f(x) = ax² + bx + c
f(1) = 6
f(2) = 11
f(3) = 18
Find:value of a,b,c
Solution:Substitute x = 1 , 2 , 3 in the given polynomial.
★ f(1) = a(1)² + b(1) + c
⟹ 6 = a + b + c -- equation (1)
Similarly,
★ f(2) = a(2)² + b(2) + c
⟹ 11 = 4a + 2b + c -- equation (2)
★ f(3) = a(3)² + b(3) + c
⟹ 18 = 9a + 3b + c -- equation (3)
Subtract equation (1) from (2).
⟹ 4a + 2b + c - (a + b + c) = 11 - 6
⟹ 4a + 2b + c - a - b - c = 5
⟹ 3a + b = 5 -- equation (4).
From equation (3) ,
⟹ 18 - c = 9a + 3b
⟹ 18 - c = 3(3a + b)
Substitute the value of 3a + b from equation (4).
⟹ 18 - c = 3 * 5
⟹ 18 - 15 = c
⟹ 3 = c
substitute the value of c in equation (1).
⟹ 6 = a + b + 3
⟹ 6 - 3 = a + b
⟹ 3 = a + b -- equation (5)
Subtract equation (5) from equation (4).
⟹ 3a + b - (a + b) = 5 - 3
⟹ 3a + b - a - b = 2
⟹ 2a = 2
⟹ a = 1
Substitute a value in equation (5).
⟹ 1 + b = 3
⟹ b = 3 - 1
⟹ b = 2
Therefore,
a = 1
b = 2
c = 3.
I hope it will help you.
Regards.
What is the solution set of the equation below? 3|5 − x| + 2 = 29
Answer:
x=-4
x=14
Step-by-step explanation:
Absolute Value Equation entered :
3|5-x|+2=29
Step by step solution :
STEP
1
:
Rearrange this Absolute Value Equation
Absolute value equalitiy entered
3|-x+5|+2 = 29
Another term is moved / added to the right hand side.
3|-x+5| = 27
STEP
2
:
Clear the Absolute Value Bars
Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.
The Absolute Value term is 3|-x+5|
For the Negative case we'll use -3(-x+5)
For the Positive case we'll use 3(-x+5)
STEP
3
:
Solve the Negative Case
-3(-x+5) = 27
Multiply
3x-15 = 27
Rearrange and Add up
3x = 42
Divide both sides by 3
x = 14
STEP
4
:
Solve the Positive Case
3(-x+5) = 27
Multiply
-3x+15 = 27
Rearrange and Add up
-3x = 12
Divide both sides by 3
-x = 4
Multiply both sides by (-1)
x = -4
Which is the solution for the Positive Case
STEP
5
:
Wrap up the solution
x=14
x=-4
Solutions on the Number Line
Two solutions were found :
x=-4
x=14
£1=$1.62
£650 in dollars
$405 in Pounds
605 pounds is 840.25 dollars
405 dollars is 313.30 pounds
Answer:
£650= 840.25$
$405= 313.30£
Step-by-step explanation:
A coordinate plane is shown. Triangle PQR has vertices P at negative 6 comma 6, Q at negative 6 comma 3, and R at negative 3 comma 3. Triangle P prime Q prime R prime has vertices at P prime negative 2 comma 2, Q prime at negative 2 comma 1, and R prime at negative 1 comma 1. What is the scale factor of dilation?
Answer:
The scale factor of dilation from ΔPQR to ΔP'Q'R' is 1/3
Step-by-step explanation:
The given information are;
The vertices of ΔPQR are;
P(-6, 6), Q(-6, 3), and R(-3, 3) and the coordinates of ΔP'Q'R' are P'(-2, 2), Q'(-2, 1), and R'(-1, 1)
Given that the length, l, of each side of the triangles is given by the formula for calculating length given the vertices we have;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
For side PQ, we have;
(x₁, y₁) = (-6, 6), (x₂, y₂) = (-6, 3)
Given that the points have equal y-values, the length is the difference of their x-values as follows;
[tex]l_{PQ}[/tex] = 6 - 3 = 3
Similarly, length QR is the difference in the y-values, since the x-values are equal. therefore, we have;
[tex]l_{QR}[/tex] = -3 - (-6) = 3
Length PR is given as follows;
(x₁, y₁) = (-6, 6), (x₂, y₂) = (-3, 3)
[tex]l_{PR} = \sqrt{\left (3-6 \right )^{2}+\left (-3-(-6) \right )^{2}} = \sqrt{18} = 3\cdot \sqrt{2}[/tex]
[tex]l_{PR}[/tex] = 3·√2
For P'Q', we have
P'(-2, 2), Q'(-2, 1)
[tex]l_{P'Q'}[/tex] = 2 - 1 = 1
[tex]l_{P'Q'}[/tex] = 1
For Q'R', we have
Q'(-2, 1), R'(-1, 1)
[tex]l_{Q'R'}[/tex] = -1 - (-2) = -1 + 2 = 1
[tex]l_{Q'R'}[/tex] = 1
For P'R', we have;
P'(-2, 2), R'(-1, 1)
[tex]l_{P'R'} = \sqrt{\left (1-2 \right )^{2}+\left (-1-(-2) \right )^{2}} = \sqrt{2} = \sqrt{2}[/tex]
[tex]l_{P'R'}[/tex] = √2
Therefore, given that we have
PQ/(P'Q') = PR/(P'R') = 3/1 = 3 and QR/(Q'R') = 3·√2/(√2) = 3
The scale factor of dilation from ΔPQR to ΔP'Q'R' = 1/3.
Please solve that problem my homework is due ✨
Answer:
1,100 miles traveled in 2 hours, 3,300 miles in 6 hours
Step-by-step explanation:
if the plane is moving at a constant speed, to find the miles per hour divide the distance traveled over the time (1650/3). this would get you 550 miles per hour. So, to get the distances at the other times multiply the times by the speed to get distance traveled. (2*550) and (6*550)
On Saturday, Kim's softball team will be having a family picnic. Hamburger patties
are sold at the local store with 12 patties in a package. Hamburger buns, however,
are only sold in packages of 9 hamburger buns. Kim's team wants to buy the exact
same number of packages for patties and buns
What is the least number of packages of patties and hamburger buns that Kim's
team should buy to have exactly the same number of patties as hamburger buns? If a
package of hamburger patties cost $4.98 and a package of hamburger buns cost
$2.16, what was the total expense?
Answer:
See below
Step-by-step explanation:
The patties (3 packs)
12x3= 36
The buns (4 packs)
9x4= 36
cost:
3x$4.98= $14.94
4x$2.16= $8.64
Add them to equal the total cost
= $ 23.58
Tell me a cool, fun fact, best fact gets. Brainliest
Answer:
The moon has moonquakes.
Step-by-step explanation:
The heads on Easter Island have bodies.
Find the value of x.
Answer:
sdf
Step-by-step explanation:
sdff
For the first one, 132 and 4 + x make a straight line, and a straight line is 180 degrees, so:
132 + 4 + x = 180
Add 132 and 4.
136 + x = 180
Subtract 136.
x = 44
You are right!
For the second one, 68 + x + 9 form a right angle, and a right angle is 90 degrees, so:
68 + x + 9 = 90
Combine 68 and 9.
77 + x = 90
Subtract 77.
x = 13
Hope this helps
Before i thought the dividing functions
I really need help..
Thanks!
write a real world problem that can be solved using the distributive property
Answer:
10 + 2. 3(10 + 2) = ? something like that I think .
Step-by-step explanation:
Given m//n, find the value of x
Answer:
117 is the value of you Question
Step-by-step explanation:
Which table represents a function?
Answer:
The table that starts with (-3, -1)
Step-by-step explanation:
For a table to represent a function the x value has to be different number. Such as, the other tables one has two -5, two -2, two -4 and etc. Do you get it
Answer: the first box
-3 -1
0 0
-2 -1
8 1
Step-by-step explanation: the x value can not repet it self but the y value can
PLS TELL ME WHICH ONE IS TRUE PLS DONT LIE
Plz help with this question
Answer:
A
Step-by-step explanation:
Given
6 ([tex]\frac{x}{2}[/tex] + 4) ≥ 9 ( distribute the parenthesis by 6 )
3x + 24 ≥ 9 ( subtract 24 from both sides )
3x ≥ - 15 ( divide both sides by 3 )
x ≥ - 5 → A
Answer:
A
Step-by-step explanation:
First, divide both sides by 6:
6(x/2 + 4) ≥ 9
x/2 + 4 ≥ 9/6
x/2 + 4 ≥ 3/2
Now, subtract 4 from both sides:
x/2 ≥ 3/2 - 4
x/2 ≥ -5/2
Finally multiply both sides by 2:
x ≥ (-5/2) * 2
x ≥ -5
The answer is thus A.
~ an aesthetics lover
The distance light travels in one year is known as a light year. A light year is equal to 5.87 × 1012 miles. The closest that Earth ever gets to Jupiter is 3.65 × 108 miles. What is a correct representation of the number of years it will take light to travel from Earth to Jupiter at this distance? Check all that apply.
Answer:
[tex]6.21\times 10^{-5}\ \text{light years}[/tex]
Step-by-step explanation:
The distance light travels in one year is known as a light year.
[tex]1\ \text{light year}=5.87\times 10^{12}\ \text{miles}[/tex]
The closest that Earth ever gets to Jupiter is [tex]3.65\times 10^8\ \text{miles}[/tex]
[tex]3.65\times 10^8\ \text{miles}=\dfrac{1}{5.87\times 10^{12}}\times 3.65\times 10^8\ \text{light years}\\\\=6.21\times 10^{-5}\ \text{light years}[/tex]
Hence, the distance it will take light to travel from Earth to Jupiter at this distance is [tex]6.21\times 10^{-5}\ \text{light years}[/tex]
do any of you know how to do algebra 2 ?
Answer: Were is the math problem at?
A portion of a map with cities A and B is shown. The map uses a scale of 1 inch =15 miles. You are making a map with a scale of 2 inches = 25 miles How far apart are cities A and B on your map?
expand and simplify 3(3x-4)-2(2x-1)
Answer:
5x-10
Step-by-step explanation:
distribute 3 & 2 thought the parenthesis
Denise buys a $100,000 condo using a $20,000
down payment on a 30-year fixed-rate loan.
After 5 years of payments, she's made
approximately $24,000 in payments and still
owes approximately $75,000. How much
equity does Denise have in her house? *
Pls help me ASAP PLS PLS PLS PLS PLS PLS ASAP
Answer:
The domain is the input value of x, which can be any real number.
There is no inequality.
Set notation x | E R. ( all real nUmbers)
Interval. Oration (-infinity, infinity)
Range: set x to 0 and solve:
3(0)^2 + 2 = 2
The lowest value is 2 and goes to infinity.
Inequality is >=
Set notation Y | >= 2
Interval notation : [2, infinity)
End behavior they both go to infinity .
Han made some hot chocolate by mixing 4 cups of milk with 6 tablespoons of cocoa
Please Help! Will mark brainliest!
Answer:<EBA=103
Step-by-step explanation:
72+31=103
Answer:
[tex]\boxed {\tt C. \ m \angle EBA=103}[/tex]
Step-by-step explanation:
∠EBA is made up of 2 angles: ∠ABC and ∠EBC
If we want to find the measure of ∠EBA, we should add the measure of ∠ABC and ∠EBC.
m∠EBA= m∠ABC+m∠EBC
The measure of angle ABC is 72. The measure of angle EBC is 31. (m∠ABC=72 and m∠EBC=31)
m∠EBA= 72 + 31
Add.
m∠EBA=103
The measure of angle EBA is 103 and choice C is correct.
how do i graph 2x+4y=12
Answer:
(0,3) (6,0)
Step-by-step explanation:
a printer can print 12 pages in 9 seconds what is the closest estimate of the number of pages it can print in 1 min
Answer:
estimated number of pages it can print will 80 in 1 min.
Step-by-step explanation:
If 12 pages/9 Seconds then by multiplying by 60 secs as there are 60 secs in 1 min.
we get
12/9 then multiply by 60 you will get 80 pages in 1 minute.
Number of pages a printer can print in 9 seconds = 12 pages
Number of pages than can be printed in 1 second =
= 12/9
= 1.3 pages
Number of pages that can be printed in 1 second = 0.75 page
Number of pages that can be printed in 1 minute =
= 1 minute = 60 seconds
Number of pages that can be printed in 60 seconds =
= 1.3 × 60
= 78 pages
Rounding off 78 , we get 80 .
Therefore , 80 pages can be printed in 1 minute .
what is 64x64? and I know if you use a calculator =)
Answer:
4096
Step-by-step explanation:
The function g(x) represents f(x) = 9 cosine (x minus StartFraction pi Over 2 EndFraction) + 3 after translating StartFraction pi Over 6 EndFraction units left and 4 units up.
Which equation represents g(x)?
Answer:
B
Step-by-step explanation:
Im almost sure it B but if not then its for sure D.
The equation that represents the function g(x) is [tex]g(x)=9cos(x-\frac{\pi }{3} )+7[/tex].
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
What is translation?Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.
The function is given as
[tex]f(x)=9cos(x-\frac{\pi }{2} )+3[/tex]
The function f(x) is first translated [tex]\frac{\pi }{6}[/tex] units left.
The rule of translation is:
[tex](x,y)=(x+\frac{\pi }{6},y)[/tex]
So, we have:
[tex]f'(x)=9cos(x+\frac{\pi }{6} -\frac{\pi }{2} )+3[/tex]
Take LCM
[tex]f'(x)=9cos(x+\frac{\pi-3\pi }{6} )+3[/tex]
[tex]f'(x)=9cos(x-\frac{2\pi }{6} )+3[/tex]
[tex]f'(x)=9cos(x-\frac{\pi }{3} )+3[/tex]
Next, translate f'(x) 4 units up.
The rule of this translation is:
[tex](x,y)=(x,y+4)[/tex]
So, we have:
[tex]g(x)=9cos(x-\frac{\pi }{3} )+3+4[/tex]
[tex]g(x)=9cos(x-\frac{\pi }{3} )+7[/tex]
Hence, the equation that represents the function g(x) is [tex]g(x)=9cos(x-\frac{\pi }{3} )+7[/tex].
Find out more information about function and translation here
https://brainly.com/question/21145944
https://brainly.com/question/23961993
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Maggie‘s brother is 11 years younger than four times her age. The sum of their ages is 54. How old is Maggie?
Answer:
Maggie is 13
Step-by-step explanation:
Honestly, I just kept trying ages starting from 10 because I knew it wasn't going to be less than that. Then I did whatever age, in this case 13, and multiply it by 4. Then minus 11 from that number. Then take that end number and add it to the beginning number(maggies age) and you should get 54.
Math Equation Explanation:
13*4 = 52 (Maggies Age) x 4
52-11= 41 The question stated that Maggie's brother was 11 -------------------------------------years younger than her age times 4.
41 + 13 =54 The sum of both their ages.
in a survey 8 out of 32 students preferred vanilla ice cream if 252 students are surveyed how many should theoretically prefer vanilla ice cream make a prediction?
Answer:
63
Step-by-step explanation:
8 / 32 = 0.25
Multiply 0.25 with 252
0.25 * 252 = 63
This process simply applies the same ratio from the first test to the second test.
Ashley is preparing for a horse riding competition. She has trained her horse for 6 hours and has completed 240 rounds. At what rate has Ashley ridden her horse in rounds per hour?
Answer:
40
Step-by-step explanation:
PLEASE HELP THERE ARE TWO PARTS!!
The graph shows the relationship between the United States dollar and
the euro, the currency of the European Union, in December 2011. Part A:
What is the constant of proportionality shown in the graph? *
Exchange Rate (December 6, 2011)
VA
(400, 300)
300
Number of euros
200
(250, 187.50)
100
(120,90)
100 200 300
400
Number of US dollars
I
Answer:
The constant of proportionality of the graph is 0.75
Step-by-step explanation:
The coordinates of the points on the lines are;
(400, 300), (250, 187.5), and (120, 90)
Which can be written in a tabular form as follows;
Number of US dollars [tex]{}[/tex] Number of euros
120 [tex]{}[/tex] 90
250 [tex]{}[/tex] 187.5
400 [tex]{}[/tex] 300
Given that the graph is a straight line graph, we can represent the graph with the straight line equation, y = m·x + c
Where;
c = The y-intercept (where the graph meets the y-axis) = 0
m = The slope = The constant of proportionality
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m =\dfrac{300-90}{400-120} = \dfrac{210}{280} = 0.75[/tex]
We have, y = m·x = 0.75·x.
Therefore, the constant of proportionality of the graph = 0.75.