Answers
A quadratic function has the form
y = ax^2 + bx + c
Use point (3, 5) in the equation above:
5 = a(3^2) + 3b + c
5 = 9a + 3b + c
9a + 3b + c = 5 Equation 1
Use point (4, 3) in the equation above:
3 = a(4^2) + 4b + c
16a + 4b + c = 3 Equation 2
Use point (5, 3) in the equation above.
5 = a(5^2) + 5b + c
25a + 5b + c = 5 Equation 3.
Now solve the system of equations of equations 1, 2, and 3 to find the coefficients, a, b, and c.
9a + 3b + c = 5
16a + 4b + c = 3
25a + 5b + c = 5
Subtract the first equation from the second equation.
Subtract the second equation from the third equation.
You get
7a + b = -2
9a + b = 2
Subtract the first equation above from the second equation to get.
2a = 4
a = 2
Substitute:
7a + b = -2
7(2) + b = -2
b = -16
9a + 3b + c = 5
9(2) + 3(-16) + c = 5
18 - 48 + c = 5
c - 30 = 5
c = 35
The equation in standard form is
y = 2x^2 - 16x + 35
We can find it in vertex form:
y = 2(x^2 - 8x) + 35
y = 2(x^2 - 8x + 16) + 35 - 32
y = 2(x - 4)^2 + 3
Related Questions
The area of a parallelogram is 3.36 square feet. the base is 2.8 feet. if the measures of the base and height are each doubled, find the area of the resulting parallelogram
Answers
Plug in values and solve for height (h).
A=3.36
b=2.8
3.36 = 2.8h
/2.8 /2.8
1.2 = h
Base and Height doubled:
b = 2.8
h = 1.2
2(2.8)=5.6
2(1.2)=2.4
Plug in new b and h to area equation given to find area:
5.6(2.4) = 13.44
Resulting parallelogram area = 13.44 ft^2
A tractor was purchased for $30,000 six years ago. what is the value of the tractor today if the depreciation rate was 2.5%?
Answers
Depreciation rate = 2.5%
Depreciation expense per year = 30,000*2.5/100 = $750
In six years,
Depreciation = 6*750 = $4,500
Value of the tractor = Initial cost - Depreciation = $30,000 - $4,500 = $25,500
Another geometry question! Please help!
Answers
∠3
The dollar amount (d) that erin earns varies directly as the number of hours (t) that she works. if she earns $206.25 in 25 hours, how many hours did she work if she earned $264?
Answers
d=dollar amount
t=hours
m=how much she earns per hour
Plug in the first set of numbers
$206.25=(25hr)*m
the amount she earns per hour is
$206.25/25hr = m = $8.25 per hr
So
$264=t*$8.25
264/8.25 = t
t = 32 hr
Amy owns a graphic design store. She purchases a new printer to use in her store.
The printer depreciates by a fixed rate of 14% per year. The function
V = 2,400(1 – 0.14)t can be used to model the value of the printer in dollars after
t years.
Question:
Part A: Explain what the parameter 2,400 represents in the equation of the function.
Part B: What is the factor by which the printer depreciates each year?
Part C: Amy also considered purchasing a printer that costs $4,000 and depreciates by 25% each year. Which printer will have more value in 5 years? Justify your answer by showing/explaining your work.
i really need help :( im working hard to get all my school work done and this one thing is making my head hurt :(
Answers
The parameter 2,400 in the depreciation function represents the initial value of Amy's printer. The printer depreciates by a factor of 0.86 each year. After calculations, the first printer has more value ($1,004.40) after 5 years compared to the second printer ($949.24).
Part A: The parameter 2,400 represents the initial purchase price or the original value of the printer that Amy owns in her graphic design store.
Part B: The factor by which the printer depreciates each year is 0.86 (which is calculated as 1 - 0.14, meaning the value retains 86% of its worth each subsequent year).
Part C: To compare which printer will have more value in 5 years, we need to calculate the future value of both printers using their respective depreciation rates:
First printer: V = 2,400(1 - 0.14)^5Second printer: V = 4,000(1 - 0.25)^5After calculating:
Value of the first printer after 5 years: V \\approx 2,400(0.86)^5 \\approx 2,400(0.4185) \\approx $1,004.40Value of the second printer after 5 years: V \\approx 4,000(0.75)^5 \\approx 4,000(0.2373) \\approx $949.24Therefore, the first printer will have more value after 5 years.
Solve for c in the equation 3x^2-18x+5=47
Answers
The general quadrilatic equation is ax²+bx+c=0.
So, arranging the equation in this form we get,
3x²-18x+5-47=0
3x²-18x-42=0
The value of C = -42
Please help me idk this
Answers
1- You have the following information given in the problem above:
- The jug helds 16 cups of milk.
- Isaac drank 1 7/8 cups and his brother drank 1 1/2 cups.
2- Keeping this on mind, you have:
1 7/8=15/8
1 1/2=3/2
=16 cups-15/8 cups-3/2 cups
=101/8 cups
The answer is: 101/8 cups
.48 divided by 9.23 rounded by nearest tenth
Answers
Answer
48/9.23=0.052
0.48/9.23 =0.05
THIS IS ROUNDED
plz help me!!!!
A cross country coach records the number of miles his athletes on the Junior Varsity and Varsity teams ran today and displays the data in the provided dot plots. Given the shape of each distribution, determine which measures of center and spread are appropriate for him to use to summarize the data from each team.
Answers
b.) For the Varsity Team, the median would be the appropriate measure of the center since the data is skewed left and not evenly distributed so median could be used since it does not account for outliers while we use IQR or interquartile range in measuring the spread of data since IQR does not account for the data that is skewed.
Answer:
Step-by-step explanation:
Which line of symmetry for the parabola (x-1)^2= 4(y-1)^?
Answers
Vertex of the parabola (1,1).
So line symmetry is x=1.
The line of symmetry for the parabola is x = 1.
The line of symmetry for the parabola is x = 1. In the given equation (x-1)^2 = 4(y-1)^2, the x-coordinate of the vertex is 1, which means the line of symmetry is a vertical line passing through x = 1.
Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 - 6x + 5 y = x2 + 7x - 11 y = -x2 - 8x - 16
pppppppllllllleeeeaaaassssseeeee ANSWER FASRT
Answers
if its <0, no real soln
its =0, 1 real soln
its >0, 2 real solns
for
y = -3x2 + x + 12, 1^2-4(-3)(12) > 0, two solns
y = 2x2 - 6x + 5, -6^2-4(2)(5) < 0, no soln
y = x2 + 7x - 11, 7^2-4(1)(-11) > 0, two solns
y = -x2 - 8x - 16, -8^2-4(-1)(-16) = 0, one soln
According to the discriminant:
[tex]y = -3x^2 + x + 12[/tex] has two real solutions.[tex]y = 2x^2 - 6x + 5[/tex] has zero real solutions.[tex]y = x^2 + 7x - 11[/tex] has two real solutions.[tex]y = -x^2 - 8x - 16[/tex] has one real solution.The number of real solutions of quadratic equation [tex]y = ax^2 + bx + c[/tex] depends on the discriminant [tex]\Delta = b^2 - 4ac[/tex].
If [tex]\Delta > 0[/tex], the equation has two real solutions.If [tex]\Delta = 0[/tex], the equation has one real solution.If [tex]\Delta < 0[/tex], the equation has zero real solutions.Equation [tex]y = -3x^2 + x + 12[/tex]
The coefficients are: [tex]a = -3, b = 1, c = 12[/tex]The discriminant is: [tex]\Delta = 1^2 - 4(-3)(12) = 145[/tex].Positive, thus two real solutions.Equation [tex]y = 2x^2 - 6x + 5[/tex]
The coefficients are: [tex]a = -2, b = -6, c = 5[/tex]The discriminant is: [tex]\Delta = (-6)^2 - 4(2)(5) = -4[/tex].Positive, thus zero real solutions.Equation [tex]y = x^2 + 7x - 11[/tex]
The coefficients are: [tex]a = 1, b = 7, c = -11[/tex]The discriminant is: [tex]\Delta = (7)^2 - 4(1)(-11) = 93[/tex].Positive, thus two real solutions.Equation [tex]y = -x^2 - 8x - 16[/tex]
The coefficients are: [tex]a = -1, b = -8, c = -16[/tex]The discriminant is: [tex]\Delta = (-8)^2 - 4(-1)(-16) = 0[/tex].Positive, thus one real solutions.A similar problem is given at https://brainly.com/question/19776811
Difference between ellipse circle parabola and hyperbola equations
Answers
(x - h)² + (y - k)² = r²
The equation of a parabola is:
(x - h)² = 4p(y - k)
The equation of an ellipse is:
[tex] \frac{(x-h) ^{2} }{ a^{2} } + \frac{(y-k) ^{2} }{ b^{2} } = 1[/tex]
where variables a and b and the two different measurements of the vertices
The equation of a hyperbola is:
[tex] \frac{((x-h)^{2} }{ a^{2} } - \frac{(y-k)^{2} }{ b^{2} } = 1[/tex] if it is with a horizontal transverse axis
[tex] \frac{ (y-k)^{2} }{ b^{2} } - \frac{ (x-h)^{2} }{ a^{2} } = 1[/tex] if it is with a vertical transverse axis
Notice these have a subtraction operation, the exact opposite ellipse.
The solution is: these have a subtraction operation, the exact opposite ellipse.
What is parabola?The parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. It fits several superficial different mathematical descriptions.
here, we have,
The equation of a circle is:
(x - h)² + (y - k)² = r²
The equation of a parabola is:
(x - h)² = 4p(y - k)
The equation of an ellipse is:
(x - h)²/ a² + (y - k)²/ b² = 1
where variables a and b and the two different measurements of the vertices
The equation of a hyperbola is:
(x - h)²/ a² - (y - k)²/ b² = 1 if it is with a horizontal transverse axis
(y - k)²/ b² - (x - h)²/ a² = 1 if it is with a vertical transverse axis
Notice these have a subtraction operation, the exact opposite ellipse.
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solve the equation 2 cos x + 1 = 0 , 0 <= x <= 2pi PLEASE HELP! WILL AWARD!
Answers
Solve this quadratic equation for cos x.
Since a + b + c = 0, use shortcut.
One real root is cos x = 1 and the other is cosx=ca=−12.
Trig table and unit circle -->
a. cos x = 1 --> arc x = 0, and arc x=2π
b. cosx=−12 --> arc x=±2π3
The arc −2π3 is co-terminal to the arc: 4π3
Answers for (0,2π):
0,2π3,4π3,and2π
The solution of the given trigonometric expression is x = 2π/3.
Use the concept of trigonometric ratio defined as:
Trigonometric ratios depend on the value of the ratio of sides of a triangle which is right-angled and contains the values of all trigonometric functions.
The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as it's trigonometric ratios.
The given expression is:
2 cos x + 1 = 0
Where,
0 ≤ x ≤ 2π
To solve it,
Subtract both sides,
2 cos x = - 1
Divide by 2 on both sides,
cos x = -1/2
Take cos inverse on both sides,
[tex]x = cos^{-1} (\frac{1}{2})[/tex]
Since cos(2π/3) = -1
x = 2π/3
Now since 2π/3 lies between 0 ≤ x ≤ 2π
Hence,
The solution of the given expression is x = 2π/3
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The quarters, buckled, and dimes totaled 20 and their value was $2.05. How many kind were there if there were 3 times as many dimes as quarters
Answers
Let q, n, d represent the numbers of quarters, nickels, and dimes, respectively. Then you have three equations in the unknowns:
q +n +d = 20
25q +5n +10d = 205
-3q +d = 0
A calculator can give the solution to this matrix equation in short order. It is
q = 3
n = 8
d = 9
There are 3 quarters, 8 nickels, and 9 dimes.
_____
If you use the third equation to write an expression for d, you can substitute that into the other two equations.
q +n +3q = 20
25q +5n +10(3q) = 205
Simplifying, these are
4q +n = 20
11q +n = 41
Subtracting the first from the second, we find
7q = 21
q = 3
From there, it is easy to find d=9, n=8.
Evaluate at the given value
4x^2+6x-5 when x=-3
Answers
Evaluate when x = -3.
4x² + 6x - 5
Plug -3 for x.
4(-3)² + 6(-3) - 5
Square -3.
4(9) - 18 - 5
Multiply 4 and 9.
36 - 18 - 5
Subtract from left to right.
18 - 5
13
Answer:
13
The equation of a parabola is 1/32 (y−2)2=x−1 .
What are the coordinates of the focus?
(1, 10)
(1, −6)
(−7, 2)
(9, 2)
Answers
The given equation of parabola is
[tex] \frac{1}{32} (y-2)^2 = x-1 [/tex]
Which can also be written as
[tex] x = \frac{1}{32} (y-2)^2 +1 [/tex]
Here vertex (h,k) is (1,2)
And value of a is
[tex] a = \frac{1}{32} [/tex]
Formula of focus is
[tex] (h+ \frac{1}{4a} , k) [/tex]
Substituting the values of h,k and a, we will get
[tex] (1+ \frac{1}{4*(1/32) } , 2} = (1+ 8,2) = (9,2) [/tex]
Therefore the correct option is the last option .
Answer: The correct option is (D) (9, 2).
Step-by-step explanation: We are given to find the co-ordinates of the focus for the following parabola:
[tex]\dfrac{1}{32}(y-2)^2=x-1~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that the standard form equation of a parabola is
[tex](y-k)^2=4p(x-h),[/tex]
where the co-ordinates of the focus are (h+p, k).
From equation (i), we have
[tex]\dfrac{1}{32}(y-2)^2=x-1\\\\\\\Rightarrow (y-2)^2=32(x-1)\\\\\Rightarrow (y-2)^2=4\times 8(x-1).[/tex]
Comparing the above equation with the standard form equation of the parabola, we get
h = 1, k = 2, and p = 8.
Therefore, the co-ordinates of the focus are
[tex](h+p,k)=(1+8,2)=(9,2).[/tex]
Thus, option (D) is CORRECT.
The function h=−16t2+26t models the height h (in feet) of the dolphin after t seconds. after how many seconds is the dolphin at a height of 5 feet? round your answers to the nearest tenth.
Answers
Answer:
The dolphin is at height 5 feet after 1.40 seconds or 0.228 seconds.
Step-by-step explanation:
Given : The function [tex]h=-16t^2+26t[/tex]models the height h (in feet) of the dolphin after t seconds.
To Find: After how many seconds is the dolphin at a height of 5 feet?
Solution:
Function: [tex]h=-16t^2+26t[/tex]
h is the height
t is the time
Now we are supposed to find After how many seconds is the dolphin at a height of 5 feet
Substitute h = 5
So, [tex]5=-16t^2+26t[/tex]
[tex]16t^2-26t+5=0[/tex]
[tex]16t^2-26t+5=0[/tex] ---1
Using quadratic formula : [tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
General quadratic equation: [tex]ax^2+bx+c=0[/tex] ---A
On Comparing equation 1 with A
a = 16
b = -26
c=5
Substitute the values in the quadratic formula.
[tex]x = \frac{-(-26)\pm\sqrt{(-26)^2-4(16)(5)}}{2(16)}[/tex]
[tex]x = \frac{26\pm 18.86796}{32}[/tex]
[tex]x = \frac{26+18.86796}{32},\frac{26-18.86796}{32}[/tex]
[tex]x = 1.4021,0.2228[/tex]
Thus the dolphin is at height 5 feet after 1.40 seconds or 0.228 seconds.
The dolphin is at a height of 5 feet at 0.2 second and 1.4 seconds.
Polynomial
Polynomial is an expression that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Let h represent the height of dolphin at t seconds.
Given the function:
h = −16t² + 26tFor a height of 5 ft.:
5 = −16t² + 26t
16t² - 26t + 5 = 0
t = 0.2 or t = 1.4
The dolphin is at a height of 5 feet at 0.2 second and 1.4 seconds.
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An isoceles triangle has congruent side of 20 cm. The base is 10 cm. Find the height of the triangle
Answers
x^2=375
x=sqrt(375)
What is the value of the rational expression 2x+1/x2 when x = 5?
Answers
[tex] \dfrac{2x + 1}{ {x}^{2} } \\ = \dfrac{2(5) + 1}{ {5}^{2} } \\ = \dfrac{11}{25} [/tex]
Answer is 11/25.
Hope this helps. - M
The solution is A = 11/25
The value of the equation A = ( 2x + 1 ) / x² is 11/25
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = ( 2x + 1 ) / x²
when x = 5 , substitute the value of x as 5 in the equation , we get
A = ( 2 ( 5 ) + 1 ) / 5²
The value of A = ( 10 + 1 ) / 25
The value of A = 11/25
Therefore , the value of A = 11/25
Hence , The value of the equation A = ( 2x + 1 ) / x² is 11/25
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Farmer toby's chickens and pigs have a total of 30 heads and 84 legs. a chicken has 2 legs, a pig has 4 legs, and each animal has 1 head. how many of each type of animal does toby have
Answers
C = h + 2l
P = h + 4l
C = 18h + 36l
P = 12h + 48l
Nikolai has a jar filled with 120 marbles. he has 72 red marbles, 17 blue marbles, 13 green marbles, and 18 purple marbles. what is the probability that he will randomly select a blue marble, without replacement, and then a purple marble from the jar
Answers
Probability of choosing a blue marble: 17/120
Probability of choosing a purple marble: 18/119
17/120 x 18/119 = 3/140
You will have a 3/140 chance of both of these occurring.
The probability of selecting a blue marble followed by a purple marble from a jar containing 120 marbles with different colors is approximately 2.2%.
The probability of grabbing a blue marble and then a purple marble is determined by multiplying the probability of grabbing a blue marble first and the probability of grabbing a purple marble second. Here's the calculation:
Probability of selecting a blue marble first: 17/120
Probability of selecting a purple marble second (after one blue marble is already taken out): 18/119
Multiplying the probabilities: (17/120) * (18/119) ≈ 0.022, or 2.2%
Which of the following sequences of numbers are arithmetic sequences? Check all that apply.
A.99, 100, 101, 102, 103, ...
B.-3, -5, -7, -9, -11, ...
C.2, -2, 2, -2, 2, ...
D.1, 6, 11, 16, 21, ...
E.-4, 7, -10, 13, -16, ...
Answers
__________________
If we observe the given options, we can note:
In option A, the difference between two consecutive terms is the same and is equal to 1.
In option B, the difference between two consecutive terms is the same and is equal to -2.
In option C, the difference is not the same.
In option D, the difference between two consecutive terms is the same and is equal to 5.
In option E, the difference is not the same.
So, the correct options are A,B and D
Graphic lesions to solve the system Y equals 1/3 X +6 and why equals 1/3 X +4
Answers
y = (1/3) x + 6
y = (1/3) x + 4
We note that both lines have the same slope in this case given by:
m = 1/3
Therefore, the lines are parallel.
As they are parallel, they are not cut at any point.
Thus, the system of equations has no solution.
Answer:
The system has no solution (parallel lines)
Following the formula: y=mx+b,where:m= slopeb=y-interceptAs observed in the given equations, they have the same slope which is equal to 1/3 but each have different y-intercept which is 6 and 4.
Note that two lines are parallel if their slopes are equal and they have different y-intercepts.
Upon graphing, it had seen that the two functions are parallel.See attached picture for the graph.
Someone please help me?
Answers
CBD = 180 - 98/2
CBD = 180 = 49
CBD = 131
Answer is the third one
An airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west of the airplane. they report the angles of elevation as 14° and how high is the airplane? round to the nearest hundredth of a mile.
Answers
An airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west of the airplane. they report the angles of elevation as 14° and 30° how high is the airplane? round to the nearest hundredth of a mile.
Check the diagram of the situation in the picture attached.
First, we are going to use the law of sines to find the measure of side [tex]a[/tex] in triangle ABC:
[tex] \frac{a}{sin(14)} = \frac{5}{sin(16)} [/tex]
[tex]a= \frac{5sin(14)}{sin(16)} [/tex]
[tex]a=4.39[/tex]
Next, we are going to use the trig function Sine in triangle BCD to find the height, [tex]h[/tex], of the plane:
[tex]sin(30)= \frac{h}{4.39} [/tex]
[tex]h=4.39sin30[/tex]
[tex]h=2.19[/tex]
We can conclude that the plane is 2.19 miles high.
The slope of a line in a blueprint must be . A line is drawn that contains the points 5/6 < | m | <7/4. Determine if the line meets the required specifications.
A.No, the rooftop does not meet the specifications, because the absolute value of the roof’s slope is greater than the parameters.
B.No, the rooftop does not meet the specifications, because the absolute value of the roof’s slope is less than the parameters.
C.Yes, the rooftop does meet the specifications, because the absolute value of the roof’s slope is within the parameters.
D.Yes, the rooftop does meet the specifications, because the absolute value of the roof’s slope is less than the parameters.
Answers
In sakura’s garden, for every 5 red flowers, there are 10 yellow flowers. There are a total of 75 yellow and red flowers in her garden. How many ref flowers are in Sakura’s garden?
Answers
We have then:
x: number of red flowers
y: number of yellow flowers.
We write the system of equations:
x + y = 75
y = 2x
Solving the system we have:
x = 25
y = 50
Answer:
there are 25 red flowers in Sakura's garden
I think its B
A researcher finds a negative correlation between the total number of people driving for pleasure and the sales of electric cars.
Which variable is most likely the lurking variable that explains the correlation?
population
gas prices
amount of rainfall
water prices
Answers
The correct answer is:
gas prices
Explanation:
As the number of people driving for pleasure goes down, the sales of electric cars go up. This is likely due to gas prices. As gas prices go up, fewer people drive for pleasure and more people purchase electric cars. Both are ways to reduce the amount of money spent on gasoline.
The option 'gas prices' variable is most likely the lurking variable that explains the correlation.
Given that a researcher finds a negative correlation between the total number of people driving for pleasure and the sales of electric cars.
It is required to find which variable is most likely the lurking variable that explains the correlation.
What is correlation?It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
We have a negative correlation between:
The total number of people driving for pleasure and the sales of electric cars.
We know that the negative correlation means one variable decreases and as the other increases and vice versa.
If the sales of electric cars increase the total number of people driving for pleasure goes down.
This can happen if the gas prices go up fewer people drive for pleasure and more people buy an electric car.
Thus, the option 'gas prices' is correct.
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the mean mark for the class was 70%. There are 30 students in the class, 20 of whom are boys. The mean mark for the boys is 62%. What is the mean mark for the girls?
Answers
Total marks for the class = 70 x 30 = 2100
Mean mark for the boys = 62%
Total marks for the boys = 62 x 20 = 1240
Total marks for the girls = 2100 - 1240 = 860
Mean marks for the girls = 860 ÷ 10 = 86%
Answer: 86%
The total cost (c) in dollars of renting a sailboat for n days is given by the inequality c≥120+60n. what is the maximum number of days for which a sailboat could be rented if the total cost was $360?
Answers
c≥120 + 60n
We substitute the value of c = 360 in the inequality:
360≥120 + 60n
We clear the value of n:
360 - 120 ≥ 60n
240 ≥ 60n
240/60 ≥ n
4 ≥ n
Answer:
The maximum number of days for which a sailboat could be rented if the total cost was $ 360 is:
4 days
Answer:
4 days
Step-by-step explanation: