Answer:
All of the them excluding f(x)=-27x+2
The required function is [tex]f(x)=-2x^2+2[/tex]. Hence, option a is correct.
Important information:
The graph of a function passes through the points (0,2), (1,0) and (-1,0).Quadratic function:The graph has two x-intercepts (1,0) and (-1,0). It means it is a quadratic function and [tex](x-1)[/tex] and [tex](x+1)[/tex] are two factors.
[tex]f(x)=a(x-1)(x+1)[/tex]
[tex]f(x)=a(x^2-1)[/tex] ...(i)
The graph passes through the point (0,2). Substitute [tex]x=0,f(x)=2[/tex] in the above function.
[tex]2=a(0^2-1)[/tex]
[tex]2=-a[/tex]
[tex]-2=a[/tex]
Substitute [tex]a=-2[/tex] in (i).
[tex]f(x)=-2(x^2-1)[/tex]
[tex]f(x)=-2x^2+2[/tex]
Therefore, the correct option is a.
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Select all the key features of the graph of the equation.
The key features of the graph of the given equation -8x + 20y = 240 include the following:
D. As x → -∞, y → ∞.
E. The y-intercept is (0, 12).
H. The x-intercept is (-30, 0).
How to determine the key features of this equation?Making y the subject of formula in order to determine the slope, we have:
20y = 8x + 240
Dividing both sides of the equation, we have:
y = 8x/20 + 240/20
y = 8x/20 + 12
Therefore, the slope is equal to 8/20.
What is y-intercept?In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
When x = 0, the y-intercept is given by;
20y = 8(0) + 240
y = 240/20
y = 12.
Therefore, the y-intercept is equal to (0, 12).
When y = 0, the x-intercept is given by;
-8x + 20(0) = 240
x = -240/8
x = -30
Y=(x-3)^2+3
vertex form to standard form
Answer:
y = x² -6x +12
Step-by-step explanation:
You want the quadratic equation Y=(x-3)^2+3 written in standard form.
Standard formDepending on where you go to school, the given equation may already be in standard form.
Other places, standard form means the equation is simplified and terms are written in order of decreasing degree.
y = (x -3)² +3 = (x² -6x +9) +3
y = x² -6x +12
Three friends went to the movies. They shared 4/5 of a candy bar. If they share the bar equally, how much of the candy bar will each person get?
The candy bar will each person get will be 4 / 15.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that three friends went to the movies. They shared 4/5 of a candy bar. If they share the bar equally.
The amount of candy shared by each person will be,
Amount = ( 4 / 5 ) ÷ 3
Amount = 4 / 15
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Can y’all help me?!
Answer:D
Step-by-step explanation:
3 is on the positive x side and 2 is on the negative y side so it will be (3,-2)
Pls help me out here
All of the equations that are true include the following:
B. 56 + 70 = 14(4 + 5).
C. 28 + 49 = 7(4 + 7).
What is the distributive property of multiplication?In Mathematics, the distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.
How to determine the true equation?In order to determine the true equation, we would apply the distributive property of multiplication and then check whether or not the right-hand side is equal to the left-hand side.
By applying the distributive property of multiplication to the given mathematical expression, we have the following:
32 + 96 = 8(4 + 14)
32 + 96 = 32 + 112 (False).
56 + 70 = 14(4 + 5).
56 + 70 = 56 + 70 (True).
28 + 49 = 7(4 + 7).
28 + 49 = 28 + 49 (True).
27 + 36 = 3(9 + 13)
27 + 36 = 27 + 39 (False).
25 + 35 = 5(5 + 6)
25 + 35 = 25 + 30 (False).
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irrational number formula
Answer:
hope it helps.
stay safe healthy and happy.
PLSSSSSSSSSSS HELPPPPPPPPP
Answer:
B and D
Step-by-step explanation:
HELPPPPP! Points scored in a basketball game vary directly with shots taken. If a player scores 50 points , and takes 40 shots , how many would she score if she takes 60 shots? Round your answer down to the nearest points scored
Answer:
Points scored in a basketball game vary directly with shots taken.
This means that this question can be solved
by proportions, using a rule of three.
How many would she have scored if she takes 60 shots?
Using a rule of three:
50 points - 40 shots
x points - 60 shots
Applying cross multiplication:
4x = 50 × 60
Divide from both sides
x = 50 × 1.25 = 75
Answer is 75
Step-by-step explanation:
Here is a easier explanation if you didn't understand clearly:
It asked for how many 60 shots would score.
You would look at the first time he scored which is 50 and took 40 shots. Divide them
50 ÷ 40 = 1.25 or 1.5
So now you know each point scores 1.25 or 1.5
Now you multiply 1.25 or 1.5 with how many shots to see how much was scored and in this case 60 shots.
60 × 1.25 or 60 × 1.5
& They both end up equaling just the same, 75.
Hope it made sense :)
If the probability of an outcome is 2/9, what are the odds against that outcome?
Answer:
7/9
Step-by-step explanation:
If the chances of an outcome are 2/9, the odds against it can be found by subtracting that from 1.
1 - 2/9
= 7/9
So, the odds against that outcome are 7/9
Seven television sets are chosen at random (i.e., without replacement) from a shipment of 240 television sets of which 15 are defective. Calculate the probability that at least 1 of the chosen televisions are defective.
Answer:
7/16
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one ids attached to the event. If it doesn't a value of zero is attached to the event.
Proportion of defective televisions in the shipment = 15/240 = 1/16
Probability that 1 of the 7 chosen is defective = 1/16 x 7 = 7/16
 Please tell me what question 4
Step-by-step explanation:
In my opinion I think the answer for this question is B you don't have to choose it because it might be wrong
Mr. Harmon ordered calculators for his math class to use. He ordered a case of 24 calculators and paid a total
of $199.20.
What is the unit rate per calculator that Mr. Harmon paid?
$4.78
$8.30
$12.05
$17.52
HELP ME PLEASE
-our classmates were asked to decorate /5 or the bulletn boara In a classroom They divided the section to be decorated equally among the 4 classmates. Whe fraction of the entire bulletin board did each classmate decorate? (5.NF.7)
The fraction of the entire bulletin board decorated by each classmate is N/20.
Fraction of a number.Fraction is a mathematical expression which is made up of denominator and a numerator. So that fractions may generally be categorized into 3 types. These are: proper fraction, improper fraction, and mixed fraction.
Considering the given question, let the size of the bulletin board be represented by N.
The section of the bulletin board to be decorated = 1/5 * N
= N/ 5
There are 4 classmates that has been selected to divide the section to be decorated equally among themselves. So.
Fraction of the board to be decorated by each student = (N/ 5)/ 4
= 1/20 N
The fraction of the board to be decorated by each student is N/20.
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Help plz:)))I’ll mark u Brainliest
Answer:
h = 9
Step-by-step explanation:
cylinder A = [tex]\pi[/tex][tex]3^{2}[/tex]*4 = 113.0973355 [tex]m^{3}[/tex]
Cylinder B = 113.0973355 [tex]m^{3}[/tex]
113.0973355 [tex]m^{3}[/tex] = [tex]\pi[/tex][tex]2^{2}[/tex]*h
113.0973355 [tex]m^{3}[/tex] / 4[tex]\pi[/tex] = h
8.999999999998 = h
I think b/c of the rounding error of rounding off pi, that h= 9
Can y’all help me?!
Answer:
4 is next in NUMBER OF DAYS
9 is the first in NUMBER OF TADPOLES
41 is the 2nd answer ON NUMBER OF TADPOLES
Step-by-step explanation:
hope this helps a lot!!
a student states that the exterior angle of a triangle can never be a right angle. find the mistake and correct it
Answer:
FALSE statement
Step-by-step explanation:
a right triangle’s exterior angle is 90 degree
The angle of elevation to the top of a Building in New York is found to be 4 degrees from the ground at a
distance of 1.75 miles from the base of the building. Using this information, find the height of the building.
Round to the nearest whole number.
Your answer is
Submit Question
feet.
The height of the building can be 649.44 ft
What is angle of elevation ?
angle of elevation states that the angle which is formed between line of sight and horizontal line.
Given, the base of the triangle is 1.75 mile. The angle opposite of the tall side, x, is 4 degrees.
height of the building is an unknown variable (x) .
tan(angle) = opposite length /adjacent length.
Opposite length is x, adjacent length is 1.75 mile, angle is 4 degrees.
tan(4º) = x / 1.75
rearrange for x
x = 1.75*tan(4º) = ~1.75*0.0699 miles.
x = ~0.123
Now to get feet, just multiply by 5,280 ft in one mile
Height of the building is 0.123 miles * 5280 ft/mile = 649.44 ft
Hence , The height of the building can be 649.44 ft .
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What is 2/3 plus 1/5 equal
Answer: 13/15
Step-by-step explanation: Hope this helps, please mark brainliest and give thanks!
2/3+1/5
15÷3*2+15÷5*1
10+3/15
13/15
Pls help me ! I rlly need help on this have a great day or night
link below!!!!!!!!!!!
Compare numbers to their opposites based on their positions on a number line. Choose ALL true statements based on these comparisons.
A) −(−7) = 7
B) Zero is its own opposite.
C) −(−10) = −10
D) −14 and 4 are equally distant from 0.
E) −12 and 12 are equally distant from 0.
Answer:
A, B, E
Step-by-step explanation:
I'm not too sure about B, but A and E are definitely true
WILL GIVE BRAINLIEST
Q1) ABCD is a square. A is the point (-2,0) and C is the point (6,4). AC and BD are diagonals of the square, which intersect at M.
a) Find the coordinates of M,B and D.
b) Find the area of ABCD.
9514 1404 393
Answer:
a) M(2,2), B(4, -2), D(0, 6)
b) 40
Step-by-step explanation:
a) The midpoint of AC is the average of the endpoint coordinates.
M = (A +C)/2
M = ((-2, 0) +(6, 4))/2 = (4, 4)/2
M = (2, 2)
There are several ways to find points B and D. One of them is to rotate points A and C 90° about M. The 90° CCW rotation transformation about the origin is ...
(x, y) ⇒ (-y, x)
About the point (2, 2), the transformation would be ...
(x, y) ⇒ (-(y -2)+2, (x -2)+2) = (4 -y, x)
Rotating point A 90° to get point B, we have ...
B = (4 -0, -2)
B = (4, -2)
And rotating C to get point D, we have ...
D = (4 -4, 6)
D = (0, 6)
__
b) The area of the square is half the square of the diagonal. The square of the diagonal can be found using the distance formula ...
d² = AC² = (6-(-2))² +(4 -0)² = 64 +16 = 80
Then the area is ...
area = AC²/2 = 80/2
area = 40 . . . . square units
7. Sarah draws a card from a standard deck, throws the card away, and then draws another card.
Are these events independent or dependent?
Answer:
dependent
Step-by-step explanation:
A family went out to dinner. The cost of their meal was $57.50, before sales tax and tip.
A sales tax of 8% was added.
The family then tipped 18% on the amount after the sales tax was added.
Part A:
What was the amount, rounded to the nearest cent, of just the sales tax?
Part B : What was the total amount the family paid , including tax and tip , rounded to the nearest cent ?
PLEASE HELP
Answer:
I hope I got this answer right
A is 4.60 and B is 8.30
Given that cot 0 =
5
-, find csc 0.
√11
According to the given cosecant function the value of csc 0 is equal to 6/5.
What is the cosecant function?The sine function has a reciprocal called the cosecant function. The cosecant function is the hypotenuse divided by the opposite side, just like the sine function is the opposite side divided by the hypotenuse. The hypotenuse and legs are terms for the two sides that are not at the right angle.
It is given that:
[tex]cot\ 0=\sqrt{\frac{11}{5} }[/tex]
According to trigonometric identity,
[tex]csc^2\ alpha - cot^2\alpha = 1\\csc^2\ 0 -\frac{11}{25} =1\\csc^2\ 0 = \frac{36}{25} \\csc\ 0= \frac{6}{5}[/tex]
Therefore the value of csc 0 is equal to 6/5.
Complete question;
Given that [tex]cot\ 0=\sqrt{\frac{11}{5} }[/tex]
find csc 0.
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In an all boys school, the heights of the student body are normally distributed with a mean of 69 inches and a standard deviation of 2.5 inches. Using the empirical rule, what percentage of the boys are between 61.5 and 76.5 inches tall?
Step-by-step explanation:
plus of yhis number and solve it oksy
Solve on the interval [0, 2pi): 4csc x +6=-2
By solving the interval : [0,2pi] 4 csc x +6=-2 is 7pi/6 , 11pi/6
What are Trigonometric identities?Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence. These are identities that, geometrically speaking, involve certain functions of one or more angles. defining sine and cosine in terms of tangent, cotangent, secant, and cosecant interactions. The sine and cosine formula according to Pythagoras. This trig identity is arguably the most significant.[tex]& 4 \csc x+6=-2 \\[/tex]
[tex]& 4 \csc x=-8 \\[/tex]
Simplifying,
[tex]& \csc x=-2 \\[/tex]
[tex]& \frac{1}{\sin x}=-2 \\[/tex]
[tex]& \sin x=-\frac{1}{2} \\[/tex]
We get,
[tex]& x=\frac{7 \pi}{6}, \frac{11 \pi}{6}[/tex]
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Shane's soccer team played three games in a tournament. Identify the sample
space (the correct list of possible outcomes) for the team's results.
W = win, L = loss
The notation WLL means Shane's team won the first game, lost the second
game, and lost the third game.
A. {WW, WL, LW, LL}
O B. (WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL}
C. {WWWW, WLWL, LLLL}
O D. {WWW, WWL, LLL}
Answer:
B
Step-by-step explanation:
the all posible situations are listed in the sample space
www =won all 3 games
wwl= won first 2 games and lost the last and so on...
Help me out:)i need an answer as soon as possible!!!
PLEASE HELP!!
For the right triangles below, find the values of the side lengths c and b.
Round your answers to the nearest tenth.
Answer:
[tex]c = 3 \tan(60 \degree) \\ c = 5.2 \\ hypotenuse \: of \: first \: triangle : \\ = \frac{ 5.2 }{ \sin(60 \degree) } \\ = 6 \\ \\ \frac{6}{4} = \frac{c}{b} \\ \frac{6}{4} = \frac{5.2}{b} \\ b = \frac{5.2 \times 4}{6} \\ b = 3.5[/tex]
Unitary method A car can cover a distance of 522km on 36litres of disesel. How far can it travel with 14litres,
Answer:
It can cover 203 km with 14 litres.
Step-by-step explanation:
Given that,
A car can cover a distance of 522km on 36litres of diesel.
522 km = 36 litres
1 l = (522/36) km
We need to find how far can it travel with 14 litres.
We can use the unitary method to solve it.
[tex]14\ L=\dfrac{522}{36}\times 14\\\\=203\ km[/tex]
So, it can cover 203 km with 14 litres.