Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.)
Vertex:
(−2, −12)
Point:
(0, −4)

As per the given function rule , y = -6x + 1 , the values will be 31, 7, 1, -5 -5 , 1, 1, -6X+1, -17.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is often represented as y = f. (x).

The relationship between the input or domain and the output or range is known as the function rule. If and only if there is a single value in the range for each domain value, a relation is a function.

As per the given function rule in the question i.e y = -6x + 1

X                         Y

-5                         31

-1                          7

0                           1

1                           -5

1                           -5

0                            1

0                            1

X                   -6X +1

3                         -17

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A reflection over a line l  moves every point P  of the plane to the point P ′  on the perpendicular from  P to the line l and on the same distance from l .

If the line is the  x  -axis, a point P  =  ( p 1   p 2 )  moves to the point  P ′  =  ( p 1 , − p 2 ) .

The image of the triangle A B C  is the triangle  A ′ B ′ C ′ with  B ′  =  ( 9 , − 5 )

A positive and a negative co - terminal angle for each given angle is 1) -π/2 and -9π / 2 and 2) 7π / 2 and -π / 2 .

Given :

a positive and a negative co - terminal angle for each given angle

1 )  

= -5π / 2

To find positive and negative co - terminal angle we need to add and subtract by 2π .

= -5π / 2 + 2π

= -5π + 4π / 2

= -π/2

= -5π / 2 - 2π

= -5π - 2 * 2π / 2

= -5π - 4π / 2

= -9π / 2

or =

2 )

= 3π / 2

= 3π / 2 + 2π

= 3π + 2 * 2π / 2

= 3π + 4π / 2

= 7π / 2

= 3π / 2 - 2π

= 3π - 4π / 2

= -π / 2

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Answer:

x = 32

y = 5

Step-by-step explanation:

2y=10

X=6y+2

Put both equations in the same format

x - 6y = 2

Manipulate the equations so that they have a common coefficient

6y = 30

Solve for one coefficient

(x - 6y = 2) + (6y = 30)

x + (-6y + 6y) = 2 + 30

x = 2 + 30

x = 32

Solve for the other coefficient

2y = 10

y = 5

x - 6y = 2

32 - 6y = 2

-6y = 2 - 32

-6y = -30

y = -30/-6

y = 5

Answer:

28p + 14q + 21r

Step-by-step explanation:

7(4p + 2q + 3r) ← multiply each term in the parenthesis by the 7 outside

= 28p + 14q + 21r

Answer:

Option A: y-9=2(x-1)

Step-by-step explanation:

Notice that the answer choices are in point-slope form which is y-y1=m(x-x1)

The slope, m, is (9-3)/(1-(-2))=6/(1+2)=6/3=2, but that's given anyway.

Option A would be right because y1=9 and x1=1 which is where the line crosses through (1,9)

B is not right because that would suggest the line crosses (2,3) as y1=3 and x1=2, but it actually crosses (-2,3) so it should've been y-3=2(x+2)

C and D are wrong because the points aren't crossed through

Answer:

The sum will be close to 1/4

Step-by-step explanation:

1/8+1/6 is 7/24, and 1/4th of that is 6/24, so it is very close.

Answer: The sum will be close to 1/4

Step-by-step explanation:

You can start by making the fractions have the same denominator, (8*6) which gets you 48

You then want to use the butterfly method, so 1/8 becomes 6/48 and 1/6 becomes 8/48. You then add these up to 14/48.

12/48 is 1/4, and 14/48 is close to 12/48, thus making the answer the first option.

she can buy 5 shirts

Step-by-step explanation:

I think the first one.Because if you rotate it it looks like the picture.

the Given

We are asked to find the x-intercept of the linear equation. This can be seen below.

Explanation

To find the x-intercept, we must recall that x-intercept is the point at which the graph of the equation crosses the x-axis. We can find this point by plotting the given equation.

From the graph, we can determine the x-intercept as

Answer: (2,0)

The table can be summarized as follows:

|          | Has a dog | Does not have a dog |

|----------|-----------|---------------------|

| Has a cat     | 2         | 3                   |

| Does not have a cat | 12        | 10                  |

To find the probability that a student chosen randomly from the class has a cat, we need to find the total number of students who have a cat (regardless of whether or not they have a dog), and divide it by the total number of students in the class.

The number of students who have a cat is 2 (those who have a dog and a cat) + 3 (those who have a cat but do not have a dog) = 5.

The total number of students in the class is the sum of all four categories: 2 (has a cat and a dog) + 3 (has a cat, does not have a dog) + 12 (does not have a cat, has a dog) + 10 (does not have a cat, does not have a dog) = 27.

So, the probability that a student chosen randomly from the class has a cat is 5/27.

Answer:

5f + 6g + 12

Step-by-step explanation:

10f - 5f is 5f, you would keep 6g as it is because there are no other numbers to add to it, and 8 + 4 is 12. Hope this helps!! :)

Step-by-step explanation:

I'm thinking of a number, let's call it X, between 0 and 10 (inclusive). If I don't tell you anything else, what would you imagine is the probability that X=0? That X=4? Assuming that I don't have any preference for any particular number, you'd imagine that the probability of each of the eleven integers 0,1,2,…,10 is the same. Since all the probabilities must add up to 1, a logical conclusion is to assign a probability of 1/11 to each of the 11 options, i.e., you'd assume that the probability that X=i is 1/11 for any integer i from 0 to 10, which we write as

Pr(X=i)=111for i=0,1,2,…,10.

Implicit in this description is the assumption that the probability that X is any other number x is zero. (Here we make a distinction between the random number X and the variable x which can stand for any fixed number.) We can write this implicit assumption as

Pr(X=x)=0if x is not one of {0,1,2,…,10}.

What would change if instead I told you that I was thinking of a number X between 0 and 1 (inclusive)? You might assume that I was thinking of either the number 0 or the number 1, and you'd assign a probability 1/2 to both options. Or, you might guess that I had more than two options in mind. There was nothing in what I said that forces you to conclude that I was thinking of an integer. Maybe I was thinking of 1/2, or 1/4, or 7/8. Once you start going down that road, the possibilities are endless. I could be thinking of any fraction between 0 and 1. But who said I was limiting myself to rational numbers? I could even be thinking of irrational numbers like 1/2√ or π/5. If we allow the possibility that the number X could any real number in the interval [0,1], then there are clearly an infinite number of possibilities. (Of course, I could have been thinking of non-integers for the number betwen 0 and 10 as well, but most people would think I was referring to integers in that case.)

Since we don't want to assume that I am favoring any particular number, then we should insist that the probability is the same for each number. In other words, the probability that the random number X is any particular number x∈[0,1] (confused?) should be some constant value; let's use c to denote this probability of any single number. But, now we run into trouble due to the fact that there are an infinite number of possibilities. If each possibility has the same probability c and the probabilities must add up to 1 and there are an infinite number of possibilities, what could the individual probability c possibly be? If c were any finite number greater than zero, once we add up an infinite number of the c's, we must get to infinity, which is definitely larger than the required sum of 1. In order to prevent the sum from blowing up to infinity, we must have c be infinitesimally small, i.e., we must insist that c=0. The probability that I chose any particular number, such as the probability that X equals 1/2, must be equal to zero. We can write this as

Pr(X=x)=0for any real number x.

What went wrong here? We know all probabilities must not be zero, because we know that the total probability must add up to one. In fact, were know that, somehow, there must be something special for the probability of numbers 0≤x≤1. We know that X is somewhere in that interval with probability one, and the probability that X is outside that interval is zero.

The function that grows at the fastest rate for increasing values of x is f(x) = 4×2ˣ.

We can see this by comparing the growth rates of the three functions for larger and larger values of x.

As x gets larger, the exponential function f(x) grows much faster than the other two functions, which are both polynomial functions.

if we plug in x = 10, we get:

f(10) = 4×2¹⁰ = 4×1024 = 4096

h(10) = 9×10² + 25 = 925

g(10) = 15×10 + 6 = 156

As we can see, f(10) is much larger than h(10) and g(10), indicating that f(x) grows at a much faster rate than the other two functions.

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Answer:

The answer is 2000. Hope this helps! If I could have brainliest I'm trying to rank up :)

Step-by-step explanation:

This question asks us to estimate the amount of money Paul gave to Charity.  

To work out an estimate we must start by rounding the numbers we are given to 1 significant figure and the

Starting with 19.95 --> this rounds to 20 and 395 rounds to 400.  

Then we have to multiply these numbers together:

20 x 400 = 8000

3. Finally subtract 6000 from our estimate

8000-6000=2000

The answer is 2000.

The population after 198 years from now will be 2,270,200.

Let a be the initial value and x be the power of the exponent function. Then the exponent is given as,

\(\rm y = 283,900\times (2)^{x/198}\)

The population after 198 years from now will be calculated as,

\(\rm y = 283,900 \times (2)^{198/66}\)

Simplify the equation, then we have

y = 283,900 x 8

y = 2,270,200

The population after 198 years will be 2,270,200.

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Number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7. This can be obtained by assuming the value of number of seats in each row, forming quadratic equation and using quadratic formula to find root.

Here in the question it is given that,

We have to find the number of seats in each row.

Let us assume that the number of seats in each row be x.

From the given statement, number of seats in each row exceeds the number of rows by 7, we can write that,

Number of seats in one row = Number of rows + 7

x = Number of rows + 7

⇒ Number of rows = x - 7

Total number of seats in the auditorium can be written as,

⇒ (Number of seats in one row)(Number of rows) = Total number of seats

(x)(x - 7) = 2244

x² - 7x = 2244

⇒ x² - 7x - 2244 = 0

By using quadratic formula we can find the root,

x = (-b ± √b² - 4ac)/2a

here in the question, a = 1, b = -7, c = -2244

√b² - 4ac = √(-7)² - 4(1)(-2244)

√b² - 4ac = √49 + 8976

√b² - 4ac = √9025

√b² - 4ac = 95

x = (-b ± √b² - 4ac)/2a

x = (7 ± 95)/2

x = 102/2 or x = -88/2

⇒ x  = 51 or x = -44

Hence number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7.

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If the measure of angles ∠DAB = 51° and the value of x is 25. Then the measure of angle ∠CAB will be 25°.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

If the measure of angles ∠DAB = 51°, ∠CAB = x, and ∠DAC = x + 1.

Then the measure of angle ∠CAB will be

We know

∠CAB + ∠CAD = ∠DAB

x + x + 1 = 51

        2x = 50

          x = 25

Then the measure of the angle ∠CAB will be

∠CAB = x

∠CAB = 25

∠CAB = 25°

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The ratio of the volumes of the two similar solids that have a scale factor of 5:3 is: 125:27.

If two solids that are similar to each other, have volumes A and B respectively, and have a scale factor of a:b, thus, the ratio of their volumes would be expressed as:

Volume of solid A/Volume of solid B = a³/b³

or

Volume of solid A : Volume of solid B = a³ : b³

Thus, the given similar solids have a scale factor of 5:3, therefore, the ratio of their volumes would be expressed as shown below:

5³ : 3³

125 : 27

Thus, the ratio of the volumes of the two similar solids that have a scale factor of 5:3 is: 125:27.

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Answer:

\(8.5x+4y=99.5,\ x+y=17\)

Step-by-step explanation:

\(\mathrm{System\ of\ equations:}\\8.5x+4y=99.5\\x+y=17\\\mathrm{where,}\ x\ \mathrm{is\ the\ number\ of\ popcorns\ and\ }y\mathrm{\is\ the\ number\ of\ candies}\)

Answer:

False

Step-by-step explanation:

a^(m/n)=sqrt_{n}a^m

The value of n such that the conditions are met is:

\(n = \frac{2x \pm \sqrt{(-2x) - 4*1*(y + 2)^2} }{2}\)

Where x and y are the coordinates of point P.

We know that:

Now, the distance of P to Q is equal than the distance of P to R, then we have that:

\(\sqrt{(x - 0)^2 + (y - y)^2} = \sqrt{(x - n)^2 + (y + 2)^2} \\\\x^2 = (x - n)^2 + (y + 2)^2\)

So we need to solve this for n.

\(x^2 = x^2 - 2xn + n^2 + y^2 + 4y + 4\\\\0 = -2xn +n^2 + (y + 2)^2\\\\\\0 = n^2 - (2x)*n + (y + 2)^2\)

Notice that this is a quadratic of n, the two solutions of n will be:

\(n = \frac{2x \pm \sqrt{(-2x) - 4*1*(y + 2)^2} }{2}\)

Such that, as you can see, the value of n depends on x and y.

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Answer:

Answer is [A]

Step-by-step explanation:

Arc length = 2πr × (θ/360) where θ is the angle of sector which is p in the question and the radius is still the symbol R

The value of p when q is 2 is 1

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.

This means that has x increases y will decrease and vice versa.

If p is inversely proportional to q , then p = kq

when p = 2, q = 4

2 = k4

k = 2/4

k = 1/2

When q = 2

p = 1/2 × 2

p = 1

Therefore the value of p is 1

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.

A’(-12,18), B’(-6,6), C’(12,-6), D’(12,12)

Answer:

Step-by-step explanation:

Answer:

A^n = [4^n 4^n

0 1]

Step-by-step explanation:

To find the solution for the 2x2 matrix A:

[4 4

0 1] to the nth power = [ ]

We can use matrix multiplication to raise A to the nth power. Let's start with n = 1:

A^1 = [4 4

0 1]

Now, let's solve for A^2 by multiplying A^1 by A:

A^2 = A x A^1

= [4 4 [4 4

0 1] 0 1]

= [16 16

0 1]

Next, let's solve for A^3:

A^3 = A x A^2

= [4 4 [16 16

0 1] 0 1]

= [64 64

0 1]

We can see a pattern emerging:

   A^1 = [4 4

   0 1]

   A^2 = [16 16

   0 1]

   A^3 = [64 64

   0 1]

We can generalize this pattern as follows:

A^n = [4^n 4^n

0 1]

Therefore, the solution for the 2x2 matrix A raised to the nth power is:

A^n = [4^n 4^n

0 1]

Answer:

Step-by-step explanation:

Answer:

yes ,because the average human hight

cannot exceed 7squared feets

Without knowing the dimensions of the box or the size of the person, we cannot determine whether the person can fit inside the box or not.

In mathematics, a box is a three-dimensional shape that has six rectangular faces.

It is also called a rectangular prism.

The faces on opposite sides of a box are congruent and parallel. A box has a height, width, and length, which are usually labeled as h, w, and l.

The volume of a box can be found by multiplying its length, width, and height: V = l × w × h.

We have,

The volume of a box is a measure of the amount of space inside the box, typically measured in cubic units such as cubic feet or cubic meters.

If a box has a volume of 42 cubic feet, it is simply telling us the amount of space inside the box.

Whether a person can fit inside the box or not depends on the size of the box and the size of the person.

Without knowing the dimensions of the box or the size of the person, we cannot determine whether the person can fit inside the box or not.

So,

We need more information to answer this question.

Thus,

Without knowing the dimensions of the box or the size of the person, we cannot determine whether the person can fit inside the box or not.

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