The composition of the functions f(x) and g(x) gives the equation:
[tex]f(g(x)) = 4x^2 + 6x - 3[/tex]
How to get the composition of functions?Here we want to get the composition of the two functions:
[tex]f(x) = x^2 + 3x - 3\\\\g(x) = 2x[/tex]
f(x) is a quadratic and g(x) is a linear equation.
Now we want to get the composition:
[tex]f(g(x))[/tex]
This means that we need to evaluate function f(x) in g(x), so we can replace all the "x" in the function f(x) by the notation "g(x)"
[tex]f(g(x)) = g(x)^2 + 3*g(x) - 3[/tex]
Now we replace all the "g(x)" by the actual function g(x) = 2x, we wll get:
[tex]f(g(x)) = g(x)^2 + 3*g(x) - 3 = (2x)^2 + 3*(2x) - 3[/tex]
finally, we can simplify this to get the composition, which is a quadratic function just like f(x).
[tex]f(g(x)) = 4x^2 + 6x - 3[/tex]
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Two containers of gasoline hold a total of 100 gallons. The big container can hold 20 gallons less than twice the small container. How many gallons does each container hold?
Answer:
The big container holds 60 gallons
The small container holds 40 gallons
Step-by-step explanation:
If the small container held 40 gallons of gasoline then double that would be 80 gallons and 20 gallons less than that would be 60 gallons.
You are designing a simulation for which day of the week people are born. You assign numbers
to each day of the week from, Sunday = 0 through Saturday = 6. You decide to use a sample
size of 20.
Use the random number table to conduct your first trial, working from left to right.
39017 66124 37046 59285 15208 47185 76426 23648
51239 88346 59268 71307 37420 69307 98648 45960
Which chart matches the results from your first trial?
Answer:
The chart should have the pattern 3332333
Step-by-step explanation:
The equation below shows the total volume (V), in cubic units, of 4 identical boxes with each side equal to s units: V = 453 If s = 2.5 units, what is the value of V?
Answer:
in cubic units, of 4 identical boxes with each side equal to s units: V = 4s3 If s = 2.5 units, what is the value of V? (5 points) 25 cubic units 30 cubic units 62.50 cubic units 156.25 cubic units
Step-by-step explanation:
Hayden's checking account balance was $145.95. After two checks were cashed, each for the
same amount, his balance was - $4.05. This problem can be represented by the equation below.
145.95 - 2x = -4.05
What does x represent?
A. amount of each cashed check
B. total amount of both cashed checks
C. beginning checking account balance
D. final checking account balance
Answer: A. Amount of each cashed check.
Step-by-step explanation:
145.95 - 2x = -4.05
2x=150
X=75
Can someone help me please
Answer:
8(n/4)
Step-by-step explanation:
Find the error.
x=40
y=90
If(x>y and x<50)
print(a+10))
ELIF(x<y or x>50):
print(b*10)
Answer:
If(x>y and x<50): # add semicolon
print(a+10) # one close bracket
add " " double quotes inside print statements
print("a+10")
Find value of x and y
Turn y=-1/5x-4 into standard form
Im willing to give 20 points maybe even more
A teacher purchased 20 calculators and 10 measuring tapes for her class and paid $495. Later, she realized that she didn't order enough supplies. She placed another order of 8 of the same calculators and 1 more of the same measure tape and paid $178.50.
The system represents the situation
`20c+10m=495`
`8c+1m=178.50`
Find the cost of one calculator and the cost of one measure tape using one of our methods of solving systems.
Answer:
Equations are
20c + 10m = 495..............(1)
8c + 1m = 178.5.................(2)
Now , equation (2) * 10 = 80c + 10m = 1785...........(3)
So, Eq. (3) - Eq(1) =
80c + 10m - 20c - 10m = 1785 - 495
60c = 1290
c= 21.5
********************************************************
Now place the value of c in Eq (2)
So , m =6.5
Mark my answer as brainlist answer
Step-by-step explanation:
Lanie's room is in the shape of a parallelogram. The floor of her room is shown below and has an area of 108 square feet. Lanie has a rectangular rug that is 6 feet wide and 10 feet long. Will the rug fit on the floor of her room? Use the drop‐down menus to explain and show your answer.
Answer:
Yes it would
Step-by-step explanation:
Lanie's room is in the shape of a parallelogram.
Lanie has a rectangular rug that is 6 feet wide and 10 feet long.
Area of a rectangle = Length × Width
Area of the rectangular rug = 10 feet × 6 feet
= 60 square feet
We are told that:
The floor of her room is shown below and has an area of 108 square feet.
Hence, the rug would fit on the floor of her room because it's area is within the area of the floor of her room.
Tan(x) *cos(x)*cos(x)= ( the answer should have sin only ) ASAP
This doesn't make any sense because you didn't give a value to cos like you did to sin.
Let me guess the actual question is tan(x)*cos(x) write this in term of sin.
Now from trigonometry identities, we know that tan(x)=sin(x)/cos(x)
So the expression can be written as sin(x)/cos(x)*cos(x)
which results in sin(x) as the answer, if I guessed the question wrong, sorry and please tell me in the comments what the correct question is, because this question doesn't seem complete :)
Solve the inequality:
-15 + 5x > 25
Answer:
x > 8
Step-by-step explanation:
-15 + 5x > 25
Add 15 on both sides
5x > 40
x > 8
Answer:
here
Step-by-step explanation:
inequality form ---- x>8
interval form ----- (8,infinite)
The figure is made up of 2 rectangles and 2 right triangles.
What is the area of the figure?
173 units2
253 units2
277 units2
325 units2
plzzzzzz answer ASAP
Answer:
Hi how are you
Step-by-step explanation:
i thhink the answer is B if im wrong im srry
Answer:
i think it would be the first answer which is, 173 units
What is the domain of the function y = 2e graphed below?
Answer:
All Real Numbers
General Formulas and Concepts:
Algebra I
Interval NotationDomain is the set of x-values that can be inputted into function f(x)Step-by-step explanation:
According to the graph and function y = 2eˣ, we see that our x-values span from negative infinity to positive infinity. We also see that we can plug in any number x into our function:
(-∞, ∞)
or
All Real Numbers
Answer: D) all real numbers
Step-by-step explanation:
determine the value of the?
25x +30=?(5x+6)
Answer:
It began after the stock market crash of October 1929, which sent Wall Street into a panic and wiped out millions of investors. Over the next several years, consumer spending and investment dropped, causing steep declines in industrial output and employment as failing companies laid off workers.
160 divided by 7 rounded to the nearest hundredth
Answer: A We round the number up to the nearest hundred if the last two digits in the number are 50 or above.
Step-by-step explanation:
6 (8j - 3l + 9 ) 12l + 14j
Answer:
5822j-15972
Step-by-step explanation:
Answer:
5822j-15972
Step-by-step explanation:
Mrs. Beppu's property has four sides. An aerial view of her property is shown below. What term best describes the shape of her property?
Answer:
rectangle
Step-by-step explanation:
From the picture attached below of the aerial view of Mrs. Beppu's house we can see that it is a rectangle. That is because it has 4 sides with only the parallels being the same size. Meaning that both the width and the length of the house are not the same. This removes the possibility of it being a square. Since all the angles seem to be right angles it also removes the possibility of it being a trapezoid. The best choice would be that it is a rectangle.
Algebraic Expression
x + y + 2
Constants | Variable/s/term/s Degree of term
Constants : 1 (the only constant term is 2)
Variables : 2 (x and y)
Terms : 3 ( x, y and 2)
Degree of term : 1
Dentro de cinco años mi abuelo tendrá el cuádruple de mi edad. Hace cinco años tenia siete veces mi edad¿que edad tenemos el y yo?
Answer:
La edad del abuelo es 75 años y la tuya es de 15 años.
Step-by-step explanation:
Si dentro de 5 años tu abuelo (A) tendrá el cuádruple de tu edad (E), tenemos:
[tex] A + 5 = 4(E + 5) [/tex] (1)
Ahora, si hace cinco años tenia siete veces tu edad:
[tex] A - 5 = 7(E - 5) [/tex] (2)
Multiplicando la ecuacion (1) por -1, tenemos:
[tex] -A - 5 = -4(E + 5) [/tex] (3)
Ahora sumando la ecuación (3) con (2):
[tex] -10 = 3E - 55 [/tex]
[tex] E = 15 [/tex]
Entonces, reemplazando el valor de E en la ecuación (1):
[tex] A + 5 = 4(15 + 5) [/tex]
[tex] A = 75 [/tex]
Por lo tanto, la edad del abuelo es 75 años y la tuya es de 15 años.
Espero que te sea de utilidad!
At the market you can buy 6 bags of apples for $25. At the orchard you can get 8 bags of apples for $35. Which is the better deal?
Answer:
6 bags for $25
Step-by-step explanation:
25/6 = 4.16666666667 = $4.17 per bag
35/8 = 4.375 = $4.37 per bag
The better deal for the bags of apples is at the market
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
To determine which is the better deal, we can compare the prices per bag of apples at the market and the orchard.
At the market:
Price of 6 bags of apples = $25
Price per bag of apples = $25 / 6 ≈ $4.17 (rounded to two decimal places)
At the orchard:
Price of 8 bags of apples = $35
Price per bag of apples = $35 / 8 ≈ $4.38 (rounded to two decimal places)
Comparing the two prices per bag of apples, we can see that the price per bag at the market is $4.17, while the price per bag at the orchard is $4.38.
Hence , the better deal is at the market where you can buy 6 bags of apples for $25, resulting in a lower price per bag compared to the orchard.
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Find the value of k, represented as a decimal rounded to the nearest tenth.
5/7 = 12/k
Answer:
We conclude that the value of k represented as a decimal rounded to the nearest tenth is: [tex]k = 16.8[/tex]
Step-by-step explanation:
Given the expression
[tex]\frac{5}{7}=\frac{12}{k}[/tex]
We need to determine the value of k, represented as a decimal rounded to the nearest tenth.
Let us solve the expression
[tex]\frac{5}{7}=\frac{12}{k}[/tex]
Apply cross-function multiply: if [tex]\frac{a}{b}=\frac{c}{d}[/tex] then [tex]a\cdot \:d=b\cdot \:c[/tex]
[tex]5k=7\cdot \:12[/tex]
[tex]5k=84[/tex] ∵ 7 · 12= 84
Divide both sides by 5
[tex]\frac{5k}{5}=\frac{84}{5}[/tex]
Simplify
[tex]k=\frac{84}{5}[/tex]
[tex]k = 16.8[/tex] (Rounded to the nearest 0.1 or the Tenths Place)
Therefore, we conclude that the value of k represented as a decimal rounded to the nearest tenth is: [tex]k = 16.8[/tex]
this question is hard help..........
Answer:
sorry i dont know
Step-by-step explanation:
Answer:
.OOF Sorry im not good in math
A young woman walked into a cafe and asked for a drink of water the man behind the counter suddenly pulled out a gun and pointed it at her a few seconds elapsed and then the women smiled and thanked the man and left
She had hiccups so she ordered a glass of water. The man noticed so he pulled out a gun to give her a scare. Being startled is said to make hiccups stop. Therefore, she thanked him for ending her hiccups and left.
I will mark you brainiest if you can answer this
Answer:
y=2x
Step-by-step explanation:
y= 2x
b is 0 because there is no y-intercept and it's going up 2 right 1 so the slope is 2
Answer:
Step-by-step explanation:
Chicken nugget
pls help me. Will mark brainliest if right
Answer:
1st one
Step-by-step explanation:
The Big Wheel at a theme park has a diameter of 5m. How far would you travel in one complete revolution of the wheel?
Answer:
15.71m
Step-by-step explanation:
One revolution is equal to the circumference of the wheel
Circumference = πD
22/7 X 5 = 15.71m
Which pair of fractions is not equivalent fractions?
A.1/9,2/18
B.7/8,5,6
C.3/16,9/48
D.6/15,4/10
Answer:
b is correct
Step-by-step explanation:
as 7/8 can't be further simplified and it is not making equivalent with 5/6
hope it helps you
please mark me as brainlist
A 45 ounce box of cereal costs $3.99. Find the unit price. Round your unit
price to the nearest cent if needed.
Answer:
0.1125 ounces per cent
Find the original price.
The discount on a toy robot is 40%. The toy robot is on sale for $54?
Answer:
$75.60
Step-by-step explanation:
Well, I don't exactly know why, but I know that you need to 54 multiply by 1.40 to get the answer.
Answer:
$75.60
Step-by-step explanation:
54 increase 40% =
54 × (1 + 40%) = 54 × (1 + 0.4) = 75.6