Answers
ANSWER
The vertex of (f o g)(x) is on the x-axis while the vertex of (g o f)(x) is on the y-axis
EXPLANATION
First, we have to find the composite functions. In this notation, this means that we have to substitute x in the first function with the second function,
\((f\circ g)(x)=f(g(x))=(g(x))^2=(3x-2)^2\)Let's expand this function using the binomial squared rule,
\((3x-2)^2=(3x)^2-2\cdot3x\cdot2+2^2=9x^2-12x+4\)For the second composition, we have,
\((g\circ f)(x)=g(f(x))=3f(x)-2=3x^2-2\)Both composite functions are written in standard form,
\(y=ax^2+bx+c\)The x-coordinate of the vertex is given by,
\(x_v=\frac{-b}{2a}\)For the first composite function, a = 9, and b = -12,
\(x_v=\frac{-(-12)}{2\cdot9}=\frac{12}{18}=\frac{2}{3}\)And the y-coordinate of the vertex is,
\(y_v=9x_v^2-12x_v+4=9\left(\frac{2}{3}\right)^2-12\left(\frac{2}{3}\right)+4=0\)So, the vertex of the first composite function is at the point (2/3, 0).
For the second composite function, a = 3, and b = 0. This means that the x-coordinate of the vertex is 0 and the y-coordinate is,
\(y_v=3\cdot0-2=-2\)So, the vertex of the second composite function is at the point (0, -2).
Therefore, the vertices are located on each axis: the vertex of (f o g)(x) is on the x-axis while the vertex of (g o f)(x) is on the y-axis.
Related Questions
Given that f(x)=x^2+2x+3
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I need help with a math problem.
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Answer:
where is the problem?
Archimedes drained the water in his tub. 62.5 liters of water were drained each minute, and the tub wascompletely drained after 8 minutes.Graph the relationship between the amount of water left in the tub (in liters) and time (in minutes).
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Start by finding the initial amount of water there was in the tub.
If it took 8 minutes to drain and it loose 62.5 liters per minute we can find the inital amount.
\((\frac{62.5L}{\min})\cdot(8\min )=500L\)continue by drawing a line between points (0,500) and (8,0)
using this line we can see how the water is being drained in the y-axis over the time in the x-axis.
Help!!!! I will give you brainiest!!!! Pls
find the solution of y=3x+5 for x=-2
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Answer:
I think the answer is B
can you also please mark me as brainliest
Answer:
The slope-intercept form is y=mx+b y = m x + b , where m is the slope and b is the y-intercept. Using the slope-intercept form, the slope is 3 .
Please break down how to do these pls
Answers
The value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08
Simplifying an equation is simply another way of saying solving a math problem. When you simplify a phrase, you are attempting to write it in the simplest way feasible. In conclusion, there should be no more adding, subtracting, multiplying, or dividing to do.
Given expression 1. -4\(x^{-2}\) + 3\(y^{0}\) 2. 2\(x^{0}\)\(y^{-2}\)
Expression for x =2 and y=5
-4x-2 + 3y0
= -4(2)-2 + 3(5)0
= 16+3
=19
Now
2x0y-2
= 2(2)0x(5)-2
= 2 x (1/25)
= 2 x 0.04
= 0.08
Therefore the value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08
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A normally distributed data set has a mean of 0 and a standard deviation of 0.5. Which is closest to the percent of values between –1 and 1?
34%
50%
68%
95%
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As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.
What is equation?A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.
For a normally distributed data set with a mean of 0 and a standard deviation of 0.5, the proportion of values between -1 and 1 is most closely related to 68%.
Approximately 68% of the data in a normal distribution lies within one standard deviation of the mean, which explains why. One standard deviation below the mean is -0.5, and one standard deviation above the mean is 0.5 since the mean is 0 and the standard deviation is 0.5. As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.
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Please anyone that can help me
Answers
Answer:
\(|\frac{x}{y} |\)
Step-by-step explanation:
Pre-SolvingWe are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.
We want to simplify it.
To do that, we can first simplify what is under the radical, then take the square root of what is left.
Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.
SolvingTo simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).
So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .
Under the radical, we now have:
\(\sqrt{x^2y^{-2}}\)
Now, we take the square root of both exponents to get:
\(|xy^{-1}|\)
The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.
However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.
Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).
So, by using that,
\(|x * \frac{1}{y} |\)
This can be simplified to:
\(|\frac{x}{y} |\)
SOMEONE PLEASE HELP ME IM GONNA FAIL
The wind force F on a sail varies jointly as the area A of the sail and the square of the wind speed w.
The force on a sail with area an area of 500 P? is 64.8 pounds when the wind speed is 18 mph. What
would be the force for a sail with an area of 250 f2 with a wind speed of 35 mph.
Answers
Answer:
405 pounds
Step-by-step explanation:
2. What is the 7th term of an A.P: 50+45+40? a. 40, b. 20, c. 15, d. 22
Answers
The 7th term of an Arithmetic Progression 50+45+40 is 20
How to determine the 7th term of an Arithmetic Progression 50+45+40?The Arithmetic Progression is given as:
50+45+40
In the above Arithmetic Progression, we have
First term, a= 50
Common difference, d = 45 - 50 = -5
The nth term of the Arithmetic Progression is calculated as:
Tn = a + (n - 1)d
Substitute the known values in the above equation
Tn = 50 + (n - 1) * -5
Substitute 7 for n in the above equation
Tn = 50 + (7 - 1) * -5
Evaluate the product
Tn = 50 - 30
Evaluate the difference
T7 = 20
Hence, the 7th term of an Arithmetic Progression 50+45+40 is 20
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Harper’s parents put $75 into her school lunch money account. Each meal she gets from school costs her $3.25. The school sends Harper’s parent’s an email when the balance reaches $19.75. Let m be the number of meals Harper has bought when they get the email. Set up and solve an equation to find the value of m.
Answers
Answer:
She has ordered 6 meals
Find the value of the expression f+ 4 1/ 2 for f = 2 Write your answer as a fraction or as a whole or mixed number.
Answers
Answer:
43/6
Step-by-step explanation:
The figure shown is composed of two cubes.
Which equation shows the surface area
ne figure?
SA = 6(5-5)+6(3-3)-2(3-3)
What is the surface area of
the figure shown?
cm²
3cm
5c
Answers
186 cm³ will be the surface area of the given figure.
To calculate the surface area of the given figure, we need to add the surface area of two cubes and reduce the area of the hidden part.
Thus,
Total surface area = Surface area of bigger cube + surface area of the smaller cube - 2* surface area of the hidden part.
So,
Total surface area = 6*(5*5)+6*(3*3)-2*(3*3)
Total surface area = 150+54-18
Total surface area = 186
Therefore, the surface area of the given figure will be 186 cm³.
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What the meaning of statement this?
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The axiom of regularity is a set theory principle which states that every non-empty set C contains an element that is disjoint from C.
Axiom of RegularityThe set theory concept rules that for every non-empty set C there is an element x of C such that x does not intersect C. The regularity axiom aims to establish that no non-empty set will have itself as an element.
The principle which is also called the axiom of foundation is a fundamental concept in set theory and credited to Zermelo–Fraenkel.
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At a high school football game, admission is $5 for students and $10 for non-students. The school made $4,000 from admissions at the first game,which 500 people attended. How many students and non-students were at the game? Earlier you wrote the system of equations that models thissituation. In this activity, you will solve this system of equations.S+ n = 5005s + 10 = 4,000Part ALooking at the two equations, which method should you use to solve this system of equations?
Answers
To solve the system of equation use substitution method:
1. Solve s in the first equation:
\(s=500-n\)2. Substitute in the second equation the s for the value you get in step 1:
\(5(500-n)+10n=4000\)3. Solve n:
\(\begin{gathered} 2500-5n+10n=4000 \\ -5n+10n=4000-2500 \\ 5n=1500 \\ n=\frac{1500}{5} \\ \\ n=300 \end{gathered}\)4. Use the value of n to solve s:
\(\begin{gathered} s=500-n \\ s=500-300 \\ s=200 \end{gathered}\)Then, in the game were 200 students and 300 non-studentsWhat is the y-intercept of the line representing Beatrice's monthly music subscription bill as a function of the number of songs she downloaded?
$$
Answers
The y-intercept of the line representing Beatrice's monthly music is 20
How to determine the y-intercept of the lineFrom the question, we have the following parameters that can be used in our computation:
y = -.95x + 20
To calculate the y-intercept of the line, we set x = 0
So, we have
y = -.95 * 0 + 20
Evaluate
y = 20
Hence, the y-intercept of the line representing Beatrice's monthly music is 20
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Question
What is the y-intercept of the line representing Beatrice's monthly music subscription bill as a function of the number of songs she downloaded?
The equation is y = -.95x + 20
A model rocket is launched with an initial upward velocity of 60 m/s the rocket's height h meters after t seconds h=60t-5t^2 find values for which rockets height is 30 meters
Answers
The model rocket will have a height of 30 meters at a time of 0.523 seconds and 11.477 seconds, respectively.
How to determine the time associated with the height of a rocket on air
In this problem we have the case of a model rocket being launched, the height of the rocket in time is described by the following quadratic equation:
h(t) = 60 · t - 5 · t²
Where:
h - Height, in meters.t - Time, in seconds.We need to determine the time associated to a given height of 30 meters above the ground. If we know that h(t) = 30, then the times are, respectively:
30 = 60 · t - 5 · t²
6 = 12 · t - t²
t² - 12 · t + 6 = 0
(t - 11.477) · (t - 0.523) = 0
t = 11.477 s. or t = 0.523 s.
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Please ANSWER!!!!!!!
Answers
Answer:
See explanation
Step-by-step explanation:
It appears that the second graph is better since it seems to be rather consistent. The graph of the first one seems out of place. Therefore it seems to be confusing and could be misleading.
if f(x)=x+2/x^2-9 and g(x)=11/x^2+3x
A. find f(x)+g(x)
B. list all of the excluded values
C. classify each type of discontinuty
To receive credit, this must be done by Algebraic methods, not graphing
Answers
The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.
A. To find f(x) + g(x), we add the two functions together:
f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)
To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:
f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]
Simplifying the numerator:
f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]
Combining like terms:
f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]
B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:
(x^2 - 9) = 0 --> x = -3, 3
(x^2 + 3x) = 0 --> x = 0, -3
So, the excluded values are x = -3, 0, and 3.
C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.
At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.
At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.
Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.
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An airplane travels 500 miles in 2 hours. What is the airplane's speed in feet per second?
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Answer:
403.3 feet per second
Step-by-step explanation:
please mark brainlest
What is the intermediate step in the form (x+a)^2=b as a result of complementing the square for the following equations
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The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.
To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.
Add the square of half of the coefficient of x to both sides of the equation:
x² + 2x + (2/2)² = 319 + (2/2)²
x² + 2x + 1 = 320
The left-hand side of the equation can now be factored as a perfect square:
(x+1)² = 320
This is the equation in the form (x+a)²=b, where a=1 and b=320.
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The complete question is as follows:
What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?
x² + 2x = 319
Which can be represented using the product (50) × (-5) ?
O saving $5 each day for 50 days
O a submarine rising by 50 feet each hour for 5 hours
O earning $50 each month for 5 months
O an airplane losing altitude by 5 feet each second for 50 seconds
Answers
Answer: D
Step-by-step explanation:
An individual is baking 3 batches of cookies. They used 1.8 oz. of vanilla in one batch of the cookies, 1.25 oz. of vanilla in the second batch and .95 oz. in the third batch. Convert these decimals into fractions, and then put them in ascending order.
Answers
Answer:
19/20 , 1 1/4 , 1 4/5
Step-by-step explanation:
1.8 = 1 4/5 (fraction)
1.8 converts to 18/10. This can be simplified twice, firstly by making it 9/5 since both 18 and 10 are divisible by two, but can be simplified further to 1 4/5
1.25 = 1 1/4 (fraction)
1.25 converts to 125/100. This can be simplified to 5/4 or 1 1/4
0.95 = 19/20 (fraction)
0.95 converts to 95/100. This can be simplified to 19/20
Ascending Order (smallest to largest)
smallest - 19/20
middle - 1 1/4
largest - 1 4/5
I believe this is the right answer, but haven't done fractions in a while so may want to double check to make sure
PLS I REALLY NEED HELP! what is the range of graph!
Answers
Solitary Savings received an initial deposit of $2000. It kept a percentage of this money in reserve based on the reserve rate and loaned out the rest. The amount it loaned out was eventually all deposited back into the bank. if this cycle continued indefinitely and eventually the $2000 turned into $40,000, what was the reserve rate?
Answers
The value of reserve rate is 5%
Given that;
Solitary savings bank received initially amount of $2000.
Now, Let x% percent be kept as reserve then (100-x)% will be loaned out which would be deposited in other bank.
The other bank would keep x% of (100 - x) and again loan the remaining amount.
Thus the total deposits of this cycle would be a geometric series as
⇒ 2000[1 + (100 - x)% + (100 - x)²%+(100-x)² +...]
Here common ratio is,
(100 - x) / 100 = 1 - 0.01x <
for all possible x
This series is infinite and sum of this would be
= sum of geometric series
= 2000 (1/ (x/100)
= 200000/x
This is given as, 40000
Hence, equate and simplify to get;
⇒ x = 5%
So, The value of reserve rate is 5%
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If I have a population of all the apples in an orchard, what would I call the subset of 1000 apples collected from the orchard knowing that the 1000 apples was less than the population of the apples? 50 points
Answers
I would call the subset of 1000 apples collected from the orchard knowing that the 1000 apples was less than the population of the apples as a sample
What is a sample?You should be aware that Set of all possible outcomes or results of a statistical trial or experiment is called a sample
The total outcome in the orchard is 1000 apples Which is the universal set.
So the sample is drawn from the universal set to give a sub set of 1000 apples.
Total population is the universal set is larger than the sample size which is the subset of 1000 apples
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Find the missing side
Answers
By using trigonometry, the missing sides are
Example 1: x = 16.7
Example 2: x = 3.2
Example 3: x = 23.5
Example 4: x = 9.3
Trigonometry: Determining the values of the missing sidesFrom the question we are to determine the value of the missing sides in the given triangles
We can determine the value of the missing sides by using SOH CAH TOA
Example 1
Angle = 42°
Opposite side = x
Hypotenuse = 25
Thus,
sin (42°) = x / 25
x = 25 × sin (42°)
x = 16.7
Example 2
Angle = 75°
Opposite side = 12
Adjacent side = x
Thus,
tan (75°) = 12 / x
x = 12 / tan (75°)
x = 3.2
Example 3
Angle = 36°
Hypotenuse side = x
Adjacent side = 19
Thus,
cos (36°) = 19 / x
x = 19 / cos (36°)
x = 23.5
Example 4
Angle = 53°
Opposite side = x
Adjacent side = 7
Thus,
tan (53°) = x / 7
x = 7 × tan (53°)
x = 9.3
Hence,
The missing sides are 16.7, 3.2, 23.5 and 9.3
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i need help asap
than you!
Answers
The highest height for the daily rainfall were for 5 and 6 inches
How to Interpret Dot Plots?Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.
From the given dot plot, we see the number of times for each height of rainfall.
Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.
Thus, we conclude those were the highest heights for the daily rainfall.
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Determine the equation of the circle graphed below.
Answers
Step-by-step explanation:
radius= √(2+2)²+(0+3)²=√4²+3²=√16+9
=√25=5
the equation is
(x+2)²+(y+3)²=25
or
x²+y²+4x+6y-12 = 0
3. Chris rode his bike along the same route every day for 60 days. He logged that he had gone exactly 127.8 miles.How many miles did he bike over the course of two weeks
Answers
Step-by-step explanation:
2wks = 24 days
If he spent 60days going 127.8 miles
He will spend 14 days going X miles
60/14 =127.8/X cross multiply
60X= 14×127.8
X=( 14×127.8)÷60
X= 29.82 miles
2k+8=0 Can someone help explain how to solves this please?
Answers
Answer:
2k + 8 = 0
2k + 8 - 8 = 0 - 8
2k = - 8
2k/2 = - 8/2
k = - 4
Step-by-step explanation:
you gotta put the 8 on the other side by subtracting and the divide both sides to get k
Answer:
k = -4
Step-by-step explanation:
2k + 8 = 0
Subtract 8 from both sides.
2k = -8
Divide both sides by 2.
k = -4