Need help with question
The composite functions and their domains are listed as follows:
a) (f ∘ g)(x) = sin(2x/(x + 5)), domain is all real values except x = -5.
b) (g ∘ f)(x) = sin(2x)/(sin(2x) + 5), domain is all real values except x = -5 and the values of x for which sin(2x) + 5 = 0.
c) (f ∘ f)(x) = sin(sin(2x)), domain is all real values.
d) (g ∘ g)(x) = x/(6x + 5), domain is all real values except x = -5 and x = -5/6.
How to obtain the composite functions and their domains?
The composite functions are found applying the inner function as the input to the outer function, according to the rule presented as follows:
(f ∘ g)(x) = f(g(x)).
The domain is the set of values that respect all the input constraints of the inner function, of the outer function, and of the composite function.
For this problem, the functions are given as follows:
f(x) = sin(2x).g(x) = x/(x + 5).For item a, the inner function g is applied as the input to the outer function f, hence:
f(g(x)) = sin(2x/(x + 5))
The sine has no constrains, the fraction cannot have a denominator zero, hence the domain is composed by all real values except x = -5.
The other composite functions are listed as follows:
g(f(x)) = sin(2x)/(sin(2x) + 5), domain is all real values except x = -5(constraint of g(x)) and the values of x for which sin(2x) + 5 = 0.f(f(x)) = sin(sin(2x)), the domain is all real values, as the sine has no restriction.[tex]g(g(x)) = \frac{\frac{x}{x + 5}}{\frac{x}{x + 5} + 5} = \frac{x}{6x + 5}[/tex]
Domain is all real values except:
x = -5 -> constraint of g(x).x = -5/6 -> constrain of the composite function.More can be learned about composite functions at https://brainly.com/question/10687170
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John painted his most famous work, in his country, in 1930 on composition board with perimeter 104.09
in. If the rectangular painting is 5.72
in. taller than it is wide, find the dimensions of the painting.
Question content area bottom
Part 1
What is the width? enter your response here
▼
in. squared
in. cubedJohn painted his most famous work, in his country, in 1930 on composition board with perimeter 104.09
in. If the rectangular painting is 5.72
in. taller than it is wide, find the dimensions of the painting.
Question content area bottom
Part 1
What is the width? enter your response here
▼
in. squared
in. cubed
in.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)John painted his most famous work, in his country, in 1930 on composition board with perimeter 104.09
in. If the rectangular painting is 5.72
in. taller than it is wide, find the dimensions of the painting.
Question content area bottom
Part 1
What is the width? enter your response here
▼
in. squared
in. cubed
in.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)John painted his most famous work, in his country, in 1930 on composition board with perimeter 104.09
in. If the rectangular painting is 5.72
in. taller than it is wide, find the dimensions of the painting.
Question content area bottom
Part 1
What is the width? enter your response here
▼
in. squared
in. cubed
in.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)John painted his most famous work, in his country, in 1930 on composition board with perimeter 104.09
in. If the rectangular painting is 5.72
in. taller than it is wide, find the dimensions of the painting.
Question content area bottom
Part 1
What is the width? enter your response here
▼
in. squared
in. cubed
in.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)John painted his most famous work, in his country, in 1930 on composition board with perimeter 104.09
in. If the rectangular painting is 5.72
in. taller than it is wide, find the dimensions of the painting.
Question content area bottom
Part 1
What is the width? enter your response here
▼
in. squared
in. cubed
in.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)John painted his most famous work, in his country, in 1930 on composition board with perimeter 104.09
in. If the rectangular painting is 5.72
in. taller than it is wide, find the dimensions of the painting.
Question content area bottom
Part 1
What is the width? enter your response here
▼
in. squared
in. cubed
in.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)
in.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)
The dimensions of the rectangular paint of perimeter 104.09 inches are given as follows:
Height: 28.88 inches.Width: 23.16 inches.How to obtain the perimeter of a rectangle?The perimeter of any polygon, including a rectangle, is given by the sum of all the lengths of the outer edges of the figure.
Hence, for a rectangle of height h and width w, the perimeter is given by twice the sum of these dimensions, hence it is given as follows:
P = 2(h + w).
In this problem, the perimeter has the value given as follows:
P = 104.09 inches.
Hence:
2(h + w) = 104.09
h + w = 104.09/2
h + w = 52.045 inches.
The painting is 5.72 inches taller than it is wide, hence:
h = 5.72 + w.
Then the height is obtained as follows:
5.72 + w + w = 52.045
2w = (52.045 - 5.72)
w = (52.045 - 5.72)/2
w = 23.16 inches.
Then the height of the rectangular painting is given as follows:
h = 5.72 + w = 5.72 + 23.16 = 28.88 inches.
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What is the value of 4n+ 7 when n
-
2?
Answer:
Either 15 or -1 see below
Step-by-step explanation:
I am not sure if you menat n = 2 or n = -2
n= 2
4n + 7 Subtitute in 2 for n
4(2) + 7
8 + 7
15
n = -2
4n + 7y
4(-2) + 7
-8 + 7
-1
At a particular restaurant, each pizza roll has 65 calories and each chicken wing has 50 calories. A combination meal with pizza rolls and chicken wings is shown to have 1015 total calories and 5 more pizza rolls than chicken wings. Determine the number of pizza rolls in the combination meal and the number of chicken wings in the combination meal
The lifetime of a certain type of battery is known to be normally distributed with standard deviation =σ17 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 95% confidence interval for the mean lifetime for this type of battery.
The point estimate for the lifetime of a certain type of battery is 120.1 hours.
How to illustrate the information?Let X represent the battery's lifetime. X has a normal distribution with a standard deviation of 20 hours. The sample size is 50, and the average lifetime is 120.1 hours.
Calculating the mean of a sample drawn from the population yields a point estimate of the population's mean. The mean is calculated as the sum of all sample values divided by the number of values.
A single value estimate of a parameter is referred to as a point estimate. A sample mean, for example, is a point estimate of the population mean. An interval estimate provides a range of values within which the parameter is expected to fall. The population mean point estimate is sample mean and this is 120.1 hours.
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Complete question
The lifetime of a certain type of battery is known to be normally distributed with standard deviation =σ17 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 95% confidence interval for the mean lifetime for this type of battery. What is the point estimated?
A paper company needs to ship papre to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weight 35 ponds and each large box of paper wight 60 pounds. There were 7 more small boxes shipped than large boxes and the total wight of all boxes was 815 ponds. Write a system of equations that could be used to determine the number of small boxes shipped and the number boxes shipped.
Setting up a system of equation, the number of small boxes shipped is 13 and large box shipped is 6
System of EquationSystem of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.
Let;
x = small boxy = large boxWe can represent this using equations;
35x + 60y = 815 ...eq(i)
x = 7 + y ... eq(ii)
Solving equation (i) and (ii)
x = 13, y = 6
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Find the average rate of change of f(x) = -x² + 3x + 1 from x=2 to x = 5.
Simplify your answer as much as possible.
Answer:
The average rate of change is: -4
Step-by-step explanation:
So to solve this we just need to plug our numbers into the formula. We are using the formula f(b) - f(a)b - a where “a” and “b” are our numbers. So we are given the intervals x=2 and x=5. When we see that we can rewrite it as (2,0) and (5,0). This is because when it is telling us just “x” we know “y” (the second number in the parentheses) is 0. So just plugging in the numbers we get: (-(5)2+3(5)+1)-(-(2)2+3(2)+1)(5 - 2). Solving it we get -4.
Give g(x)=4x-4 , solve for x when g (x) =0
Answer:
x = 1
Step-by-step explanation:
Given:
g(x) = 4x - 4
To Find:
x when g(x) = 0
[tex] \rm \implies 4x - 4 = 0 \\ \\ \rm \implies 4x - 4 + 4 = 0 + 4 \\ \\ \rm \implies 4x = 4 \\ \\ \rm \implies \cancel{\frac{4}{4}} x = \cancel{ \frac{4}{4} } \\ \\ \rm \implies x = 1[/tex]
A company estimates that 0.5% of their products will fail after the original warranty period but within 2 years of the purchase, with a repair cost of $300. The company offers an extended two-year warranty.
If a consumer does not purchase the extended warranty, then the consumer will need to pay for any necessary repairs. What is the expected value of their repair costs?
The expected value of their repair costs is $41.50.
How to calculate the repair cost?Given the probability of failure as 0.5%, this can be illustrated as 0.005.
The cost of repair is given as $300.
The expected value of the company will be:
= Earnings - [(Cost × P(failure)]
= 43 - (300 × 0.005)
= 43 - 1.50
= 41.5
The value is $41.50.
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Complete question
company estimates that 0.5% of their products will fail after the original warranty period but within 2 years of the purchase, with a repair cost of $300. The company offers an extended two-year warranty.
If a consumer does not purchase the extended warranty, then the consumer will need to pay $43 for any necessary repairs. What is the expected value of their repair costs?
Express the angle in radian measure.
-22½°
a. -π/8
b. -π/4
c. -π/16
the answer is a, -π/8
what the slopes and y intercepts for both of these?
Answer:
First graph: slope = [tex]\frac{2}{3}[/tex] & y-intercept = (0, -1). Second graph: slope = 2 & y-intercept = (0,2)Step-by-step explanation:
They're both linear graphs, so they both follow the formula y = mx + b.
The y-intercept is when the graph crosses the y-intercept, so when x = 0.
First graph:
(x, y₁) = (0, -1)(x₂, y₂) = (-3, -3)Slope(m): [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{-3-(-1)}{-3-0} =\frac{-2}{-3} =\frac{2}{3}[/tex]
y-intercept(b): (0, -1)
Second graph:
(x, y₁) = (0, 2)(x₂, y₂) = (-3, -4)Slope(m): [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{-4-2}{-3-0} =\frac{-6}{-3} =2\\[/tex]
y-intercept(b): (0, 2)
I need assistance with this math assignment
a) The maximum height of the ball is 100 feet.
b) The velocity of the ball on its way up is +16 feet per second.
c) The velocity of the ball on its way down is - 16 feet per second.
How to analyze quadratic equations to find the main features of a free fall
A free fall is an uniformly accelerated motion experimented by a particle due to the effects of gravity. The position of the ball (s) in time (t), in seconds, is described by a quadratic equation.
a) First, we find the maximum height reached by the ball:
s(t) = 80 · t - 16 · t²
16 · t² - 80 · t + s(t) = 0
Then, by using the discriminant:
(- 80)² - 4 · 16 · s(t) = 0
64 · s(t) = (- 80)²
s(t) = 100 ft
b) Second, find the function velocity by derivatives:
v(t) = 80 - 32 · t
Third, find the time related to the position s(t) = 96 ft:
s(t) = 80 · t - 16 · t²
100 = 80 · t - 16 · t²
16 · t² - 80 · t + 96 = 0
Then, by quadratic equation:
t = 3 s or t = 2 s.
Fourth, evaluate the function velocity:
v(2) = 80 - 32 · 2
v(2) = 16
v(3) = 80 - 32 · 3
v(3) = - 16
The velocity of the ball when s(t) = 96 ft on its way up is 16 feet per second.
c) The velocity of the ball when s(t) = 96 ft on its way down is - 16 feet per second.
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H
3/21
(5,4)
Type here to search
U2FsdGVkX19Gmq6NxFwchHwtmTuzdHdnF2526%252BPKnZnmk4prUc006/EXe%252BwFFIHOATvP2Lrdy RyLSEw3w%253D%253D%
(5,2)
[12]
Triangle RST has vertices R(1, 1), S(1, 4), and T(3, 1).
Graph the figure and its rotated image after a
counterclockwise rotation of 180° about the origin.
What are the coordinates of T'?
6
(-3,-1)
6048 4787 3
(-3,-2)
721 PM
11/10/2012
The coordinates of T' are, T'(-3, -1).
What is rotation?
A rotation is a transformation in which each point of a preimage is turned through a predetermined angle and direction around a fixed point. The center of rotation is the fixed point. The term for the amount of rotation is the angle of rotation, and it is expressed in degrees. Measure the specified angle in the anticlockwise direction using a protractor.
Given: Triangle RST has vertices R(1, 1), S(1, 4), and T(3, 1).
We have to find the coordinates of T' after counterclockwise rotation of 180°.
Since, The rule for a rotation by 180° about the origin is (x, y) → (−x, −y).
So, the coordinates R(1, 1), S(1, 4) and T(3, 1) changes to R'(-1, -1), S'(-1, -4) and T'(-3, -1).
Therefore, the coordinates of T' are T'(-3, -1).
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Rewrite
barrel
hour
о
as a unit rate.
O A. 2 barrels/hour
OB. barrel/hour
OC. 6 barrels/hour
D. barrel/hour
Please I need it asap
Unit rate of (1 /5 barrel) / (1/2hour) is equals to (2/5) barrels /hour.
What is unit rate?
"Unit rate is defined as the representation of the ratio of the two different units with value of the denominator equals to 1."
According to the question,
Given,
1/5 barrel/1/2 barrel
⇒ (1/2) hour = (1/5) barrel
⇒ 1 hour = (2/5) barallel
⇒ (2/5) barrel per one hour.
Therefore,
Unit rate of given value is rewritten as
2/5 barrel/hour
hence option b is correct.
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Your question is incomplete. Please find the missing content below.
Rewrite 1/5 barrel 1/2 hour as a unit rate.
A. 2 1/2 barrel/hour
B. 2/5 barrel/hour
C. 10 barrels/hour
D. 1/10 barre./hour
This is due tomorrow, please help!
Mr. Phone stayed in a hotel room for 2 nights that cost $210. The hotel room tax rate is 12% what is the total cost for the hotel room?
Answer:
$235.20
Step-by-step explanation:
the tax :
[tex] \frac{12}{100} \times 210 = 25.20[/tex]
total cost :
$210 + $25.20 = $235.20
Darren and Clara live in a tall building. Clara lives 12 floors above Darren. One day Darren went up to visit Clara and he took the stairs up from his apartment to Clara’s. Half-way up he was on the 8th floor. On what floor does Clara live? Show your work.
If Clara lives 12 floors above Darren, Clara lives on the 16 floor while Darren lives on the 4 floors.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
Given that Darren and Clara reside in a towering structure, this is expected. Twelve stories above Darren, Clara resides. One day, Darren climbed the stairs from his apartment to Clara's and went to see her. He was halfway up, on the eighth floor.
Suppose Darren and Clara live on x and y number of floor respectively.
If Clara lives 12 floors above Darren.
x-y=12
If in halfway he is on the 8th floor the total number of floors in the building will be 16.
As a result, we can say that Clara lives on the 16 floors while Darren lives on the 4 floor.
Thus, if Clara lives 12 floors above Darren, Clara lives on the 16 floors while Darren lives on the 4 floors.
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Solve the following equation below. Show each step and check your work.
72y - 126 = 522 + 144
Answer: y = 11
Step-by-step explanation:
Our problem: 72y - 126 = 522 + 144
1. Simplify 552 + 144 to 666
72y - 126 = 666
2. Add 126 to both sides
72y = 666 + 126
3. Simplify 666 + 126 to 792
72y = 792
4. Divide both sides by 72
y = [tex]\frac{792}{72}[/tex]
5. Simplify [tex]\frac{792}{72}[/tex] to 11
y = 11
A species of bacteria has a population of 80 at noon. It double every 8 hours. The function that models the growth of the population, P, at any hour, t, is
P(t) = 80(28) 8 a. Why is the exponent ?
b. Why is the base 2?
c. Why is the multiplier 80?
d. Determine the population at noon the next day.
e. Determine the time at which the population first exceeds 60 Thousand.
Answer:123
Step-by-step explanation:
31231231232131
75°
64°
2
The measure of the exterior angle of the triangle is
Answer:
exterior angle = 139°
step-by-step explaination:(I'm using "X" instead of "2")
to find the exterior angle, find the interior angle first and then use the straight line.
interior angle = 180° therefore,
75° + 64° + X = 180
139° + X = 180°
X = 180° - 139°
X = 41° (not the answer)
a straight line = 180°
X = 41°
Y - the exterior angle
41° + Y = 180°
Y = 180° + 41°
Y = 139°
hope this is clear :)
Answer the question in the picture
The area of the semicircle is A = 1187.9 cm².
What is the area of a circle?The area of a circle with a radius of r is A = πr².
Given that, the diameter of the semicircle is 55 cm.
The radius of the semicircle is,
r = 55/2
The area of a semicircle is given by,
A = (1/2)πr²
Substitute the values,
A = (1/2)π(55/2)²
A = 1187.9
Hence, the area of the semicircle is A = 1187.9 cm².
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The demand for an item is given as Q=2500-6P where P is the pric supply is Q=1750 +4P. How many units Q must be made for supply to equ
The quantity of items tha must be made for supply to equal demand is 2050 items
What is demand?Demand simply means a consumer's desire to buy goods and services without any hesitation and pay the price for it.
To calculate the unit of quantity Q that must be made for demand to be equal to supply, we equate the demand and supply equation.
From the question,
For Demand
Q = 2500-6P............... Equation 1From Supply,
Q = 1750+4P........... Equation 2When supply is equal to demand
2500-6P = 1750+4PSolve for P
10P = 2500-175010P = 750P = 750/10P = 75Substitute the values of P into equation 1
Q = 2500-6(75)Q = 2500-450Q = 2050Hence, the quantity of items tha must be made 2050 items.
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Mike staples 10 sheets of paper together to make a packet.
He makes fewer than 8 packets. He uses all of the paper. How
many sheets of paper could Mike have used? Explain how you
know.
Answer:
70
Step-by-step explanation:
8 - 1 = 7
7 x 10 = 70
He used 70 sheets.
factorise 6x^2+11x+4
Answer:
(2x+1)(3x+4)
Step-by-step explanation:
6x² + 11x + 4
multiply the first and last term
i.e (6x²)(4) = 24x²
find two terms that multiplies to give 24x² and when added would give 11x
¶ 8x and 3x
Therefore; 6x² + 11x + 4
6x² + 8x + 3x + 4
2x(3x + 4) + 1(3x + 4)
Answer; (2x + 1)(3x + 4)
Find the points on the graph for the function f (x) =x²-8x/7x+12 at the value f(x) = 3.
The points on the graph of the given function at the value f(x)=3 would be x=5.0971 and x=1.5695.
What is a graph of a function?
A function's graph is the set of all points in the plane of the form (x, f(x)). The graph of f could also be defined as the graph of the equation y = f(x).
The given function is
[tex]f(x)=\frac{8-x}{x^2-7x+12}\\\\\[/tex]
Now we put f(x) = 3, we get
[tex]3=\frac{8-x}{x^2-7x+12}\\\\\\\3x^2-21x+36=8-x\\3x^2-20x+24=0\\[/tex]
Solving we get
x=5.09717
x=1.5695
So the points on the graph of the given function at the value f(x)=3 would be x=5.0971 and x=1.5695.
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The length of the longer side of a rectangle is 2 in. less than twice the length of
the shorter side. The area of the rectangle is 60 in2. What is the difference
between the lengths of the longer and shorter sides?
Simplify
15x²y³-10x²y² +5xy² divided by 5xy
Answer:
y(3xy-2x+1)
Step-by-step explanation:
I'm pretty sure it'd be y(3xy-2x+1).
Answer:
3xy²-2xy +y
Step-by-step explanation:
15x²y³-10x²y² +5xy² = 5xy(3xy²-2xy +y)
then
5xy(3xy²-2xy +y) / 5xy = 3xy²-2xy +y
92. Which key word would help you decide which operation to use to solve the following: If Kay has 5 pencils, but gives 1 to Mary, how many would she have left? (a) has (c) pencils (b) give (d) left
Answer:
Step-by-step explanation:
the correct answer is A.
because if Kay has 5 pencils and it is given to Merry 1, it means that Kay still has 4 pencils.
In AGHI, h = 300 inches, ZG=30° and H=29°. Find the
length of i, to the nearest inch.
The length of i will be 531.3 inch when h is 300 inch and ∠G is 30° and ∠H is 29°.
What is angle?When two straight lines or rays intersect at a shared terminal, an angle is generated. An angle's vertex is the common point of contact. The difference in direction between two lines or surfaces is defined as an angle. Angles are expressed in degrees. From a same point, the two hands draw separate sets of lines. Angle refers to these groups of lines that originate from a common point. Every minute, the two hands create various angles. In real life, one example of an angle is a clock.
Here,
∠I=180-(30+29)
=180-59
∠I=121°
h/sin H=i/sin I
300/sin 29=i/sin 121
i=300*sin 121/sin 29
i=531.3 inch
When h is 300 inches, G is 30 degrees, and H is 29 degrees, the length of I is 531.3 inches.
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Question 9 of 10
Mark all the statements that are true.
A. This graph is not a function because the value x = 3 is assigned to
more than one y-value.
B. The equation of this line is x = 3.
C. This graph is a function whose range is the set (3).
D. This graph is a function because the value of x is the same for
every value of y.
E. This graph is a function whose domain is the set (3).
True statement are:
A. This graph is not a function because the value x = 3 is assigned to
more than one y-value.
D. This graph is a function because the value of x is the same for
every value of y.
Given,
In the question:
To see the graph :
Mark all the statement that are true.
Now, According to the question:
From the graph,
Equations are expressions of two mathematical expressions t such as two numbers, functions. An equality between quantities and operations, usually with an equal sign "=".
Functions is a correspondences between two sets that are not empty each element in the set of input values can corresponds to a element in a set of output values that is unique.
Hence, True statement are:
A. This graph is not a function because the value x = 3 is assigned to
more than one y-value.
D. This graph is a function because the value of x is the same for
every value of y.
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5. Mrs. Hans bought a house for $35,000 ten years ago. If she sells it this year for $119,000, what percent profit will she make?
Answer:
340%
Step-by-step explanation:
119000/35000