When the result of one function is utilized as the input for another, this is known as a composite function. If f(x) = (6x³ - 7)³ and g(x) = 6x³ - 7 then the value of h(x) = x³.
What is meant by composition functions?A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function exists essentially applied to the output of another function.
Function composition is an operation used in mathematics that takes two functions, f and g, and creates a function, h = g ° f, such that h(x) = g. The function g is applied in this operation on the outcome of applying the function f to x.
Let the two functions be f(x) = (6x³ - 7)³ and g(x) = 6x³ - 7.
f(x) = (h° g)(x)
⇒ f(x) = (h(g(x))
If f(x) = (h° g)(x) (6x³ - 7)³ = (h(g(x)) then h(x) = x³.
The complete question is:
Let f(x) = (6x³ - 7)³ and g(x) = 6x³ - 7. Given that f(x) = (h° g)(x), find h(x).
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Answer:
h(x) = x³
Step-by-step explanation:
Given:
[tex]f(x)=(6x^3-7)^3[/tex]
[tex]g(x)=6x^3-7[/tex]
[tex]f(x)=(h \circ g)(x)[/tex]
The relationship between f(x) and g(x) is that function f is function g cubed:
[tex]f(x)=(g(x))^3[/tex]
(h o g)(x) means we replace the x-variable of function h(x) with function g(x). So:
[tex](h \circ g)(x)=h(g(x))[/tex]
If (h o g)(x) equals f(x), then h(x) must be h(x) = x³.
Check by replacing the x-variable of function h(x) with the function g(x) and comparing it to f(x):
[tex]\begin{aligned}(h \circ g)(x)&=h(g(x))\\&=(g(x))^3\\&=(6x^3-7)^3\\&=f(x)\end{aligned}[/tex]
Hence proving that h(x) = x³.
13 What value of x makes the equation modeled below true? PHONE 1 1 1 A x = 1 B x = -1 C x = 7 D x = -5 I
SOLUTION
Step 1 : We need to recognize the value of x in 5 places means 5 x
and the value of 1 in 6 times means 6,
so we have that: 5 x + 6 = 1 .
Step 2 : We need the linear equation: 5 x + 6 = 1
collecting like terms, we have that:
5 x = 1 - 6
5 x = - 5
Divide both sides by 5 , we have that:
x = - 1
CONCLUSION : The value of x = -1 ( OPTION B )
Find the value of each variable
Answer:
x = 58°
y = 74°
z = 106°
w = 42°
Step-by-step explanation:
Finding the value of unknown variables:
x + 32° = 90°
x = 90 - 32
[tex]\sf \boxed{\bf x = 58^\circ}[/tex]
x + y + 48 = 180 {Angle sum property of triangle}
58 + y + 48 = 180
y + 106 = 180
y = 180 - 106
[tex]\sf \boxed{\bf y = 74\°}[/tex]
y + z = 180 {Linear pair}
74 + z = 180
z = 180 - 74
[tex]\sf \boxed{\bf z = 106\°}[/tex]
32 +z + w = 180 {Angle sum property of triangle}
32 + 106 +w = 180
138 + w = 180
w = 180 - 138
[tex]\sf \boxed{\bf w = 42\°}[/tex]
3 x blank x blank x blank = 36
Answer:
3x2x2x3
Step-by-step explanation:
3x2x2x3= 36
I hope that was helpful!
My pleasure to help!!
the larger number is 18 more than twice the smaller. If the sum of the two numbers is 93, find
oth numbers.
Answer:
The larger number is 68 and the small number is 25
Step-by-step explanation:
Large number y
small number is x
y=2x+18
x+y=93
Larry plants to invest 275,000 for 30 years at an anticipated rate of 6% per annum compounded yearly what is the approximate difference in his ending balance of the actual rate is 5% instead of six
Answer:
$390,000
Explanation
To do this, we will use the compound interest formula;
A = P(1+r)^t
P = 275000
rate r = 6%
Time t = 30years
Substitute
A = 275000(1+0.06)^30
A = 275000(1.06)^30
A = 275000(5.7435)
A = 1,579,460.07
For the rate of 5%
A = 275000(1+0.05)^30
A = 275000(1.05)^30
A = 275000(4.3219)
A = 1,188,534.15
Takeing their difference;
Difference = 1,579,460.07-1,188,534.15
Difference =390,925.92
Hence the approximate difference in his ending balance of the actual rate is 5% instead of six is about $390,000
how long would it take to drive 1km at a speed of 1.71km/h (with working)
It would take 35 minutes to drive 1 km at a speed of 1.71 km/h.
How do distance and speed compare?Speed is the ratio of distance traveled in a given time. Speed is given by distance/time.
The time can be computed by dividing distance by speed.
This implies that time is the quotient of distance and speed.
The total distance drove = 1 km
The driving speed = 1.71 km/h
Time = Distance/Speed
= 1/1.71
= 0.58 hours
= 0.58 x 60 seconds
= 35 minutes 5 seconds
Thus, to travel 1 kilometer at the speed of 1/71 kilometers per hour would take 35 minutes.
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A triangle has been plotted on the coordinate plane.
Which series of transformations will result in Point B” being the greatest distance from the x-axis.
A - reflect over the x-axis then rotate 90° clockwise
B - rotate 80° clockwise then reflect over the line x= -1
C - rotate 90° clockwise then translate following the rule (x+1, y-1)
D - translate (x+1,y-1) then reflect over the y-axis
REALLY NEED THIS
When a point is reflected across the x-axis, the x-coordinate remains unchanged, but the y-coordinate is assumed to be the additive inverse. Point (x, yreflection )'s across the x-axis is (x, -y). A point's reflection over the y axis is shown. The reflection rule over the y axis is (x,y)(x,y).
What exactly is a coordinate plane?A coordinate plane is a two-dimensional plane formed by two number lines intersecting. One of these number lines is a horizontal number line known as the x-axis, and the other is a vertical number line known as the y-axis.
1) Determine the absolute value of x1(y2-y3) + x2(y3-y1) + x3(y1-y2).
2) The area of the triangle is calculated by dividing this value by two.
3) Use our area of a triangle with coordinates calculator to confirm this result.
The coordinate plane can be used to draw lines and points. This system allows us to visually describe algebraic relationships, as well as create and interpret algebraic concepts.
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5(1-1)+10=
5(2-1)+10=
5 (3-1) +10=
5(4-1)+10=
Step-by-step explanation:
First is
5(1-1)+10= 5×0+10= 0+10 = 10
2nd is
5(2-1)+10=5× 1+10= 5+10=15
3rd= 5(3-1)+10= 5×2+10=10+10=20
4th=5(4-1)+10=5×3+10=15+10=25
I hope it will be helpful for you.
Over the last four months, your investment lost
10%, 20%, 30%, and then 40%. What percent
of the original investment do you have left?
Answer:
30.24%
Step-by-step explanation:
Each time you lose x%, you end up with 1 - 0.01x.
For example, if you lose 10% of an amount, you end up with 1 - 0.01(10), or 0.9 times the original amount.
Let's say you started with x.
You lost 10%. Now you have 0.9x.
Then you lost 20% of the remaining amount. Now you have 0.8(0.9x).
Then you lost 30% of the remaining amount. Now you have 0.7(0.8)(0.9x).
Finally you lost 40% of the remaining amount. Now you have 0.6(0.7)(0.8)(0.9x).
The final amount you have is
0.6(0.7)(0.8)(0.9x) = 0.3024x = 30.24% of x
Answer: 30.24%
Find the range, variance & standard deviation of the following sample dataset. Round all answers to the nearest tenth.
The following data represent the number of students from each school that attended a debate tournament: 75, 47, 50, 71, 64, 50, 52, 56, 53, 47, 55
Answer:
The range is 28
The variance is 90.855
The mean is 56.36
The median is 53
The sample standard deviation is 9.532
Step-by-step explanation:
Which of the following is a balanced equation?
KCIO(3)-->KCI + O(2)
KCIO(3)-->3 KCI + O(2)
2KCIO(3)-->KCI + 3 O(2)
2KCIO(3)-->2 KCI + 3 O(2)
Select one:
a. A
b. B
c. C
d. D
Based on the chemical equations given, the balanced equation would be d. D.
How to find a balanced equation?In Chemistry, a balanced equation is one that has the same number of atoms on the left side of the equation, as on the right side of the equation.
The balanced equation is therefore:
2KCIO₃ -->2 KCI + 3 O₂
This is because there are 2 KCI atoms and 6 Oxygen atoms on the left side, and there are also 2 KCI atoms and 6 Oxygen atoms on the right side.
In conclusion, option D is correct.
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Find the area of the figure below, formed from a triangle and a parallelogram. A figure is formed from a triangle and a parallelogram. The base of the triangle is 8 millimeters and the height is 2 millimeters. The bottom and top of the parallelogram are 6 millimeters and the height is 4 millimeters.
The total area of the figure is; 32 millimeters sq.
What is the area of a parallelogram?The area of a parallelogram is the product of the base and the height of the figure.
The area of a parallelogram = Base x Height
We have been given that a parallelogram has a base is 6 millimeters and a height is 4 millimeters
The area of a parallelogram = Base x Height
= 6 x 4
Area = 24 millimeters sq.
Similarly, The area of the triangle = 1/2 x b x h
= 1/2 x 8 x 2
= 8 millimeters sq.
The total area of the figure is;
Total = area of the triangle + area of a parallelogram
Total = 24 + 8 = 32
Hence, the total area of the figure is; 32 millimeters sq.
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What is 39,400,000 in scientific notation?
Answer:
3.94*10^7
Step-by-step explanation:
Answer:
3.94 * 10^7
Step-by-step explanation:
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Nitin and Sharat were going to Delhi by different trains.
Their trains were scheduled to reach at 10:30 am and 11:15am respectively.
Nitin’s train reached late but Sharat’s train reached on time.
Nitin’s train reached 10 minutes AFTER Sharat’s train.
By how many minutes was Nitin’s train late?
Answer:
55 minutes
Step-by-step explanation:
sharat's train arrived on time (11.15) but Nitin's was after and 10 mins later it'd be 11.25
arif's backyard is 22 by 32 meters. he wants to put a flower garden in the middle of the backyard, leaving a strip of grass of uniform width around the flower garden. to be happy, arif must have 288 m^2 of grass. under these conditions what will the length and width of the garden be?
The dimension of the flower garden, which located in the middle of the backyard surrounded by a strip of grass, is 26 m length and 16 m width.
The situation can be depicted on the attached picture.
We need to translate the word problem into algebraic expressions.
Let x be the width of the grass strip.
Let A be the area of the grass strip.
Then,
A = 2 . 22x + 2 . (32 - 2x)x
288 = 2 . 22x + 2 . (32 - 2x)x (divide by 2)
144 = 22x + x(32 - 2x) (divide by 2)
72 = 11x + x(16 - x)
72 = 27x - x²
x² - 27x + 72 = 0
This is a quadratic equation. One of the methods to solve a quadratic equation is by factorization.
Factorize the left side:
(x - 3) (x - 24) = 0
x = 3 or x = 24
The length of the flower garden = 32 - 2x
The width of the flower garden = 22 - 2x
Substitute x = 3:
The length of the flower garden = 32 - 2 . 3 = 32 - 6 = 26 m
The width of the flower garden = 22 - 2 . 3 = 16 m
Note that if we substitute x = 24, it will results in negative values while the dimension is always positive.
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13 gallon of water in a 3-gallon container. What fraction of the container is filled?
Answer:
1/9
Step-by-step explanation:
There is 1/3 gallon of water in a 3 gallon container. The fraction of the container that is filled is 1/9
(1/3 of a gallon divided by 3 gallons equals 1/9)
Two exponential functions, f(x) and g(x), are graphed on the same coordinate plane. Graph of f of x equals 2 to the x power going through points 0 comma 1 and 1 comma 2 and graph of g of x equals 2 to the x power plus 4 going through points 0 comma 5 and 1 comma 6. What effect does adding 4 to the parent function have on the transformed function? a Adding 4 to the parent function shifts the function down four units. b Adding 4 to the parent function shifts the function up four units. c Adding 4 to the parent function shifts the function right four units. d Adding 4 to the parent function shifts the function left four units.
Answer:
b Adding 4 to the parent function shifts the function up four units.
Step-by-step explanation:
The original function is y(x) = 2^x
Adding four is y(x) = 2^x + 4
We've simply told y to take whatever value is generated for x and add four to it.
So the new value for the same x would have 4 added to y: (x,y+4),
Point (1,2) would shift to point (1,6).
Adding four to the parent function will shift the entire graph up by 4. See ate attached graph.
-53 = 8y + 4y - 17 solve for y and simplify as much as possible
Answer:
y = -3
Step-by-step explanation:
-53 = 8y + 4y - 17
combine y terms on right side:
-53 = 12y - 17
add 17 to both sides:
-53 + 17 = 12y - 17 + 17
-36 = 12y
divide both sides by 12:
-36/12 = 12y/12
y = -3
Refer to Expression 1 and Expression 2.
Expression 1
6-7-3².9+43
r:
Expression 2
5+4+2+6-2-2-1
(a) What is the value of Expression 1?
(b) Insert parentheses in Expression 2 so that it has a value of 19. Then show why your expression has a
value of 19.
a) Value of Expression 1 is 29.833.
b) After inserting the parentheses the expression is (5+4) * 2 + 6 -2 * 2 - 1.
The order of operations to solve in expression 1 is:
First parenthesis, then multiplication and division, and then addition and subtraction.
So, the expression is:
6 × 7 - 3 ÷ 2 × 9 + 4 ÷ 3
First, solve division and then multiplication:
= 42 - 1.5 × 9 + 1.34
= 42 - 13.5 + 1.34
= 29.84
b) Because the parenthesis is the initial action, so insert it in 5+4 which provides the following result:
(5 + 4) × 2 + 6 - 2 × 2 - 1
First, calculate the parenthesis, then the multiplication and division, and finally perform addition and subtraction:
= (9) × 2 + 6 - 4 - 1
= 18 + 6 - 4 - 1
= 19
The final value is 19.
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a certain bacteria doubles every 2 seconds. Starting from a single bacterium, how many bacteria will be there after 20 seconds?
The answer will de 10 bacterias
Answer: 1024
Step-by-step explanation: Since there's only 1 bacteria at first, we can just do 2^x. x being the amount of time divided by the amount of time between each time it doubles. Since the bacteria doubles every 2 seconds, and 20/2 = 10 we get 2^10 which is 1024.
A star shape is made out of 5 congruent triangles. the peak of 1 triange is 25°. what are the sizes of the base angles?
Answer:
77.5
Step-by-step explanation:
180-25=155
155/2=77.5
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Vinny is serving punch to guests at a party. He has $\frac{3}{4}$ of a gallon of punch, and he pours $\frac{5}{64}$ of a gallon into each guest's cup, filling each to the top. At the most, how many guests' cups can he fill to the top?
In serving punch to guests at the party, Vinny can fill 9 guests' cups to the top based on this unit rate.
What is a unit rate?The unit rate is the ratio of a variable to another.
The whole number here is the total gallons of punch available to serve the guests.
The unit rate is the volume that each guest's cup can hold or contain.
This implies that the ratio is 5/64: 3/4
The total number of gallons of punch = 3/4 or 0.75 gallons.
The volume or capacity of each guest's cup = 5/64 gallons or 0.078125.
The number of guests' cups to fill to the brim = 9.6 cups (0.75/0.078125)
= 9 guests' cups.
Thus, Vinny can fill 9 guests' cups to the brim, using the given ratio or unit rate.
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Which of the following values are in the range of the function graphed below?
Check all that apply.
The range of the function is 1
As seen by the graph in the following figure
As can be seen, x's value falls between
nonetheless, y is equal to 1 for all values of x.
This holds true regardless of x's value.
Consequently, the function's range is 1.
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Find the equation of the line that contains the given point and is perpendicular to the given line. Write the equation in slope-intercept form, if possible.
(2,-6); y = 2/3x-4
Answer:
Step-by-step explanation:
2
Combine multiplied terms into a single fraction
3
Find common denominator
4
Combine fractions with common denominator
5
Multiply the numbers
Please help me with this. Show the solution as well. Thank you
Step-by-step explanation:
any ordered pair is a solution, if we can use its coordinates in the equation, and the equation stays true.
for x - 3y = 6
1. (3, -1)
3 - 3×-1 = 6
3 + 3 = 6
6 = 6
true, this is a solution.
2. (0, 2)
0 - 3×2 = 6
-6 = 6
false, this is not a solution.
3. (3, 1)
3 - 3×1 = 6
3 - 3 = 6
0 = 6
false, this is not a solution.
The team's engagement score was 5.20 this month. the score has been improving at a rate of 8% per month. what was the score 3 months ago? 1.60 3.95 4.13 4.78 5.12
The score 3 months ago was 4.130.
What is rate of increase?
Rate of increase is defined the change in rate that describes how one quantity changes in relation to another quantity.
Assume the score 3 months ago was x. This means that the above can be expressed as:
Current score = x × ( 1 + rate) ^ number of months
5.20= x(1+8%)^3
5.20 = x(1.259)
x= 5.20/1.259
x= 4.130
therefore, the score was 4.130
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The art club had an election to select a president. 42 out of the 60 members of the art club voted in the election. What percentage of the members voted?
The percentage of members that voted is 70%.
How to find the percentage of members that voted?The art club had an election to select a president. 42 out of the 60 members of the art club voted in the election.
Therefore, the percentage of the members that voted can be calculated as follows;
percentage that voted = number of people that voted / total number members × 100
Therefore,
number of people that voted = 42
total number members = 60
Hence,
percentage that voted = 42 / 60 ×100
percentage that voted = 4200 / 60
Therefore,
percentage that voted = 70%
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What is the slope of this image?? I NEED HELP
Answer:
Positive, so the answer would be y=4/2 or 2. y=2x-4
Step-by-step explanation:
Slope formula y=mx+b
The mx is the rise/ over run
The b is the y-intercept
You can check in the end by checking so to see if the rise over the run is correct
Also, you can check the b by looking at the y-intercept, which is -4
Hope this helps!
The length of the rectangle is 5 more than twice the width. If the perimeter is 10 times that of the width, what is the width, length, and perimeter of the rectangle?
The length of the rectangle is 10, the width is 2.5 and the perimeter is 25
Let the width of the rectangle be x
The length of rectangle = 2x + 5
The overall length of the outline determines a rectangle's perimeter in two dimensions. We add the lengths of all four corners of a rectangle to find its perimeter. Since the opposite sides of a rectangle are always equal, we must determine the length and width of the rectangle in order to determine its perimeter.
Perimeter = 10 times of width
= 10*x
= 10x
The formula for the perimeter of a rectangle is given:
Perimeter = 2(Length+Breadth)
10x = 2(x + 2x+5)
10x = 2(3x+5)
10x = 6x + 10
4x = 10
x=2.5
Length = 10
Width = 2.5
Perimeter = 25
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