (5)
y = 310 miles
Elijah will pass John after 5 hours, and they each will have traveled 310 miles.
Then the correct option is C.
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Answer:
c
Step-by-step explanation:
i took the quiz
You buy 100 file folders for 7.72. how much are you paying for each file folder?
Answers
Each folder would cost 0.0772.
What is Rate?Rate is used to express the change in a quantity with respect to a standard quantity.
Analysis:
If 100 file folders cost 7.72, then each folder will cost 7.72/100 = 0.0772
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Answer: 0.8 or whatever has 8 last since i forgot sorry!, but it was correct for me!
Step-by-step explanation:
I dont know if its right for you but its right for me
factor completely 4a^3b^5-18a^2b^3+8a^3b^3
Answers
The factored expression of the expression 4a^3b^5 - 18a^2b^3 + 8a^3b^3 is 2a^2b^3(2ab^3 - 9 + 4a)
How to factor the expression?The expression is give as:
4a^3b^5 - 18a^2b^3 + 8a^3b^3
Factor out 2
2(2a^3b^5 - 9a^2b^3 + 4a^3b^3)
Factor out a^2b^3
2a^2b^3(2ab^3 - 9 + 4a)
Hence, the factored expression of the expression 4a^3b^5 - 18a^2b^3 + 8a^3b^3 is 2a^2b^3(2ab^3 - 9 + 4a)
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pls answer, will mark brainliest
Answers
Answer:5200-0.0005x=2800+0.0003x
Step-by-step explanation: Ignore the supply and demand stuff. Just focus on what value of x will make the two equations equal, which is all the question is asking.
5200-0.0005x=2800+0.0003x
solve for x
This is now a very simple one variable equation, try to solve this yourself and message me if you still need help.
Evaluate P(4, 2)
O 24
O 12
06
Answers
Hope i helped!! :)
elect the correct answer. graph A graph B graph C graph D A credit card company uses these rules to calculate the minimum amount owed: For a bill of less than $100, the entire amount is due. For a bill of at least $100 but less than $500, the minimum due is $100. For a bill of at least $500 but less than $1,000, the minimum due is $300. For a bill of $1,000 or more, the minimum due is $500. Which graph shows the minimum amount due for a credit amount of x (given that the credit limit is $2,000). A. graph A B. graph B C. graph C D. graph D
Answers
The graph that correctly shows the minimum amount due for a credit amount (x) is graph B.
How to determine the graph with the minimum amount due?First of all, we would assign a variable to the different amount of money as follows:
Let x be the credit amount.Let y be the minimum amount due.Translating the word problem into an algebraic expression, we have;
For a bill of less than $100, the entire amount is due:
0 ≤ x < $100, therefore, y = x
For a bill of at least $100 but less than $500, the minimum due is $100: $100 ≤ x < $500, therefore, y = 100
For a bill of at least $500 but less than $1,000, the minimum due is $300:
$500 ≤ x < $1000, therefore, y = $300
For a bill of $1,000 or more, the minimum due is $500:
Since the credit limit is equal to $2000, we have $1000 ≤ x < $2000 and y = $500
In conclusion, the graph that correctly shows the minimum amount due for a credit amount (x) is graph B.
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A basketball trophy is 1.5 feet tall and casts a 2 foot shadow.
if a basketball hoop casts a 16 foot shadow, how tall is the hoop
Answers
Answer:
12 feet
Step-by-step explanation:
Given that the trophy is 1.5 feet tall which casts a 2 feet shadow and the basketball hoop casts a 16 feet shadow, we can identify the height of the basketball hoop by doing (16÷2)×1.5= 12 feet
Hope this helps with your work
If x and y are adjacent angles, then x and y are ______ acute.
answer choices - always, sometimes, or never.
Answers
Answer:
sometimes
Step-by-step explanation:
adjacent angles are two angles that share a vertex, common side/ray between them, and do not overlap.
only supplementary adjacent angles always add up to 180 degrees,
both x or y could be any angle, as long as they're sharing a common side and vertex.
Please help!!! will mark brainliest!!!!!!
Answers
The compound interest will be equal to $13.57.
What is compound interest?The interest on a loan or deposit that accrues on both the initial principal and the accumulated interest from prior periods is known as compound interest.
The compound interest will be calculated by:-
[tex]CI = P(1+\dfrac{r}{12})^{12t}-P[/tex]
[tex]CI = 250(1+\dfrac{0.053}{12})^{12}-250[/tex]
CI = $13.57
Therefore the compound interest will be equal to $13.57.
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y is inversely proportional to x when x =3, y = 8 work out the value of y when x = 8
Answers
y is inversely proportional to x: yx = k, such k is constant
Did you know?
Inversely proportional is also known as inverse variation.Given:
x = 3y = 8To determine the constant of variation, substitute the first two given values to the equation of variation.
yx = k(8)(3) = k24 = kTo determine the value of y, substitute the second given value of x including the constant of variation.
x = 8, y = ?yx = 248y = 24y = 24/8y = 3Answer:
The value of y is 3.Wxndy~~
If the assessment rate is 46% and the tax rate is $37.84 per $1,000 of assessed value, the property tax on a house with a market value of $170,000 is
Answers
The property tax on a house with a market value of $170,000 is $2,959.09.
What is property tax?Property tax is a tax levied on the assessed value of property owned by an individual or a corporation.
Data and Calculations:Assessment rate = 46%
Tax rate = $37.84 per $1,000
Market value of house = $170,000
Assessed value = $78,200 ($170,000 x 46%)
Property tax = $2,959.09 ($78,200 x $37.84/$1,000)
Thus, the property tax on a house with a market value of $170,000 is $2,959.09.
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Please help me on this.
Answers
Answer: B; 4
Explanation: The squares means that's how many numbers there are.
The example : -- There's 4 of 4. = 16. 6 of 2. = 12.
All of them add up to 64.
There are 16 numbers.
The mean means adding up all the numbers then divide by how many numbers are there.
64 / 16 = 4.
Whats 2 plus 0 bc I can't figure it out ......
Answers
Answer:
this is the hardest one yet gee
Step-by-step explanation:
2 + O = 2
If P(x)=6+9x−5x^2 represents the profit in selling x thousand Boombotix speakers, how many speakers should be sold to maximize profit?
Answers
The number of speakers that should be sold to maximize profit is 0.9
Vertex of a quadratic equationGiven the function that represents the profit made in selling x thousand Boombotix speakers expressed as:
P(x)=6+9x−5x^2
In order to maximize the profit, p'(x) = 0, hence;
P'(x) =9 - 10x
0 = 9 - 10x
x = 9/10
Hence the number of speakers that should be sold to maximize profit is 0.9
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please answer this question!
Answers
A bag of paper clips contains:
. 9 pink paper clips
• 7 yellow paper clips
• 5 green paper clips
• 4 blue paper clips
A random paper clip is drawn from the bag and replaced 50 times. What is a
reasonable prediction for the number of times a yellow paper clip will be
drawn?
Answers
Answer:
14 times
Step-by-step explanation: add all colors up for total which is 25
since 7 out of the 25 total paper clips are yellow you would have a 7/25 chance of getting yellow after 1 pick.
since you pick and replace 50 times do (7/25) X 50 which gives you 14 times yellow will be drawn.
Step-by-step explanation: add all colors
up for total which is 25
since 7 out of the 25 total paper clips are
yellow you would have a 7/25 chance of
getting yellow after 1 pick.
since you pick and replace 50 times do
(7/25) × 50 which gives you 14 times
yellow will be drawn.
PLEASE HELP URGENTLY! RIGHT ANSWERS ONLY!
Answers
Answer:
Hi! The answer is B!
I would suggest using a graphing calculator to compare all the lines. You can use this free one called Desmos, sorry i was not able to attach a link :)
Which of the following is a point on the plane curve defined by the parametric equations?
x=3t
y=18t^2+12t+2
The ANSWER is (-1,0) ---- PLEASE EXPLAIN!!! THANK YOU x1000000!!!
Answers
By eliminating the parameter t and evaluating the function at x = -1 we conclude that the parametric equations contains the point (x, y) = (-1, 0).
How to determine that point belongs to a set of parametric functions
In this case we must determine if a point in rectangular format belongs to a set formed by two parametric functions. The functions are parametric as they are based in a parameter t. A quick approach consist in reduce the number of equations by eliminating the parameter.
The first equation is represented below:
t = x/3
And the parameter is substituted in the second equation:
y = 18 · (x/3)² + 12 · (x/3) + 2
y = 2 · x² + 4 · x + 2
If we know that x = -1, then the y-value is:
y = 2 · (- 1)² + 4 · (- 1) + 2
y = 0
By eliminating the parameter t and evaluating the function at x = -1 we conclude that the parametric equations contains the point (x, y) = (-1, 0).
Remark
The statement is incomplete, the complete definition is presented below:
Which of the following is a point on the plane curve defined by the parametric equations?
x = 3 · t, y = 18 · t² + 12 · t + 2
A. (-1, 0)
B. (-3, -28)
C. (-1, 8)
D. (-3, 128)
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The formula for density is given by p equals startfraction m over v endfraction, where p is density, m is mass and v is volume. if a substance has a mass of 27.82 grams and a volume of 3.6 ml, what is the most accurate density of the substance in g/ml? 7.7 7.7278 7.73 0.1
Answers
Answer:
it is 7.73
Step-by-step explanation:
Get smarter
Do subtraction
Answer:
The Answer is 7.73
Step-by-step explanation:
do some basic math lol
Please help quickly! and Correctly. :)
There are 30 homes in Neighborhood A. Each year, the number of homes increases by 20%. Just down the road, Neighborhood B has 45 homes. Each year, 3 new homes are built in Neighborhood B.
Part A: Write functions to represent the number of homes in Neighborhood A and Neighborhood B throughout the years. (4 points)
Part B: How many homes does Neighborhood A have after 5 years? How many does Neighborhood B have after the same number of years? (2 points)
Part C: After approximately how many years is the number of homes in Neighborhood A and Neighborhood B the same? Justify your answer mathematically. (4 points)
(10 points)
Answers
Answer:
We know that:
Neighbourhood A = 30 homes and the number increases by 20% each year
Neighbourhood B = 45 homes, and each year 3 new homes are built.
A.
Neighbourhood A and B are as follows:
For neighbourhood A: f(x) =
For neighbourhood B: f(x) = 45 + 3x
B.
Over five years:
Neighbourhood A has =
Neighbourhood A =
Neighbourhood A = 74.65 homes
Neighbourhood B: = 45 + 3(5)
Neighbourhood B: = 45 + 15
Neighbourhood B: = 60 homes
C.
To determine how many years the number of homes are the same for neighbourhood A and B, we need to equate both together.
So x= 3.3
so, hence after 3.3 years, the number of homes will be the same.
Step-by-step explanation:
Hope this helped, good luck