What are the solutions to the quadratic function. f(x) = x^2+4x-12
Answers
Answer:
2, -6
Step-by-step explanation:
x^2 + 4x - 12
A = 1
B = 4
C = -12
i used the "X" method to solve for the solutions. i think it's easier than using the quadratic formula but it doesn't always work
for the "X" method you have to multiply your A value and your C value together so 1 x (-12) = -12. that is going to be the top part of the X
the bottom part of the x will be your B value which is 4
we have to find multiples of -12 that will also add to 4
so -2 and 6 multiply to -12 but also add to 4 so we know these numbers will work
i added added two drawings to show how i found the solutions using the "X" method and the quadratic formula
(x - 2) (x + 6)
Explanation:
A p 3 x
Related Questions
3. Find the difference between the two expressions.
(3/5x - 5y) - (4/5x + 2y
Answers
Answer:
[tex]^{-1}/_{5}x-7y[/tex]
Step-by-step explanation:
Our equation is
[tex](^{3}/_{5}-5y)-(^{4}/_{5}+2y)[/tex]
now we distribute the - and we get
[tex]^{3}/_{5}-5y-^{4}/_{5}-2y[/tex]
[tex]Combine[/tex] [tex]like[/tex] [tex]terms[/tex]
and now we have [tex]^{-1}/_{5}x-7y[/tex]
expand and simplify (3x-2)2
Answers
Answer:
9x² - 12x + 4
Step-by-step explanation:
(3x - 2)² = (3x - 2)(3x - 2)
Each term in the second factor is multiplied by each term in the first factor , that is
3x(3x - 2) - 2(3x - 2) ← distribute both parenthesis
= 9x² - 6x - 6x + 4 ← collect like terms
= 9x² - 12x + 4
Inequalities definition
Answers
Answer:
a inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Step-by-step explanation:
hope it helps :)
Answer:
In Algebra, inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol. The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa. If the relationship between two algebraic expressions is defined using the inequality symbols, then it is called literal inequalities. If two real numbers or the algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality.
A family pays $34.56 for souvenirs on vacation if the sales tax is 7.5% what is the total amount the family spent on souvenirs
Answers
Answer: $37.15
Step-by-step explanation:
$31.958
Step-by-step explanation:
I'm not sure guys if that's right answer
Differential Equation
Answers
1. The given equation is probably supposed to read
y'' - 2y' - 3y = 64x exp(-x)
First consider the homogeneous equation,
y'' - 2y' - 3y = 0
which has characteristic equation
r² - 2r - 3 = (r - 3) (r + 1) = 0
with roots r = 3 and r = -1. Then the characteristic solution is
[tex]y = C_1 e^{3x} + C_2 e^{-x}[/tex]
and we let y₁ = exp(3x) and y₂ = exp(-x), our fundamental solutions.
Now we use variation of parameters, which gives a particular solution of the form
[tex]y_p = u_1y_1 + u_2y_2[/tex]
where
[tex]\displaystyle u_1 = -\int \frac{64xe^{-x}y_2}{W(y_1,y_2)} \, dx[/tex]
[tex]\displaystyle u_2 = \int \frac{64xe^{-x}y_1}{W(y_1,y_2)} \, dx[/tex]
and W(y₁, y₂) is the Wronskian determinant of the two fundamental solutions. This is
[tex]W(y_1,y_2) = \begin{vmatrix}e^{3x} & e^{-x} \\ (e^{3x})' & (e^{-x})'\end{vmatrix} = \begin{vmatrix}e^{3x} & e^{-x} \\ 3e^{3x} & -e^{-x}\end{vmatrix} = -e^{2x} - 3e^{2x} = -4e^{2x}[/tex]
Then we find
[tex]\displaystyle u_1 = -\int \frac{64xe^{-x} \cdot e^{-x}}{-4e^{2x}} \, dx = 16 \int xe^{-4x} \, dx = -(4x + 1) e^{-4x}[/tex]
[tex]\displaystyle u_2 = \int \frac{64xe^{-x} \cdot e^{3x}}{-4e^{2x}} \, dx = -16 \int x \, dx = -8x^2[/tex]
so it follows that the particular solution is
[tex]y_p = -(4x+1)e^{-4x} \cdot e^{3x} - 8x^2\cdot e^{-x} = -(8x^2+4x+1)e^{-x}[/tex]
and so the general solution is
[tex]\boxed{y(x) = C_1 e^{3x} + C_2e^{-x} - (8x^2+4x+1) e^{-x}}[/tex]
2. I'll again assume there's typo in the equation, and that it should read
y''' - 6y'' + 11y' - 6y = 2x exp(-x)
Again, we consider the homogeneous equation,
y''' - 6y'' + 11y' - 6y = 0
and observe that the characteristic polynomial,
r³ - 6r² + 11r - 6
has coefficients that sum to 1 - 6 + 11 - 6 = 0, which immediately tells us that r = 1 is a root. Polynomial division and subsequent factoring yields
r³ - 6r² + 11r - 6 = (r - 1) (r² - 5r + 6) = (r - 1) (r - 2) (r - 3)
and from this we see the characteristic solution is
[tex]y_c = C_1 e^x + C_2 e^{2x} + C_3 e^{3x}[/tex]
For the particular solution, I'll use undetermined coefficients. We look for a solution of the form
[tex]y_p = (ax+b)e^{-x}[/tex]
whose first three derivatives are
[tex]{y_p}' = ae^{-x} - (ax+b)e^{-x} = (-ax+a-b)e^{-x}[/tex]
[tex]{y_p}'' = -ae^{-x} - (-ax+a-b)e^{-x} = (ax-2a+b)e^{-x}[/tex]
[tex]{y_p}''' = ae^{-x} - (ax-2a+b)e^{-x} = (-ax+3a-b)e^{-x}[/tex]
Substituting these into the equation gives
[tex](-ax+3a-b)e^{-x} - 6(ax-2a+b)e^{-x} + 11(-ax+a-b)e^{-x} - 6(ax+b)e^{-x} = 2xe^{-x}[/tex]
[tex](-ax+3a-b) - 6(ax-2a+b) + 11(-ax+a-b) - 6(ax+b) = 2x[/tex]
[tex]-24ax+26a-24b = 2x[/tex]
It follows that -24a = 2 and 26a - 24b = 0, so that a = -1/12 = -12/144 and b = -13/144, so the particular solution is
[tex]y_p = -\dfrac{12x+13}{144}e^{-x}[/tex]
and the general solution is
[tex]\boxed{y = C_1 e^x + C_2 e^{2x} + C_3 e^{3x} - \dfrac{12x+13}{144} e^{-x}}[/tex]
Are the following polynomial sets open or closed?
6. (x ^ 2 + x - 4) - (x ^ 2 + x + 8)
7. (2 - x)(1 + 3x)
8. (5b - 3c)(7b - 3c)
Answers
Answer:
All closed.
Addition, subtraction as well as multiplication of polynomials result into another polynomial. Therefore, the set of polynomials is closed under addition, subtraction and multiplication.
Open polynomial set is (x² + x - 4) - (x² + x + 8)
Closed polynomial sets are (2 - x)(1 + 3x) and (5b - 3c)(7b - 3c)
What is polynomial?A polynomial is an expression consisting of variables and their coefficients, operations of addition, subtraction, multiplication, and positive-integer powers of variables are involved in polynomial. If the result of a polynomial set applying different operations is polynomial then it is closed under that operation.
Given, polynomial sets
(x² + x - 4) - (x² + x + 8)
Applying subtraction operation
x² + x - 4 - x² - x - 8
Subtracting like terms
-12
The result is integer, it is open polynomial set
(2 - x)(1 + 3x)
Applying multiplication operation
2 - x - x - 3x²
= 2 - 2x - 3x²
The result is polynomial, it is closed polynomial set
(5b - 3c)(7b - 3c)
Applying multiplication operation
35b² - 15bc - 21bc + 9c²
= 35b² - 36bc + 9c²
The result is polynomial, it is closed polynomial set
Hence, (x² + x - 4) - (x² + x + 8) is an open polynomial set
(2 - x)(1 + 3x) and (5b - 3c)(7b - 3c) are closed polynomial sets.
Learn more about polynomials here:
https://brainly.com/question/11536910
#SPJ2
A school needs to buy new notebook and desktop computers for its computer lab. The
notebook computers cost $325 each, and the desktop computers cost $250 each. How
many total computers would someone buy if they get 20 notebooks and 17 desktop
computers? How many total computers would someone buy if they get n notebooks
and d desktop computers?
Answers
A committee is formed consisting of one representative from each of the 4 departments (CS-IS-IT-SW) in the computer science college, where the representative from a department is either the president or one of the two representatives from that department. How many ways are there to form this committee?
Answers
Step-by-step explanation:
each department has 3 options for their representative.
and each of these options can be associated with the 3 options of the next department. and so on.
so, we have
3×3×3×3 = 3⁴ = 81
possibilities to firm that committee overall.
Keshawn is planning to drive from City X to City Y. The scale drawing below shows the distance between the two cities with a scale of ¼ inch = 5 miles.
Answers
Answer:
14 m actural sif 124075n
Step-by-step explanation:
no link no bot right answer
Answers
What is the slope of the line between the points ( 2 , 7 ) and ( 7 , 1 )?
Answers
Answer:
slope = - [tex]\frac{6}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 7 ) and (x₂, y₂ ) = (7, 1 )
m = [tex]\frac{1-7}{7-2}[/tex] = [tex]\frac{-6}{5}[/tex] = - [tex]\frac{6}{5}[/tex]
Hello there! :)
To find the slope of the line when we are given 2 points, we use the following formula:
m=[tex]\frac{y2-y1}{x2-x1}[/tex]
m=[tex]\frac{1-7}{7-2} \\\frac{-6}{5}[/tex]
So the slope is -6/5. Hope this helps!
~Just a cheerful gal
#CarryOnLearning
[tex]MysteriousNature :)[/tex]
Order from least to greatest -0.4, -1/5, and -0.65
Answers
-0.65, -0.4, -1/5.
Tell me if want step by step!!
Hope this helped. :(
2(x + 1) - 3x
howwwwwww
Answers
Answer:
a = -x + 2
Step-by-step explanation:
First, you must distribute to get 2x + 2 and adding in the -3x it equals 2x + 2 - 3x = a
Combine the like terms to get -x + 2 = a
Since there is 2 variables then the answer will stay a = -x + 2 because x or a must be substituted in order to find the other variable
Write the ratio as a ratio of whole numbers using fractional notation.
45 days to 24 days
The ratio of 45 days to 24 days can be written in fractional form as
(Type the ratio as a simplified fraction.)
Answers
Answer:
15:8=15/8
Step-by-step explanation:
45:24=45/24
15/8=15:8
Is ( - 1, 2) a solution of the system y > x and x + y > 0?
O No, because ( - 1, 2) is a solution to only one of these inequalities.
O Yes, because ( – 1, 2) is a solution to both inequalities.
O Yes, because ( - 1, 2) is the point of intersection of the two boundary lines of this system.
No, because ( – 1, 2) is not a solution to either inequality.
Answers
Answer:
Yes, because (-1,2) is a solution to both inequalities
Step-by-step explanation:
2>-1 so the first inequality is correct
-1+2>0 so the second inequality is correct
4.
Classify the function as linear or quadratic and identify the quadratic, linear, and constant terms.
f(x) = 6x2 + x − 12
A. linear function; linear term: x; constant term: −12
B. quadratic function; quadratic term: −12x2; linear term: −6x; constant term: −12
C. quadratic function; quadratic term: 6x2; linear term: x; constant term: −12
D. linear function; linear term: 6x2; constant term: −12
Answers
9514 1404 393
Answer:
C. quadratic function; quadratic term: 6x^2; linear term: x; constant term: −12
Step-by-step explanation:
A function is "quadratic" when the degree (exponent) of the highest-degree term is 2. The "quadratic" term is the one with degree 2.
The "linear" term is the one that has degree 1.
The "constant" term has no variable.
In the quadratic function ...
f(x) = 6x^2 +x -12
the quadratic term is 6x^2
the linear term is x
the constant is -12
Answer: The answer is either letter B or letter C
C. quadratic function; quadratic term: 6x2; linear term: x; constant term: −12
Step-by-step explanation:
Find the degree of the function to determine if linear. f ( x ) = 6 x 2 + x − 12 is not a linear function
Nothing further can be done with this topic. Please check the expression entered or try another topic. f ( x ) = 6 x 2 + x − 12
The union of { 1, 2, 3, 4, 5, 6 } and { 4, 5, 6, 7, 8, 9, 10} is ( 4, 5, 6 }. True or false?
Answers
Answer:
Below:
Step-by-step explanation:-
The answer is in the comment!! someone answered your question!!
Answer:
false this is because the answer would contain all the values in both sets
PLEASE HELP! Economics
Answers
100 francs = 50 dollars
Exchange rate = 50/100
= 1/2
= 0.50 dollars per franc (C)
Note :-
It's dollars per franc because here the dollar has more value.
______
RainbowSalt2222 ☔
Answer:
Im pretty sure it is c
Step-by-step explanation:
Which situation involves permutations? A. choosing 5 people out of 15 to participate in a survey B. choosing 3 flavors of ice cream out of 15 for an ice-cream sundae C. choosing a dozen flowers out of 30 to create a bouquet D. choosing first second-, and third-place winners in a cooking contest
Answers
9514 1404 393
Answer:
D. choosing first second-, and third-place winners in a cooking contest
Step-by-step explanation:
Permutations are involved when order matters. The order of people surveyed, sundae flavors, and flowers are irrelevant. The order of first-second-third is entirely relevant.
Cooking contest winners involve permutations.
You exchange 50 AED, and receive 12 Euro. How many Euros would you receive for 1 AED? Please explain step by step on how you solved the problem. (Using equations like multiplication, devision, adding, subtracting.)
Answers
Answer:
Step-by-step explanation:
if 50 AED= 12 Euro
for 1 AED ? Euro
50AED/1AED= 12Euro/x
cross multiplication:
50*x=12*1
50*x=12
x=12/50
x=0.24 Euro
so for 1AED you will get 0.26 Euro
Can someone help me please I’ve been stuck for a week :(
Answers
Answer:
8/25.
Step-by-step explanation:
As a fraction it is 32/100 but simplified is 8/25 :)
convert this fraction to a decimal 1/200
Answers
Answer:
0.005
Step-by-step explanation:
what is 351.86 in terms of pi?
Answers
Answer:
It can either be 17593pi/9000 rad or if youre looking for a decimal answer is it 1.95pi and rad=6.14
Step-by-step explanation:
On a coordinate grid, point L is at (−4, 4) and point S is at (8, 4). The distance (in units) between points L and S is ______. Input only whole numbers, such as 2.
Answers
Answer:
12 this is da a answer
12 twelve
Carrie loves carrots so much that she ate 30 of them for lunch. Her sister doesn’t like carrots as much and only ate 5 of them for lunch. The number of carrots Carrie ate is how many times greater than the number that her sister ate?
Answers
Which means she at 6 times the amount of carrots than her sister.
1 32 multiplied by 0.32 when rounded to the nearest hundredths
Answers
Answer:
42.20
Step-by-step explanation:
132 ×0.32
=42.24
rounded off it give 42.20
In a Parallelogram CARS , <C = 5x-20 and <A = 3x+20. Find the value of x ?
Answers
Given that
In a Parallelogram CARS ,∠C = (5x-20)°
∠A = (3x+20)°
angle C and angle A are adjacent angles
We know that
In a Parallelogram the adjacent angles are supplementary.
⇛∠C + ∠A = 180°
⇛ (5x-20)°+(3x+20)° = 180°
⇛5x°-20°+3x°+20° = 180°
⇛(5x°+3x°)+(20°-20°) = 180°
⇛8x°+0 = 180°
⇛8x° = 180°
⇛ x° = 180°/8
⇛ x° = 22.5°
Answer:-The value of x = 22.5°
also read similar questions: In parallelogram MATH, m= (3x+ 20) and t= (5x-4) find A
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find the value of x (5x+12) (3x+8) a 10 b 15 c 20 d 25
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1) Company A charges $55 per hour and a service charge of $250 and Company B charges $60
per hour and a service charge of $225. At what time are they equal?
Answers
Answer:
5 hours
Step-by-step explanation:
100 raspberries weigh 40 grams. if there is a proportional relationship between raspberries and weight, how many raspberries does it take to weigh 100 grams
Answers
Answer:
250 raspberries
Step-by-step explanation:
So if 100 raspberries weigh 40 grams, each raspberry weighs 40/100 grams, which is 4/10 of a gram. so, you need to do 100/ 4/10=250
45 cows can graze a field in 13 days. How many cows will graze the same field in 9 days
Answers
Answer:
65 cows
Step-by-step explanation:
Inverse rule of three
[tex]45-------13\\x -------- 9[/tex]
[tex]x=\frac{(45)(13)}{9}=585/9=65[/tex]
Hope this helps
