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
3x+45=60 solve for x
Answer:
x = 5
Step-by-step explanation:
you subtract 45 from both sides
3x = 15
you divide both sides by 3
x = 5
Answer:
x = 5
Step-by-step explanation:
Simplify: -2 root -3 x root negative -18. What are the steps to get the answer?
Answer:
6 squareoot 6
Step-by-step explanation:
1) In 2000, there were approximately 109 million cell phone users in the United States. The number of cell
phone users grew to approximately 189 million after one year.
a) Write an exponential model that represents the number of cell phone users in the United States, where t
represents the number of years after 2000.
[2]
[1]
b) What is the percent rate of change?
[1]
c) What would be the number of cell phone users in 2015?
[3]
2) Which statement applies to the graph of f(x)=e* below.
Answer:
the answer is 298
Step-by-step explanation:
Jennifer had 3 \frac{3}{4}
4
3
lbs of tomatoes. She used \frac{1}{3}
3
1
OF that amount to make a salad. How many pounds OF tomatoes did she use? (LEAVE ANSWER AS A MIXED NUMBER)
Answer:
She used 1/4 of a pounds for salad
Step-by-step explanation:
Here, we want to calculate the amount of pounds of tomatoes used to make salad
From the question, she has 3/4 pounds and used 1/3 of what she has to make salad
What she used will be;
3/4 * 1/3 = 1/4
Emma earns $2 less than three times as much as Rachel. Nick earns twice as much as Emma. Together they earn $594 per week. How much does each person earn per week?
Answer:
290$
Step-by-step explanation:
Answer:
Mei earn $2 less than three times as much as Olivia. Shane earns twice as much as mei. Together they earn $594 per week. How much does each person earn per week?
***
Step-by-step explanation:
let x=amt Olivia earns
3x-2=amt Mei earns ($2 less than three times as much as Olivia).
2(3x-2)=amt Shane earns (twice as much as mei)
..
x+3x-2+2(3x-2)=594
x+3x-2+6x-4=594
10x=600
x=60
3x-2=178
2(3x-2)=356
amt Olivia earns=$60
amt Mei earns=$178
amt Shane earns=$356
Which equation describes the line that passes through (-3,1) and is parallel to the line described by y =4x+1
Zola and her friends are going bowling. The bowling alley charges each person a $14 fee to rent shoes, plus $4.50 per game. Which equation represents the cost, y, for each friend to go bowling in terms of the number of games played, x?
Answer:
X+14=y
Step-by-step explanation:
Help plzzzzzzzzzzzzzz
Answer:
∠E
Step-by-step explanation:
∠E is between PE and EN
Which function is equivalent to g (k) = -k'+ 6k-9?
a g(k) = -(k- 3)
g(k) = (-k+ 3)(k+ 3)
© g(k) =-(k+3)
O
g(k) = (-k- 3)(–k+ 3)
Answer:
I believe it’s g(k)=(-k- 3)(-k+3)
Step-by-step explanation:
The equivalent function is g(k) = -(k - 3)².
The correct option is A.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
We can start by completing the square of the quadratic function g(k) = -k² + 6k - 9:
g(k) = -(k² - 6k + 9 ) = -(k - 3)²
Option A can be simplified as:
g(k) = -(k - 3)²
Compared with the completed square form of g(k), we can see that option A is equivalent to g(k).
Therefore, the answer is A. g(k) = -(k - 3)²
To learn more about the quadratic function;
https://brainly.com/question/11485644
#SPJ5
The complete question:
Which function is equivalent to g (k) = -k²+ 6k-9?
A. g(k) = -(k- 3)²
B. g(k) = (-k+ 3)(k+ 3)
C. g(k) = -(k+3)²
D. g(k) = (-k- 3)(–k+ 3)
Which line on the graph below has an undefined slope?
○ P
○ Q
○ R
○ S
Answer:
R
Step-by-step explanation:
Answer:
R
Step-by-step explanation:
A mom mixes 9 ounces of juice with 3 ounces of water. What present of the drank is juice?
Answer:
6 ounces of juice
Step-by-step explanation:
Answer:
12 ounces
Step-by-step explanation:
A mom mixes 9 ounces of juice with 3 ounces of water. This means that the total ounces of drink= 9+3 = 12 ounces. The percent of the drink which is juice is: Ratio of the quantity of juice to the total quantity of drink and multiplying this obtained quantity by 100.
PLEASE HELP ME ASAP!!!!!!
Answer:
b
Step-by-step explanation:
solve -1 < x + 1 ≤ 6
Answer:
-2<x≤5
Step-by-step :
-1<x+1≤6 So fisrt what every we do to one side we must do to the other. In this case it's a bit different since we are dealing with inequalities.
-1<x+1≤6 I would start off by isolating x in the middle.
-1<x+1≤6 I subtracted 1 from all three sides.
-1 -1 -1
Now your equation should look like this:
-2<x≤5 Now there is really nothing much we can do here since we were just trying to get x by its self.
Answer : -2<x≤5
(Need help ASAP)
How many solutions does the equation have:
3x - 5 = -5 + 3x
Answer:
Infinitely many
Step-by-step explanation:
Add 5 to both sides and subtract 3x on both sides. that results in 0=0. if the numbers are the same, than its infinitely many.
Answer:
0=0
Step-by-step explanation:
3x-5=-5+3x
0=0
Last year, Ivy's pant measured 12 inches. This year, her plant is 75% taller.
How many inches did her plant grow?
Answer:
The plant grew 9 more inches since last year.
Step-by-step explanation:
75% of 12 is 9 and the initial plant growth was 12 inches.
So, the plant grew 9 more inches since last year.
The plant is now 21 inches.
Answer:
9
Step-by-step explanation:
Divide 12 by 4 to get 25% = 3
25% x 3 = 75%
3 x 3 = 9
28. How much plain yogurt will you need to make 2 1/2 dozen cookies? Show your work.
Answer:
[tex]\frac{5}{6}[/tex] cups
Step-by-step explanation:
Normally, when working with mixed numbers, I would prefer to turn them into improper fractions first before evaluating.
1 [tex]\frac{1}{2}[/tex] cookies --- [tex]\frac{1}{2}[/tex] cup plain yogurt
[tex]\frac{3}{2}[/tex] cookies --- [tex]\frac{1}{2}[/tex] cup plain yogurt
2[tex]\frac{1}{2}[/tex] cookies --- ? cup plain yogurt
[tex]\frac{5}{2}[/tex] cookies --- [tex]\frac{5}{3}[/tex] × [tex]\frac{1}{2}[/tex] cup plain yogurt = [tex]\frac{5}{6}[/tex] cups plain yogurt
Mary bought these art supplies: 4 paint brushes at $1.29 each, 6 dowel rods at $1.49 each, a jar of paste at $1.25, and 2 canvases at $6.00 each. How much change did she get from $40?
A. $8.25
B. $9.35
C. $10.45
D. $12.65
I'll give brainliest!
Answer: The answer is D.
Step-by-step explanation:
Multiply the art supplies with their assigned prices, then combine like terms.
I need help with this
Answer: 0.6 grams
Step-by-step explanation: divide grams by cm and its 0.6
Enter an equation to describe the linear relationship.
The temperature, y, of a pot of water is 45 °F. The temperature increases by 25 °F per minute,x , when being heated.
The equation is y=
Jen and Kamlee are walking to school. After 20 minutes, Jen has walked 45 mile. After 25 minutes, Kamlee has walked 56 mile. Find their speeds in miles per hour. Enter the correct answers in the boxes.
Answer:
Jen's speed = 135 miles per hour (Approx)
Kamlee's speed = 134 miles per hour (Approx)
Step-by-step explanation:
Given:
Jen walk = 45 miles
Jen's time = 20 min = 20/60 = 0.333 hour
Kamlee walk = 56 miles
Kamlee's time = 25 min = 25/60 = 0.416667 hour
Find:
Speed
Computation:
Jen's speed = 45 / 0.333
Jen's speed = 135 miles per hour (Approx)
Kamlee's speed = 56 / 0.416667
Kamlee's speed = 134 miles per hour (Approx)
write at least four rational numbers between -2/5 and -1/3.
Answer:
-47/120 -23/60 -3/8 -11/30
Step-by-step explanation:
fractions are always rational. give both numbers the same denominator and list any numbers between the two. (-2/5 is equal to -6/15) (-1/3 is equal to -5/15) make sure to simplify though
The length of the rope was cut from 30 inches to 24 inches. By what percent was the price of the rope reduced?
The club sold shirts and capes to raise money for new stage equipment. The club sold each shirt for $20.00. The club made profit of $4.00 for each shirt. Sold. Part A: The drama club sold a total of $480.00 worth of shirts. How much profit did the club make from the shirt sale?
Answer:
The club made a profit of $96 from the shirt sale.
Step-by-step explanation:
First, you have to find the number of shirts sold by dividing the total amount sold by the price per shirt:
480/20=24
Now, that you know the number of shirts that were sold, you can multiply the profit per shirt for the number of shirts sold:
4*24=96
According to this, the answer is that the club made a profit of $96 from the shirt sale.
Which expressions are equivalent to 5x?
(Didn’t expect the test to be this hard ;C)
A: 5x + 0
B: x (0) + 4x
C: x + (0 + 4x)
D: 4x + (1) x
E: 5x multiplied by 0
F: 5x (1)
Answer:
A, E, F
Step-by-step explanation:
Your welcome
Answer:
its a,d,c,e, and f
Step-by-step explanation:
Find the slope of the line. Write your answers in simplest form
Answer:
-3/5
Step-by-step explanation:
using the picture and the rise over run method, you can see that from the coordinate farthest to the right, you move 3 spaces up (positive), and 5 spaces to the left (negative), which gives you your answer of -3/5.
You can also use the formula to find the slope:
1) y₂-y₁/x₂-x₁
2) -2-1/1-(-4)
3) -3/5
HELP THIS IS TIMED
i need answers asap
Answer:
7
Step-by-step explanation:
I am 100% sure
[tex]\sf{\bold{\green{\underline{\underline{Given}}}}} [/tex]
⠀⠀⠀⠀
AD = 24cmDB = 25 cm______________________[tex]\sf{\bold{\green{\underline{\underline{To\:Find}}}}} [/tex]
⠀⠀⠀⠀
AB = d = ?? ______________________[tex]\sf{\bold{\green{\underline{\underline{Solution}}}}} [/tex]
⠀⠀⠀⠀
Using Pythagoras theorem ;
⠀⠀⠀⠀
[tex]\sf{\red{\boxed{\bold{( hypotenuse )^2 = ( base )^2 + ( height )^2 }}}}[/tex]
⠀⠀
First , lets understand the concept ;
⠀⠀
What is Pythagoras theorem ??
⠀⠀⠀⠀
In Pythagoras theorem the square of hypotenuse is equal to the square of base in the square of corresponding height when one angle is 90° .⠀⠀⠀⠀
What is hypotenuse ?
⠀⠀⠀⠀
The side in the front of right angle is known as hypotenuse .⠀⠀⠀⠀
In the given Δ ;
⠀⠀⠀⠀
Hypotenuse = DB = 25 cm
⠀⠀
Acc. to the formulae ;
⠀⠀⠀⠀
➠ 25² = 24² + d²
⠀⠀⠀⠀
➠ d² = 25 ² - 24 ²
⠀
➠ d² = 625 - 576
⠀⠀⠀⠀
➠ d² = 49
⠀
➠ d = √49
⠀⠀⠀⠀
➠d = 7cm
⠀⠀⠀⠀
______________________[tex]\sf{\bold{\green{\underline{\underline{Answer}}}}} [/tex]
⠀⠀⠀⠀
Value of d is 7cmneed help finding out something, refer to picture
Answer:
He made a mistake in the second line.
Step-by-step explanation:
He factored out x out of 6-2x and 5+4x, which is not possible because there is not an x in both 6 and 5.
I’ll name brainliest✨
Answer: -5 1/2 or -5.5
Step-by-step explanation: Negative five and a half. Its technically -5 2/4 but simplify 2/4 its 1/2
Answer:
Point B is located at -5.5
Step-by-step explanation:
Point B is located at the mid point between -6 and -5 on the scale. So, the answer would be 5 and 1/2 or -5.5
I hope this helped to answer your question.
On the radio one morning, a weather reporter stated that the tempature was two degrees below zero, but the tempature would cotinue to rise throughout the day. Which inequality can be used to represent readings, T, that day? A. T < -2 B. T < -2 ( _ UNDER < ) C. T > - 2 D. T > -2 ( _ UNDER >)
Answer:
T ≥ -2
Step-by-step explanation:
Given
Temperature = 2° below 0°
Required
Represent as an inequality
First, we need to calculate the temperature in the morning.
2° below 0 means.
Temperature = 0° - 2°
Temperature = -2°
Next, we determine the temperature at any time.
The question says the temperature continues to rise during the day.
Represent this with T
This means T will be greater than -2°
However, we need to consider where the temperature started from.
In other words, T = -2
Combine T = -2 and T = -2 together, we have:.
T ≥ -2
Hence, the inequality that represents the scenario is T ≥ -2
plssss help me mathh
Answer:
C and E
Step-by-step explanation: