Marla was given the point (1,3), (2, 1), and (-2, -15). She was asked to find a quadratic function that fit these 3 given
points. Marla created a system of three equations with three variables to solve the problem and then used the
matrix functions on her graphing calculator to find the equation. Which equation can be written given these 3
points?
Answers
The linear equations [tex]c_{2}+c_{1}+c_{o} = 3[/tex], [tex]4\cdot c_{2} + 2\cdot c_{1}+ c_{o} = 1[/tex] and [tex]4\cdot c_{2} - 2\cdot c_{1} + c_{o} = -15[/tex] can be written given the points [tex](x_{1}, y_{1}) = (1, 3)[/tex], [tex](x_{2}, y_{2}) = (2, 1)[/tex] and [tex](x_{3}, y_{3}) = (-2, -15)[/tex].
A quadratic function ([tex]p(x)[/tex]) is a second order polynomial of the form:
[tex]p(x) = \Sigma\limits_{i= 0}^{2} c_{i}\cdot x^{i} = c_{2}\cdot x^{2}+c_{1}\cdot x + c_{o}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable[tex]i[/tex] - Monomial index[tex]c_{i}[/tex] - i-th coefficientTo determine the value of all coefficients, we need three distinct points on plane and create a resulting system of linear equations.
If we know that [tex](x_{1}, y_{1}) = (1, 3)[/tex], [tex](x_{2}, y_{2}) = (2, 1)[/tex] and [tex](x_{3}, y_{3}) = (-2, -15)[/tex], then the system of linear equations is:
[tex]c_{2}+c_{1}+c_{o} = 3[/tex] (2)
[tex]4\cdot c_{2} + 2\cdot c_{1}+ c_{o} = 1[/tex] (3)
[tex]4\cdot c_{2} - 2\cdot c_{1} + c_{o} = -15[/tex] (4)
The linear equations [tex]c_{2}+c_{1}+c_{o} = 3[/tex], [tex]4\cdot c_{2} + 2\cdot c_{1}+ c_{o} = 1[/tex] and [tex]4\cdot c_{2} - 2\cdot c_{1} + c_{o} = -15[/tex] can be written given the points [tex](x_{1}, y_{1}) = (1, 3)[/tex], [tex](x_{2}, y_{2}) = (2, 1)[/tex] and [tex](x_{3}, y_{3}) = (-2, -15)[/tex].
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Related Questions
x+y=5
x-1=y
Please help
Answers
Rearrange the second to give
x - y = 1
Add the two equations
(x + y) + (x - y) = 5 + 1
2x = 6
x=3
Substitute 3 into either equation
3 - 1 = y
y = 2
Write the equation of the line with a slope of 3 and passes through the point (0,5).
Answer can be in either slope-intercept
form or point-slope
form
Answers
Answer:
y=3x+5
Step-by-step explanation:
y-y1=m(x-x1)
y-5=3(x-0)
y-5=3(x)
y-5=3x
y=3x+5
Note that the slope intercept form is y=mx+b where m=slope and b=y-intercept.
If you're satisfied with the answer, then please mark me as Brainliest. Thank you.
Sarah has 150 marbles. Of the marbles, 2/5 are blue, 3/10 are clear, and the rest are green. What is the ratio of blue marbles to clear marbles to Green marbles in simplest form?
Answers
Answer:
4 : 3 : 3
Step-by-step explanation:
2/5 of 150 = 300/5 or 60; therefore, there are 60 blue marbles
3/10 of 150 = 450/10 or 45; therefore, there are 45 clear marbles
150 - (60 + 45) = number of green marbles; there are 45 green marbles
Blue : Clear : Green ratio is 60 : 45 : 45 or 4 : 3 : 3
Need someone to help me with this
Answers
Formula- y=mx+b
B is y intercept
M is slope
Hope this helps!!
I will give these ponts for free if u answer 100+100x100. (help me get brnliest)
Answers
100x100=10.000+100=
10.100result…
Answer:
10,100
Step-by-step explanation:
100*100=10000+100=10,000
pls help me answer this
Answers
Step-by-step explanation:
hope it would help you...
I need these answers in 5 MINUTES PLZ HELP
Answers
Answer: 1. w=-30%
2. c=361
Step-by-step explanation: 1. 15+15=30 2. a looks the same size as c so c is 361 or same as a
Matthew wants to buy a new pair of jeans. If the jeans were originally $65.00, but are on sale with a 10% discount, how much will Matthew have to pay for the jeans?
Answers
10% off means the jeans will sell for 90% of the original price ( 100% - 10% = 90%)
Multiply the original price by 90%
65.00 x 0.90 = 58.50
He will pay $58.50
Consider the figure below. Write the equation of the line of reflection.
_____ = ______
Answers
Answer:
y = 0
Step-by-step explanation:
(03.02 MC)
The vertices of AGHI are G (2, 4), H (4,8), and I (8,4). The vertices of AJKL are ) (1.), K (2, 3), and L (4,1). Which conclusion is true about the triangles?
whats the answer
Answers
Answer:
The coordinates of J are missing. Plus, I don't see options for the conclusions. I made an imaginary point J, which you could correct to form the proper triangle.
Step-by-step explanation:
See the attachment. Plot all the vertices, including a corrected point J and draw the resulting triangle. It might be that AJKL is a slightly smaller, shifted version of AGHI. Enter the correct coordinates and then compare.
What is the domain of f(x) = (x + 2)2 – 1?
Answers
Simplify
[tex]\\ \tt\Rrightarrow f(x)=(x+2)^2-1[/tex]
[tex]\\ \tt\Rrightarrow f(x)=x^2+4x+2-1[/tex]
[tex]\\ \tt\Rrightarrow f(x)=x^2+4x+1[/tex]
The Domain is set of all real numbers
[tex]\\ \tt\Rrightarrow Domain\in R[/tex]
Which of the following statements is meaningless?
A.There was a 3% decrease in the price of sugar.
B.There was a 200% increase in the population of a town.
C.There was a 120% decrease in the amount of water in a dam. D.There was a 0% change in the temperature in the room after 1 hour.
Answers
Answer:
(C)
Step-by-step explanation:
If can't have a meaning as something can't decrease more than 100% of itself.
The statement that is meaningless is
There was a 120% decrease in the amount of water in a dam.
Option C is the correct answer.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
A percentage increase can be of any number.
A percentage decrease can not be below 100%.
Now,
A.
There was a 3% decrease in the price of sugar.
This is possible.
B.
There was a 200% increase in the population of the town.
This is possible.
C.
There was a 120% decrease in the amount of water in a dam.
This is not possible.
The highest percentage decrease can be up to 100%.
D.
There was a 0% change in the temperature in the room after 1 hour.
This is possible.
Thus,
There was a 120% decrease in the amount of water in a dam is meaningless.
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8:07, 8:58, ?, 10:43, 11:37
9:51
9:50
9:53
9:49
Answers
Answer:
9:50
Step-by-step explanation:
because, 8:07 ->8:58 +51
...+52
...+53
A pattern can either follow an arithmetic sequence, a geometric sequence or a user defined sequence.
The term that completes the sequence is (d) 9:49
The sequence is given as:
8:07, 8:58, ?, 10:43, 11:37
The above sequence follows an arithmetic sequence, and the common difference (d) is calculated using:
d = 8:58 - 8:07
This gives
d = 51 seconds
The missing term (which is the third term) is then calculated using:
T3 = 8:58 + 51 seconds
This gives
T3 = 9:49
Hence, the term that completes the sequence is (d) 9:49
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8) The height of a stack of CD cases is Proportional to the number of CDs in the stack. A stack of 6 CDs is 66mm high.* Find the unit rate**
a) How high is a stack of 10 CDs?
b) Write an equation that relates the height (y) of a stack of CDs and the number of CD cases(x) in the stack.
please help I will mark your answer as brainliest
Answers
Answer:
a) 110 mm
b) y = 11x
Step-by-step explanation:
The unit rate for 6 CD at 66 mm is
66mm / 6 CD = 11 mm per CD
a) 10 CD's
66 mm x mm
--------- = ------------
6 CD 10 CD
Using cross products
66 * 10 = 6x
660 = 6x
Divide by 6
660/6 = x
110 mm for 10 CD's
b) y = 11 x
We use the rate and multiply by the number of cases to get the height
Shania bought a $1,455 drum set on an installment plan. The Installment agreement included a 15% down payment and 18 monthly payments of $80.78 each
a. How much is the down payment
b. What is the total amount of the monthly payments?
c. What is the total cost of the plan?
d. What is the finance charge?
Answers
Down Payment=15% of $1455
a.Down Payment=(15/100)*1444=$218.25
b.Total amount of the monthly payment=$80.78*18=$1454.04
c.Total cost of the plan=$1454.04+$218.25=$1672.29
d.Finance charge=$1672.29-$1455=$217.29
The down payment will be $218.25, the total amount of the monthly payments is $1454.04.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
Shania bought a $1,455 drum set on an installment plan.
The installment agreement included a 15% down payment and 18 monthly payments of $80.78 each
Down Payment = (15/100)x1444
= $218.25
The total amount of the monthly payment = $80.78x18
= $1454.04
Total cost of the plan = $1454.04 + $218.25
= $1672.29
Finance charge = $1672.29 - $1455
= $217.29
Thus, the down payment will be $218.25, the total amount of the monthly payments is $1454.04.
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(6) Arrange the decimals in increasing order..
(a) 0.8, 0.25, 0.21
(b) 0.85, 3/4' 0.857
Answers
A) 0.21, 0.25, 0.8
B) 3/4, 0.85, 0.857
hope this is helpful!
2 x 3 2 x 7 = what Prime Factorization ?
A. 42
B. 84
C. 126
D. 252
Answers
Answer:
It's B
And Prime Factorization is when 2 numbers have the same answer.
Example: 3x8=24 and 4x6=24
Step-by-step explanation:
Solve the proportion
x/10=9/5
Answers
Answer:
X = 10*9/5
= 2*9
= 18
Answer = 18
Answer:
[tex]x=18[/tex]
Step-by-step explanation:
First way (equivalent fractions):
[tex]\frac{x}{10}=\frac{9}{5}[/tex]
[tex]\frac{x}{10}=\frac{18}{10}[/tex]
[tex]x=18[/tex]
Second way (cross multiplication):
[tex]\frac{x}{10}=\frac{9}{5}[/tex]
[tex]5x=90[/tex]
[tex]x=18[/tex]
Describe the possible length of the third side of the triangle given that the links of the other two sides of 5 inches and 12 inches
___in.
Answers
Answer:
60
Step-by-step explanation:
your welcome
Use the table from a random survey about the preferred service for streaming movies. Out of 750 people, how many would you expect to prefer Company B?
Answers
Answer:
The correct answer option is 192
Step-by-step explanation:
We are given the results of a random survey about the preferred service for streaming movies.
We are to find the number of people we would expect to prefer Company B.
Number of people using service B = 32
Total number of people = 125
Number of people expected to prefer Company B =32/125 x 750 = 192
How many angles are formed with a pair of parallel lines and a transversal
Answers
Answer:
what i learned was 8 are formed
Step-by-step explanation:
Luis made an error when he used the distributive property to write an equivalent expression.
Which sentence describes the error?
35x−15====(5⋅7)−(5⋅3)5(7−3)5(4)20
Answers
Answer:
35x does not equal 5 times 7Step-by-step explanation:
The second step ''(5 × 7) - (5 × 3)'' has an error.
Given that;
Luis made an error when he used the distributive property to write an equivalent expression.
Here the expression is,
35x - 15
It can be written as;
(5 × 7)x - (5 × 3)
Take 5 as common,
5 (7x - 3)
Therefore, the second step ''(5 × 7) - (5 × 3)'' has an error.
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A bag has 25 beads in it.the probability of picking a white bead is 3/5.how many white beads are in the bag
Answers
A truck left a station at 6:00am traveling at a rate of 45km/h. A van left the same place 2 hours later heading in the same direction at a rate of 54km/h. At what time will the van catch up with the truck?
Answers
The Van would catch up with the truck at 6:00 pm
Speed is the ratio of distance travelled to time taken. It is given by:
Speed = distance / time
Let us say the van catch up with the truck after t hours at a distance d.
For the truck:
45 = d/t
d = 45t
For the Van:
54 = d / (t - 2)
d = 54t - 108
45t = 54t - 108
9t = 108
t = 12 hours
The Van would catch up with the truck at 6:00 pm
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Answer:
The Van would catch up with the truck at 6:00 pm
Speed is the ratio of distance travelled to time taken. It is given by:
Speed = distance / time
Let us say the van catch up with the truck after t hours at a distance d.
For the truck:
45 = d/t
d = 45t
For the Van:
54 = d / (t - 2)
d = 54t - 108
45t = 54t - 108
9t = 108
t = 12 hours
The Van would catch up with the truck at 6:00 pm
The area of a rectangular pool is 5628 m^(2). If the width of the pool is 67m, what is its length?
Answers
Answer: 84 m
Step-by-step explanation:
To find area, you multiply the width by the length ( A = L x W). Here, it is asking for the length, giving the area of the pool and the width. With this information, you can inverse operation ( division) to find the length of the pool. So:
5628 / 67 = 84
This tells us that the length of the pool is 87 meters. To check this answer, multiply 67 and 84. If it's equivalent to 5628, the given area, then 84 is indeed the length of the pool.
67 x 84 = 5628.
Thus, the length of the pool is 84 m.
An exponential growth function has an asymptote of y = –3. Which might have occurred in the original function to permit the range to include negative numbers?
A whole number constant could have been added to the exponential expression.
A whole number constant could have been subtracted from the exponential expression.
A whole number constant could have been added to the exponent.
A whole number constant could have been subtracted from the exponent.
Answers
The right choice is: A whole number constant could have been subtracted from the exponential expression.
Let be an exponential function of the form [tex]y = A\cdot e^{B\cdot x}[/tex], where [tex]A[/tex] and [tex]B[/tex] are real numbers. A horizontal asymptote exists when [tex]e^{B\cdot x} \to 0[/tex], which occurs for [tex]B\cdot x \to - \infty[/tex].
For this function, the horizontal asymptote is represented by [tex]y = 0[/tex] and to change the value of the asymptote we must add the parent function by another real number ([tex]C[/tex]), that is to say:
[tex]y = A\cdot e^{B\cdot x} + C[/tex] (1)
In this case, we must use [tex]C = -3[/tex] to obtain an horizontal asymptote of -3. Thus, the right choice is: A whole number constant could have been subtracted from the exponential expression.
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Answer: C. A whole number constant could have been added to the exponent.
Step-by-step explanation: On Edge!
Write the fraction 35/42 simplest form
Answers
Answer:
5/6
Step-by-step explanation:
how to factorize 5x^2-20y^2
Answers
Answer:
Step-by-step explanation:
[tex]5x^2-20y^2\\=5(x^{2} -4y^2)\\=5[x^{2} -(2y)^2]\\=5(x+2y)(x-2y)[/tex]
Answer:
Step-by-step explanation:
Solve x/2 - 8 = y for x
Answers
Answer:
B) x=2y + 16
Step-by-step explanation:
First, you'd multiply the x/2 by 2 to get x by itself.
You do the same throughout the whole equation.
Then isolate the x by getting rid of the -16 to the other side by adding 16
Your final answer should be:
B) x=2y + 16
The value of x for the given equation x/2 - 8 = y will be x = 2y + 16 thus option (B) is correct.
What is the equation?A formula known as an equation uses the same sign to denote the equality of two expressions.
In another word, the equation must be constrained with some constraints.
As per the given equation,
x/2 - 8 = y
Add 8 both sides,
x/2 - 8 + 8 = y + 8
x/2 = y + 8
Multiply by 2 both sides,
x/2 × 2 = (8 + y) × 2
x = 2y + 16
Hence "x = 2y + 16 will be the value of x in the equation x/2 - 8 = y".
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The area of a rhombus is 40 sq cm and one of its diagonals is 8 cm long. Find the length of the other diagonal.
Answers
Answer: The length of the other diagonal is 10 cm...
So the diagonal formula is - 1/2* (d1*d2) d1 is the first diagonal and d2 is the second diagonal.
So,
1/2 * (8*d2) = 40
8d2= 40*2
d2= 80/8
d2= 10