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 value of x is in the solution set of 9(2x + 1) < 9x – 18?
-4
-3
-2
-1
Answer:
c = -3
Step-by-step explanation:
Which of the following is true of the angle measures in the diagram below.
Answer:
B
Step-by-step explanation:
Answer:
it's B
Step-by-step explanation:
the sum of two interior angle of a triangle are always equal to the degree of the adjoined angle to the 3 angle
sorry i don't know how to explain this better
Pleaseeeeeeeeeeeeeeeee solve this
Answer:
x=25
Step-by-step explanation:
All angles in a triangle add up to 180°, so add all the angles together
(2x+15)+(x+10)+(3x+5)=6x+30
So that means... 6x+30=180°
Get rid of the 30, so... 180-30=150
6x=150°
Divide each by 6
6x/6=x
150/6=25
x=25
Sorry if that was hard to understand!!
What is the length of a rectangle with width 15 in, and area 93 in 2?
if 2^6=y^3 what is y?
Answer:
y=4
Step-by-step explanation:
simplify 2^6 --> 64
find the cube root of 64,
y=4
Which expression does the number line represent? A number line going from 0 to StartFraction 9 Over 4 EndFraction in increments of one-fourth. Arrows go from 0 to three-fourths, from three-fourths to six-fourths, and from six-fourths to nine-fourths.
Answer: 9/4 divided by 3/4
Step-by-step explanation: i took the test
Answer:
D
Step-by-step explanation:
2021 moment
6. One of Mollie's favorite toys is a set of hollow rectangular plastic blocks that can be filled with water to use as bath toys. The red block has dimensions 4 1/4 inches by 6 1/4 inches by 5 1/4 inches. Which represents the volume of the red block? Select all that apply. a. 30 cubic inches b. 2,231 and 1/4 cubic inches c. 139 and 29/64 cubic inches d. 557 cubic inches e. (17/4) (25/4) (21/4) cubic inches f. 8,925/64 cubic inches
Answer:
Option c. is correct
Step-by-step explanation:
Given: The red rectangular block has dimensions [tex]4\frac{1}{4}[/tex] inches by [tex]6\frac{1}{4}[/tex] inches by [tex]5\frac{1}{4}[/tex] inches.
To find: volume of the red block
Solution:
Volume of the rectangular box = length × breadth × height
First convert [tex]4\frac{1}{4}[/tex], [tex]6\frac{1}{4}[/tex] and [tex]5\frac{1}{4}[/tex] inches into improper fractions.
[tex]4\frac{1}{4}=\frac{17}{4} \\6\frac{1}{4}=\frac{25}{4} \\5\frac{1}{4} =\frac{21}{4}[/tex]
So,
Volume of the rectangular box [tex]=4\frac{1}{4} (6\frac{1}{4})(5\frac{1}{4} )=\frac{17}{4}(\frac{25}{4})(\frac{21}{4} )=\frac{8925}{64}=139\frac{29}{64}[/tex] cubic inches
Which graph shows the solution to the inequality −2(2x+3)≤26?
pls help
Answer:
the answer is c
Step-by-step explanation:
Problem 11. *
11. Grace has $6 to buy a gallon of milk and some apples. The gallon of milk costs $3.59 and the apples
cost $0.60 each. Which inequality could she use to find out how many apples she can buy?
A) 6 2 0.6x + 3.59
B) 6 S 0.6x + 3.59
C) 6 S 0.6x - 3.59
D) 6 2 0.6x - 3.59
Answer:
Step-by-step explanation:
a
Evaluate the following expression when x = -1, y = 2, z = -3, and
w = 4.
x² - y²
Answer:
-3
Step-by-step explanation:
-1*-1=1
2*2=4
1-4
=-3
Need all these questions answer plz
Step-by-step explanation:
1 result(s) found
x
2
−x−3
Step by Step Solution:
More Icon
STEP
1
:
Equation at the end of step 1
STEP
2
:
x3 + 3x2 - 7x - 12
Simplify ——————————————————
x + 4
Checking for a perfect cube :
2.1 x3 + 3x2 - 7x - 12 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3 + 3x2 - 7x - 12
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -7x - 12
Group 2: x3 + 3x2
Pull out from each group separately :
Group 1: (7x + 12) • (-1)
Group 2: (x + 3) • (x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
2.3 Find roots (zeroes) of : F(x) = x3 + 3x2 - 7x - 12
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is -12.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,3 ,4 ,6 ,12
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -3.00
-2 1 -2.00 6.00
-3 1 -3.00 9.00
-4 1 -4.00 0.00 x + 4
-6 1 -6.00 -78.00
-12 1 -12.00 -1224.00
1 1 1.00 -15.00
2 1 2.00 -6.00
3 1 3.00 21.00
4 1 4.00 72.00
6 1 6.00 270.00
12 1 12.00 2064.00
The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms
In our case this means that
x3 + 3x2 - 7x - 12
can be divided with x + 4
Polynomial Long Division :
2.4 Polynomial Long Division
Dividing : x3 + 3x2 - 7x - 12
("Dividend")
By : x + 4 ("Divisor")
dividend x3 + 3x2 - 7x - 12
- divisor * x2 x3 + 4x2
remainder - x2 - 7x - 12
- divisor * -x1 - x2 - 4x
remainder - 3x - 12
- divisor * -3x0 - 3x - 12
remainder 0
Quotient : x2-x-3 Remainder: 0
Trying to factor by splitting the middle term
2.5 Factoring x2-x-3
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3
Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is -1 .
-3 + 1 = -2
-1 + 3 = 2
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Canceling Out :
2.6 Cancel out (x+4) which appears on both sides of the fraction line.
Final result :
x2 - x - 3
Terms and topics
More Icon
Polynomial root calculator
Polynomial long division
Related links
More Icon
Root Finder -- Polynomials Calculator
How to factor five term polynomial - Yahoo Answers
Long Polynomial Division
Polynomial long division - Wikipedia
Polynomial Long Division
Polynomials - Long Division
Write , or = to make the statement true. 9.008 ___ 9.08
Answer:
9.008 < 9.08
Step-by-step explanation:
9.08 is greater because you compare the number 9 and 9 are the same, 0 and 0 still the same, but then 0 and 8 you know eight is greater. was this helpful enough
3(q − 16) + –8 = –14
Answer:
q = 14
Step-by-step explanation:
3 (q - 16) + -8 = -14
3q - 48 + -8 = -14
3q - 56 = -14
+56 +56
3q = 42
/3. /3
q = 14
hope this helps :)
What is the average rates of change of f(x) = x2-5 over the interval [-2,0].
(a+b) to the power of two a= -3 and b= 6.
Answer:
9
Step-by-step explanation:
-3+6 is 3
3*3 is 9
Mrs adeolu spent 1/4 of her monthly income at a shopping mall 1/3 at a open market and 2/5 of the remaining amount at a mechanic workshop. if she had 225,000 naira left .
find her monthly income
find the amount spent at the open market
Answer: it's c
Step-by-step explanation:
Order these in descending order (greatest to least). 1 is the greatest. 2 is the middle. 3 is the least.
Answer:
3/20 then 0.015 then 0.15%
Step-by-step explanation:
3/20 then 0.015 then 0.15%
3/20 is 0.15
0.15% is .0015
0.015 is 0.015
What is the solution for -x+10<4??
Answer:
x=6
Step-by-step explanation:
subtract 10 on both sides you will get -x<-6 divide both sides by a negative 1 that is how you get 6
Jeremy bought a 5-kilogram can of peanuts for $4.50. What is the unit price?
Answer:
$0.90
Step-by-step explanation:
you would divide it by 5
$4.50/5=$0.90
hope this helps
brainliest?
PLS help in this questions. Thanks !
Answer:
D
Step-by-step explanation:
You are given the two sides and the abgle inbetween.
The sum of three numbers is 36. The first number is two times the second number, and the second number is
four less than the third number. What are the numbers?
o (8, 12, 16)
12<8, 16)
(12, 16,8)
o (16, 8, 12)
Please help out
Answer:
o (16, 8, 12)
Step-by-step explanation:
1st number: 8*2 =16
2nd number:12-4=8
3rd number: given
Answer:
16,8,12
Step-by-step explanation:
its 16,8,12 because:
8x2=16
12-4=8
youre welcome
Two congruent figures
have the same perimeter.
O sometimes
O Never
O Always
Answer:
always
Step-by-step explanation:
Rachel needs to know if the triangle shown is a right triangle. Which equation could he use to help? 36 25 49 (triangle)
A. 136 + 25 = 49
B. 25 + 36 = 49
C. 252 + 362 = 492
D. 362-252 = 492
Miles
Minutes
Martin's running ability is measured by this proportion:
1 3
7 21
1
7
Use the proportion to identify the values of the variables
that complete the rate table
3
21
a =
7
a
b=
CE
b
70
15
c
Answer:
the answer is
a=49
b=10
c=105
14 out of 22 students surveyed enjoyed playing baseball. If 308 students are surveyed, how many would you expect to say they enjoy playing baseball?
Answer:
124
Step-by-step explanation:
14 -22=8
8= the number of students that didn't like playing baseball
Somehow 8 = 800%
if you subtract 800%-308 it gives you -124
124 students don't like playing baseball
A race dog is initially running at 10 m/s but is slowing down. How fast is the dog moving when its kinetic energy has been reduced by half?
5.37 m/s
7.07 m/s
5.00 m/s
6.10 m/s
Answer: 7.07 m/s
Step-by-step explanation:
I took the quiz and that was the correct answer 5 is wrong
The speed of the dog at half of its kinetic energy is 7.07 m/s. The correct option is (B).
What is Proportionality?When two quantities have some dependence in their values they can be said proportional to each other.
It can be of two types such as direct and indirect.
The direct proportionality means the values of both the quantities are increasing or decreasing at the same time while the indirect proportionality implies value of one quantity is increasing while the other is decreasing.
Given that,
The present speed of the dog is 10 m/s.
Suppose the mass of the dog be m kg.
Since, the kinetic energy of an object is given as K = 1/2mv².
As per the question, the following expression can be written,
Initial energy, K₁ = 1/2m × 10²
= 50m
Final energy, K₂ = K₁/2
= 50m/2
= 25m
Using the expression for kinetic energy,
1/2mv² = 25m
=> v² = 50
=> v = √50
= 7.07
Hence, the speed of the dog when its kinetic energy is reduced to half is 7.07 m/s.
To know more about proportionality click on,
brainly.com/question/22620356
#SPJ2
since i tried looking it up and it gave me a dum answer heres the real answer since i got it wrong lol
The equation a = StartFraction one-half EndFraction left-parenthesis b 1 plus b 1 right-parenthesis.(b1 + b2)h can be used to determine the area, a, of a trapezoid with height, h, and base lengths, b1 and b2. Which are equivalent equations? Check all that apply.
StartFraction 2 a Over h EndFraction minus b 2 equals b 1.– b2 = b1
StartFraction a Over 2 h EndFraction minus b 2 equals b 1. – b2 = b1
StartFraction 2 a minus b 2 Over h EndFraction equals b. = b1
StartFraction 2 a Over b 1 plus b 2 EndFraction equals h. = h
StartFraction a Over 2 left-parenthesis b 1 plus b 1 right-parenthesis EndFraction equals h.= h
Answer:
the answer to your question is A and D i just got it right
Step-by-step explanation:
i hope this helps your welcome
StartFraction 2 a Over h EndFraction minus b 2 equals b 1.– b2 = b1
StartFraction 2 a Over b 1 plus b 2 EndFraction equals h. = h
Answer:
A and D
Step-by-step explanation:
correct on edge
The number of pupils in a school increases by 15% every year. If there are 1058 pupils this year, what was the enrollment last year?
Hi there
I think I maybe able to help.
Here is my answer:
996
Hope this helps
SOLVE PLS I WILL GIVE BRAINIEST AND 5 STARS
Solve for b:
3.5b + (-8) = (-6.25b) - 6.5
Solve for x:
-5x + 3 > (-7x) - 12
Answer:
1)b=0.153846
2)x > -15/2
Step-by-step explanation:
I used this site called math-
way
Company XYZ has 97 employees. 31 Of the employees are vegetarian, 36 of the employees owns a Nissan Leaf and 6 of the employees are vegetarian and own a Nissan Leaf. If you randomly select an employee from company XYZ, what is the probability that the employee is vegetarian or that she/he owns a Nissan Leaf?
Answer: [tex]\dfrac{61}{97}[/tex]
Step-by-step explanation:
Let V = Event of selecting vegetarian employee
N = Event of selecting employee who owns a Nissan Leaf.
Given: Total employees = 97
n(V) = 31
n(N) = 36
n(N and V) = 6
By formula,
n(N or V) = n(V) + n(V) - n(N and V)
= 31+36-6
=61
By probability formula,
[tex]P(N \ or \ V)=\dfrac{n(N\ or\ V)}{Total }\\\\=\dfrac{61}{97}[/tex]
Hence, the probability that the employee is vegetarian or that she/he owns a Nissan Leaf = [tex]\dfrac{61}{97}[/tex]