Evaluate compositions of function. Let f(x) = 3x + 2, g(x) = -x2, and h(x) = x-2/5. Find the indicated value. (SHOW WORK PLEASE))
Answers
The indicated numeric values for the composite functions are given as follows:
1. f(g(-3)) = -25.
2. g(f(2)) = -64.
3. h(f(-5)) = -3.
4. g(g(-3)) = -81.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is according to the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function. Hence, to calculate f(g(-3)), for example, we calculate g(-3), then we calculate the numeric value of function f(x) at x = g(-3).
For this problem, the functions are given as follows:
f(x) = 3x + 2.g(x) = -x².h(x) = (x - 2)/5.For item 1, the numeric values are found as follows:
g(-3) = -(-3)² = -9.f(g(-3)) = f(-9) = 3(-9) + 2 = -27 + 2 = -25.For item 2, the numeric values are found as follows:
f(2) = 3(2) + 2 = 6 + 2 = 8.g(f(2)) = g(8) = -(8)² = -64.For item 3, the numeric values are found as follows:
f(-5) = 3(-5) + 2 = -15 + 2 = -13.h(f(-5)) = h(-13) = (-13 - 2)/5 = -3.For item 4, the numeric values are found as follows:
g(-3) = -(-3)² = -9.g(g(-3)) = g(-9) = (-9)² = -81.More can be learned about composite functions at https://brainly.com/question/10687170
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Related Questions
How many units is 523 from 0?
Answers
Using proportions, it is found that the number 523 is 523 units from zero.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using arithmetic operations such as multiplication and division with the unit rates of the measures.
One example of application is for the digit values of a number, as:
Each unit is worth 1.Each tenth is worth 10.Each hundredth is worth 100.Each thousandth is worth 1000.And so on...
For the number 523 given in this problem, since each unit is worth one, the number of units that it is away from zero is given by:
523/1 = 523 units.
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4) Krysta is attending a school orchestra concert. She sees her math teacher seated 12 meters ahead of her and her science teacher seated 9 meters to her right. How far apart are the two teachers? Submit meters Work it out Not feeling ready yet? These can help: Pythagorean theorem: find the missing leg or hypoten... (80) Distance/direction to starting point
Answers
Pythagoras's theorem - The two teachers are both seated at a distance of 15 meters from each other.
What is Pythagoras' theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of the square with the hypotenuse (the side across from the right angle) is equal to the sum of the areas of the squares with the other two sides. The Pythagorean equation, which generally refers to the relationship between the lengths of the legs a, b, and the hypotenuse c, can be used to represent this theorem.
We are given,
the distance between Krysta and her math teacher to be 12 meters, and the distance between Krysta and her science teacher to be 9 meters
for simplicity, we'll let
the distance between Krysta and her math teacher to be KM =12 meters
and the distance between krysta and her science teacher to be KS =9 meters we need to find the distance between the maths teacher and the science teacher, i.e. MS.
all three people's sitting arrangement makes a triangle, with them sitting on the vertex of it.
Using Pythagoras' theorem,
(KM)² + (KS)² = (MS)²
(12)² + (9)² = (MS)²
144 + 81 = (MS)²
225 = (MS)²
√225 = (MS)
thus, MS = 15 meters
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Julie says that the constant of proportionality in the equation below is 0.45. Is Julie correct?
P = 0.45n
Answers
The constant of proportionality in the equation:
P = 0.45*n
Is k = 0.45, so we can conclude that Julie is correct.
What is the constant of proportionality?A proportional relationship between two variables x and y is written as:
y = k*x
Where k is the constant of proportionality.
In this case, we have the variables P and n, and the proportional relationship is:
P = 0.45*n
So we can see that the value of the constant of proportionality is k = 0.45, so yes, Julie is correct.
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A monthly produce box is
delivered to Ms. Jones'
door. There is an initial set
up fee of $25.00 plus
$30.00 each week. If Ms.
Jones spent $265, then
how many weeks did she
receive the produce
box?
Ahmed says eight weeks
because
25+ 30x = 265.
Amy says nine weeks
because
30+ 25x = 265.
Answers
Answer: 8 weeks
Step-by-step explanation:
HELP ASAP WILL GIVE 20 POINTS AND BRAINLIEST TO WHOEVER SOLVES THIS
The length of a bacterial cell is about 4 x 10−6 m, and the length of an amoeba cell is about 2.5 x 10−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant digits. A 6.25 x 10^2
B 2 x 10^2
C 6 x 10^1
D 16 x 10^1
Answers
The bacterial cell is 6.25 x 10 times smaller than the amoeba cell.
The length of the Bacterial cell is 4 x 10⁻⁶ meters.
The length of the Amoeba cell is 2.5 x 10⁻⁴ meters.
The length L of the bacterial cell can be written as,
L = 0.000004 meters.
Also, the length L' of the amoeba cell can be written as,
L' = 0.00025 meters.
Let us say that the bacterial cell is N times smaller than the amoeba cell.
So. we can write,
Length of bacterial cell x N = length of amoeba cell.
LN = L'
0.000004(N) = 0.00025
N = 0.00025/0.000004
N = 62.5
So, now we can say that the length of the bacterial cell is 62.5 times smaller than he amoeba cell.
As we have to state our answer in scientific notation,
We can write 62.5 as 6.25 x 10.
Now the number of significant figure is has are three.
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Maria paid $240 for a table set after a discount of 40%. What was the original price? Use scratch paper to create a model to help solve the problem (e.g., tape diagram, table, double number line diagram, 10×10 grid).
The original price was $
Answers
Answer:
$400
Step-by-step explanation:
We see that the discount price is (100-40) = 60% of the original price
If 60% corresponds to $240, than 10% corresponds to 240/6 = $40
Since the original price is 100% = 10*10%, the original price is 10* $40 = 400.
I can't make something with scratch paper right now, i hope you will be able yourself to put the above information is a table :-)
Good luck with it!
If A=B and B=C, which property let's us say A=C?
Answers
Answer:
By using commutative property, if a = b and b = c, then a = c.
Step-by-step explanation:
Answer:
translative property
Step-by-step explanation:
Renz wishes to make an open box froma square piece of cardboard with a sidethat measures 15 inches by cuttingequal squares from the four cornersand folding the sides. what will be thevolume of the box if he cuts a squarewith 2 inch sides?
Answers
2.5 inches will be the volume of the box if he cuts a square with 2 inch sides.
What is volume ?
Every three-dimensional item takes up space in some way. The volume of this area is what is being measured. The area contained by an object's limits in three-dimensional space is referred to as its volume. It is sometimes referred to as the object's capacity.Let each side of he square that's cut-off from each corner be represented by x.
This means that the base of the box will be of dimension of the side 15−2x while the height of the box will be x.
Thus;
Volume of box is:
V = (15 − 2x)(15 − 2x)x
V = (15 − 2x)²x
V = (4x² - 60x + 225)x
V = 4x³ - 60x² + 225x
Let's differentiate with respect to x to get;
dV/dx = 12x² - 120x + 225
Maximum value of x is at dV/dx = 0
12x² - 120x + 225 = 0
Using quadratic formula, we arrive at;
x = 2.5 or 7.5
Now, let's find the second derivative of the volume;
d²V/dx² = 24x - 120
Putting x = 2.5 gives;
d²V/dx² = 24(2.5) - 120
d²V/dx² = -60Thus, V is maximum at x = 2.5, since d²V/dx² is negative
At x = 7.5;
d²V/dx² = 24(7.5) - 120
d²V/dx² = 60
Thus, V is minimum at x = 7.5, since d²V/dx² is negative
Thus,we will use x = 2.5
Maximum volume; V = (15 − 2(2.5))(15 − 2(2.5))(2.5)
V = 10 × 10 × 2.5
V = 250 Sq.inches
Dimensions are;
(15 − 2x) = 15 - 2(2.5) = 10 inches
(15 − 2x) = 15 - 2(2.5) = 10 inches
x = 2.5 inches
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rewrite this expression as an addition equation -4 3/8 - (-1 1/4)=
Answers
Given the equation:
[tex]\text{ - 4 }\frac{3}{8}\text{ - (-1 }\frac{1}{4})[/tex]Please helppp <3
The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over times, x measured in seconds. During what interval(s) of the domain is the water balloon's height staying the same?
A. 0 ≤ x ≤ 2
B. 2 ≤ x ≤ 5
C. 5 ≤ x ≤ 6
D. 6 ≤ x ≤ 8
Answers
Answer:
B
Step-by-step explanation:
it shows that it doesn't go anywhere in the interval of 2 and 5, other ones would be wrong bcs it's either go up or down
The function h
(
t
)
=
−
0. 25
t
2
+
1. 9
t
+
17
, where h
(
t
)
is height in feet, models the height of an "angry bird" shot into the sky as a function of time (seconds). Use this function to answer the following questions. Round all answers to two decimal places
Answers
The height of an "angry bird" shot into the sky as a function of time (seconds) is h = 8.65 ft.
The height of the bird is given by the following equation
h(t)= -0.25t2 + 1.9t + 17
t= 1
= -0.25 + 1.9 + 17
= -8.35 + 17
h = 8.65 ft.
The following are the three equations:
-First equation of motion: v = u + at
-Second equation of motion: s = u t + 1/2 at2
Third equation of motion: v2 = u2 + 2as
t is the time, in seconds.
h(t) is the height, in feet, which is dependent of the time.
h(t) is height in feet and t is time in seconds
then h = 8.65 ft.
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Consider the first 2 terms of the sequence 28, 14, ...
Determine whether the sequence is arithmetic or geometric. Explain your reasoning.
please help me with 1 and 2
Answers
1. The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.
2. The common difference of the sequence 28, 14 ..... will be;
d = - 14
And, Next three terms of the arithmetic sequence are;
0, -14, -28
What is Geometric sequence?
An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
Given that;
The first two terms of the sequence,
28, 14 .....
Now,
Let the sequence is in arithmetic sequence, then;
28, 14 ......
The common difference of the sequence is;
d = 14 - 28
d = - 14
And, Let the sequence is in geometric sequence, then;
28, 14 ......
The common difference of the sequence is;
d = 14/28
d = 1/2
Thus, The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.
2. If the given sequence is in arithmetic sequence, then;
28, 14 ......
The common difference of the sequence is;
d = 14 - 28
d = - 14
And, The nth term of the arithmetic sequence is;
⇒ [tex]a_{n} = a + (n - 1)d[/tex]
Where, 'a' is the first term and 'd' is the common difference of the sequence.
So, The 3rd term of the arithmetic sequence is,
⇒ [tex]a_{n} = a + (n - 1)d[/tex]
[tex]a_{3} = 28 + (3-1)(-14)\\ \\a_{3} = 28 - 2 * 14\\\\a_{3} = 28 - 28\\\\a_{3} = 0[/tex]
And, The 4th term of the arithmetic sequence is,
[tex]a_{4} = 28 + (4-1)(-14)\\ \\a_{4} = 28 - 3 * 14\\\\a_{4} = 28 - 42\\\\a_{4} = -14[/tex]
And, The 5th term of the arithmetic sequence is,
[tex]a_{5} = 28 + (5-1)(-14)\\ \\a_{5} = 28 - 4 * 14\\\\a_{4} = 28 - 56\\\\a_{5} = -28[/tex]
Therefore, Next three terms of the arithmetic sequence are;
⇒ 0, -14, -28
Thus,
1. The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.
2. The common difference of the sequence 28, 14 ..... will be;
d = - 14
And, Next three terms of the arithmetic sequence are;
0, -14, -28
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JP Computers produces both laptop
and desktop computers. Laptop
computers take up 2 cubic feet of
space and desktop computers take up
5 cubic feet of space. The maximum
capacity on the delivery truck is 800
cubic feet. Due to demand, they need
to load at least 300 laptop computers.
They profit $225 on each laptop and
$280 on each desktop computer. How
many of each should they load on the
truck to maximize profit?
Answers
The load each should get to maximize the profit is $67,500, $78,700 and $90,000
What Is Profit?
In accounting, a profit is an income that is given to the owner throughout a successful market producing process. Profitability, which is the owner's primary interest in the income-formation process of market production, is measured by profit. There are various profit metrics that are frequently used.
Let x represent the total number of laptops and y represent the total number of desktop computers.
A laptop computer occupies 2 cubic feet, hence x laptops each use 2x cubic feet. Desktop computers take up 5 cubic feet of space, hence 5y cubic feet of room is required for 5y desktop computers.
They require 2x + 5y cubic feet in total.
Since the delivery truck's maximum capacity is 800 cubic feet,
2x + 5y <= 800.
They must load at least 300 laptops because of the demand,
hence, x >= 300
They make $225 on each laptop, which translates to $225 times as many computers. They make a profit of $280 on each desktop computer, or $280y on y desktops.
Total profit is:
P=$(225x + 280y)
Draw the inequality system (see attached diagram)
2x + 5y <= 800.
x >= 300
One of the common region's three vertices will have the most profit:
P(300,0) = 225(300) + 280(0) = $67,500
P(300,40) = 225(300) + 280(40) = $78,700
P(400,0) = 225(400) + 280(0) = $90,000
Hence, each should load $67,500, $78,700 and $90,000 on the truck to maximize profit
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Which measuring cups do you use to measure out 1 3/4 cups if you don't have a 3/4 cup measuring cup?
1 cup, 1 cup
1 cup, 1/2 cup
1/4 cup, 1/3 cup, 1/2 cup
1 cup, 1/2 cup, 1/4 cup
Answers
Answer:
d
Step-by-step explanation:
1 = 1 cup
1/2 can be 2/4
2/4+1/4=3/4
1+3/4 = 1 3/4
Need help please : Given the equation 6x + 18 = 72: Part A: Write a short word problem about a purchase made to illustrate the equation. Part B: Solve the equation showing all work. Part C: Explain what the value of the variable represents.
Answers
A. A short word problem about a purchase made to illustrate the equation is that John bought six pens and bought books for $18. The total amount is $72. Find the cost of each pen.
B. The cost of each pen is $9
C. The variable is x.
How to illustrate the equation?A. The problem is that John bought six pens and bought books for $18. The
B. The equation to illustrate this will be:
6x + 18 = 72
Collect like terms
6x = 72 - 18
6x = 54
Divide
x = 54 / 6.
x = $9
The cost of each pen is $9.
C. The variable is x = 9. This is the cost of the pen.
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a gardener has 760 feet of fencing to fence in a rectangular garden. one side of the garden is bordered by a river and so it does not need any fencing.
Answers
The dimensions that would guarantee that the garden has the greatest possible area is 190 feet on the shorter side and 380 feet on the longer side to produce an area of 72,200 square feet.
A dimensions of a rectangle is the length of each side.
Let x = length of the shorter side
y = length of the longer side
If one side of the garden is bordered by a river and so it does not need any fencing, and assume that the longer side is this side, then the perimeter that only needs to be fenced by 760 feet of fencing materials is
2x + y = 760
y = 760 - 2x
The area of the rectangular garden is the product of the shorter side and the longer side of the garden. Hence,
A = xy
A = x(760 - 2x)
A = 760x - 2x²
To obtain the largest area possible, the first derivative of the area should be equal to zero.
A(x) = 760x - 2x²
A'(x) = 0
760 - 4x = 0
Solve for x.
760 - 4x = 0
4x = 760
x = 190
length of the shorter side = 190 feet
y = 760 - 2x
y = 760 - 2(190)
y = 380
length of the longer side = 380 feet
Solve for the greatest possible area.
A = xy
A = 190 feet(380 feet)
A = 72,200 square feet
" A gardener has 760 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing. What dimensions would guarantee that the garden has the greatest possible area? "
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Click on the graph to choose the correct answer to the equation. y ≥ 2 x + 1
Answers
The graph of the linear inequality can be seen in the image at the end.
How to identify the graph of the inequality?
Here we have the linear inequality:
y ≥ 2x + 1
To graph this, we first need to graph the line.
y = 2x + 1
With a solid line, because we have the symbol ≥, which means that the points on the line are solutions.
Once we graphed that line, we look at our inequality:
y ≥ 2x + 1
It says that y is larger than or equal to the values on the line, so once the line is graphed we need to shade all the region above that line.
The shaded region (and the line itself) represent all the solutions of the linear inequality.
And the graph can be seen below.
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May you guys/girls please help me I have to submit this before midnight and I do not fail because my parents will get me , so may y'all please help me out!?
Answers
Answer:
Answer down below!
Step-by-step explanation:
Let's try and find a point that we can easily start on (a point that lands perfectly on the graph)
The point that we will use is (2,2)
So, starting from there we use rise/run to get our answer
We go up 1 and over -2
So, our slope will be (since we cannot simply it...)
-1/2
Hello!
To find the slope:
==> need to pick two points on the line
(x₁, y₁): (0,3)
(x₂,y₂): (4,1)
[tex]Slope = \dfrac{y_2-y_1}{x_2-x_1} =\dfrac{1-3}{4-0} =\dfrac{-2}{4} =-\dfrac{1}{2}[/tex] <== Answer
Hope that helps!
18.75 = u/3 solve for u please
Answers
Answer: 56.25 = u
Step-by-step explanation:
1) Multiply 3 on both sides to leave u by itself
18.75 = u/3
18.75*3 = u
56.25 = u
Explanation:
Question 22 of 27
Question 22
On Sunday, Jax biked 25.91 miles. This is 3.3 fewer miles than the number of miles he biked on Saturday. Let b represent the number of miles
Jax biked on Saturday.
Write a subtraction equation that could be used to find the number of miles Jax biked on Saturday.
Answers
PLS HELP
Yan is climbing down a ladder. Each time he descends 4 rungs on the ladder, he stops to see how much farther he has to go. If Yan made 8 stops with no extra steps, which expression best shows another way to write the product of the number of ladder rungs that Yan climbed?
4 + 4 + 4 + 4
8 + 8 + 8 + 8
(Negative 1) (4 + 4 + 4 + 4)
(Negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4)
Answers
The expression shows the product of the number of ladder rungs that Yan climbed is D. (Negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4)
What is an expression?
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We have been given that each time Yan descends 4 rungs on the ladder.
SInce, each time the number of ladder rungs that Yan climbed is negative 4, where negative sign represent descends.
Yan made eight stops with no extra steps.
-4 x 8 = -32
It can also written as; (-4) + (-4)+(-4)+(-4)+(-4)+(-4)+(-4)+(-4)
The correct answer is D. (Negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4)
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HELP IS DUE AT 10pm AND IM IN THE LAST QUESTION SOMEBODY PLEASE SOS
Answers
Notice how the graph has a sudden drop, and then slowly makes its way back up.
Boris received a $20.50 gift card for a photo center. He used it to buy prints that cost 6 cents each. The remaining balance, B
(in dollars), on the card after buying x prints is given by the following function.
B(x)=20.50-0.06.x
What is the remaining balance on the card if Boris bought 15 prints?
Answers
Answer:
$19.6
Step-by-step explanation:
B=20.50-0.06.x
B=20.50-0.06*15
B=20.50-0.9
B=19.6
HELP PLEASE <3: quadratic functions, (image contains question)
not too hard I'm just bad at math-
THANK YOU :)
Answers
Answer:
f(x)=(x-4)^2-4
The parent function (x^2) is shifted to the right 4 times (x-4) and down 4 times (-4).
I need help with this math problem. Find the distance between points J and M
Answers
Answer:
0.75
Step-by-step explanation:
in the pic
goodluck
work out the length of x
Answers
Answer:Tes icahd
Step-by-step explanation:
Physical Science: A ball was dropped from a height of 100 meters. Its height above the ground
in meters at different times after its release is given in the table. Do these ordered pairs satisfy a
linear function? Explain.
Time (s)
Height (m)
0
1
2
100 90.2 60.8
3
11.8
Answers
Answer: Yes they do.
1) [tex]\frac{2x-3}{3} +\frac{x-1}{5}[/tex]
Answers
Answer:
4_62
Step-by-step explanation:
its is just leave me
Qué número sumado igual da 60 que no sea 20
Answers
Answer: 30
Step-by-step explanation:
uppose p ( t ) p(t) represents the population of a certain mosquito colony, where t t is measured in days. the current population of the colony is known to be 578 578 mosquitos; that is, p ( 0 )
Answers
The size of the population of mosquito follows an exponential model.
the size of the population in 10 days is 1370
The size of the population in 10 days is 1370
The given parameters are:
p(0) = 574
p'(0)= 50
An exponential function is represented as:
p(t) =p(0) * e^ rt
So, we have:
p(t)=574*e^rt
Differentiate
p'(t)=574*r*e^rt
Substitute 0 for t
50=574 r
Divide both sides by 574
r=0.087
The function becomes
p(t)= 574*e^rt
= 574*e^0.087 t
In 10 days, t = 10.
So, we have:
p(10)=574*e^0.87
Solve
p(0)=1370
Hence, the size of the population in 10 days is 1370
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