g∘f(x) or g(f(x)) is equal to 27x + 43.
To find g∘f(x) or g(f(x)), we need to substitute the function f(x) into the function g(x).
Given:
f(x) = 3x + 4
g(x) = 9x + 7
To find g∘f(x), we substitute f(x) into g(x) as follows:
g(f(x)) = g(3x + 4)
Now, we substitute 3x + 4 for x in the function g(x):
g(f(x)) = 9(3x + 4) + 7
Expanding and simplifying:
g(f(x)) = 27x + 36 + 7
g(f(x)) = 27x + 43
Therefore, g∘f(x) or g(f(x)) is equal to 27x + 43.
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5.
Factorise each of the following.
(a)-15ab-6ab²
(b) 6x(2y-5)-3(5-2y)
A local farmer built a rectangular pen for her chickens using 12 meters of fence. She used part of one side of her barn as one length of the rectangular pen. She maximized the area using 12 meters of fence. She then build a rectangular pen for her pigs using 16 meters of fence. She used part of one side of her barn as one length of the rectangular pen. The length of her pen was 2 meters more than the length of the chicken pen. The width of her pen was 1 meter more than the width of the chicken pen. How much larger is the pig pen than the chicken pen
The pig pen is 14 sq. meters larger than the chicken pen built by the former.
What are the perimeter and area of a rectangle?Consider a rectangle with length 'L' and width 'W'.
So, its perimeter = 2(L + W) units and area = L × W sq. units.
Calculating the dimensions of the rectangular pen for chicken:It is given that a farmer built a rectangular pen for chickens.
The chicken pen's perimeter is 12 meters, and she used only one side of the barn as one length of the rectangular pen.
So,
L + 2W = 12
⇒ L = 12 - 2W
Then its area is calculated as below:
Area = L × W
= (12 - 2W) W
= 12W - 2W²
Consider A' = 0 for finding the larger area.
So, differentiating the area w.r.t W,
dA/dW = 12 - 4W
0 = 12 - 4W
⇒ 4W = 12
∴W = 3 meters
Then,
L = 12 - 2W = 12 - 2(3) = 6 meters
So, the area of the chicken pen = 6m × 3m = 18 m²
Calculating the dimensions of the rectangular pen for the pig:It is given that,
The length of the pig pen was 2 meters more than the length of the chicken pen. I.e., L' = L + 2
The width of the pig pen was 1 meter more than the width of the chicken pen. I.e., W' = W + 1
On substituting L and W values to find the dimensions of the pig pen,
L' = 6 + 2 = 8m
W' = 3 + 1 = 4m
Then,
Area = L' × W'
= 8m × 4m
= 32 m²
Finding how much larger is the pig pen than the chicken pen:
Area of the pig pen - Area of the chicken pen
⇒ 32 m² - 18 m² = 14 m²
Therefore, the pig pen is 14 m² larger than the chicken pen.
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how do I solve for x? (the picture has the problem)
Answer:
x = 21.013155617496
Step-by-step explanation:
we have a right triangle then ,
[tex]\cos \left( 36\right) =\frac{17}{x}[/tex]
Then
[tex]x=\frac{17}{\cos \left( 36\right) } = 21.013155617496[/tex]
Then
x ≈ 21
Step-by-step explanation:
imagine this right-angled triangle is the sine and cosine scenario in a circle. just turn it in your mind or on the paper until it looks like this.
the point with the 36° angle is the center of this circle.
x is the radius of the circle, that is under 36° connecting the center of the circle with the arc of the circle.
17 is the cosine of the angle multiplied by the radius (as the standard cosine function is normed for the standard circle with radius 1).
and the other leg is the sine of the angle multiplied by the radius (this is FYI, we don't need that for the solution here).
so,
17 = cos(36) × x
x = 17/cos(36) = 21.01315562...
10. A drawer contains only green marbles. After
5 red marbles are added to the drawer, the
probability of picking a red marble is
How many marbles were there in the drawer
originally?
(A) 5
(B) 7
(C) 12
(D) 30
(8)
Answer:
(D) 30
Step-by-step explanation:
number of green marbles = x
number of red marbles = 5
total number of marbles = x + 5
p(red) = (number of red marbles)/(total number of marbles)
p(red) = 5/(x + 5)
p(red) = 1/7
5/(x + 5) = 1/7
(x + 5) × 1 = 5 × 7
x + 5 = 35
x = 30
Answer: (D) 30
To remain a member of the student council, a student must attend at least Three-fourths of the activities. Joey attends 15 of the activities and remains on the student council. Which inequality represents the total amount of student council activities, a?
Answer:
20
Step-by-step explanation:
so we need to see that
3/4 x ? = 15
so we say
3 x ? = 15x4
? =60/3
?= 20
Find the missing segment in the image below.
Using the proportionality theorem, the length of the missing segment is 25 units.
What is the Proportionality Theorem?According to the proportionality theorem, the middle segment in the diagram given divides the two sides it intersects proportionally.
Therefore, we would have:
x = missing segment
36/21 = (35 + x)/35
Cross multiply
35(36) = 21(35 + x)
1,260 = 735 + 21x
1,260 - 735 = 21x
525 = 21x
525/21 = x
x = 25
The missing segment is: 25 units.
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Determine the unknown length or angle measurement. Round each answer to the nearest whole number.
The unknown sides and angles of the triangle are 18 cm and 39 degrees respectively.
How to find the side and angle of a triangle?The side and angle of a triangle can be found as follows:
using sine law,
Angle A = 180 - 68 - 59 = 53 degrees
19.5 / sin 59 = a / sin 53
19.5 sin 53 = a sin 59
a = 19.5 sin 53 / sin 59
a = 15.5733924459 / 0.8571673007
a = 18.1680280047
a = 18 cm
15 / sin ∅ = 20 / sin 57
15 sin 57 = 20 sin ∅
sin ∅ = 12.5800585192 / 20
sin ∅= 0.62900292595
∅ = sin ⁻¹ 0.62900292595
∅ = 38.9763828249
∅ = 39 degrees.
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Solve ΔABC with ABC=51°, c=8 and a=11. Draw a diagram.
To solve a triangle means to obtain al the missing parts of the triangle.
How do you solve a triangle?To solve a triangle means to obtain al the missing parts of the triangle. Now we have the following information;
<ABC = 51°
c = 8
a = 11
Then;
b^2 = a^2 + c^2 - 2acCos B
b^2 = (11)^2 + (8)^2 - [2 * 11 * 8 * cos 51]
b^2 = 121 + 64 - 55.38
b = 11.39
Now;
a/sinA = b/sinB
asinB = bsinA
sinA = asinB/b
sinA = 11 * sin 51/11.39
A = 48.6 or 49°
C = 180 - (49 + 51)
C = 80°
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A designer created a kitchen floor tile in a triangular shape. two sides of the tile have lengths of 8 inches and 9 inches. what is the range of the possible lengths, x, of the third side of the tile?
Considering that it is a triangle, the range of the possible lengths, x, of the third side of the tile is: (1, 17).
What is the condition for 3 lengths to represent a triangle?In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.
Hence, if 9 is the greater side:
8 + x > 9
x > 1.
If 8 and 9 are the smaller sides:
x < 8 + 9
x < 17.
Hence the range of possible lengths is:
(1, 17).
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simplify 1/5 (-16-9) + 4^2 ÷ 8 A.-3 B.7 C. -7/5 D.3/5
The simplified form of the expression [1/5 (-16-9) + 4² ÷ 8] is -3.
Option A) is the correct answer.
What is the simplified form of the expression?
Given the expression; 1/5 (-16-9) + 4² ÷ 8
First we remove the parentheses and perform the operations using the guidelines of BODMAS
1/5 (-16-9) + 4² ÷ 8
1/5 × -25 + 4² ÷ 8
1/5 × -25 + 16 ÷ 8
-25/5 + 16/8
-5 + 2
-3
The simplified form of the expression [1/5 (-16-9) + 4² ÷ 8] is -3.
Option A) is the correct answer.
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A snail crawls at the rate of 1cm in 3 minutes.how long will it take to cover 1m distance? answer asap
Answer:
Step-by-step explanation:
velocity = distance divided by time
velocity of the snail = 1cm / 3min
v of snail = 0.333 cm per minute
to calculate the time of 1 meter displacement, we use the formula t = d/V
time = distance divided by velocity
time = 1meter / 0.333cm/min
time = 100cm / 0.333cm/min
time = 300 minutes
hope it helped!
for pet food: how would adopting a process costing system benefit the managers responsible for the production of this product? list two specific decisions you think a process costing system could help these managers make. identify and describe two or three processes involved in making this product. for each, describe the direct materials used and at least one conversion cost associated with the process. explain how managers would be able to estimate the cost of the units being processed at a given point in time.
Job order costing also gives managers the advantage of being able to keep track of individuals' and teams' performance in terms of cost control, efficiency, and productivity. A disadvantage of job order costing is that employees are required to track all materials and labor used during the job.
With the standardization of products, managers track performance, productivity, and costs over time. Process costing allows for greater flexibility when making changes in the production process. Managers can target specific departments' processes or materials to lower production costs.
With process costing, companies track the flow of costs from department to department, rather than tracking costs for each individual item. Each department adds direct labor and manufacturing overhead costs, plus the cost of any raw materials it uses.
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Which number(s) satisfy a ∩ c? 16, 81 1, 16, 81 1, 4, 9, 16, 25, 36, 49, 81, 100 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Answer:
Step-by-step explanation:
B: 1, 16, 81
WHY?
Set A is perfect squares from A to 100:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100
Set A = 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Set C is perfect fourths
1^4 = 1
2^4 = 16
3^4 = 81
4^4 = 254 (This is greater than 100)
Set C = 1, 16, 81
Hope this helps :)
John, and bill shared $900 in the ratio 7:3 respectively. how much money did each person get?
John get money $630 and bill get money $270.
Given that John and bill shared $900 in the ratio 7:3 respectively.
The ratio is defined as the comparison of two quantities of equal units, indicating the quantity of one quantity contained in the other quantity.
The total ratio is 7+3=10
For john:
John has money seven out of 10 for the $900, we get
J=900×(7/10)
J=90×7
J=630
For bill:
Bill is three out of ten for $900, we get
B=900×(3/10)
B=90×3
B=270
Hence, john get money $630 and bill get $270 when they both shared $900 in the ratio 7:3 respectively.
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The distance to your uncle's house is 444 miles, and the distance to Atlanta is 555 miles. If it took 12 hours to drive to your uncle's house, how long would you estimate the drive to Atlanta to take
It takes 15 hours to drive to Atlanta. Using the distance-time-speed formula the required time is calculated.
What is the distance-time-speed formula?The relation between distance 'd', time 't', and speed 's' is given by the formula,
s = d/t or
d = st or
t = d/s
Calculation:It is given that,
The distance to uncle's house = 444 miles
The time taken to drive to uncle's house = 12 hours
So,
speed = (444)/12 = 37 miles/hour
Then the time to drive 555 miles(to Atlanta) is calculated by,
time t = (555)/37 = 15 hours
Therefore, it takes 15 hours to drive to Atlanta at 555 miles of distance.
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Drag each equation and coordinate to the correct location on the table. Not all equations or coordinates will be used.
In the table below, quadratic equations are given in standard form. Rewrite each equation in the form that reveals the maximum or
minimum value, and then identify the coordinate point of that extreme value.
Completing the squares, we have that:
For the parabola of standard form y = x² - 6x + 17, we have that the equivalent form is (x - 3)² + 8 and the extreme value is (3,8).For the parabola of standard form y = x² + 8x + 21, we have that the equivalent form is (x + 4)² + 5 and the extreme value is (-4,5).For the parabola of standard form y = x² - 16x + 60, we have that the equivalent form is (x - 8)² - 4 and the extreme value is (8,-4).What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For the parabola of standard form y = x² - 6x + 17, we have that it can be written as follows, completing the squares:
y = x² - 6x + 17 = (x - 3)² + 8, hence the extreme value is (3,8).
For the parabola of standard form y = x² + 8x + 21, we have that it can be written as follows, completing the squares:
y = x² + 8x + 21 = (x + 4)² + 5, hence the extreme value is (-4,5).
For the parabola of standard form y = x² - 16x + 60, we have that it can be written as follows, completing the squares:
y = x² - 16x + 60 = (x - 8)² - 4, hence the extreme value is (8,-4).
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Triangle ABC is transformed to triangle A′B′C′, as shown below: A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0. A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0. Which equation shows the correct relationship between the measures of the angles of the two triangles?
A. m
B. m
C. m
D. m
The triangle ABC was reflected over the x axis to form triangle A'B'C, hence the measures of the corresponding angles are congruent.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
The triangle ABC was reflected over the x axis to form triangle A'B'C, hence the measures of the corresponding angles are congruent.
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Solve for x sim b (10, 0.75) for x = 5
The value of [tex]x \sim B (10, 0.75)[/tex] for x = 5 is 0.06
How to solve the probability?The expression is given as:
[tex]x \sim B (10, 0.75)[/tex]
This means that:
n = 10
p = 0.75
The probability is then calculated as
[tex]P(x)= ^nC_x * p^x *(1 - p)^{n-x[/tex]
This gives
[tex]P(5)= ^{10}C_5 * 0.75^5 *(1 - 0.75)^5[/tex]
Evaluate the combination expression
[tex]P(5)= 252 * 0.75^5 *0.25^5[/tex]
Evaluate
P(5)= 0.06
Hence, the value of [tex]x \sim B (10, 0.75)[/tex] for x = 5 is 0.06
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Examine the first two steps for solving this equation. 3x - 6(5x 3) = 9x 6 1. distribute: 3x - 30x - 18 = 9x 6 2. combine like terms: -27x - 18 = 9x 6 what could be the coefficient of x once the variable term is isolated on one side of the equation? check all that apply. –36 –27 –24 24 27 36
Answer:
-36 and 36
Step-by-step explanation:
moving the 9x to the left it changes to -9x and that plus -27x is -36x
-27-9 = -36
moving -27x to the right it changes to 27x so that plus 9x is 36x
27+9 = 36
Answer:
A. -36
F. 36
Step-by-step explanation:
Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?
The table that describes the behavior of the graph of f(x) = 2x3 – 26x – 24 is known to be table B.
What is the function about?To be able to tell the function one need to use a graphing tool and see the attached figure to better tell and know the problem.
The Relation of graph to the x-axis are shown below
Interval (-∞,-3)- below (the function is said to be negative) - x axisInterval (-3,-1) - above (the function is said to be positive) - x axisInterval (-1,4)- below (the function is said to be negative)- x axisInterval (4,∞) - above (the function is said to be positive) - x axisNote also that in the image attached, the vertical line is the y-axis and the horizontal line is the x- axis.
Hence, the table that describes the behavior of the graph of f(x) = 2x3 – 26x– 24 is known to be table B.
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Answer:
B
Step-by-step explanation:
Which expression is not equivalent to 8+(n-4) (8-4+n) 12+n n+4 (8+n)-4
The expression which is not equivalent to (8 + (n - 4)) is (12+n) and this can be determined by using the arithmetic operations.
Given :
Expression - 8 + (n - 4)
To simplify the given expression following steps can be used:
Step 1 - Rewrite the given expression.
= (n - 4) + 8
Step 2 - Now, remove the parenthesis in the given expression.
= n - 4 + 8
Step 3 - Now, write 8 as the addition of 4 and 4.
= n - 4 + 4 + 4
Step 4 - Subtract 4 by 4.
= n + 4
Therefore, the correct answer is (12+n).
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For 2-3, Name a postulate or theorem that can be used to prove that the two triangles are similar. Then, write a similarity statement.
Postulate: AA
Similarity statement: [tex]\triangle CBA \sim \triangle FED[/tex]
The tuition costs, c, for a local community college are modeled by c(h) = 250 200h, where h represents the number of credit hours taken. the local state university has tuition costs, s, modeled by the function s(h) = 300 180h. how many credit hours will a student have to take for the two tuition costs to be equal? round the answer to the nearest tenth of an hour. 250 200h = 300 180h 250 200h = 300 180h − 180h − 180h 250 20h = 300 h = credit hours
The number of credit hours a student have to take for the two tuition costs to be equal is 2.5 hours. Option A
Equationlocal community college;c(h) = 250 + 200h
local state University;s(h) = 300 + 180h
Where,
number of credit hours taken = hTo have equal tuition in both schools,
equate both function
250 + 200h = 300 + 180h
200h - 180h = 300 - 250
20h = 50
h = 50/20
h = 2.5 hours.
The number of credit hours a student have to take for the two tuition costs to be equal is 2.5 hours.
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A newspaper reports the following changes in temperature of the city over 4 days.
3.24 degrees celsius, -3/8 degrees celsius! -0.15 degrees celsius, 7/9 degrees celsius
. write an expression to show the daily average change in the temperature of the city.
write the steps to solve the expression round your answer to the nearest hundreth
(you will get 50 points if you answer my question correct)
The average change in the temperature of the city is 0.87°C.
The average quantity is the sum of all quantities divided by the number of quantities.
In the question, we are informed that a newspaper reports the changes in the temperature of the city over 4 days to be 3.24°C, - 3/8 °C, - 0.15 °C, and 7/9 °C.
We are asked to write an expression to show the daily average change in the temperature of the city.
As we know, the average quantity is the sum of all quantities divided by the number of quantities.
Thus, average = {(3.24 - 3/8 -0.15 +7/9)/4} °C,
or, average = {{324/100 - 3/8 - 15/100 + 7/9}/4} °C,
or, average = [{(23328 - 2700 - 1080 + 5600)/7200}/4] °C,
or, average = 25148/28800 °C,
or, average = 6287/7200 °C = 0.8732 °C ≈ 0.87 °C.
Thus, the average change in the temperature of the city is 0.87°C.
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Simplify the expression Β. 15ω – 6ω + 1402
Answer:
9w+1402
Step-by-step explanation:
What are two methods that can solve x^2+14x=-8
The two methods which can be used to solve the quadratic equation are; The completing the square method and the factor method.
Which two methods can be used to solve the quadratic equation?Although, not limited to the aforementioned methods of solving quadratic equations, the two methods are major methods of solving quadratic equations.
The completing the square method (also used in expressing quadratic equations in vertex form) and the factor method are very efficient method of solving quadratic equations.
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what is the measure.. PLS HELP THIS IS URGENT
The angle of the given ray is of x = 150º.
What is the angle of the ray?The angle of the ray is given by the sum of the angles that compose the ray.
In this problem, the angles are of 65º, 40º and 45º, hence:
x = 65 + 40 + 45 = 150º
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find the y intercept of the line on the graph
PLEASE HELP AND EXPLAIN
See below for the interpretation of the graph
How to interpret the graph?From the graph, the initial values of x and y are 0
As x increases, y decreases.
This means that the first statement is
Initially, as x increases, y decreases.Slope is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
Using the graph values at the interval x =0 to x = 3, we have:
[tex]m = \frac{-3 - 0}{3 - 0}[/tex]
m = -1
This means that the second statement is
The slope of the graph is equal to -1 for all x between x = 0 and x = 3From the graph, y = -3, when x = 3
As x increases at this point, y increases.
This means that the third statement is
Starting at x = 3, the function value y increases as x increasesUsing the graph values at the interval x = 3 to x = 5, we have:
[tex]m = \frac{3 + 3}{5 - 3}[/tex]
m = 3
This means that the fourth statement is
The slope of the graph is equal to 3 for x between x = 3 and x = 5All y values at x = 0 to x = 4 are less than 0, while all y values at x = 4 to x = 8 are greater than 0
So, the last two statements are
For x between x = 0 and x = 4, the function value y is less than 0For x between x = 4 and x = 8, the function value y is greater than 0Read more about functions at:
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A line passes through the points (p,a) and (p,−a) where p and a are real numbers and p ≠ 0. Describe each of the
following. Explain your reasoning.
.slope of the line
.equation of the line
.y-intercept
.slope of a line perpendicular to the given line
Answer:
slope: undefined
equation: x = p
y-intercept: there is none
slope of perpendicular: 0
Step-by-step explanation:
points: (p, a), (p, -a)
slope = (-a - a)/(p - p) = -2a/0
The slope is undefined since the line is vertical.
equation: x = p
Since p ≠ 0, the vertical crosses the x-axis at a point that is not x = 0 and never intersects the y-axis, so the is no y-intercept.
A line perpendicular to he given line is a horizontal line.
slope = 0