Function g can be thought of as a scaled version of f(x)=x^2
Write the equation for g(x)
Answers
A scaled version means that our leading coefficient will change. Let's set up an equation to find our leading coefficient, a.
g(x) = a * x^2
Now that we have our equation, we need a point that is on g(x). The point given is (4,8). Let's use that point and plug x and y into our equation so that we can solve for a.
8 = a * (4)^2
8 = a * 16
a = 1/2
All that's left to do is plug in our a value into g(x).
g(x) = 1/2 x^2
Hope this helps!! :)
Related Questions
The equation of three other functions are given which function or functions have a slope equal to the slope of Function 1
Answers
Answer:
See Explanation
Step-by-step explanation:
Required
Function(s) with the same slope as function 1
The question is incomplete as function 1 and the three additional functions are not given.
However, I will provide a general explanation.
A slope is represented as:
[tex]y = mx + b[/tex]
Where
[tex]m \to[/tex] slope
So, considering the following equations
[tex]y = 2x + 3[/tex]
[tex]y = \frac{3x}{2} + 9[/tex]
[tex]y = 2x - 5[/tex]
[tex]y = -2x + 3[/tex]
The following equations have the same slope
[tex]y = 2x + 3[/tex] and [tex]y = 2x - 5[/tex]
Because: [tex]y = mx + b[/tex] implies that:
[tex]m = 2[/tex] for [tex]y = 2x + 3[/tex] and [tex]y = 2x - 5[/tex]
[tex] \sqrt[3]{( - 64)} [/tex]
Answers
Answer:
[tex]-4[/tex]
Step-by-step explanation:
Step 1: Apply the rule
[tex]\left(-64\right)=-64\\\\=\sqrt[3]{-64}[/tex]
Step 2: Apply the radical rule
[tex]\sqrt[3]{-64}=-\sqrt[3]{64}\\\\=-\sqrt[3]{64}[/tex]
Step 3: Factor the number
[tex]\:64=4^3\\\\=-\sqrt[3]{4^3}[/tex]
Step 4: Apply the radical rule
[tex]\sqrt[3]{4^3}=4\\\\=-4[/tex]
Therefore, [tex]\:\sqrt[3]{\left(\:-\:64\right)}\:=\:-4[/tex]
Answer:
-4
Step-by-step explanation:
Juan tiene que salir de su casa a estrenar futbol 20 minutos antes de las 4 PM. Escribe 4 formas diferentes de decir esa hora
Answers
Respuesta:
03:40 pm;
15: 40;
20 minutos antes de las 4 pm;
40 minutos después de las 3 pm
Explicación paso a paso:
20 minutos antes de las 4 de la tarde se pueden expresar de las siguientes formas:
Basado en un tiempo de 12 horas, podría escribirse tiene: 3: 40 pm
Usando el formato de reloj de 24 horas; donde 3 pm es equivalente a 15; por lo tanto, podría escribirse como: 15:40
Además, el tiempo se puede informar en palabras de la siguiente manera:
20 minutos antes de las 4 pm
También ;
40 minutos después de las 3 pm
The mean of 5 numbers is 11.The numbers are in the ratio 1:2:3:4:5 ?
Please help me!!!!
Answers
consider the numbers are x,2x,3x,4x,5x
Given;
(x+2x+3x+4x+5x)/5 = 11
15x = 55
x= 55/15 = 11/3
The numbers are
11/3, 22/3, 11, 44/3, 55/3
11(5)= 55
15x=55
x=55/15
x= 11/3
x=3.67–>3.7
I hope my answers help you..
I need help with this question
Answers
-3 -12 -5 in that order
Answer:
-3
-12
-33
Step-by-step explanation:
sorry if i m wrong.
Erin has 5 cans of juice and drinks 13 of a can daily. In how many days will she empty all the cans she has?
Answers
Answer:
15 days
Step-by-step explanation:
Don't you mean 1/3? If so,
5 cans
-------------------- = 15 days
1/3 can/daily
Question 8 (1 point)
At your high school, you are trying to determine the probability that a student takes
Spanish given that the student is taking Marketing. Which of the following
statements explains how to BEST gather the data to determine this probability?
Determine the number of students taking Marketing, the number of students
taking Spanish, the total number of students, and the distribution of students.
Survey students taking Marketing to determine how many also take Spanish.
Survey students taking Spanish to determine how many also take Marketing.
Determine the number of students taking Marketing, the number of students
taking Spanish, and the total number of students.
Answers
the function h=-16t^2+48t represents the height h (in feet) of a kickball t seconds after it is kicked from the ground
Answers
Answer:
36 feet
Step-by-step explanation:
Given
[tex]h(t) = -16t^2 + 48t[/tex]
Required
Determine the maximum height attained
First, calculate the time to reach maximum height;
In a quadratic equation;
[tex]y = ax^2 + bx + c[/tex]
The maximum is:
[tex]x = -\frac{b}{2a}[/tex]
So, we have:
[tex]t = -\frac{b}{2a}[/tex]
Where
[tex]a = -16; b = 48[/tex]
So:
[tex]t = -\frac{b}{2a}[/tex]
[tex]t = -\frac{48}{2 * -16}[/tex]
[tex]t = -\frac{48}{-32}[/tex]
[tex]t = \frac{48}{32}[/tex]
[tex]t = 1.5[/tex]
The maximum height is at: [tex]t = 1.5[/tex]
So, we have:
[tex]h(t) = -16t^2 + 48t[/tex]
[tex]h_{max}=-16 * 1.5^2 + 48 * 1.5[/tex]
[tex]h_{max}=36[/tex]
A 10-foot ladder is leaning against a wall. If the ladder reaches 8 feet up the wall, how fare is thr base of the ladder from the wall?
Answers
Answer:
6ft
Step-by-step explanation:
The answer is 6 feet
Have a good day:)
PLZ HELP PLZ PLZ ILL MARK AS BRAINLIESTT!!
Answers
4x-6=30
i need help really bad !!!
Answers
Answer:
4x-6=30
4x=36
x=9
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
x = 9
Explanation:
Move all terms that do not contain x to the right side and solve.
The function h(t)=−16t2+7t+63 represents the height of a t-shirt launched from a t-shirt cannon after t seconds. a. Write an equation that tells us when the t-shirt hits the ground. b. At what time does the t-shirt hit the ground. SHOW ALL WORK. Round to 2 decimal places.
Answers
Answer:
[tex](a)\ -16t^2 + 7t + 63=0[/tex]
[tex](b)\ t = 2.215[/tex]
Step-by-step explanation:
Given
[tex]h(t) = -16t^2 + 7t + 63[/tex]
Solving (a): Equation when it hits the ground.
This means that [tex]h(t) = 0[/tex]
So, we have:
[tex]h(t) = -16t^2 + 7t + 63[/tex]
[tex]-16t^2 + 7t + 63=0[/tex]
Solving (b): The value of t in (a)
[tex]-16t^2 + 7t + 63=0[/tex]
Using quadratic formula, we have:
[tex]t = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
This gives:
[tex]t = \frac{-7 \± \sqrt{7^2 - 4*-16*63}}{2*-16}[/tex]
[tex]t = \frac{-7 \± \sqrt{49+ 4032}}{2*-16}[/tex]
[tex]t = \frac{-7 \± \sqrt{4081}}{-32}[/tex]
[tex]t = \frac{-7 \± 63.88}{-32}[/tex]
Split
[tex]t = \frac{-7 + 63.88}{-32}; or\ t = \frac{-7 - 63.88}{-32}[/tex]
[tex]t = \frac{56.88}{-32}; or\ t = \frac{-70.88}{-32}[/tex]
[tex]t = -1.7775; or\ t = 2.215[/tex]
Time can't be negative; So:
[tex]t = 2.215[/tex]
How to solve it?
[tex]\int\limits^a_b {x^2+2x} \, dx[/tex]
Answers
Hi there! Assume that this is your question.
[tex] \large{ \int \limits^a_b ( {x}^{2} + 2x)dx}[/tex]
Before we get to Integral, you have to know Differentiation first. If you know how to differentiate a polynomial function then we are good to go in Integral!
We call the function that we are going to integrate as Integrand. Integrand is a function that's differentiated. In Integral, Integrating requires you to turn the function from differentiated to an original function.
For Ex. If the Integrand is x² then the original function is (1/3)x³ because when we differentiate (1/3)x³, we get x²
[tex] \large{f(x) = \frac{1}{3} {x}^{3} \longrightarrow f'(x) = {x}^{2} } \\ \large{f'(x) = 3( \frac{1}{3} ) {x}^{3 - 1} } \\ \large{f'(x) = {x}^{2} }[/tex]
So when we Integrate, make sure to convert Integrand as in original function. From the question, our Integrand is x²+2x. The function is in differentiated form. We know that x² is from (1/3)x³ and 2x comes from x²
[tex] \large{ f(x) = {x}^{2} \longrightarrow f'(x) = 2x} \\ \large{f'(x) = 2 {x}^{2 - 1} } \\ \large{f'(x) = 2x}[/tex]
Thus,
[tex] \large{ \int \limits^a_b ( {x}^{2} + 2x)dx} \\ \large{\int \limits^a_b ( \frac{1}{3} {x}^{3} + {x}^{2}) }[/tex]
Normally, if it's an indefinite Integral then we'd just put + C after (1/3)x³+x² but since we have a and b, it's a definite Integral.
[tex] \large{ \int \limits^b_a f(x)dx = F(b) - F(a)}[/tex]
Define F(x) as our anti-diff
From our problem, substitute x = a in then subtract with the one that substitute x = b
[tex] \large{ (\frac{1}{3}{a}^{3} + {a}^{2} ) - ( \frac{1}{3} {b}^{3} + {b}^{2}) }[/tex]
Simplify as we get:
[tex] \large \boxed{ \frac{1}{3}{a}^{3} + {a}^{2} - \frac{1}{3} {b}^{3} - {b}^{2}}[/tex]
What is 2000% as a fraction
Answers
Answer:
20000/10
Step-by-step explanation:
Answer:
Step-by-step explanation:
2000%=2000/100=20/1
Translate this sentence into an equation. 59 decreased by Vanessa's score is 7. Use the variable v to represent Vanessa's score.
Answers
So, Vanessa's score = v. Let's work from there.
We know that 59 is decreased by Vanessa's score, which is subtraction, and thus: 59 - v
Then, we're told that that quantity is 7. "Is" can be used in place of an equals sign: = 7
Therefore, our equation is as follows: 59 - v = 7
Hope this helps!! :)
A population of beetles is modeled by the equation b(t) = 3,000 (2)t where t represents the number of weeks since the population was first measured?
Answers
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]b(t) = 3000 * 2^t[/tex]
The question is incomplete;
A possible question could be to calculate the initial amount of beetle
An exponential function is represented as:
[tex]f(x) = ab^x[/tex]
Where
[tex]a \to Initial\ amount[/tex]
By comparison:
[tex]a = 3000[/tex] --- The initial number of beetles
Another question could be to solve for f(t), after a certain number of weeks (say 3)
Substitute 3 for t in: [tex]b(t) = 3000 * 2^t[/tex]
[tex]b(3) = 3000 * 2^3[/tex]
[tex]b(3) = 3000 * 8[/tex]
[tex]b(3) = 24000[/tex]
In the month of September, a bird population increased by a factor of 1.25 every day for those 30 days. The function below shows the number of birds, f(x), after x days:
Answers
Answer:
0 ≤ x ≤ 30
Step-by-step explanation:
In the month of September, a bird population increased by a factor of 1.25 every day for those 30 days. The function below shows the number of birds, f(x), after x days:
f(x) = 250(1.25)ˣ
Which of the following is a reasonable domain for the function?
0 ≤ x ≤ 250
0 ≤ x ≤ 30
All positive integers greater than 100
All real numbers
Solution:
Given that f(x) = 250(1.25)ˣ, where x is the number of days and f(x) is the population of the birds after x days. This means that at the beginning of the month of September (i.e. at x = 0), the population of the birds was 250. And as each day goes by, the population of the bird increases by a factor of 1.25.
The domain of a function is the set of all possible independent variables. In this case the number of days (x) is the independent variable. Since in the month of September there are 30 days, therefore the domain is:
0 ≤ x ≤ 30
how to graph linear standard 3x−4y=24
Answers
Graph the linear equation. 3x-4y= 24
---------------------
Let x = 0, then y = -6
Let y = 0, then x = 8
----------------------------
Plot (0,-6) and (8,0) and draw a line thru them to get:
A thin wire inform of an equilateral triangle of side 11 cm find the area of a circle whose circumference is equal to the length of the wire
Answers
Answer:
86.70 cm^2
Step-by-step explanation:
circumference = 11 x 3 = 33
circumference of a circle = nD
33 = 3.14 X D
D = 10.51
r = 10.51 / 2 = 5.25
Area = nr^2
3.14 x 5.25^2 = 86.70 cm^2
Please help me solve this math it’s due in 1 hour
Answers
15 yard line would be the answer.
If f (x) = StartRoot x EndRoot + 12 and g (x) = 2 StartRoot x EndRoot, what is the value of (f – g)(144)?
–84
Answers
Answer:
hmm very diffecult.
Step-by-step explanation:
if f (x) = StartRoot
Determine if each equation will have 0, 1, or 2 solutions. Equation A: x(x−3)=0 This equation has ____ solutions because... Equation B: x2=−81 This equation has ____ solutions because... Equation C: (x−1)(x−1)=0 This equation has ____ solutions because...
Answers
Answer:
See below
Step-by-step explanation:
Given the expression
x(x-3) = 0
This can be written as x = 0 and x - 3 = 0
x = 0 and x = 0+3
x = 0 and x = 3
Hence the equation has 2 solutions since it is a quadratic equation
B) Given x^2 = -81
Take the square root of both sides
√x² = ±√-81
x =±√-81
Note that √-1 = i
x = ±9i
x = 9i and -9i
Hence this equation has 2 solutions because of its quadratic nature
C) (x−1)(x−1)=0
x - 1 = 0 and x = 1 = 0
x = 1 twice
Hence this equation has 1 solution because of its repitition of root
Find the product. Write your solution in standard form.
(b-6)(b-6)
Answers
Answer:
b² - 12b + 36
Step-by-step explanation:
use the FOIL method:
b² - 6b - 6b + 36
combine the 'like' terms in the middle:
b² - 12b + 36
Largest 3 digit number which is divisible by 6
Answers
Answer:
996
Step-by-step explanation:
largest 3 digit number is 999
then just reduce slowly to find ans
Answer:
The largest 3-digit number divisible by 6 is 996.
PLSS HELP ME BO LINKSSS
Answers
Answer:
x=5.657 or because rouded 5.7
Step-by-step explanation:
ill give explaniation if want
Answer:
(I don't understand 36 sorry, but I can help you with 35)
C. 5.7 feet
Step-by-step explanation:
35. This question is asking you to use the pythagorean theorem, this is the formula:
a² + b² = c²
--------
So we know the lengths of a and b,
a² = 16
b² = 16
We add those together:
16 + 16 = 32
-------
The next step is to calculate [tex]\sqrt{32}[/tex]
[tex]\sqrt{32}[/tex] ≈ 5.7
------
Have a good day :)
Can Some one help fast easy question
Answers
Answer: x = 2
Step-by-step explanation:
4x + 4 = 2x + 8
2x = 4
x = 2
Answer: x = 2.
Step-by-step explanation: 4x+4=2x+8 subtract 4 from both sides.
4x = 2x+4 subtract 2x on both sides
2x = 4 divide both sides by two
x = 2
I hope this helps, have a nice day.
A machine cuts 25 circuit boards every 5 minutes. What is the unit rate of production for the machine?
A- 1/5 minute/boards
B- 5/1 boards/minutes
C- 5/25 minutes/boards
D- 25/5 boards/minutes
Answers
Answer:
B- 5/1 boards/minutesStep-by-step explanation:
Unit rate is the number of circuit boards a minute:
25 boards every 5 minutes >> 25/5 boards every 5/5 minutes >> 5/1 boards/minutesCorrect choice is B
Which of the following shows the coordinates of Q(3,-5) after a translation of
3 units right?
Q'(0,-5)
Q'(6,-5)
Q'(6,-2)
Q'(3,-2)
Answers
Answer:
(0,-5)
Step-by-step explanation:
move the x point to the right three times im pretty sure
Which of the following is (−5x + 4) − (3x2 − 7x + 4) simplified and written in standard form?
A. 3x2 − 12x + 8
B. 2x − 3x2
C. −3x2 + 7x − 5x
D. −3x2 + 2x
Answers
Answer:
D)
Step-by-step explanation:
-5x + 4 - 3x² + 7x - 4
-3x² + 2x
Answer:
(–5x + 4) – (3X²–7x + 4) = ( – 3x² + 2x )
A woman weighs herself. Her mass is 43.4 kg and she is trying to increase .She successfully increases her mass by 8%. a) Work out the increase in her mass. b) Work out her new mass.
Answers
Answer:
Increase in her mass = 3.472 kg
Her new mass = 46.872 kg
Step-by-step explanation:
Her original mass = 43.4 kg
Percentage increase in her mass = 8%
Increase in her mass = 8% of 43.4 kg
= 8/100 * 43.4 kg
= 0.08 * 43.4 kg
= 3.472 kg
Increase in her mass = 3.472 kg
b) Work out her new mass
Her new mass = Her original mass + Increase in her mass
= 43.4 kg + 3.472 kg
= 46.872 kg
Her new mass = 46.872 kg