Find the equation of the parabola with the given x-intercepts and point on the graph. Use y = a(x-p)(x-q).

3. x-int: (-4,0) , (7,0)
P (3,8)

Answer:

15$

Step-by-step explanation:

Answer:

Hence, the value of y = b^2 = (-3/2)^2 = 9/4 is your answer

Step-by-step explanation:

only if your answers are
A) 3/2

B) 9/4

C) 6

D) 9

Answer: y=x+4

Step-by-step explanation:

The formula for slope-intercept form is y=mx+b where

m is the slope and b is the y-intercept.

Formula for working out the slope: y2-y1/x2-x1

Put the values in the equation: 4-3/0-(-1). Answer is 1/1 which is 1.

y-intercept: put one of the x and y values from the graph into the equation y=mx+b. Here, I'm going to choose the point (0,4).

The equation is now 4=1(0) + b

Working out for equation:

4=0+b

4=b

The final equation is y=x+4.

You can also use the graph to help you find the y-intercept! First, look at the y-axis. Then the point that passes it is your y-intercept!(Remember it's the y value not the x)

Answer:

20

Step-by-step explanation:

3-point shots made : 3-point shots attempted = 2 : 5

If the team made 24 points out of 3-point baskets, then since 24/3 = 8, it made 8 3-point baskets.

Proportion:

8 made is to 2 as x attempted is to 5

8/2 = x/5

2x = 40

x = 20

The length and the width of the rectangle are 61 inches and 19 inches, respectively

The mathematical statement from the question is given as

Length of a rectangle is four more than triple its width.

Mathematically, this can be represented as

Length = 3Width + 4

The perimeter is given as

Perimeter = 160 meters

The perimeter is calculated as

Perimeter = 2 x (Length + Width)

So, we have

2 x (3Width + 4 + Width) = 160

Divide by 2

3Width + 4 + Width = 80

This gives

4Width= 76

Divide by 4

Width = 19

Recall that

Length = 3Width + 4

So, we have

Length =  3 * 19 + 4

Evaluate

Length =  61

Hence, the dimensions are 61 inches by 19 inches

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With annual growth rate of 1.2% per year, the projected world population in 2044 is 10.5 billion

The formula for the exponential growth model is:

X(t) = Xo (1 + r)^t

Where:

X(t) = value of X at time t

Xo = initial value

t = time interval

r = growth rate

Parameters given:

Xo = 7 billion = 7 x 10⁹

t = 2044 - 2010 = 34

r = 1.2% = 0.012

Hence,

X(t) =  7 x 10⁹ (1 + 0.012)³⁴

X(t) = 10.5 x 10⁹ = 10.5 billion

Therefore,

The projected world population in 2044 = 10.5 billion

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Answer:

3/5=w

Step-by-step explanation:

the 2 onthe numerator and the 2 on the denominator cancel each other out leaving w byitself.

Answer:

16/5

Step-by-step explanation:

10x3/5=10x w-2/2

Answer:

Step-by-step explanation:

Angles f and g are congruent as opposite sides are congruent. Therefore:

Angles h, 76°, g and the right angle all together form 360°:

0.015 the radius of the balloon changing at the instant the radius is 50cm  

given that

a spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute

radius = 50 centimeters

now we need to find the volume of the balloon

Let V  = volume of the balloon at time t

    r = radius of the balloon at time t

   V = (4/3)πr3

  Given:  dV/dt = 500  

   Find:  dr/dt when r = 50

   dV/dt = (4/3)(3πr^2)(dr/dt)

   500 = 4π(50)^2(dr/dt)  

   dr/dt = 1/(20π)

   dr/dt = 0.015 cm/min

  0.015 the radius of the balloon changing at the instant the radius is   50cm  

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Answer:

The area of the circle would be 113.04

Step-by-step explanation:

If you plug the radius into the formula for finding the area of a circle (π·r²), or (3.14 · r²) then you'll get 113.04

Hope this helps! :D

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The starting term of the function  f(x) = 300 (1.16)^x is 300

This is a type of function that are of 3 main parts

Considering the given problem,  f(x) = 300(1.16)^x

the starting = 300

the base = 1.16

the exponents = x

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so forth.

The base is what determines exponential growth or decay

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If Mr. Fitch applies for the 5-year loan, the amount  he will pay in interest  with the 3-year loan is: $565.24.

First step is to find the cost of replacement left

Cost of replacement  = $4,348 x 6.5%

Cost of replacement =$282.62

Second step is to calculate the amount of  5-year loan

Loan = $282.62 x 5

Loan = $1413.1

Third step is to calculate the amount of the 3-years loan

Loan = $282.62 x 3

Loan = $847.86

Now let find the amount he will pay in interest with the 3-year loan

Amount = $1,413.1- $847.86

Amount =$565.24

Therefore the interest amount is $565.24.

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Answer:

11r+2

Step-by-step explanation:

combine the two numbers with the same variable and then leave the 2 by itself, that would be 4r+7r=11r and then bring the 2 down that makes 11r+2

The value of the x, y, and z for the given system of equations are; x =  -2/3, y = -1/2, and z = 1.

First, let us understand the equation:

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given the system of equations;

3x − 4y + z = 2                ...........equation 1

−9x + 12y − 3z = − 6       ...........equation 2

4x − 2y − z = -16             ...........equation 3

Add equation 1 to equation 3, we will get;

(3x − 4y + z ) + (4x − 2y − z ) =  2 -16

7x - 6y = -14  ...........equation 4

Multiply equation 3 by 3 and subtract from equation 2, we will get;

3(4x − 2y − z) - (−9x + 12y − 3z ) = -48 + 6

12x - 6y - 3z + 9x - 12y + 3z = 42

21x  - 18y = 42   ...........equation 5

Multiply equation 4 by 3 and add it to equation 4, we will get;

3(-3x + 3z) + (9x + 4z) = 5×3 - 2

-9x + 9z + 9x + 4z = 15 -2

13z = 13

z = 1

Put z = 1 in equation 5, we will get;

-3x + 3×1 = 5

-3x + 3 = 5

-3x = 5 - 3

x = -2/3

y = -1/2

Thus, the value of the x, y, and z for the given system of equations are; x =  -2/3, y = -1/2, and z = 1.

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Answer:

the number is 24 good luck :)

Answer:

24

Step-by-step explanation:

1) Break down the question

We are told that a number increased by 6 is 30 meaning a number added to 6 will get 30.

2) Work you way backwards to get your answer

To find the answer to this question we have to subtract 30 from 6.

This is because we are told that a number is added to get 30 so we should subtract to find our number!

3) Check you answer

Every question that you may be unsure of or had been struggling with should always be checked.

To check our answer we have to go backwards and see if the numbers match

As we can see the numbers match together and are correct in our equation

Hope this helps, have a great day!

The Answer is : 64

I took the test and it showed this is the correct answer, hope this helped :)

The money A has is #150 and the money B has is #125.

According to the question,

We have the following information:

Half of A's money plus one-fifth of B's makes #100. Two-thirds of A's money plus two-fifth of B's makes # 150.

So, we will convert these verbal phrases into expression.

Now, let's take the amount of A to be #x and the amount of B to be #y.

x/2 + y/5 = 100

Using the least common factor of 2 and 5:

5x+2y = 1000

5x = 1000-2y ...(1)

2x/3 + 2y/5 = 150

Adding the fractions using the least common multiple of 3 and 5:

(10x+6y)/15 = 150

Using the cross multiplication method:

10x+6y = 2250

Now, putting the value of 5x from equation 1:

2(1000-2y)+6y = 2250

2000-4y+6y = 2250

2y = 2250-2000

2y = 250

y = 250/2

y = #125

Now, putting this value of y in equation 1:

5x = 1000-2y

5x = 1000-2*125

5x = 1000-250

5x = 750

x = 750/5

x = #150

Hence, the money A has is #150 and the money B has is #125.

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Answer:

=================

The slope- intercept form:

Use two points on the graph to find the slope:

Find the slope:

The y-intercept is b = - 4.

The equation is:

Answer:

Step-by-step explanation:

3 * 4 = 12 3 * 5 = 15 List of the First 5 Multiples of 3: 3, 6, 9, 12, 15 Notes: The listed multiples are the First 5 Multiples of 3 that are positive (greater than 0) The sum of the digits in Multiples of 3 are divisible by 3

list <- value, value, value, value

x<-value

FOR EACH item IN the list

{

             IF item=x

                display "found"

}

Pseudocode is an informal manner of programming description that does not require any strict programming language syntax or underlying era concerns. it is used for growing an outline or a rough draft of a program. Pseudocode summarizes an application's flow but excludes underlying info.

Pseudocode is a synthetic and casual language that facilitates programmers' to increase algorithms. Pseudocode is a "text-primarily based totally" element (algorithmic) layout device. The policies of Pseudocode are fairly straightforward. All statements showing "dependency" are to be indented. the Python pseudocode is a syntax-loose representation of code. So, the Python pseudocode no longer involves any code in it. The Python pseudocode should be a very near illustration of algorithmic good judgment.

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Answer:

9l^5n-8l-3<15

Step-by-step explanation:

The standard form of quadratic function is f(x) = 1(x-2)2 - 6

A quadratic function is a two-degree function. A parabola is the graph of a quadratic function. A quadratic function has the general form f(x)=ax2+bx+c, where a, b, and c are real numbers and a0. A quadratic function has the standard form f(x)=a(xh)2+k. The vertex (h,k) has the coordinates h=-b2a,k=f(h)=f(b2a).

Given points (5,3) and (2,-6)

We know that the General form of a quadratic function is

f(x) = ax2+bx+c

Standard form = a(x-h)2 + k

Here point(x,y) = (5,3) and vertex (h,k) = (2,-6)

y =  a(x-h)2 + k

3 = a(5-2)2 – 6

3 = a(3)2 – 6

3 + 6 =9a2

9= 9a2

a2 = 9/9

a2=1

a=1

Now substitute a value in standard form

f(x) = 1(x-2)2 – 6

Therefore the standard form of quadratic function is f(x) = 1(x-2)2 – 6

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For the given data, 1 free download song and cost of each additional download song is $0.59 ,then total downloaded songs in $15.34 including  28 free songs is equal to 54 songs.

As given in the question,

Total free download songs is equal to 28

Let us consider variable 'x' to represent  the number of downloaded songs at the rate of $0.59

Total monthly bill of downloaded songs = $15.34

Equation formed :

0.59x = $15.34

⇒ x = 15.34 / 0.59

⇒ x = 26 songs

Total number of downloaded songs including 28 free songs

= 26 + 28

= 54 songs

Therefore, for the given data, 1 free download song and cost of each additional download song is $0.59 ,then total downloaded songs in $15.34 including  28 free songs is equal to 54 songs.

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According to the the concept of hypothesis testing, there is no evidence that the proportion of Americans who are afraid to fly has decreased.

Hypothesis testing:

Basically, in math hypothesis, it test the population on the basis of the sample data taken from the population using a simple random sampling.

Given,

According to a study conducted by an​ organization, the proportion of Americans who were afraid to fly in 2006 was 0. 10. A random sample of 1300  Americans results in 117 indicating that they are afraid to fly.

Now, we need to explain why this is not necessarily evidence that the proportion of Americans who are afraid to fly has.

While we looking into the given question,

Sample size, n = 1300

Number of Americans who were afraid to fly, x = 117

Now, we have to computing the sample proportion of Americans who afraid to fly,

Therefore, p = 117 / 1300 = 0.09

Then the Formulation of Hypotheses is written as,

Here the Null Hypothesis: H0: p≥0.10

And the alternative Hypothesis: Ha: p<0.10

Then the Left-tailed test of Test statistic is written as,

Here Let us assume that the level of significance, α = 0.05.

Then the Critical value, z≈−1.645

And the Decision rule is written as

If the value of  |z|<|z0.05|≈1.645: Do not reject the null hypothesis.

Otherwise If value of  |z|≥|z0.05|≈1.645: Reject the null hypothesis.

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Answer:

B, or y - 1 = 1/2(x + 2)

Step-by-step explanation:

when you solve B, you get y = 1/2x + 2, which is the equation being shown on the graph.

We have that the data is: (x₁ =–9.3, y₁=3) and (x₂=– 9.3, y₂=–7.5). The formula to calculate two distance between two points is:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(x_1-x_2)^2+(y_1-Y_2)^2 } } \end{gathered}$}}[/tex]

When we calculate the distance between two points, we solve what goes inside the parentheses, then it is calculated to the power of 2, and we continue adding the two numbers of the previous results, and finally the square root is calculated.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(-9.3-(-9.3))^2+(-7.5-3)^2 } } \end{gathered}$}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(0)^2+(-10.5)^2 } } \end{gathered}$}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{0+110.25 } } \end{gathered}$}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{110.25 } } \end{gathered}$}}[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=10.5 } \end{gathered}$}}}[/tex]

Using the z test the value of z is -0.9404 and  the value of z the research team should 0 - retain the null hypothesis.

In the given question,

They randomly selects a sample of 12 people, and with their permission, provides them a treatment.

So n = 12

The mean for their sample is 99.

x = 99

The mean for the population is 102.

μ=102

A standard deviation of 11.

σ = 11

Test statistic z:

z = (x-μ)/σ /√n

Now putting the value

z = 99-102/11/√12

z=-3/11/3.45

z=-3/3.19

z= -0.9404

Test statistic z = -0.9404

From the value of z the research team should 0 - retain the null hypothesis.

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The range of the given function, using it's concept, is given by the following option.

y≤3: y is less than or equal to 3.

The range of a function is the set that is composed by all the output values on a function.

Om the graph of a function, we have that:

Hence from the graph, the range of the function is given by the values of y of the function.

From the graph of the function given at the end of the answer, the function assumes values of 3 and greater, hence the first option is the correct option giving the range of the function.

The function is given by the image presented at the end of the answer.

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