Given:
Functions are
[tex]f(x)=\dfrac{1}{3}x^2+4[/tex]
[tex]g(x)=9x-12[/tex]
To find:
The value of [tex]g(f(x)).[/tex].
Solution:
We have,
[tex]g(f(x))=g(\dfrac{1}{3}x^2+4)[/tex] [tex][\because f(x)=\dfrac{1}{3}x^2+4][/tex]
[tex]g(f(x))=9(\dfrac{1}{3}x^2+4)-12[/tex] [tex][\because g(x)=9x-12][/tex]
[tex]g(f(x))=9(\dfrac{1}{3}x^2)+9(4)-12[/tex]
[tex]g(f(x))=3x^2+36-12[/tex]
[tex]g(f(x))=3x^2+24[/tex]
Therefore, the required function is [tex]g(f(x))=3x^2+24[/tex].
Following are the calculation to the given function:
Given:
[tex]f(x)=\frac{1}{3}x^2+4 \\\\g(x)=9x-12[/tex]
To find:
[tex]g(f(x))=?[/tex]
Solution:
[tex]f(x)=\frac{1}{3}x^2+4 \\\\g(x)=9x-12[/tex]
[tex]\to g(f(x))=g( \frac{1}{3} x^2+4) \\\\[/tex]
[tex]=9( \frac{1}{3} x^2+4)-12 \\\\=\frac{9}{3}x^2+36-12 \\\\=3x^2+24 \\[/tex]
Therefore, the answer is "[tex]24+3x^2[/tex]" .
Learn more about the g(f(x)):
brainly.com/question/17022176
8 - 10 is the same as
A. -8 + -10
B. 8 + (-10)
C. -8 + 10
D. 8 + 10
will mark brainliest for the correct answer! just read the english, okay? the other language is the translation for the english.
Answer:
Step-by-step explanation:
Given equation is,
y = 3x² - 6x + 11
a). y = 3x² - 6x + 11
= 3(x² - 2x) + 11
= 3(x² -2x + 1 - 1) + 11
= 3(x² - 2x + 1) - 3 + 11
= 3(x - 1)² + 8
Comparing this equation with y = a(x - b)² + c
a = 3, b = 1 and c = 8
b). For minimum value of x,
Since, vertex of the graph is given by (b, c),
Minimum value of x will be,
x = b
x = 1
c). Vertex of the parabola → (b, c)
→ (1, 8)
For y-intercept,
By substituting x = 0 in the equation,
y = 3(0 - 1)² + 8
y = 11
Now we can sketch the graph by using the table of input - output values.
x -2 -1 0 1 2 3
y 35 20 11 8 11 20
In ΔEFG, e = 82 cm, ∠G=35° and ∠E=51°. Find the length of f, to the nearest 10th of a centimeter.
Answer:
105.3
Step-by-step explanation:
deltamath
You put $2500 in a bank account with 5% interest
1. How much money will you earn in interest?
2. How much money will be in your account after 1 year?
Calculate the constant of proportionality, k, for the given table.
Employees at a hardware store are receiving pay raises. Dan's hourly pay rate is increasing from $12 to $14. Kathy's hourly pay rate is increasing from $13 to $15.
Part A
Complete the proportions that can be used to find the percent change, x, in Dan's and Kathy's pay rates.
Answer:
1/6 or like 15 or 16 percent comment for
my snop chot
Clare estimates that her brother is 4 feet tall. When they get measured at the doctor’s office, her brother’s actual height is 4 feet, 2 inches.
1.What was the error, expressed in inches?
2.What was the error, expressed as a percentage of the actual height?
Percentage of error by Clare is estimated as 4.1667 %
Height measured by Clare = 4 feet
Height measured by Doctor = 4 feet, 2 inches
Percentage error = ?
Percentage error = Difference/ Actual height *100
Percentage error = (2/ (4*12))*100
Percentage error = 4.1667 %
The accurate height is measured by Doctor, as he have more accurate measurement system.
A fastball is hit straight up over home plate. The ball's height, h (in feet), from the ground is modeled by ℎ = −16푡 ଶ+103푡+5 where t is time (in seconds).
Question:
A fastball is hit straight up over home plate. The ball's height, h (in feet), from the ground is modeled by h(t)=-16t^2+80t+5, where t is measured in seconds. Write an equation to determine how long it will take for the ball to reach the ground.
Answer:
[tex]t = 5.0625[/tex]
Step-by-step explanation:
Given
[tex]h(t)=-16t^2+80t+5[/tex]
Required
Find t when the ball hits the ground
This implies that h(t) = 0
So, we have:
[tex]0=-16t^2+80t+5[/tex]
Reorder
[tex]-16t^2+80t+5 = 0[/tex]
Using quadratic formula, we have:
[tex]t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
Where
[tex]a = -16[/tex] [tex]b =80[/tex] [tex]c = 5[/tex]
So, we have:
[tex]t = \frac{-80\±\sqrt{80^2 - 4*-16*5}}{2*-16}[/tex]
[tex]t = \frac{-80\±\sqrt{6400 +320}}{-32}[/tex]
[tex]t = \frac{-80\±\sqrt{6720}}{-32}[/tex]
[tex]t = \frac{-80\±82.0}{-32}[/tex]
This gives:
[tex]t = \frac{-80+82.0}{-32}[/tex] or [tex]t = \frac{-80-82.0}{-32}[/tex]
[tex]t = \frac{2}{-32}[/tex] or [tex]t = \frac{-162}{-32}[/tex]
[tex]t = -\frac{2}{32}[/tex] or [tex]t = \frac{162}{32}[/tex]
But time can not be negative.
So, we have:
[tex]t = \frac{162}{32}[/tex]
[tex]t = 5.0625[/tex]
Hence, time to hit the ground is 5.0625 seconds
what is the sum of three consecutive even numbers is 30?
Answer:
here:
you can make an equation
x + ( x + 2) + (x + 4) = 30
then by combining like items you get
3x + 6 = 30
then solve
3x = 30 - 6 ; then 3x = 24 , and x = 8
so the three numbers are 8 ; 10 and 12.
Besty has $27 saved. This month she saved an additional $9. She wants to buy packs of colored string to make bracelets. Each pack costs $6. Besty says she now has enough money to buy 6 packs. Carl says she has enough money to buy only 3 pack. I Besty or Carl correct? Explain your answer
Answer:
Yes, Besty is correct.
Step-by-step explanation:
$27 + $9 = 36. 36 divided by 6 is 6. Besty would only be able to buy 3 packs if each pack costed $12 (36 divided by 12 is 3).
Question 8 of 8
Find the slope-intercept equation of the line.
Plz help last question
I need the equation plz
Answer:
[tex]y = 2x + 2[/tex]
Step-by-step explanation:
To find the slope you look at how much the line rises after going 1 unit to the right. In this equation it rises 2 after going over, or running, 1 unit to the right. So the rise over run is 2 over 1. It can be represented in a fraction 2/1. The slope is the rise over run, being 2.
The constant in the equation, or the y-intercept, is the point where the line intersects the y axis, the dark vertical line. You can count how many units it is from the origin where the 2 black lines intersect. The y-intercept in this is 2.
The slope is the number bedfore the x and the y intervept is the constant after the x.
Answer:
y = -2x + 2
Step-by-step explanation:
y=mx+b
find slope(m) first:
choose two points: (1,0), (0,2)
(y2-y1)/(x2-x1)
= (2-0)/(0-1)
= 2/-1
= -2
6) Find the value of y. (pic below)
A. 90 degrees
B. 135 degrees
C. 45 degrees
D. 180 degrees
Answer:
the answer is c
Step-by-step explanation:
if it is a right triangle most of the time the 2 acute angles will most likely be 45 degrees
Answer:C.45 degrees
Step-by-step explanation:
135º+yº=180º
y=180º-135º
y=45º
If r = 1 and θ = 4π/3 what is the approximate arc length
Answer: 4.189 units
Step-by-step explanation:
AP EX
As per linear equation, the required approximate arc length is 4.19 units.
What is a linear equation?"An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line.
The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant."
Given, length of the radius (r) = 1 units
The value of the given angle(θ) = 4π/3 radian.
Therefore, the approximate arc length is
= length of the radius × value of the given angle
= r × θ
= 1 × 4π/3 units
= 4π/3 units
= 4.19 units
The required approximate arc length is 4.19 units.
Learn more about linear equation here: https://brainly.com/question/11897796
#SPJ2
Give the domain and range of the relation. Tell whether the relation. Tell whether the relation is a function.
Answer:
It is the 4th option. Domain -3 ≤ x ≤ 3. Range -2 ≤ y ≤ 2. This is not a function since it does not pass the vertical line test.
What is - 2 x 6 - 5^2?
Answer:
The answer is -300
Step-by-step explanation:
The answer is -300 because -2 multiplied by 6 is -12 and -12 times 25 is -300
Use the graph below to answer the question.
On a coordinate plane, a horizontal line is at y = 4.
What is the slope of a line that is parallel to the line in the graph?
Answer:
0
Step-by-step explanation:
edg 2020
Answer:
0
Step-by-step explanation:
if its parallel then its gonna be the same slope
When writing a recursive formula, whose initial term is 14 and whose
common difference is -4. Which one represents that theory
Answer:
thx
Step-by-step explanation:
If 1 1/2 sections are 3/4 mile long, how long is each section?
Answer:
1/2 mile
Step-by-step explanation:
.75 mile /1.5 sections = .5 mile/section
I need help with this plzzz percent equations blank % of $900,000 = $270,000
Answer:
30%
Step-by-step explanation:
If 99 candies are needed to fill in a jar, calculate the total candies needed to fill in 108 jars.
Answer:
10,692 candies
Step-by-step explanation:
Answer:
207
Step-by-step explanation:
10
8
6
4
2
X
-10
-8
-6
-4
-2
0
2
4
6
8
10
-2
-4
What is the equation of the line in slope-intercept form?
arm
N
Answer:
This link has all the answers for that quiz: https://brainly.com/question/19699782?answering=true&answeringSource=greatJob%2FquestionPage%2F1
URGENT 20 POINTS AND BRAINLIEST DUE TODAY
Answer:
I would help you but i usally know how todo this but i can't figure this out when i figure this out ill come back to it and edit my answer
Step-by-step explanation:
lus
Donna is making blueberry muffins. She
wants to make a batch that is six times
larger than her recipe makes. Her recipe
calls for 1 cup of blueberries. How many
cups of blueberries will she need?
Answer:
6? cause it is six times bigger so six
is (6,5) for y = 5x - 25 a solution
Answer:
Yes.
Step-by-step explanation:
When you plug in 6 for x and solve for y, you get 5.
y=5(6)-25
y=30-25
y=5
When X is 6, Y is 5.
Karen correctly solved
X^2 + 3x = 18 using the factoring method what solutions did Karen find?
A. {-3, 6}
B. {-6, 3}
C. {2, -9}
D. {-2, 9}
Answer
d
Step-by-step explanation:
what is 5[tex]5\frac{1}{3} divide by \frac{2}{3}[/tex]
Please help me please!!!
Round 25 to two decimal places
Answer:
To round off a number to 2 decimal places, look at the digit in the thousandths place. If the digit in the thousandths place is greater or equal to 5, the hundredths digit is increased by one unit.
Step-by-step explanation:
whats nine plus ten if anyone knows this meme put the answer in
Answer:
jnoioikop
Step-by-step explanation:
Answer:
21
Step-by-step explanation:
Hahahahahahhahahahhahaha
what is the y-intercept of this line: y=5-7x
Answer:
5
Explanation: y-intercepts are just numbers that don't have any variables and they can be found on the y axis.
Answer:
5
Step-by-step explanation:
Rewrite the equation as y=-7x+5.
y=mx+b is slope-intercept form with mx representing slope and b representing the y-intercept.