Answers
The combinations between the linear function g(x) = 4 · x + 1 and the quadratic function g(x) = 4 · x + 1 are f ° g (x) = 16 · x² + 44 · x + 10 and g ° f (x) = 4 · x² + 36 · x + 1, respectively.
How to use composition between two functions
Let be f(x) and g(x) a linear function and a quadratic function, respectively. The composition between two functions is represented below:
f ° g (x) = f [g(x)]
g ° f (x) = g [f(x)]
Where the input of the former function is substituted by the latter function. Now we proceed to find the resulting function:
f(x) = x² + 9 · x
g(x) = 4 · x + 1
f ° g (x) = (4 · x + 1)² + 9 · (4 · x + 1)
f ° g (x) = 16 · x² + 8 · x + 1 + 36 · x + 9
f ° g (x) = 16 · x² + 44 · x + 10
g ° f (x) = 4 · (x² + 9 · x) + 1
g ° f (x) = 4 · x² + 36 · x + 1
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Related Questions
please help me thank you
Answers
Answer:
D) Perpendicular
Step-by-step explanation:
Red: 5y+4x=-30
Blue: y=5/4x-5
2)Jeremy buys 5 pencils and a notebook. If each
pencil costs $0.59 and a notebook is $2. How
much will Jeremy pay all together?
Answers
Answer:
$4.95
Step-by-step explanation:
Answer:
4.59
Step-by-step explanation:
0.59x5=$2.95
2.95+2=4.59
Please please give answer , the numbers on the side are the options
Answers
Answer:
24 tiles (none of the options given is correct)
Step-by-step explanation:
Number of tiles required to floor the room = area of the room/area of 1 tile
Area of the room = 36m * 24m = 864 m²
Area of 1 tile = 6² = 36 m²
Number of times required = 864/36 = 24 tiles
170
The following problems were in your worksheet on direct and inverse proportion. Reformulate the
relationships as algebraic expressions and remember to define the variables you use. You do not
have to solve the expressions.
5. The students in class usually drink a lot of water to help with their studies. I have found that
with five students in the class at least 30 litres of water is needed. How much water will be
needed when there are 30 students in the class?
Answers
Answer:
For s students, at least 6s liters of water will be needed. So, for 30 students, at least 6*30 = 180 liters of water will be needed.
Step-by-step explanation:
This question is solved by proportions, using rule of three.
I am going to say that:
s is the number of students.
l is the number of liters of water needed for s students.
I have found that with five students in the class at least 30 litres of water is needed.
This means that:
[tex]\frac{s}{l} = \frac{5}{30}[/tex]
[tex]5l = 30s[/tex]
[tex]l = \frac{30s}{5}[/tex]
[tex]l = 6s[/tex]
This means that for s students, at least 6s liters of water will be needed. So, for 30 students, at least 6*30 = 180 liters of water will be needed.
Solve 5x + 34 = –2 + 7x for x.
Question 14 options:
A)
x = 12
B)
x = 18
C)
x = –16
D)
x = –24
Answers
Answer:
x = 18
Step-by-step explanation:
Find m
3x-6
8x+4
130
Answers
Answer:
<A = 30°
The steps are given in the pic. Hope it will help :)
Need help ASAP. Just solve what you can and make sure to tell me what is what.
100 POINTS
Answers
Answer:
9x3+5x2=37
8-(7-5)^2+8=12
10-3+5+5x4=32
ill solve rest in comments
9x3+5x2=37
8-(7-5)^2+8=12
10-3+5+5x4=32
PLEASE HELP The value of x in A is _, and the value of y in B is_.
Answers
A server sees 90 customers over 6 hours. How many customers did they see in 1 hour? *
Answers
Answer:
They saw 15 customers per hour.
Step-by-step explanation:
Because its 90 divided by 6 basically
What is the sum of 1 2 + 1 4 12+14? Use the fraction strip to help.
Answers
Answer:
6/8 or in simple terms, 3/4
Step-by-step explanation:
[tex] \frac{1}{2} + \frac{1}{4} \\ = ( \frac{1}{4} + \frac{1}{4} ) + \frac{1}{4} \\ = ( \frac{1}{8} + \frac{1}{8} ) + (\frac{1}{8} + \frac{1}{8} ) + (\frac{1}{8} + \frac{1}{8} ) \\ = ( \frac{2}{8} ) + ( \frac{2}{8} ) + ( \frac{2}{8} ) \\ = \frac{6}{8} \\ = \frac{2 \times 3}{2 \times 4} \\ = \frac{3}{4} [/tex]
The given operation of the two fractions can be found as 6/8. The correct option is (D).
What is a fraction?A fraction is a number written in the form a / b, where a and b are integers and b ≠ 0.
The number a is called as the numerator and b is the denominator.
The given expression is 1/2 + 1/4.
It can be solved using the strip given as below,
The number of 1/8 sections under 1/2 in the strip is 4.
And, the number of 1/8 sections under 1/4 in the strip is 2.
Then, the addition of the two fractions is equivalent to the total number of 1/8 sections under both of them.
It can be written in mathematical form as,
⇒ 1/2 + 1/4
⇒ 4 × 1/8 + 2 × 1/8
⇒ 6/8
Hence, the required sum of the given fractions can be evaluated as 6/8.
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you work at a coffee house roasted coffee beans retain 3/5 of the initial weight approximately what percentage of the initial weight do they retain
Answers
Answer:
they retain 3/5 or 60% of their initial weight
Step-by-step explanation:
Find the Area Please
Answers
This should be the correct answer
3
What is the remainder when 2,308 is divided by
nine? Give your answer as a fraction.
Answers
Answer:
254 R 6
Step-by-step explanation:
Answer:
256 7/16
Step-by-step explanation:
2308/9 = 256 7/16
Which equation has the steepest graph?
Answer Choices:
y = 2x + 4
y = -4x – 1
y = 1/2 x + 10
y = 5x + 2
Answers
Answer:
y = 5x + 2
Step-by-step explanation:
in order to find if a line is steeper, you need to look at the slope
the greater the slope, the steeper the line will be
y = 2x + 4
y = -4x - 1
y = 1/2x + 10
y = 5x + 2
out of all of these options, y = 5x + 2 has the largest slope. this means that it is the steepest one.
The value of a house wa shilling 600,000 in 2005.It increased by 25% in 2006 and 10% in 2007 but dropped by 15% in 2007 find its value in 2008
Answers
Given:
The value of a house is 600,000 in 2005.
It increased by 25% in 2006 and 10% in 2007 but dropped by 15% in 2007.
To find:
The value of the house in 2008.
Solution:
We have,
Value of house in 2005 = 600,000
It increased by 25% in 2006.
Value of house in 2006 = [tex]600,000+\dfrac{25}{100}600,000[/tex]
= [tex]600,000+150,000[/tex]
= [tex]750,000[/tex]
It increased by 10% in 2007
Value of house in 2007 = [tex]750,000+\dfrac{10}{100}750,000[/tex]
= [tex]750,000+75,000[/tex]
= [tex]825,000[/tex]
But it dropped by 15% in 2007.
Value of house in 2008 = [tex]825,000-\dfrac{15}{100}825,000[/tex]
= [tex]825,000-123,750[/tex]
= [tex]701,250[/tex]
Therefore, the value of the house in 2008 is 701,250.
(5 pts) It takes Jack 3 hours longer to write holiday cards than it takes Jill. Together, they can write them
in 2 hours. How long does it take each person to write the cards working alone?
Answers
Answer:
Jack needs 6 hours and Jill needs 3 hours.
Step-by-step explanation:
Let's define the variables:
X = rate at which Jack can write a holiday card.
Y = rate at which Jill can write a holiday card.
Each of them will need a given time to write a card, such that:
X*T = 1 card
We know that Jack needs 3 more hours to write a card than Jill, then Jill needs 3 hours less than Jack, so if Jack needs T hours, Jill will need T - 3 hours
Then we have the equation:
Y*(T - 3 hr) = 1 card
And we also know that when they work together, they need 2 hours, then:
(X + Y)*2 hr = 1 card.
So we have 3 equations:
X*T = 1 card
Y*(T - 3 hr) = 1 card
(X + Y)*2 hr = 1 card.
Now let's ignore the card part just for the equations, then we get:
X*T = 1
Y*(T - 3 hr) = 1
(X + Y)*2 hr = 1
To solve it, we first need to isolate one variable in one of the equations, let's isolate T in the first equation, we get:
T = 1/X
Now we can replace this in the second equation to get:
Y*((1/X) - 3hr) = 1
So now we have two equations:
(X + Y)*2 hr = 1
Y*((1/X) - 3hr) = 1
We need to do the same, isolate one variable in one of the equations, let's isolate Y in the above one:
Y*2hr = 1 - X*2hr
Y = (1 - X*2hr)/2hr
Now we can replace this in the other equation to get:
((1 - X)/2hr)*((1/X) - 3hr) = 1
Now we can solve this for X:
((1 - X)/2hr)*((1/X) - 3hr) = 1
(1 - X)*((1/X) - 3hr) = 2 hr
1/X - 3hr - X*2hr/X + X*2hr*3hr = 2hr
1/X - 3hr - 2hr + X*6hr^2 = 2hr
1/X + X*6hr^2 = 2hr + 3 hr + 2 hr = 7hr
1/X + X*6hr^2 = 7hr
Now we can multiply all by X to get:
X/X + X*(X*6hr^2) = 7hr*X
Now we have the quadratic equation:
(6hr^2)*X^2 - (7hr)*X + 1 = 0
We can find the solutions of this equation if we use the Bhaskara's formula, the solutions are:
[tex]X = \frac{-(-7hr) +- \sqrt{(-7hr)^2 - 4*(6hr^2)*1} }{2*6hr^2} = \frac{7hr +- 5hr}{12 hr^2}[/tex]
Then we have two solutions:
X = (7hr + 5hr)/12hr = 1 hr^-1
And this is the rate at which Jack writes a card, so the actual units are:
X = 0.167 card/hr
Then Jill's rate will be:
Y = (1 - X*2hr)/2hr = (1 - 1card/hr*2hr)/2hr = -0.5 card/hr
So we have a negative rate, this makes no sense, so we can discard this option. The other solution for X is:
X = (7hr - 5hr)/12hr = 0.166... hr^-1
And this is the rate at which Jack writes a card, so the actual units are:
X = 0.166... card/hr
If we have this, then the rate for Jill will be:
Y = Y = (1 - X*2hr)/2hr = (1 - 0.167card/hr*2hr)/2hr = 0.333 card/hr
Then we have:
X = 0.167 card/hr
If we use the first equation, we get:
(0.166... card/hr)*T = 1 card
T = 1 card/((0.166... card/hr)) = 6 hours
Then Jack needs 6 hours to write a card.
And we know that Jill needs 3 hours less than that, then Jill needs 3 hours.
The tape diagram represents an equation. w 1.3 2.7
Answers
Answer: 2/3
Step-by-step explanation:
Answer: w + 1.3 = 2.7
Step-by-step explanation: i did it in khan academy ∩(︶▽︶)∩ HOPE IT HELPS
What do you get when you distribute the -4 to the (11 - 2x)
Answers
helppppp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
I need help!
Benjamin had 1/3 of a can of paint left after he painted his room. Instead of throwing it away, he decided to use 3/4 of the remaining paint to make a picture for his sister. How much of the paint will he use to make the picture for his sister?
Answers
Answer:
1/4 of a can
Step-by-step explanation:
He had 1/3 of a can.
He used 3/4 of the 1/3 of the can.
He used 3/4 * 1/3 of a can.
3/4 * 1/3 = 3/12 = 1/4
Answer: 1/4 of a can
What is the diameter or the radius?
Please help
Answers
Answer:
Radius, Diameter and Circumference
The Radius is the distance from the center outwards. The Diameter goes straight across the circle, through the center. The Circumference is the distance once around the circle.
:)
Answer:
Radius = 8.7 cm
Step-by-step explanation:
The height and hypotenuse of the triangle is provided, so all we have to do is use the Pythagorean Theorem. [tex]\sqrt{15^{2}-12.2^{2}}[/tex] and this yields the answer.
you have 60 oz of egg noodles. yiu need 5 oz to make one serving of chicken noodle soup. how maby servings can you make
Answers
Answer:
The answer is 12
Step-by-step explanation:
You have to divide 5 and 60 or you can multiply by 5 until you get to 60.
Answer:
12
Step-by-step explanation:
60/5=12
Choose the inequality that represents the following graph.
Answers
Answer:
a
Step-by-step explanation:
the answer is a because the rrow is pointing right so the symbol is > and the point starts at -5
Find the segment lengths
Answers
Answer:
y = 18
Step-by-step explanation:
[tex] \frac{21 + 7}{21} = \frac{y + 6}{y} [/tex]
[tex] \frac{28}{21} = \frac{y + 6}{y} [/tex]
Cross multiply
28*y = 21(y + 6)
28y = 21y + 126
28y - 21y = 126
7y = 126
y = 126/7
y = 18
3.5-5.5n-4n+8 help please
Answers
HELP PLEASEEEE
The larger of two number is ten more than three times the smaller number The sum of the two numbers is fifty four
Answers
Answer:
hasta no se pero nimodoa esta bien adiós baybau
1000003842638476238476+2837428734682764283746
Answers
Answer:
3.8374326e+21
Step-by-step explanation:
id.k goo.gle said this
Is 5.3 a possible solution to x > 5 ?
Answers
Yes 5.3 is greater than 5
5.3 > 5
Answer:
yes, it is.
Step-by-step explanation:
its a solution because in the graph below, 5.3 is in the shaded region. hope this helped!!
A collection agent earns a fixed amount for each call that he makes, as
shown in the graph below.
If the collection agent makes 11 calls, how much will he earn in total?
Answers
Answer:
The answer is $9.90
Step-by-step explanation:
A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Find the expected frequency for the cell E2,2 to determine if there is enough evidence to conclude that the number of minutes spent online per day is related to gender. Round to the nearest tenth if necessary. Gender| 0-30| 30-60| 60-90| 90+ Male| 23|35|76|46 Female|31|42|46|16
Answers
Answer:
The expected frequency for the cell E2,2 is = 33
Step-by-step explanation:
The given data is
Gender | 0-30| 30-60| 60-90| 90+ Totals
Male | 23 | 35 | 76 | 46 180
Female | 31 | 42 | 46 | 16 135
Totals 54 77 122 62 315
The expected frequency for the cell E2,2 is :
Expected for the (30-60 box for females) = Total of (30-6)/ (total )* females
= ( 77/315)135= 33
Here p= 77/315 and n= 135
therefor X= pn = 33
χ²= (33-42)²/33= 2.455 ( for the single value of E2,2=33)
Expected for the (30-60 box for males) = Total of (30-6)/ (total )* males
= ( 77/315)180= 44
χ²= (44-42)²/44= 0.09
The critical region is χ² (0.05) 3 ≥ χ²= 11.34
Let the null and alternate hypothesis be
H0:the number of minutes spent online per day is not related to gender
against
Ha: the number of minutes spent online per day is related to gender
The single value of χ² for E2,2 = 2.45 is less than the critical value of 11.34.