(HELP ASAP) Use numerals instead of words.
What is the equation of the parabola passing through the points 2,3 , 6,9and 8,0?
Answers
Answers:
-1 in the first box19/2 or 9.5 in the second box-12 in the third box=================================================
Work Shown:
We'll use the template y = ax^2 + bx + c
If (x,y) = (2,3) is on the parabola, then y = ax^2+bx+c turns into 3 = a(2)^2 + b(2) + c. That simplifies to 4a+2b+c = 3If (x,y) = (6,9) is on the parabola, then y = ax^2+bx+c turns into 9 = a(6)^2 + b(6) + c. That simplifies to 36a+6b+c = 9If (x,y) = (8,0) is on the parabola, then y = ax^2+bx+c turns into 0 = a(8)^2 + b(8) + c. That simplifies to 64a+8b+c = 0The system of equations is
[tex]\begin{cases}4a+2b+c = 3\\36a+6b+c = 9\\64a+8b+c = 0\end{cases}[/tex]
We have 3 equations and 3 unknowns.
-----------------------------------
Let's solve the first equation for c
4a+2b+c = 3
2b+c = 3-4a
c = 3-4a-2b
c = -4a-2b+3
Plug that into the second equation and simplify
36a+6b+c = 9
36a+6b+(-4a-2b+3) = 9
32a+4b+3 = 9
32a+4b = 9-3
32a+4b = 6
2(16a+2b) = 6
16a+2b = 6/2
16a+2b = 3 .... we'll use this later
Plug that value of c into the third equation as well
64a+8b+c = 0
64a+8b+(-4a-2b+3) = 0
60a+6b+3 = 0
3(20a+2b+1) = 0
20a+2b+1 = 0
20a+2b = -1
--------------------------
We have a new system of equations. This time it deals with 2 variables instead of 3. We can think of this as a reduced equivalent system.
[tex]\begin{cases}16a+2b = 3\\20a+2b = -1\end{cases}[/tex]
Note how subtracting the terms straight down has the b terms canceling (since 2b-2b = 0b = 0)
The 'a' terms subtract to 16a-20a = -4a
The terms on the right hand side subtract to 3-(-1) = 3+1 = 4
We end up with the equation -4a = 4 which solves to a = -1
Use this value of 'a' to find b
16a+2b = 3
16(-1)+2b = 3
-16+2b = 3
2b = 3+16
2b = 19
b = 19/2
b = 9.5
Now use the values of a and b to find c
4a+2b+c = 3
4(-1)+2(9.5)+c = 3
-4+19+c = 3
15+c = 3
c = 3-15
c = -12
--------------------------
Summary:
The values of a,b,c we found were
a = -1b = 19/2 = 9.5c = -12So the function is
f(x) = -x^2 + (19/2)x - 12
which is equivalent to
f(x) = -x^2 + 9.5x - 12
To check this answer, plug in x = 2, x = 6, x = 8 one at a time. You should get y = 3, y = 9 and y = 0 in that order.
Answer:
f(x)=-x^2+9.5-12
Step-by-step explanation:
- for the first box
9.5 for the second box
-12 for the third box
Related Questions
A baseball uniform costs x dollars for a shirt, $15 for pants and $3 for SockS.
Which expression represents the total cost of 25 uniforms if each person
receives only one shirt, one pair of pants and one pair of socks?
Answers
(18+x)*25
A typical tip in a restaurant is 15% of the total bill. If the bill is $90, what would the typical tip be?
Answers
Answer:
$13.50 typical tip
Step-by-step explanation:
So to find the percentage
multiply 0.15*90
You’ll get 13.5
Answer:
13.50
Step-by-step explanation:
Find 15% of 90 dollars
90 * 15%
Change to decimal form
90 * .15
13.50
Dacă 4 kg de nectarine și 6 kg de piersici costă 48 de lei, iar 3 kg de nectarine şi 9 kg de piersici costă 54 de lei, află cât costă un kilogram de nectarine şi cât costă un kilogram de piersici.
Answers
Answer:
Costul unui kilogram de nectarine = x = 6 lei
Costul kilogram de piersicilor = y = 4 lei
Step-by-step explanation:
Lăsa
Costul nectarinelor = x
Costul piersicilor = y
Prin urmare:
Dacă 4 kg de nectarine și 6 kg de piersici costă 48 de lei
4x + 6y = 48 .... Ecuația 1
3 kg de nectarine și 9 kg de piersici costă 54 de lei
3x + 9y = 54 .... Ecuația 2
Combinând ambele ecuații
4x + 6y = 48 .... Ecuația 1
3x + 9y = 54 .... Ecuația 2
Rezolvăm folosind metoda Eliminare
Înmulțiți ecuația 1 cu 3 și ecuația 2 cu 4 pentru a elimina x
12x + 18y = 144 .... Ecuația 3
12x + 36y = 216 ... Ecuația 4
Scădeți ecuația 4 din 3
-18y = -72
y = -72 / -18
y = 4 lei
Pentru a rezolva pentru x: y = 4
4x + 6y = 48 .... Ecuația 1
4x + 6 × 4 = 48.
4x + 24 = 48
4x = 48 - 24.
4x = 24
x = 24/4
x = 6 lei
Prin urmare:
Costul unui kilogram de nectarine = x = 6 lei
Costul kilogram de piersicilor = y = 4 lei
Braniliest
find the remainder 7,852 ÷ 6
A) 2
B) 3
C ) 4
D) 5
Answers
Answer:
C
Step-by-step explanation:
you divide 7852 by 6 to get 1308.6666666 (etc.)
then you multiply 1308 by 6 (so you take away the .6666) to get 7848
your answer is 4
What is the equation of the line passing through the points (–25, 50) and (25, 50) in slope-intercept form?
y = negative 50 x
y = negative 50
y = 50 x
y = 50
Answers
Answer:
y=50
Step-by-step explanation:
this is the answer.
Answer:
Y=50x
Step-by-step explanation:
I just took the test have a good day remember god love u
please help!! i’ll give brainliest
Answers
Q1. p=a-i
Q2. l= 1/2p-w
Q3. t=d/s
I think that these are correct
Missing Angles in Triangles Worksheet
I need help with everything on this sheet (A-U) please and thank you.
Answers
Answer:
Step-by-step explanation:
This question is based on the angles of the triangle.Therefore, the angles of the triangle is 180 degree.
We need to determined the all the angles of triangle in the figure.
In the triangle ABC,
All sides are equal, therefore it is equivalent triangle. Hence, all angles are also equal.
Therefore, angle A = 60 degree, angle B = 60 degree, angle C = 60 degree.
Now, find the angle N.
In triangle PAN, one of the angle is 69 degree, and the other is 90 degree.
We know that,
Sum of angles of the triangle is 180 degree.
Thus, angle N = 180-69-90
Angle N = 21 degree
From the figure, it is observe that,
Angle P = 90 -69 = 21 degreeAngle O = 90 - angle N = 90 - 21 = 69 degree.Angle R = 90 degree - 15 = 75 degreeAngle Q = 90- 15 = 75 degreeAngle S = 90 - 48 = 42 degreeAngle T = 180- 48-90 = 42 degreeAngle J = 180 - 75 - 90 = 15 degreeAngle L = 180 - 15 - 90 = 75 degreeAngle H = 180 - 75- 60 = 45 degreeAngle I = 90 - 45 = 45 degreeAngle M = 180 - 60 = 120 degreeAngle K = 180 - 120 - 45 = 15 degreeAngle E = 90 - 55 =35 degreeAngle G= 180 - 35 - 90 =55 degreeAngle F = 90 - 55 = 35 degreeAngle U = 69 degree ( from the figure)Angle D = 180 - 69 - 69 = 42 degreeTherefore, these are the all the angles of the given figure.
For finding details, prefer this link:
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Help me plz and merry Christmas
Find the area of a trapezoid whose parallel sides are 12 and 23 centimeters respectively.
Answers
Answer:
The answer is 12 times 23
Answer:
12.5h cm²
Step-by-step explanation:
Area of trapezoid
=h×(12+13)/2 cm²
=h×25/2 cm²
=12.5h cm² ( in algebraic way)
In a box of chocolates, 1/5 of the chocolates contain nuts.
The rest of the chocolates do not contain nuts.
Write down the ratio of the number of chocolates that contain nuts to number of chocolates that do not contain nuts.
Give your answer in the form of 1:n
Answers
Answer:
1:4
Step-by-step explanation:
Ratios and Fractions
It's given 1/5 of the chocolates in a box contain nuts. The rest do not contain nuts. The portion that does not contain nuts is:
[tex]1 - \frac{1}{5}=\frac{4}{5}[/tex]
We need to calculate the ratio of the number of chocolates that contain nuts to the number of chocolates that do not contain nuts.
This can be done by dividing 1/5 by 4/5:
[tex]\displaystyle \frac{\frac{1}{5}}{\frac{4}{5}}[/tex]
Operating:
[tex]\displaystyle \frac{1}{5}\cdot\frac{5}{4}=\frac{1}{4}[/tex]
Expressing it as a ratio: 1:4
The regular price of a watch is $28.25. During a sale, the watch was marked 12% off. What was the price of the watch during the sale? (5 points)
a
$2.35
b
$3.39
c
$16.25
d
$24.86
Answers
Answer:
I believe the answer would be D, $24.86
please help! (One question)
Answers
Answer:
An equilateral triangle is never similar to a scalene triangle, because you can never map one onto the other using only dilations and using rigid transformations
Step-by-step explanation:
Round 3.3453 to 2 decimal place
Answers
Answer:
its 3.35
Step-by-step explanation:
need thanks and make me brainiest if it helps you
its all in the picture v
Answers
F(x) = -2x^2 +32
F(3) =-2(3)^2 +32
F(3)=-2(9)+32
F(3) =-18+32
F(3) = 14
X=14
Answer:
lynns is correct
Step-by-step explanation:
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What is the value of x in the equation 3(2 - x) = 8(x - 2)?
Answers
Answer:
2
Step-by-step explanation:
The equation is equal to 6-3x=8x-16. This gives 11x=22. x=2
Which expression are equivalent to -3.5 - (-8.2)? Choose ALL that apply.
-3.5 + (-8.2)
3.5 + (-8.2)
-3.5 + 8.2
3.5 + 8.2
-3.5 + (+8.2)
Answers
Answer: Your answer is D becasue when you add -3.5 - (-8.2) you get 4.7, and its the same as -3.5 + (+8.2). I hope that kinda explaines it.
Step-by-step explanation:
HELP MEEEEE (find the values of z and y)
Answers
Determine which type of graph is most appropriate for each set of data. Explain your choice. Question: average new car prices over a ten-year period.
Answers
Answer:
A line graph would be nice
Step-by-step explanation:
It would show how the prices increase over time
***im probs too late
What is (f+g) (x)???
Answers
Answer:
A.
Step-by-step explanation:
To get to the answer, add both f(x) and g(x) together. This would be (2x^2 +3x -4) + (-4x^2 + 5x - 8). Remember that adding a negative number is the same as subtracting the positive of that number, for example, 3 + (-4) is the same as 3 - 4.
The chef at LaBerge started the week with 50 pounds of cheese and used 15 4/5 pounds. How much cheese
remains in inventory?
Answers
Answer: 34.2 pounds
Step-by-step explanation:
First, convert 15 4/5 into an improper fraction. You should get 79/5. Then, convert 50 into a fraction that has a denominator of 5. Right now, 50= 50/1 so just multiply the top and bottom by 5 to make it 250/5. Then, subtract 79/5 from 250/5. You should get 171/5. Lastly, simplify. You should get 34.2 pounds as your final answer. Hope this helps!
find quotient and remainder b)diving 2x^3- 5x² +x+2
by x - 2
photo of the answer in notebook
Answers
Given:
Dividend = [tex]2x^3-5x^2+x+2[/tex]
Divisor = [tex]x-2[/tex]
To find:
The quotient and remainder.
Solution:
We have,
Dividend = [tex]2x^3-5x^2+x+2[/tex]
Divisor = [tex]x-2[/tex]
Divide [tex]2x^3-5x^2+x+2[/tex] by [tex]x-2[/tex] as shown in the below picture.
Dividing [tex]2x^3-5x^2+x+2[/tex] by [tex]x-2[/tex], we get
[tex]Quotient=2x^2-x-1[/tex]
[tex]Remainder=0[/tex]
Therefore, [tex]Quotient=2x^2-x-1[/tex] and [tex]Remainder=0[/tex].
A tornado drops a piece of wood from a
height of 4,624 ft. If the equation for
height as a function of time is
h(t) = -16t2 + initial height where t is time
in seconds and h(t) is height in feet, how
many seconds will it take for the piece of
wood to hit the ground?
Answers
Answer:
Step-by-step explanation:
H(t) = -16[tex]t^{2}[/tex]+4.624 ( in feet)
0 = -16[tex]t^{2}[/tex] + 4,624
-4,624 = -16[tex]t^{2}[/tex]
-4,624 / -16 = [tex]t^{2}[/tex]
289 = [tex]t^{2}[/tex]
17 = t
so.. 17 seconds to hit the ground.. :)
The piece of wood 17 seconds takes to hit the ground.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
A tornado drops a piece of wood from a height of 4,624 ft.
Given that the equation for the height as a function of time is
h(t) = -16t² + initial height
Substitute height = 4,624 ft. in the equation,
h(t) = -16t² +4.624
At ground level, the value of h(t) is zero,
0 = -16t² + 4,624
16t² = 4,624
t² = 4,624/16
t² =289
t = 17
So, 17 seconds to hit the ground
Hence, the piece of wood 17 seconds takes to hit the ground.
Learn more about Arithmetic operations here:
https://brainly.com/question/25834626
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How to convert To prepare for a bake-off, Louise used 0.61 kilogram of flour each day for 3 weeks. How many grams did Louise use in those 3 weeks? 1 kg = 1,000 g
Answers
Given:
Louise used 0.61 kilogram of flour each day for 3 weeks.
To find:
How many grams did Louise use in those 3 weeks?
Solution:
We know that,
1 kg = 1000 g
Flour used by Louise each day for 3 weeks = 0.61 kg
1 week = 7 days
3 week = 21 days
Flour used by Louise for 3 weeks (21 days) = (21 × 0.61) kg
= 12.81 kg
= (12.81 × 1000) [ 1 kg = 1000 g]
= 12810 g
Therefore, flour used by Louise for those 3 weeks is 12,810 grams.
Find the value of x.
Answers
Answer:
7
Step-by-step explanation:
this is an isosceles triangle so you know the two longer sides must be equal.
2x-7=7
2x=14
x=7
Answer:
The answer to this question is A) 7
The table shows the price for different numbers of icecream treats:
Number of Icecream Treats Price(in dollars)
2 6
5 15
7 21
12 36
Does this table of numbers represent a proportional relationship? (5 points)
a
Yes, because the price is 3 times the number of icecream treats
b
Yes, because 3 times the price is the number of icecream treats
c
No, because the price of 5 icecream treats should be $12 and not $15
d
No, because the price of 12 icecream treats should be $48 and not $36
Answers
In the equation, 1/4n+5=5 1/2 what is n equal to?
Answers
Answer:
n=2
Step-by-step explanation:
1/4n + 5= 5 1/2
1/4n= 1/2
(multiply both sides by 4 to cancel out the fraction on the left side of rhe equation)
n=2
In the equation 5x-2=-x-20, What is the value of x?
a. 2
b. -1
c. -3
d. -2
Answers
Answer:
C choice.
Step-by-step explanation:
[tex]5x - 2 = - x - 20 \\ [/tex]
First, we move the same terms to the same side.
[tex]5x + x = - 20 + 2 \\ 6x = - 18[/tex]
Then we move 6 to divide - 18.
[tex]x = \frac{ - 18}{6} \\ x = - 3[/tex]
solve for Y (2x+2y=4)
Answers
Answer:
[tex]y=-x+2[/tex]
Step-by-step explanation:
[tex]2x+2y=4[/tex]
[tex]2y=-2x+4[/tex] (Subtract 2x from both sides of the equation)
[tex]y=\frac{-2x+4}{2}[/tex] (Divide both sides of the equation by 2 to get rid of y's coefficient)
[tex]y=-x+2[/tex] (Simplify RHS)
Hope this helps!
An indoor soccer field is a rectangle that is 700 feet long by 250 feet wide. Coach Garza is having his players run diagonally from one corner of the field to the opposite corner. What is the distance the players must run?
Answers
Answer: 743.30343766 . . . ft
Round it to whatever place your teacher requires it to be at.
Step-by-step explanation: So, this question can be treated as one in which you need to find the hypotenuse. If you cut the soccer field diagonally, the length and width are still the same. The two legs of our triangle are 700 ft and 250 ft. The formula for finding the hypotenuse is a²+b²=c². Input the numbers, and it becomes 700²+250²=c². 700² is 490,000 and 250² is 62,500. 490,000 + 62,500 = 552,500. This means that 552,500 is c², and in order to find c, or the hypotenuse/diagonal, we need to find the square root of 552,500. The square root of 552,500 is 743.3034376 . . . , which you can round to whatever place you need it to be at.
In a right triangle the measure of one acute angle is 4 times the difference of the measure of the other acute angle and 5. Find the measure of each acute angle
Answers
Answer:
The measures are 22 and 68 degrees
Step-by-step explanation:
for a right triangle, the total angle measure gives 90
Let one of the acute angle be x and the other be y
The measure of one of the acute angle is 4 times the the difference of the measure of the other angle and 5
x = 4(y-5)
Also x + y = 90
Put i into ii
4(y-5) + y = 90
4y-20 + y = 90
5y-20 = 90
5y = 90 + 20
5y = 110
y = 110/5
y = 22
But;
x = 4(y-5)
x = 4(22-5)
x = 4(17)
x = 68
The sum of the acute angles in a right-angled triangle is 90.
The acute angles are 22 and 68 degrees
Let the acute angles be x and y, such that:
[tex]\mathbf{y = 4(x - 5)}[/tex]
So, we have:
[tex]\mathbf{x + y = 90}[/tex]
Substitute 4(x - 5) for y
[tex]\mathbf{x + 4(x - 5) = 90}[/tex]
Open brackets
[tex]\mathbf{x + 4x - 20 = 90}[/tex]
Add x and 4x
[tex]\mathbf{5x - 20 = 90}[/tex]
Add 20 to both sides
[tex]\mathbf{5x = 110}[/tex]
Divide both sides by 5
[tex]\mathbf{x = 22}[/tex]
Recall that:
[tex]\mathbf{y = 4(x - 5)}[/tex]
So, we have:
[tex]\mathbf{y = 4(22 - 5)}[/tex]
[tex]\mathbf{y = 68}[/tex]
Hence, the acute angles are 22 and 68 degrees
Read more about acute angles at:
https://brainly.com/question/10388714
help me out due in a week
Answers
Answer:
SAS ( Side, Angle, Side)
Step-by-step explanation:
Both triangles - shown by the arcs labelled on them - have two known congruent sides, and an angle which they are both equal to.
(No units are needed as this shows already that both triangles are congruent to each other)
Hope this helps