Create the quadratic function that contains the points (0,2), (1,0), and (3,10). Show all of your work for full credit.

Answers

Answer 1

Answer:

y=7/3x²-13/3x+2

Step-by-step explanation:

Determine the value of c:

y=ax²+bx+c

2=a(0)²+b(0)+c

2=c

Substitute (1,0) into the quadratic and create an equation with a and b:

y=ax²+bx+2

0=a(1)²+b(1)+2

0=a+b+2

-2=a+b

Do the same with (3,10) to get a second equation:

y=ax²+bx+2

10=a(3)²+b(3)+2

10=9a+3b+2

8=9a+3b

Set the two equations equal to each other and solve for a and b:

-2=a+b

8=9a+3b

Multiply first equation by 3 and eliminate b to find a:

 -6=3a+3b

- (8=9a+3b)

_______

-14=-6a

14/6=a

7/3=a

Substitute 7/3=a into the first equation:

-2=7/3+b

-2-(7/3)=b

-13/3=b

Final equation:

y=7/3x²-13/3x+2

See the graph for a visual representation

Create The Quadratic Function That Contains The Points (0,2), (1,0), And (3,10). Show All Of Your Work

Related Questions

An equation is shown. What values of x makes the equation true?
5x + 3x = 5x + 15/2

Answers

Step-by-step explanation:

1) Add 5x and 3x.

Now you have 8x = 5x + 15/2

2) Subtract 5x from the right side of the equation.

(You also do this to the left side)

Now you have 3x = 15/2

3) Now we want the value of x not 2 or 3x, so we will need to divide 3x by 3 to get the value of x.

3x/3 = 15/2 /2 (If the fraction divided by 3 looks confusing you can convert it into a decimal)

So you would have 3x/3 = 7.5/2

3x/3 = x

7.5/3 = 2.5

x = 2.5

Hope this helps !

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[tex]\sqrt{18}+\sqrt{50}[/tex]

Answers

[tex]3\sqrt{2} +5\sqrt2}\\=8\sqrt{2}[/tex]

Answer:

8√2

Step-by-step explanation:

Both 18 and 50 are easily factorable, the first as 2*9 and the second as 2*25.  Taking the square root of 18 results in 3√2 and that of 50 in 5√2/

Thus, the original problem √18 + √50 simplifies to (3 + 5)√2, or 8√2

Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42

Answers

From the equation, the value of x is 13

What is a Square Number?

When an integer is multiplied by the same integer, the resultant number is known as a square number. Simply put, a square number is a number that is obtained by the product of two same numbers but in this case, it is an equation, so the equation in the bracket multiplies itself.

Properties of Square NumbersSquare numbers always end with the digits 0, 1, 4, 5, 6, and 9. The number of zeros at the end of a square number is always even. This means if a number has an odd number of zeros at the end, then the number is not a square number. The square of even numbers is always even, and the square of odd numbers is always odd

(x – 7)² = 36

Raising both sides by 1/2

x-7 = √36

x - 7 = 6

x = 6+7

x = 13

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please give a step by step explanation for this question

Answers

Answer:

[tex]108\pi[/tex] or approx. [tex]339.3 m^{2}[/tex]

Step-by-step explanation:

The question asks us to find the total surface area of the given hemisphere. The question gave us the formula for total surface area of a sphere, [tex]SA_{tot} =4\pi r^2[/tex]. But we need it for a hemisphere, so multiply the equation by [tex]\frac{1}{2}[/tex].

[tex]SA} = (\frac{1}{2}) 4\pi r^2[/tex] => [tex]SA} =2\pi r^{2}[/tex]

We also need the area of the base, which is circle. [tex]A_{circle}=\pi r^{2}[/tex].

Now add these equations together to get our equation.

[tex]SA_{tot} =2\pi r^2 +\pi r^{2}[/tex] => [tex]SA_{tot} =3\pi r^2[/tex]

Now we have the proper equation for total surface area of a hemisphere, [tex]SA_{tot} =3\pi r^{2}[/tex]. Plug in the value of [tex]r[/tex] which is given in the problem, [tex]r=6m[/tex].

=> [tex]SA_{tot} =3\pi (6)^{2}[/tex] => [tex]SA_{tot} =3\pi (36)[/tex] => [tex]SA_{tot} =108\pi m^{2}[/tex] or approx. [tex]339.3 m^{2}[/tex]

SOMEONE HELP ME I DONT UNDERSTAND THIS

Answers

Answer:

Pretty sure there's 90 tens.

The answer is 90 tens because:

9 hundreds means 900 so they are asking you how many tens will it take to make 900 so the answer 90 tens. To see if I am correct multiply 90 time 10 and you should get 900. If helped mark me the brainiest!!

PAST DUE HOMEWORK! NEED HELP QUICK!!

Answers

Answer:

d = 46.15

A = 1672.76

Hope this helps!

Answer:

Diameter = 46.18 inches

Area = 1,674.09 square inches

Step-by-step explanation:

Circumference = pi x diameter

145 = 3.14d

divide both sides by 3.14

d = 46.1783 inches

------------------------

radius = 1/2 x diameter

r = 23.09

Area = (pi)(r)^2

A = (3.14)(23.09)(23.09)

A = 1,674.09 square inches

Please read photo! Thanks for anyone that helps.

Answers

Answer:

1= 66

2= 66

3 = 114

Step-by-step explanation:

Plsss help ASAP!!!! I need to finish this now!!

Answers

Answer:

your answer code would end up being 9862

composite numbers are: 40,42,44,45,46,48,49,50

4's are gone: 0,2,5,6,8,9,50

repeat are gone: 2,6,8,9

greatest to least: 9,8,6,2

Ms. Sack earns $125 teaching five workout classes at Orange Theory. If she gets a 10% raise, how much will Ms. Sack earn per class after the raise?

Answers

125•0.10 = 12.5 125+12.5= 137.5 this basically means that you take 10 percent of what’s shes earning which would be $12.50, and add that on to her original salary ($125) so the answer is $137.5

47.3 , 48.1 ,47.4 ,47.16 , 47.07 least to greatest,please help(,:

Answers

Answer:

47.07, 47.16, 47.3, 47.4, 48.1

Step-by-step explanation:

lol

What is the formula to find the side?

Answers

The formula to find the side of a geometric shape depends on the shape itself. Few details like area or perimeter of a shape or surface area or volume of a solid with few other parameters should be known.

Few examples :

For a square, the formula to find the side (s) is:

s = √(A)

where A is the area of the square.

For a rectangle, the formula to find the length (l) and width (w) are:

l = A/w and w = A/l

where A is the area of the rectangle.

For a triangle, the formula to find the base (b) and height (h) are:

A = (b*h)/2

where A is the area of the triangle.

For a cube, the formula to find the side (s) is:

V = s^3

where V is the volume of the cube.

Keep in mind that these are a few examples of formulas that can be used to find the side of a geometric shape. Depending on the specific problem, different formulas may be required.

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Given f(x) = 3x - 5.
What is fl-4)?

Answers

Answer:

f(4)=7

Step-by-step explanation:

f(x)=3x-5

f(4)=3(4)-5

f(4)=12-5

f(4)=7

If this helps please mark as brainliest

f (4)=7 have a nice day !

The perimeter of a rectangle is 84 feet long. The
length is six more than two times its width. What are
the dimensions of the rectangle? (Hint: P = 2L + 2W)

Answers

Therefore , the solution of the given problem of perimeter comes out to be length = 16.8 and width = 50.4

Establish a perimeter.

The perimeter, or total length, of a shape is referred to as its perimeter in geometry. A shape's perimeter is calculated by summing the lengths of all of its sides and edges. By adding together the lengths of all a shape's sides, one may determine its perimeter.  The circumference of a field, for instance, will be 78 yards for a rectangle with dimensions of 24 yards long by 15 yards wide.

Here,

Given :

Perimeter of rectangle = 84 feet

Thus,

Length is 6 times more than its 2 time width

=> 6L = 2W

=> W = 3L

In the perimeter formula:

=> 3L + 2L =84

=> 5L = 84

=>L = 84/5

=>16.8

and

W = 3L

=> W = 3*16.8

=> W = 50.4

Therefore , the solution of the given problem of perimeter comes out to be length = 16.8 and width = 50.4

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What’s the formula to find principal please tell me please

Answers

Answer:

Step-by-step explanation:

(100xInterest)(RatexTime)

hope this helps

Step-by-step explanation:

The formula for calculating Principal amount would be P = 100I / (RT) where Interest is Interest Amount, R is Rate of Interest and T is Time Period.

Solve each by elimination
x+y =19
x - y = -7

Answers

x + y = 19
x - y = -7
Subtract both
2y = 26, y = 13
Plug into first equation
x + 13 = 19
x = 6

Solution: x = 6, y = 13

Answer:

x = 6

y = 13

Step-by-step explanation:

x + y = 19

x - y = -7

To eliminate x, subtract ther second equation from the first

2y = 26

y = 13

To eliminate y, add the equations

2x = 12

x = 6

Ben's mom is 22 years older than ben. In 5 years she will be 3 times as old as he will be. How old are they now?

Answers

In linear equation, Ben is 9 years old currently.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Ben's mom = 22 years

Ben is 9 years old currently.

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A lottery game contains 24 balls numbered 1 through 24. What is the probability of choosing a ball numbered 25

Answers

Selecting ball number 25 has no chance of happening.

Explain about the probability?

Probability is only the likelihood that something will occur. When we don't know how something will turn out, we might discuss the likelihood of various outcomes or the potential of one. Statistics is the scientific study of events that conform to a probability distribution.

It is predicated on the likelihood that something will take place. The rationale for probability serves as the theoretical probability's essential tenet. A coin has a 12% chance of landing on its head, for instance, when it is flipped.

Probability is a statistic that is used to indicate the likelihood or potential for an event to occur. Both fractions from 0 to 1 and percentages from 0% to 100% can be used to indicate probabilities.

In 25th Ball it is 0

Because there is no 25th ball

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Can someone explain the signs between positive and negative number ?


Your gonna get so much points from me and brainlist❤️❤️❤️

Answers

Answer:

A positive value is a value greater than zero on the right handside of the number line while a negative value is less than zero on the left handside of the number line.

Negative numbers are less than the number 0 and contain “-“ this symbol. Positive numbers are greater than 0

What is the slope of the line that goes through (-7, -13) and (1,-5).

Answers

Answer:

1

Step-by-step explanation:

The slope would be 1. Using the equation y^2 - y^1 / x^2 -x^1, you would substitute the plots into the equation. -5 + 13 / 1 + 7 = 8/8 or 1. The 13 and 7 would be added because subtracting a negative is the same as adding a positive.

Can you please help me with this question? :)​

Answers

Answer:

First rational exponent means that ;Rational exponents (also called fractional exponents) are expressions with exponents that are rational numbers (as opposed to integers ). While all the standard rules of exponents apply,

Step-by-step explanation:

We take here the root of 4 which means that it gives us the exactly same the answer is 2 which we again square on two it exactly gives us the answer 4 so the bas eis given as, = √4

= ±2

as squaring on it; = 2²

= 4

→ the base in 2² where 2 is the base and 2 of the power is called index.

PLZ MARK ME AS BRAINLIEST

Please help asap..............

Answers

Answer:

what's the context of this?

Jose took a trip to South Lake Tahoe that took 65 minutes. Jose forgot to check the time as he
left, but when he got to South Lake Tahoe, his phone read 8:12 AM. What time did Jose start his
trip?

Answers

Answer:

7:07

Step-by-step explanation:

he started at 7:07 because if you take away 5 minutes from 8:12 you get 8:07 and we all know 60 minutes is an hour so 8:07 minus an hour is 7:07 hope this helps

n \triangle NOP,△NOP, \overline{PN}\cong \overline{OP}
PN

OP
and \text{m}\angle P = 50^{\circ}.m∠P=50

. Find \text{m}\angle O.m∠O.

Answers

The value of the measure of ∠O in the given triangle will be 65°

What is triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In ΔNOP;

PN ≅ OP

So, ∠O = ∠N

And, Measure of ∠P = 50°

Now,

In the ΔNOP;

The sum of all the three angles are 180°.

The value of the measure of ∠O = x

We get;

∠O + ∠N + ∠P = 180°

Substitute ∠P = 50° and ∠O = ∠N = x we get;

x + x + 50 = 180

2x + 50 = 180

2x = 180 - 50

2x = 130

x = 65

Thus, The value of the measure of ∠O will be 65°.

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Jeanette took two tests. Find her z-score for each test. (Remember: The number of standard deviations between a score and the mean score is indicated by a z-score.) On which did she score better compared with others in her class

Answers

The z-score is compared as Test A : 3.25; Test B : 3.5; Test B.

What is the z-score to be compared?The Z-score is a statistical measure that describes the relationship of a value to the mean of a group of values. The Z-score is expressed in standard deviations from the mean. A Z-score of 0 indicates that the data point's score is the same as the mean score.

Here given that,

Test A

Jeanette's score 90

Mean score 64

Standard deviation 8

Test B

Jeanette's score 95

Mean score 60

Standard deviation 10

The formula =

z = x - µ / σ

By substituting,

test A : z = (90 - 64) / 8 = 26 / 8 = 3.25

test B : z = (95 - 60) / 10 = 35/10 = 3.5

So Test A : 3.25; Test B : 3.5; Test B

The data of the question is attached below:

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Z-score in test A = 3.25, Z-score in test B = 3.5. She performed better in test B.

What is Z-score?

Z-score represent the difference between a given value and standard deviation.

What is the Z-score of the above question?

given, Jeanette scored 90 in the Test A

 mean score of test A = 64

standard deviation = 8

we know, the Z-score is calculated by the following formula.

Z-score = (X - μ) /σ

where, σ denotes the standard deviation.

          μ denotes the mean value

    X is the actual value

Test A has Z- score = (actual score - mean score) / standard deviation

                             = (90 -64)/8

                           Z = 3.25

In the test B, she scored 95.

actual score = X = 95

mean score in test B = 60

standard deviation in test B = 10

hence, Z-score for test B = (X - μ)/ σ

                                        = (95 -60)/ 10

       Z-score = 3.5

Therefore, Jeanette scored better in her test B.

                                               

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In the figure where 3x20 and 4x-36, which value of x will make aob, a traight line

Answers

The value of x that will make aob a straight line equation is x = -6.

To make aob a straight line, we need to make the gradients of both lines equal.

The gradient of the first line is 3x20 = 60.

The gradient of the second line is 4x-36 = 4x-36.

To make the gradients equal, we need to solve the equation 4x - 36 = 60.

Subtracting 36 from both sides gives us: 4x = 96.

Dividing both sides by 4 gives us x = -6.

Therefore, the value of x that will make aob a straight line is x = -6

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Annie has two boxes of markers. The first box is 7/10 full and the second box is 6/10 full. How many total markers does Annie have?

Answers

Answer: 1 3/10

Step-by-step explanation:

Since we are informed that Annie has two boxes of markers and that the first box is 7/10 full while the second box is 6/10 full.

Therefore, the total markers that Annie has will be the addition of both boxes and this will be:

= 7/10 + 6/10

= 13/10

= 1 3/10

What is the difference between an undecidable problem and an intractable problem?

Answers

Therefore , the solution of the given problem of tractable problem comes out to be Undecidable troubles are those for which there will never be a computer solution.

What does a tractable problem actually mean?

a technique that completes a manageable task in a polynomial period of time. Utilizing the polynomial upper bound is advantageous. A problem is said to be intractable if it cannot be solved in a polynomial amount of time. The bound has a minimum that is exponential.

Here,

Intractable problems would be those in which there is significant proof that, while they can be solved by a desktop, they cannot be solved quickly enough to be actually useful in practice.

Undecidable troubles are those for which there will never be a computer solution, whereas undecidable difficulties are those for which there will never be a computer solution.

Therefore , the solution of the given problem of tractable problem comes out to be Undecidable troubles are those for which there will never be a computer solution.

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What is the inverse of 12?

Answers

The inverse of 12  as calculated by the given data is found to be 1/12.

The inverse can be found by finding its reciprocal the number ,

inverse of 1 = 1 / 12

There are two types of inverse , additive inverse and multiplicative inverse .

The additive inverse can be found by finding the negative of  the number.  The multiplicative inverse, often known as the reciprocal, is another inverse of a number.

The multiplicative inverse, often known as the reciprocal, is another inverse of a number. The product of a reciprocal multiplied by the original number is always 1.

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What is the radius of circle M?

Answers

Answer:

The radius is just under 4 cm.

Step-by-step explanation:

The central angle for the entire circle is 360 degrees.

The fraction (89/360)(total circle area) = 12.36m^2.

Solving for the total circle area, we get (360/89)(12.36m^2) = 50 cm^2.

Area of a circle (in general) is A = πr²

Here we know A and π and must find r² and then r:

                                        A

A = πr² becomes r² = ----------

                                        π

Here, r² = 50 cm^2 / 3.14 = 15.92 cm^2

and r = square root of r² = 3.99, or approximately 4 cm

A cook wants to make enough cookies for 150 students. The cookie recipe makes
1 1/4 dozen cookies. A dozen equals 12 cookies.
How many batches does the cook need to make if each student gets one cookie?
A.3
B. 7
C.10
D. 13
E. 15

Answers

The answer is D 150 divided by 12= 12.5 :)

Answer:

C 10

Step-by-step explanation:

1 1/14 of a dozen is 15

then 150 divided by 15 = 10

I hope this is the right answer

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