What is the correct standard form of the equation of the parabola? Enter your answer below. Be sure to show each step of your work.
Answers
The equation of parabola is y = -6x² + 24x - 30
Define Parabola
A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side collide. Ideally, a projectile travelling under the pull of gravity will travel along a curve similar to this one.
We know the equation of parabola in vertex form,
y = a(x - h)² + k
And , we know the vertex (h, k) = (2, -5) and a = -6
put these values in given equation,
y = a (x - h)² + k
y = -6(x - 2)² + (-6)
y = -6(x² + 4 - 4x) - 6
y = -6x² - 24 + 24x - 6
y = -6x² + 24x - 30
Hence, the equation of parabola is y = -6x² + 24x - 30
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Related Questions
which of the following transformation carry the given regular polygon onto itself
Answers
The required transformation of the regular polygon to onto itself is a rotation by the angle of 360° around its own center or any point in the plane.
Given that,
To determine which transformation carries the given regular polygon onto itself.
Here,
According to the question as asked.
There are only 2 usual possible ways of transforming a regular polygon that will onto itself as,
(1) A perfect rotation of 360° around its own center.
(2) A rotation of 360° around any point in the space and plane containing the regular polygon.
Thus, the required transformation of the regular polygon to onto itself is a rotation by the angle of 360° around its own center or any point in the plane.
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y varies directly as x. y = 60 when x = 5. Find y when x = 17. Y=
Answers
Answer:
204
Step-by-step explanation:
Hello!
If y varies directly with x, that means y is a result of multiplying a number by x.
When x is 5 and y is 60, x is being multiplied by 12 to get y. That means, the direct variation equation is y = 12x.
Replace 17 with x to find y.
Evaluatey = 12x; x = 17y = 12(17)y = 204The value of y when x is 17 is 204.
what is the equation is x+9<2
Answers
Answer: Look at image
Step-by-step explanation: Look at image
[tex]x+9 < 2[/tex]
Subtract 9 from both sides:
[tex]x+9-9 < 2-9[/tex]
[tex]x < -7[/tex]
(6.18 × 10¯¹) (8.7 x 10²)
Answers
Answer:
(6.18 × 10¯¹)=(0.618) (8.7 x 10²)=(870) so 0.618+870 is 870.618
Step-by-step explanation:
First derivative of f(x) = (5x + 3)^3
Answers
Answer:
f'(x) = 15(5x + 3)²
Step-by-step explanation:
using the chain rule to differentiate
f(x) = g(h(x) , then
f'(x) = g'(x) × h'(x)
f(x) = (5x + 3)³
f'(x) = 3(5x + 3)² × [tex]\frac{d}{dx}[/tex] (5x + 3)
= 3(5x + 3)² × 5
= 15(5x + 3)²
Solve x² - 2x - 23= 0, giving your answers correct to one decimal places
Answers
Answer:
x ≈ - 3.9 , x ≈ 5.9
Step-by-step explanation:
x² - 2x - 23 = 0 ( add 23 to both sides )
x² - 2x = 23
using the method of completing the square
add ( half the coefficient of the x- term)² to both sides
x² + 2(- 1)x + 1 = 23 + 1
(x - 1)² = 24 ( take square root of both sides )
x - 1 = ± [tex]\sqrt{24}[/tex] ( add 1 to both sides )
x = 1 ± [tex]\sqrt{24}[/tex]
then
x = 1 - [tex]\sqrt{24}[/tex] ≈ - 3.9 ( to 1 dec. place )
x = 1 + [tex]\sqrt{24}[/tex] ≈ 5.9 ( to 1 dec. place )
Please help me with this!!
Answers
Answer: 33 in.
Step-by-step explanation: If the triangles are similar, you have to compare the same sides and find the scale. If you rotate the image, you see the 6 is the same side as the 18. A scale of 18:3 is the same as 3:1. Using this, you can see the missing side and 11 are the same, so you multiply the 11 by 3 to gett 33 as the length, and in. as your label.
I hoped this help and if I could get brainliest that would be nice <3
Answer
Step-by-step explanation:
Solve the inequality.
4x + 2 <2
5
x≤ [?]
Enter the number that belongs in the
green box.
Enter
Answers
The solution of the inequality in the variable x <0.
Any monotonically rising function can, by definition, be applied to both sides of an inequality without violating the asymmetry connection (provided that both expressions are in the domain of that function). The inequality relation is flipped when a monotonically decreasing function is applied to both sides of an inequality. In the criteria for the basic inverse and the multiplicative inverse for positive values, a monotonically decaying function is utilized.
The given inequality is
4x + 2 <2
subtracting 2 from both sides
4x+2-2<2-2
or,4x < 0
or, x < 0
If the inequality is strict (a< b, a > b) and the function is strictly monotonic, the inequality remains strict. If only one of the preceding conditions is met, the ensuing imbalance does not exist. Indeed, the rules for addition and multiplicative exponentiation use a monotonically decreasing function.
Hence the solution of the inequality in the variable x <0.
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please help me with this please
Answers
Answer:
Slope-intercept form: y = 9/4x - 53/4
Point-slope form: y + 2 = 9/4(x - 5)
PLEASE HURRY! I'LL GIVE BRAINLIEST
James reads at a constant rate that allows him to read 4 chapters each week. He begins reading a book that has 42 chapters. Which equation models the number of chapters James still has left to read, y, after x days?
y=42-4/7x
y=42-7x
y=42-4x
y=42-7/4x
Answers
Answer:
it is a. hope it helps
Step-by-step i think
There are 60 in one hour.How many minutes are in 1 1/4 hours ?
Answers
Answer:
75
Step-by-step explanation:
Answer: 11/4
Step-by-step explanation:
11/4x60/60=11/4
please help tomorrow is my exam
Answers
The radius of the pond is found to be 17.32m.
What is angle of elevation?
The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.
Given;
Length of the pole above= 30m
Angle of elevation = 60°
From the given information we can draw the diagram as the pole becomes the opposite of the angle of elevation and radius becomes the base.
Therefore,
Opposite / Base = tan 60°
=> base = 30 / √3
=> base = 17.32m
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i neeeeeed help pls 6th grade easy
Answers
The information that is not needed to determine the total bill after tax is is the tax was 7%.
The total bill is $11.
What is the total bill?The total bill paid is the sum of the cost of the meal, tax and the tip paid. The tip and tax would increase in the total amount that is paid by the customers.
Tax is a compulsory amount that is levied by the government on certain goods and services.
Percentage is the fraction of an amount expressed as a number out of hundred. To convert a number from percentage to a number, divide the percentage by 100.
Tax paid = 10% x total bill
$1.10 = 0.1 x b
1.10 = 0.1b
b = 1.10 / 0.1
b = $11
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a. The information that is needed to solve the problem is D. All of this information is needed to solve the problem.
b. The total bill is $117.
What is an expression?It should be noted that an expression shows the relationship between the numbers or the variables
The total bill will be:
Tip = $1.10
Tax = 7%
Tip = 10% of cost:
$10 = 10% × c
0.1c = $10
c = $10/0.1 = $100
Cost = $100
The total bill. = Cost + Tip + Tax
= $100 + $10 + (7% × $100)
= $100 + $10 + $7
= $117
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I can find percentages and values using the 68-95-99.7 rule, z-scores, and the standard normal distribution.only answer please if you know the answer
Answers
Let X be the weight of fish in the lake.
Given that the mean and standard deviation as 20 and 6 respectively,
[tex]\begin{gathered} \mu=20 \\ \sigma=6 \end{gathered}[/tex]Consider the formula,
[tex]z=\frac{x-\mu}{\sigma}[/tex]The proportion of fish weighing less than 15 pounds is calculated as,
[tex]\begin{gathered} P(X<15)=P(z<\frac{15-20}{6}) \\ P(X<15)=P(z<-0.83) \\ P(X<15)=P(z<0)-P(-0.83From the Standard Normal Distribution Table,[tex]\emptyset(-0.83)=0.2967[/tex]Substitute the value,
[tex]\begin{gathered} P(X<15)=0.5-0.2967 \\ P(X<15)=0.2033 \end{gathered}[/tex]Mulyiply by 100 to get the equivalent percent,
[tex]P(X<15)=20.33\text{ percent}[/tex]Thus, 20.33% of fish in the lake will weigh less than 15 pounds.
Yannick bought a bicycle. He paid $194.25, including tax. If the sales tax rate is 5%, how many dollars did Yannick pay for tax?
Answers
Yannick paid $9.25 as sales tax on the bicycle.
Here, we are given that Yannick bought a bicycle and paid $194.25 for it, including tax.
Let the cost of the bicycle without tax be x
We are given that the rate of sales tax is 5%
Thus, the amount of tax on bicycle will be-
5% of x
= (5/100)*x
= 0.05x
Thus, we can form an equation as follows-
x + 0.05x = 194.25
1.05x = 194.25
x = 194.25/ 1.05
x = 185
Thus, the cost of bicycle without tax is 185
Therefore, the tax paid will be-
0.05x
= 0.05*185
= 9.25
Thus, Yannick paid $9.25 as sales tax on the bicycle.
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Based on only the info given and what you see in the picture, which pair(s) of angles and which pair(s) of sides are congruent? DONT SAY ED & AB
Answers
Answer:
EC and CB
DC and AC
Angle DCB and Angle ECA
Step-by-step explanation:
Line EC and Line CB both have the same measure of 32ft.
Line DC and Line AC both have the same measure of 28ft.
The angles are the sum of the same measures.
What is the equation of the line that passes through the point (−2,−6) and has a slope of -1/2
Answers
Angelina bought a 64-ounce can of lemonade mix.She uses 4 ounces of mix for each pitcher of lemonade.How many pitchers of lemonade can Angelina make from the can of mix?
Answers
Answer:She can make 16 pitchers of lemonade
Step-by-step explanation:
1. Divide the amount of ounces needed for one pitcher of lemonade by the amount of ounces she has to get 16 pitchers of lemonade.
what is 220/275 simplified?
Answers
Answer:
4/5, 0.8 decimal form
Step-by-step explanation:
Hope this helps
Marco needs to buy some cat food. At the nearest store, 2 bags of cat food costs $9.50. How much would Marco on 3 bags?
Answers
Answer:
$14.25 for 3 bags
Step-by-step explanation:
First of all, the question is stating that 2 bags of cat food cost $9.50. This means each bag (1 bag) would cost ($4.75) So u would multiply that by 3, which is easy!
consider the matrices. what are the dimensions of the project matrix of two of these matrices
Answers
When multiplying matrices, we have the following rule:
If the first matrix dimensions are 'a' and 'b' (that is, it has 'a' rows and 'b' columns) and the second matrix dimensions are 'c' and 'd', the product is only possible if we have b = c. Also, the resulting matrix dimensions will be 'a' and 'd'.
Knowing that rule, we have that:
[tex]\begin{gathered} A\to3x1 \\ B\to2x2 \\ C\to2x3 \\ D\to2x1 \\ \\ BD=2x2\cdot2x1\to2x1 \\ CA=2x3\cdot3x1\to2x1 \\ BC=2x2\cdot2x3\to2x3 \end{gathered}[/tex]Sipho buys peanuts in bulk at r5 per kg and sells them in 100g packets for r1 each .his aunt owns a packaging business and supplies sipho with free packets for packaging the peanuts .write sipho profit as a. a rate per kg b. a rate per 100g packet c.calculate the percentage profit that sipho makes on his peanuts
Answers
Answer:
the percentage is 100g divided by 5 to get 20
Answer:
Step-by-step explanation: a rate per 100 g packet
PLEASE ANSWER ILL GIVE MY LEFT KIDNEY, MOST BRAINLIEST AND 50 POINTS. plane x and plane y are parallel and plane z intersects plane x. Line ab is in plane x line cd is in plane y and line ef is in plane z. Determine whether each statement is always, sometimes, or never true. Justify your answer.
A) Line AB is skew to Line CD
B) Line AB intersects Line EF
Answers
Line AB is always skew to line CD as the two lines are in different planes.
Line AB will sometimes intersect line EF as the two planes intersect at some point.
We know that a plane represents a 2 dimensional surface in a 3 dimensional area.
A plane is a two-dimensional, flat surface in mathematics that never ends. A plane is a point's (zero dimensions), a line's (one dimensions), and space's (three dimensions) two-dimensional equivalents. A plane may appear as a subspace of a higher-dimensional space, such as the indefinitely long wall of a room, or it may enjoy a separate status in and of itself, such as in the context of two-dimensional Euclidean space.Now it is given that planes x and y are parallel to each other, therefore they will never intersect at any place.
Now two separate lines on these two separate planes will also not intersect with each other as they are on different planes and the ploanes do not meet.
Hence Line AB is always skew to line CD as the two lines are in different planes.
Again for Line AB it will intersect EF as the plane z intersects the plane x on which the line AB is located.
We know that the lines can still be skew lines but there is a possibility that they will meet.
Hence Line AB will sometimes intersect line EF as the two planes intersect at some point.
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Which point lies on the line with a slope of m = ⅔ that passes through the point (-3, -2)?
Answers
Answer:
Step-by-step explanation: you would use point form slope in the equation and plug it in like this
y+2= 2/3(x+3)
y+2=2/3x+2
y= 2/3x
and whatever point goes through this line is your answer
Remember the y-intercept is 0!
A baby weights 7 1/8 pounds at birth. After 4 months the baby weighs 15 2/3 pounds. How much weight did the baby gain
Answers
Answer: = 8.54166666667
Step-by-step explanation:
15 2/3 - 7 1/8
malik is younger than daniel. their ages are consecutive integers. find malik’s age if the product of their ages is 42.
Answers
Answer:
go to gogle
Step-by-step explanation:
The consecutive age is 6 and 7 and Malik is 6 years old.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let their Consecutive age be x, x+1
So, x(x+ 1)= 42
x²+ x - 42 = 0
x² + 7x- 6x - 42=0
x( x+ 7)- 6 ( x+ 7)= 0
(x+ 7)( x-6)= 0
x = 6, -7
Hence, the consecutive age is 6 and 7.
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solve for x.
A) x = 11
B) x = 21
C) x = 17
D) x = 8
Answers
Answer:
A. x = 11
Step-by-step explanation:
so, the angle D corresponds to angle T.
therefore, the side BD corresponds to RT.
and CD to ST.
since both triangles are similar, they must have the same angles, and all corresponding sides and other lengths must have the same scaling factor.
so,
RT × f = BD
and the same f must then apply to
ST × f = CD
21 × f = 98
f = 98/21 = 14/3 = 4.666666666...
33 × 14/3 = 15x - 11
11 × 14 = 15x - 11
154 = 15x - 11
15x = 165
x = 11
Find the average rate of change
Answers
The average rate of change is D. 2.
What is the average rate of change?The average rate of change simply means the measure of how the function will change let unit of time.
In this case, it is important to look at the input and the output that wee given. It can seen that the difference between the output is given as:
13 - 11 = 2
15 - 13 = 2
In this case, the average change is 2.
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At 59°F, crickets chirp at a rate of 76 times per minute, and at 65°F, they chirp-100 times per minute. Whats the input
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We have a relationship between temperature and chirp rate, such that the input in this case is the temperature.
What is the input?
We define a relation as an operator that maps elements from one set (the domain, set of the inputs) into elements of another set (the range, set of the outputs).
Particularly, the relations are written as:
x → y
Where y is the output and x is the input.
In this case, we have two pairs of the relation, these are:
At 59° F, the chirp rate is 76 times per min.At 65° F, the chirp rate is 100 times per min.So we are giving the temperature as the input, and the output is the chirp rate of the crickets at that particular temperature.
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Hello could you please help me with question number 10?
Answers
Exponential Model
Some phenomena can be modeled as an exponential function of the form:
[tex]P=P_o(1+r)^t[/tex]Where Po is the initial value, r is the rate of change, and t is the time.
If the value of P decreases in time (decaying function), then r is negative. If the value of P increases in time (growth), then r is positive.
We know an investment of Po=$4500 has been losing value (decay) at a rate of r = -2.5% = -0.025 each year.
The value of the investment when t = 5 years is:
[tex]P=4500(1-0.025)^5[/tex]Calculating:
[tex]\begin{gathered} P=4500(0.975)^5 \\ P=4500\cdot0.8810957 \\ P=3964.93 \end{gathered}[/tex]The investment will be worth $3964.93 in 5 years
