20.
Find a quadratic function to model the values in the table.
A. y = -2x^2 - 3x + 3
B. y = 3x^2 + 3x - 3
C. y = -3x^2 - 3x - 3
D. y = 2x^2 + 3x + 2
Answers
Answer:
B. y = 3x^2 + 3x - 3
Step-by-step explanation:
Find the function rule.
y = 3 x ^2 + 3 x − 3
\table[[x,y],[-1,-3],[0,-3],[3,33]]
The quadratic function to model the values in the table is,
⇒ y = 3x² + 3x - 3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The values of x and y in the table are,
⇒ x = - 1, 0, 3
⇒ y = - 3, - 3, 33
Now, We know that;
The standard form of the quadratic equation is,
⇒ y = ax² + bx + c
Put x = - 1, y = - 3;
⇒ - 3 = a (- 1)² + b (- 1) + c
⇒ - 3 = a - b + c .. (i)
Put x = 0, y = - 3;
⇒ - 3 = a (0)² + b (0) + c
⇒ - 3 = c
Put x = 3, y = 33;
⇒ 33 = a (3)² + b (3) + c
⇒ 33 = 9a + 3b - 3
⇒ 36 = 9a + 3b
⇒ 36/3 = 3a + b
⇒ 3a + b = 12 .. (ii)
From (i);
⇒ - 3 = a - b + c
⇒ - 3 = a - b - 3
⇒ a - b = 0 .. (iii)
Solve for (i) and (iii), we get;
⇒ a = 3, b = 3
Hence, The quadratic function to model the values in the table is,
⇒ y = ax² + bx + c
⇒ y = 3x² + 3x - 3
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Related Questions
Last month 288 people attended the monthly bingo night. This month 243 people attended bingo night. To the nearest tenth of a percent, what is the percent decrease in attendance from last month to this month? Enter your answer as a decimal in the box. %
Answers
Answer:
15.625
Step-by-step explanation:
old number = 288
new number = 243
percent decrease = (old - new / new ) * 100
= (288 - 243 / 288) * 100
= 45 / 288 * 100
= 15.625
Answer:
15.6 (rounded)
Step-by-step explanation:
I took the test
PLEASE HELP WITH THIS ONE QUESTION (what is meant by “describe” is give all the values of the key features).
Answers
Answer:
x-intercepts: (1,0), (−2,0) and (2,0)
y-intercept: (0,4)
The graph is rising and crosses 3 times the x-axis and 1 time the y-axis as shown above.
NEED HELP!! THANK YOU
Answers
Answer:
Expression: -7 + 8f - 2b - f + 3b + 6
# of Terms: 6
Like Terms: 8f and f, -2b and 3b, and -7 and 6
Coefficients: 8, 1, -2, and 3
Constants: -7 and 6
Expression: -11x + 4 + 8x - 4 + 3x
# of Terms: 5
Like Terms: -11x, 8x, and 3x & 4 and -4
Coefficients: -11, 8, and 3
Constants: 4 and -4
Step-by-step explanation:
The coefficient is the number in front of the variable.
The variable is any letter that you may see in an expression.
Terms are the numbers and variables, that are separated by the different signs.
Like terms are the terms that share the same variable/exponent.
Constants are the terms without variables.
Hope this helps you :)
Sorry if it's somehow wrong.
problem referred below
please help
Answers
Answer:
60
Step-by-step explanation:
Perimeter = 2l + 2w
57x2 = 114
234 - 114 = 120
120 / 2 = 60
which one is true and why
Answers
Answer:
the first one is true
Step-by-step explanation:
√36>5 = 6>5
7<√10 = 7<3.162
√9>√25 = 3>5
Therefore, the first one is correct
Please help with the homework thanks
Answers
Answer:
1. 7
2. 8
3. 17 cars
4. 6 guppies
5. 54
6. 15 pencils
Step-by-step explanation:
Have a great day! Feel free to mark as brainliest! :)
see question above ^^
Answers
Determine which consecutive integers do not have a real zero of f(x) = x3 + 9x2 + 8x – 5 between them.
Answers
The difference between the two is 4,5
What is m + 5n where m = 1 and n = 5?
CHOOSE THE RIGHT ANSWER:
A. 26
B. 52
C. 25
D. 62
HELP! (T^T)
Answers
Answer:
A. 26
Step-by-step explanation:
substitute the number in for the variables (letters).
[tex]m + 5n \\ \\ 1 + 5(5) \\ 1 + 25 \\ 26[/tex]
is 6 x 8 4 x 12 equal or not equal
Answers
Answer:
both is 48
Step-by-step explanation:
What is the net pay for these details?
$764 gross pay
Federal withholding $128
FICA $41.87
State $45.15
Health $19.25
A. $529.73
B. $568.23
C. $658.53
D. $703.77
Answers
Answer:
Its a
Step-by-step explanation:
(3[tex]x^{2}[/tex]+[tex]y^{2}[/tex])Y+([tex]y^{2}[/tex]-[tex]x^{2}[/tex])x×[tex]\frac{dy}{dx}[/tex]=0
Answers
It looks like the given differential equation is
(3x² + y²) y + (y² - x²) x dy/dx = 0
Multiply both sides by 1/x³ to get
(3 + y²/x²) y/x + (y²/x² - 1) dy/dx = 0
(Note that in order to do this, we must have x ≠ 0, which means that if a solution exists, it would have to be on either (-∞, 0) or (0, ∞).)
Now substitute z = y/x, or y = xz, from which we get dy/dx = x dz/dx + z. Making this replacement and simplifying yields a separable equation:
(3 + z²) z + (z² - 1) (x dz/dx + z) = 0
(3 + z²) z + (z² - 1) x dz/dx + (z² - 1) z = 0
(z² - 1) x dz/dx = -(2z³ + 2z)
x dz/dx = (2z³ + 2z)/(1 - z²)
(1 - z²)/(2z (z² + 1)) dz = dx/x
Integrate both sides. On the left, split up the expression into partial fractions.
[tex]\dfrac{1-z^2}{z(z^2+1)} = \dfrac az + \dfrac{bz+c}{z^2+1}[/tex]
[tex]\dfrac{1-z^2}{z(z^2+1)} = \dfrac{a(z^2+1)+(bz+c)z}{z(z^2+1)}[/tex]
[tex]1-z^2 = (a+b)z^2 + cz + a[/tex]
for which we find a = 1, b = -2, and c = 0:
[tex]\dfrac{1-z^2}{2z(z^2+1)} = \dfrac12 \left( \dfrac1z - \dfrac{2z}{z^2+1} \right)[/tex]
Integrating and simplifying yields
1/2 ∫ (1/z - 2z/(z² + 1)) dz = ∫ dx/x
1/2 (ln|z| - ln(z² + 1)) = ln|x| + C
1/2 ln|z / (z² + 1)| = ln|x| + C
ln(√(z/(z² + 1))) = ln|x| + C
exp[ln(√(z/(z² + 1)))] = exp[ln|x| + C]
√(z/(z² + 1)) = exp[ln|x|] exp[C]
√(z/(z² + 1)) = Cx
z/(z² + 1) = Cx²
Replacing z = y/x then gives us an implicit solution of
(y/x) / (y²/x² + 1) = Cx²
xy / (y² + x²) = Cx²
y / (y² + x²) = Cx
y = Cx (y² + x²)
Cxy² - y + Cx³ = 0
though we can solve for y explicitly (assuming x > 0) using the quadratic formula to end up with
y = (1 + √(1 - Cx⁴))/(Cx)
(the other solution only differs by the sign on the square root)
Write the first five terms for the following recursive rule.
f(1)=7
f(n)=f(n-1)+12
Answers
Answer:
PLEASE MARK ME AS BRANLIEST!!!!!
Step-by-step explanation:
a1 = first term; an= an-1 + d a1 = the first term in the sequence an = the nth term in the sequence an-1 = the term before the nth term n = the term number d = the common difference.
{10, 15, 20, 25, 30, 35, } first term = 10, common difference = 5 recursive formula: a1= 10; an= an-1 + 5
f(n) = f(n-1) + 12
f(1) = 7
f(2) = (7-1) + 12 = 18
f(3) = (18-1) + 12 = 29
f(4) = (29-1) + 12 = 40
f(5) = (40-1) + 12 = 51
7, 18, 29, 40, 51
Express x2 + 4x - 7 in the form (x + a)? - b where a and b are integers.
Answers
Answer: (x+2)^2 -11
Step-by-step explanation:
X^2 +4x -7
Half the middle term, add it to x and put them into a bracket and square it
(X+2) ^2 -7
Square the second term to get 4 and then take that away from 7. (We do this because if we had the extra 4, our answer when’s we multiplied out of the brackets wouldn’t be x^2 +4x -7.)
(X+2)^2 -7 -4
Now simplify the whole numbers outside the bracket
(X+2) ^2 -11
does the graph represent a function?
Answers
Answer:
No
Step-by-step explanation:
yes it is
for it to not be a function it would need to have a curve or somthing that make it go somehwere else
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
What is the area of the figure below?
16 square units
14 square units
10 square units
12 square units
Answers
How do you get this answer?
start by counting the boxes there’s a total of six in the first rectangle and 6 on the other so 6+6= 12!!!
Just count the boxes and that’s it:)
1) Write a system of equations to describe the situation below, solve using any method, and
fill in the blanks.
)) Erin is training for a triathlon and needs to swim a certain distance for today's workout.
If she swims at the rec center pool, she will complete a 239-meter warmup and then swim
laps in a lane that is 32 meters long. If Erin swims at the indoor pool at her gym, she will
complete a 223-meter warmup, plus a main set that consists of 33 meters per lap. If Erin
swims the correct number of laps, she can complete the same distance in either pool. How
many laps will that take? How long will Erin's workout be in total?
Erin swims
meters
laps at either pool, she can complete a total workout of
Answers
y = 33x + 223
y = 32x + 239
I still like substitution, so let’s plug in 33x + 223 into the second equation
33x + 223 = 32x + 239
Move the terms into appropriate sides
33x - 32x = 239 - 223
Combine like terms
x = 16
Then plug in x for any equation
y = 32(16) + 239
y = 751
Erin will have to swim 16 laps for a total of 751 meters
Solve the following equation for x: 5x-3 1/2 = 9x+4 Enter answers as a decimal with no variable, no spaces, and no equal sign. DO NOT ROUND.
Answers
Answer:
− 1.875
Step-by-step explanation:
Do you want an explanation?
Triangle ABC is similar to triangle DEF.
Side AB is the longest side of ABC. It measures 12 centimeters.
Side DE is the longest side of DEF. It measures 8 centimeters.
What is the scale factor that takes triangle ABC to triangle DEF?
Answers
Answer:
1.5
Step-by-step explanation:
12 / 8 = 1.5
5.
Emily is currently being paid monthly and earns $3,500 in gross pay with every paycheck. Her
employer has decided to shift their pay schedule to a biweekly schedule.
How much less will Emily receive in gross pay per paycheck after the shift?
Answers
Answer:
Emily receives $1,750 less after the shift
Step-by-step explanation:
WILL GIVE BRAINLIEST
(7x-17)
(4x-5)
(2x+3)
The perimeter of this triangle is _____m.
Answers
x = 4
Perimeter = 33
[2] A car is traveling at 55 MPH.
How long in minutes will it take, in minutes, to travel 33 miles?
Answers
Answer:
Step-by-step explanation:
So at 55 miles per hour you go 12 miles in a little over 13 minutes.
.
Hope this helps you to understand the problem and how to use the formula to solve it.
Distance = Speed * Time
.
You might be able to understand this by thinking, "If I go at 60 miles per hour for 2 hours,
how far do I travel?" The answer is:
.
Distance = 60 miles per hour* 2 hours = 120 miles
.
In the problem you are told that the distance to be covered is 12 miles. The speed is 55 miles
per hour. Put these into the equation and you get:
.
12 miles = 55 miles per hour * Time
.
You can then solve for the Time by dividing both sides of this equation by 55 to get:
.
12/55 = Time
.
So it takes 12/55 hours to go 12 miles. The fraction 12/55 converts to a decimal by dividing
55 into 12 to get 0.218181818 of an hour. Since an hour has 60 minutes, you can convert
the answer to minutes by multiplying 60 by 0.218181818 to get about 13.09 minutes.
brainy heart rate 190 per minute her heart rate is 70% of her MHR
what is target heart rate
70
120
133
190
217
Answers
Answer:
120
Step-by-step explanation:
trough dependent sarcasm
The ratio of girls to boys on the school field trip is 6 to 7. There are 24 girls on the field trip. What is the total number of students on the field trip? NO LINKS!!!
A.28
B.52
C.4
D.13
Answers
Answer:
B.52 is the answer i think for the total number of kids
& Cassandra took 87 pads from Louie. Louie now only has 15 left. Mr. Flynn doesn't like ipads.
How many did Louie have BEFORE Cassandra took some?
Answers
9514 1404 393
Answer:
102
Step-by-step explanation:
87 more than 15 is ...
15 +87 = 102
Louie had 102 iPads before Cassandra tool some.
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.
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A particular county with a population of 7.9 million people. In that county, an average of 96 people per year die by falling from a balcony each year.Assuming that these figures are current, what is the probability that a randomly selected individual from this country will die by falling from a balcony in a given year? Express your answer as a decimal rounded to 8 decimal places. Do not convert it to a percentage
Answers
Answer:
7.9000000÷96
=0.0822916667
MARK ME BRAINLIEST PLS I WILL GET A NEW RANKMegan opened a savings account with a $500 deposit. The account pays 1.25% simple interest each year. If she neither adds nor withdraws money from the account, how much interest will she earn after 3 years? help
Answers
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 1.25\%\to \frac{1.25}{100}\dotfill &0.0125\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (500)(0.0125)(3)\implies \boxed{I = 18.75}[/tex]
If 6 units equal 12 inches, what is the value of 1 unit?