If f(x) = 3 – 2x and 1/x+5, what is the value of (f/g)(8)? –169 –1 13 104
The value of (f/g)(8) is -169 if the f(x) = 3 – 2x and g(x) = 1/(x+5) option (A) -169 is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have functions:
f(x) = 3 – 2x and
g(x) = 1/(x+5)
To find the value of (f/g)(8):
First, find the value of f(x) at x = 8
Plug x = 8 in the function f(x)
f(8) = 3 - 2(8)
f(8) = 3 - 16
f(8) = -13
Now plug the x = 8 in the function g(x)
g(8) = 1/(8 + 5)
g(8) = 1/13
(f/g)(8) = f(8)/g(8)
(f/g)(8) = -13/(1/13)
(f/g)(8) = -169
Thus, the value of (f/g)(8) is -169 if the f(x) = 3 – 2x and g(x) = 1/(x+5) option (A) -169 is correct.
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7p + 20 – 13q – 4q – 18 + 6p
A.
13p + 17q – 2
B.
13p – 17q + 2
C.
3q + 38
D.
3q – 6
Answer:
c i just took it
Step-by-step explanation:
The given expression simplifies to B. 13p - 17q + 2 by combining like terms.
The given expression that requires simplification is 7p + 20 - 13q - 4q - 18 + 6p. To simplify an algebraic expression, combine like terms, which are terms that contain the same variable raised to the same power. In this case, we combine the terms with p and the terms with q, as well as the constant terms separately.
First, combine the terms with p: 7p + 6p equals 13p.
Second, combine the terms with q: -13q - 4q combines to -17q.
Lastly, combine the constant terms: 20 - 18 equals 2.
Putting it all together, the simplified expression is 13p - 17q + 2, which corresponds to option B.
A stuntman jumps from a rooftop 315 ft off the ground. how long will it take him, falling freely, to reach the ground? (use the formula s = 16t2.)
The stuntman will take approximately 3.98 seconds to reach the ground when falling freely from a rooftop 315 ft high.
To calculate the time it takes for the stuntman to reach the ground when falling freely:
Given s = 315 ft and using the formula s = 16t^2, where s represents the distance and t represents time.Plug in the value of s into the formula: 315 = 16t^2.Solve for t by isolating the variable: t = sqrt(315/16) ≈ 3.98 seconds.Part A: The area of a square is (9x2 − 18x + 9) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work.
Part B: The area of a rectangle is (25x2 − 4y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work.
PLEASE HELP
what is the value of x in the diagram?
a. 15
b. 5 2/5
c. 19
d. 3/5
Answer: The answer is (a) 15.
Step-by-step explanation: We are given a figure with two similar triangles with sides of lengths x, 15 and corresponding sides of lengths 15 and 25 respectively.
Since the given triangles are similar, so their sides will be proportional.
Therefore, we have
[tex]\dfrac{x}{9}=\dfrac{25}{15}\\\\\\\Rightarrow \dfrac{x}{9}=\dfrac{5}{3}\\\\\\\Rightarrow x=\dfrac{5\times 9}{3}\\\\\Rightarrow x=15.[/tex]
Thus, the value of x is 15.
Which properties did Carmen use to solve the following problem? 17 + (45 + 23) 17 + (23 + 45) (17 + 23) + 45 40 + 45 85 distributive property identity property of addition associative property of addition commutative property of addition
Carmen used the associative property of addition to solve the given problem.
The associative property means one can add or multiply the given numbers regardless of how they are grouped. In other words, if one is adding or multiplying it does not matter where the brackets are placed.
The given problem is -
17 + (45 + 23), 17 + (23 + 45), (17 + 23) + 45
So here the sum of all the three patterns is 85. This clearly proves that forming groups does not affect the sum. So this is based on associative property of addition.
10. Does the table represent an exponential function? Explain why or why not.
x 1 2 3 4
y 2 8 32 128
I REALLY NEED HWLP WITH THIS
At Saturday night’s football game there were 18 less fans than half the fans at Friday night’s game. There were “x” fans at Friday’s game. Write an expression to represent the number of fans at Saturday’s game
The expression to represent the number of fans at Saturday's game when there were 'x' fans on Friday is (1/2)x - 18.
Explanation:To find the number of fans at Saturday's football game based on the given information that there were 'x' fans at Friday's game, we will write a mathematical expression. According to the statement, there were 18 fewer fans than half of the fans on Friday night. The expression for half of the fans at Friday's game is (1/2)x and we subtract 18 from this to account for the 18 fewer fans. Therefore, the expression representing the number of fans at Saturday's game is (1/2)x - 18. This expression can be used to determine the number of fans at Saturday's game once the number of fans on Friday (x) is known.
The expression representing the number of fans at Saturday's game, based on the fact that there were 18 less than half the number of fans at Friday's game (represented by x), is (x/2) - 18.
Explanation:The question we are addressing involves writing an expression to represent the number of fans at Saturday's football game, with the information that there were 18 less fans than half the number of fans at Friday night's game, and there were x fans at Friday's game.
Let's start with the number of fans at Friday's game, which is represented by x. Since we know that Saturday's game had 18 less than half of that amount, we first need to find half of x. To do that, we divide x by 2: (x/2). Now, to reflect that there were 18 fewer fans on Saturday, we subtract 18 from half of x: (x/2) - 18. Consequently, the expression that represents the number of fans at Saturday's game is (x/2) - 18.
This expression allows us to plug in the actual number of fans from Friday's game (when we know it) to determine the number of fans that attended Saturday's game.
For which interval is the function constant?
(0, 2)
(−∞, −6)
(2, ∞)
(−6, 0)
Answer:
(−6, 0)
Step-by-step explanation:
The section where the function is constant is where it is horizontal. This is from x = -6 to x = 0; in interval notation, this is (-6, 0).
A function assigns the value of each element of one set to the other specific element of another set. The function is constant in the interval (-6 to 0).
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A function is known to be constant if the value of one of the variables is not changing the value of the other.
In the function as we can see that the value of y is not changing with the change in the value of x between x=-6 to 0, therefore, the function is constant in the interval (-6 to 0).
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Describe the translation in the figure from A to A’
Answer:
d
Step-by-step explanation:
For which intervals is the function positive?
Select each correct answer.
(−6, −2)
[−8, −6)
(4, 8]
(−2, 4)
Positive is when the lines are above the X axis
in this graph it is positive from [−8, −6) and (−2, 4)
The function is positive in intervals [tex]\boldsymbol{[-8,-6),(-2,4)}[/tex]
A function is positive in intervals where the graph lies above the [tex]\boldsymbol{x-}[/tex]axis.
A function is negative in intervals where the graph lies below the [tex]\boldsymbol{x-}[/tex]axis.
In intervals [tex]\boldsymbol{(-6,-2),(4,8]}[/tex], the graph lies below the [tex]\boldsymbol{x-}[/tex] axis.
In intervals [tex]\boldsymbol{[-8,-6),(-2,4)}[/tex], the graph lies above the [tex]\boldsymbol{x-}[/tex] axis.
So, the function is positive in intervals [tex]\boldsymbol{[-8,-6),(-2,4)}[/tex]
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The table lists the test scores William and Andre received on five math assessments William's scores 89 97 78 81 91 Andre's score 90 74 73 87 82
Which statement best describes the difference of the mean of the two sets?
A)It is equal to about 0.5 times the mean absolute deviation of either data set. B)It is equal to about 1 times the mean absolute deviation of either data set. C)It is equal to about 1.5 times the mean absolute deviation of either data set. D)It is equal to about 2 times the mean absolute deviation of either data set.
A surveyor, Toby, measures the distance between two landmarks and the point where he stands. He also measured the angles between the landmarks in degrees.
What is the distance, x, between the two landmarks? Round the answer to the nearest tenth.
Answer:
It is D. 98.5
Step-by-step explanation:
Got it right on edge
230 is equal to _____.
solution:
230 degree is 50 degrees past 180 degrees into the third quadrant where both sin and cos are negative.
What is the missing reason in Step 8?
Step 8 involves identifying the gap, researching if needed, and crafting a concise reason. Ensure coherence with existing content, verify consistency, and integrate the reason seamlessly. Finally, review for clarity and implement the revised explanation.
Step 8 is to implement a missing reason in a explanation, broken down step by step:
Identify the Gap: Review the existing explanation to pinpoint where a reason is lacking.
Understand the Context: Ensure comprehension of the topic to provide an accurate reason.
Research if Necessary: Gather relevant information to support the reason.
Craft the Explanation: Write a concise statement that fills the gap logically.
Check for Coherence: Ensure the new reason aligns seamlessly with the existing content.
Review for Clarity: Confirm that the explanation is clear and understandable.
Integrate into the Content: Insert the reason into the appropriate section of the explanation.
Verify Consistency: Double-check that the added reason maintains coherence with the overall argument or narrative.
Final Review: Reevaluate the entire explanation to guarantee completeness and accuracy.
Implement and Test: Incorporate the revised explanation and assess its effectiveness.
By following these steps, the missing reason can be seamlessly integrated into the explanation, ensuring clarity and coherence.
Harrison plays a game in which he uses a net to catch balls that are randomly launched from holes in the ground. The height of one ball after t seconds is represented by the function f(t) = –After how many seconds does the ball return to the ground? Round to the hundredths place as needed.16t2 + 20t.
Evaluate e−12fe-\dfrac12f e− 2 1 f e, minus, start fraction, 1, divided by, 2, end fraction, f when e=15e=15 e=15 e, equals, 15 and f=2f=2 f=2 f, equals, 2 .
Answer:
the answer is 14
Step-by-step explanation:
If the value of e is 15 and f is 2. Then the value of the expression [e - (1/2)f] will be 14.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The expression is given below.
⇒ e - (1/2)f
If the value of e is 15 and f is 2.
Then the value of the expression will be
⇒ e - (1/2)f
⇒ 15 - (1/2) x 2
⇒ 15 - 1
⇒ 14
Thus, the value of the expression will be 14.
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Suppose the ages of cars driven by employees at a company are normally distributed with a mean of 8 years and a standard deviation of 3.2 years. What is the z score of a car that is 6 years old?
Answer:
z=(6-8)/3.2=(-2)/3.2=-0.625
Step-by-step explanation:
z=(6-8)/3.2=(-2)/3.2=-0.625
A bike rental company rented out 6 bikes in its first month. The number of bikes it rented tripled each month.
What was the total number of bikes the company rented out for the first 6 months?
Answer:
Step-by-step explanation:
HELP I WILL FAN AND MEDAL
Which of the following statements about special angle relationships is not correct?
A. It is possible for angles to be both vertical and complementary.
B. It is possible for an obtuse angle to have both a complement and a supplement.
C. It is possible for an acute angle to have both a complement and a supplement.
D. It is possible for angles to be both congruent and supplementary
Answer:
B.) It is possible for an obtuse angle to have both a complement and a supplement.
Step-by-step explanation:
Rules for an obtuse angle:
It cannot be smaller than or be 90°It can not be bigger than or be 180°To create a complementary or supplementary angle, you can use 2 angles and no more than 2.
Say we used an obtuse angle (like the one in the picture below), since an obtuse angle can not be or be greater than 90°, an obtuse angle can not be complementary.
We can not fit 2 obtuse angles at 180°, because of that, an obtuse angle(s) can not create a supplementary angle.
Therefore, B would be the correct answer.
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Two trains left the station traveling in opposite directions. The distance Train A traveled is modeled by the function d(t)=81t where d represents distance in miles and t represents time in hours.
Train B traveled a total of 324 miles in 4 hours.
How does the distance Train A traveled in 1 hour compare to the distance Train B traveled in 1 hour?
The distance Train A traveled in 1 h is equal to the distance Train B traveled in 1 h.
The distance Train A traveled in 1 h is greater than the distance Train B traveled in 1 h.
The distance Train A traveled in 1 h is less than the distance Train B traveled in 1 h.
Answer:
Option A - The distance Train A traveled in 1 h is equal to the distance Train B traveled in 1 h.
Step-by-step explanation:
Given : The distance Train A traveled is modeled by the function [tex]d(t)=81t[/tex]
where d represents distance in miles and t represents time in hours.
To find : How does the distance Train A traveled in 1 hour compare to the distance Train B traveled in 1 hour?
Solution :
Distance traveled by Train A in 1 hour is
[tex]d(t)=81t[/tex]
[tex]d(t)=81(1)=81[/tex]
Distance traveled by Train B in 1 hour is
[tex]d(t)=81t[/tex]
[tex]d(t)=81(1)=81[/tex]
or for B, we have 324 miles in 4 hours. If that is at a constant speed, it travels 324/4 = 81 miles in one hour
Therefore, The distance Train A traveled in 1 h is equal to the distance Train B traveled in 1 h.
Hence, Option A is correct.
Answer:
The distance Train A traveled in 1 h is equal to the distance Train B traveled in 1 h.
Step-by-step explanation:
What is the mode for the following set of data?
5, 7, 9, 11, 13, 13
8
9.7
10
13
please please help me
Pre-calculus Help Please! Express the complex number in trigonometric form.
3
A. 3(cos 0° + i sin 0°)
B. 3(cos 90° + i sin 90°)
C. 3(cos 180° + i sin 180°)
D. 3(cos 270° + i sin 270°)
Which sequence is geometric and has 1/4 as it’s fifth term and 1/2 as common ratio is it A)...,1,1/2,1/4,1/8,...
B)...,1/4,1/2,1,2,...
C)...,1/72,1/36,1/18,1,9,
D)...,8,4,2,1,...
Answer:
Option A - [tex]......,1,\frac{1}{2},\frac{1}{4},\frac{1}{8}...[/tex]
Step-by-step explanation:
Given : A geometric has [tex]\frac{1}{4}[/tex] as its's fifth term and [tex]\frac{1}{2}[/tex] as common ratio.
To find : Which sequence is geometric ?
Solution :
The geometric sequence is defined as [tex]a,ar,ar^2,ar^3...[/tex]
where, a is the first term and r is the common ratio.
The nth term of the sequence is [tex]a_n=ar^{n-1}[/tex]
We have given, [tex]r=\frac{1}{2}[/tex] and [tex]a_5=\frac{1}{4}[/tex]
The 5'th term is
[tex]a_5=ar^{5-1}[/tex]
[tex]\frac{1}{4}=a(\frac{1}{2})^{4}[/tex]
[tex]\frac{1}{4}=a(\frac{1}{16})[/tex]
[tex]\frac{16}{4}=a[/tex]
[tex]a=4[/tex]
The sequence form is [tex]4,4(\frac{1}{2}),4(\frac{1}{2})^2,4(\frac{1}{2})^3,4(\frac{1}{2})^4,4(\frac{1}{2})^5...[/tex]
[tex]4,2,1,\frac{1}{2},\frac{1}{4},\frac{1}{8}...[/tex]
From the given sequence Option A matched with result.
Therefore, Option A is correct.
You have $1,998.00 on a credit card with a 14.5% APR. You miss your minimum payment the first month and there is a late fee of $37.00. How much is your balance at the beginning of the second month?
The answer is:
$2,059.14
I have attached a picture of a question I am stuck on. It is about Riemann sums. I have attempted the question but did not get the correct answer :( Here is my work:
I see that this graph has the same area repeating 12 times.
I did (b - a)/n, or (12 - 0)/36, and found that the width of each rectangle should be 1/3. Because we are asked to find the area using "circumscribed angles," I will use right-endpoint rectangles on the first part of the graph that shows a decreasing interval from 0 to 1:
t = 1/3, r(t) = 2.01745506
t = 2/3, r(t) = 2
t = 1, r(t) = 1.45369751
These values for r(t) represent heights of the rectangles. I can add them and multiply by the width of each rectangle:
1/3(2.01745506 + 2 + 1.45369751) = 1/3(5.47115257) = 1.823717523
I can multiply the area by 12 to find the area under the entire function:
1.823717523 * 12 = 21.88461028
This is not an answer choice, so I clearly did something wrong! Can someone help me find my mistake?
The number 1,054 is:
A. < 1,045
B. = 1,045
C. > 1,045
D. None of the choices are correct.
Write a pair of parametric equations for an object moving along the unit circle
Are lines of symmetry for any given polygon also diagonal?