The function f(x) is translated 3 units right and 5 units down then the function f(x) is coincident with the function g(x).
What is a function?A function is an assertion, conception, or regulation that establishes a partnership between two variables.
The functions f(x) and g(x) are given below.
f(x) = 1 / x
g(x) = 1 / (x - 3) - 5
Translate the function 3 units right, then replace x with (x - 3). And translate the function 5 units down, then replace f(x) with (g(x) + 5). Then we have
g(x) + 5 = 1 / (x - 3)
g(x) = 1 / (x - 3) - 5
The function f(x) is translated 3 units right and 5 units down then the function f(x) is coincident with the function g(x).
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Find the sum. Write your answer in simplest form. 3 3/4 + 1 2/4=
Answer: 5 1/4
Step-by-step explanation:
I don’t understand this can someone help
The ordered pair (2,10) means that the cost to feed 200 animals is of $10,000.
How to interpret the ordered pair?The general format of an ordered pair is given as follows:
(x,y).
The meaning of an ordered pair (x,y) is that y = f(x), meaning that the numeric value of the function at the value of x is of y.
The variables for this problem are given as follows:
x -> number of animals, in hundreds, hence x = 2 means that there are 200 animals.y -> cost to feed the animals, in thousands, hence y = 10 means that the cost is of $10,000.More can be learned about ordered pairs at brainly.com/question/1528681
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A cylinder has a base diameter of 6m and a height of 12m what is the volume in cubic m, to the nearest tenths place
Answer:
339.3 cubic m
Step-by-step explanation:
r = Base radius
= [tex]\frac{Diameter}{2}[/tex]
= [tex]\frac{6}{2}[/tex] m
Base radius = 3 m
h = Perpendicular height
= 12 m
Volume of a cylinder: [tex]\pi r^{2} h[/tex]
= [tex]\pi (3 m)^{2} (12 m)[/tex]
= [tex]\pi (108)m^{3}[/tex]
= 339.3 cubic m (Rounded to the nearest tenths place)
can someone please help i don’t understand
Which statements describe the graph of 2 8/9>x
There is an open circle on ²9.
21909.
The graph contains the point 0
,8
There is a closed circle on ²ğ.
The arrow points to the left.
The arrow points to the right.
2x on a number line? Select three options.
The inequality 26/9 > x represents a line with an open circle at 26/9 going toward positive infinity represented by an arrow.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, An inequality [tex]2\frac{8}{9} > x[/tex].
26/9 > x.
Now, As the inequality is strictly greater than 26/9 it would be represented by a line open circled at 26/9 and going towards +∞.
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prove by induction that if we remove the root of a k-th order binomial tree, it results in k binomial trees of the smaller orders. you can only use the definition of bk. per the definition, bk is formed by joining two bk−1 trees.
To prove that removing the root of a k-th order binomial tree results in k binomial trees of smaller orders, we will use mathematical induction.
Base case: For k = 1, removing the root of a 1st order binomial tree results in zero smaller binomial trees, which is true.
Inductive hypothesis: Assume that removing the root of a k-th order binomial tree results in k binomial trees of smaller orders, for some positive integer k.
Inductive step: We want to prove that removing the root of a (k+1)-th order binomial tree results in (k+1) binomial trees of smaller orders.
By definition, a (k+1)-th order binomial tree, denoted by B(k+1), is formed by joining two k-th order binomial trees, denoted by Bk, with one of them as the leftmost child of the root of the other. Let us remove the root of B(k+1) to obtain a new binomial tree, denoted by B'.
Since B(k+1) is formed by joining two k-th order binomial trees, we can apply the inductive hypothesis to each of them to obtain that removing their roots results in k smaller binomial trees each. Let these smaller binomial trees be denoted by B1, B2, ..., Bk and C1, C2, ..., Ck,
respectively.
Now, consider B' and observe that it is a k-th order binomial tree, since it has k children, each of which is a smaller binomial tree. Moreover, B' is obtained from B(k+1) by removing the root, which is the parent of the two k-th order binomial trees Bk and Ck. Thus, we have decomposed B' into k smaller binomial trees, namely B1, B2, ..., Bk and C1, C2, ..., Ck.
Therefore, we have shown that removing the root of a (k+1)-th order binomial tree results in (k+1) binomial trees of smaller orders, which completes the induction.
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among the cast aluminum parts manufactured on a certain day, 80% were awless, 15% had only minor aws, and 5% had ma jor aws. find the probability that a randomly chosen part (a) has a aw and (b) has no ma jor aw.
Probability that a randomly chosen part (a) has a P(flaw) = 0.2 and
has no major flaws b) P(No major flaws) = 0.95
The probability that an event will occur is determined by probability: P(A) = f / N. Probability and odds are related, but probability determines what the odds are. Probability is required before calculating the likelihood that an event will occur.
To find the probability of flaws, we can find the probability of no flaws first by dividing by 100:
P(no flaw) = 80/100 = 0.8
So then:
P(flaw) = 1 - P(no flaw) = 1 - 0.8 = 0.2
P(flaw) = 0.2
B) First, we need to find the probability of major flaws:
P(major flaws) =
P(Major flaws) = 0.05
So to find the probability of no major flaws:
P(No major flaws) = 1 - P(major flaws) = 1 - 0.05 = 0.95
P(No major flaws) = 0.95
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How does the distance change during the last section of tom’s journey? What does this mean? Explain your reasoning
The distance is decreasing with time meaning that the object is going back to the starting point.
What does it mean when distance decreases with time?When distance decreases with time, it means that the object is moving towards its starting point or moving in the opposite direction from its initial position. In other words, the object is moving backwards or reversing its direction of motion.
Distance is a measure of the total amount of ground covered by an object in motion, while time is a measure of how long it takes the object to cover that distance. If the object is moving towards its starting point, it means that it is covering less and less distance over time, or the distance it covers is decreasing.
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Find the area bounded by y=x-13/x^2-6x-27, x=2, x=7, and y=0
Answer
Step-by-step explanation:
Jonathan rides his bicycle at a velocity of 12 m/s East. He
comes to a hill and over the next 23 seconds, his velocity
decreases to 5 m/s East. What is Jonathan's acceleration?
Jonathan's acceleration is -0.3043 m/s² East, which means he is slowing down.
What is Acceleration?Acceleration is the rate of change of the velocity of an object with respect to time.
Jonathan's initial velocity, u = 12 m/s East
His final velocity, v = 5 m/s East
The time taken, t = 23 seconds
We can use the formula for acceleration:
a = (v - u) / t
Substituting the given values, we get:
a = (5 m/s - 12 m/s) / 23 s
a = -7 m/s / 23 s
a = -0.3043 m/s^2 East
Therefore, Jonathan's acceleration is -0.3043 m/s² East, which means he is slowing down.
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Lena estimate is there a bottle contains 500 mm of water but actually contains 473 mm of water what is the percent error and Lena's estimate rounded to the nearest 10th of a percent HURRY FAST PLS!!!
5.4% is the percent error .
What is the formula for errors?
The difference between the estimated value and the actual value in relation to the actual value is given as a percentage and is known as the percent error.
The relative error is multiplied by 100 to calculate the % error, in other words. The absolute value of the difference between the measured value and the actual value is divided by the actual value, then multiplied by 100 to get the percent error.
= 500 - 473/500 * 100
= 27/500 * 100
= 5.4%
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pls help due now!!!!!!!!!!!!!!!
Answer: D. 6 cm
Step-by-step explanation:
V = 4/3πr^3
r = (3 V/4π)^1/3 = (3* 900/4*π)^1/3 = 5.98942
Work out 135% of 160
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{135\% of 160}}{\left( \cfrac{135}{100} \right)160}\implies \text{\LARGE 216}[/tex]
Gloria traveled a total of 888 miles to get from school to her apartment. Gloria took the bus from school and then walked the remaining 880880880 yards home.
Gloria walked 500500 Miles from nearest bus stop to home.
How to convert yards into miles ?
To convert a yard measurement to a mile measurement, divide the length by the conversion ratio.
Since one mile is equal to 1,760 yards, you can use this simple formula to convert:
miles = yards ÷ 1,760
The length in miles is equal to the yards divided by 1,760.
Given:
Gloria traveled : 888 miles
1 Mile = 1760 yards
880880880 yards = 500500 Miles
So she walked 500500 Miles from nearest bus stop to home.
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Suppose a magazine ranks the best paying college degrees in a country. The following data show the median starting salary, the mid-career salary, and the percentage increase from starting salary to mid-career salary for the 20 college degrees with the highest mid-career salary. Degree starting salary mid-career salary : Degree Starting Salary Mid-Career Salary % Increase
College Degree A 59,400 105,000 77
College Degree B 56,400 101,000 79
College Degree C 54,800 101,000 84
College Degree D 64,800 105,000 62
College Degree E 53,500 93,400 75
College Degree F 61,200 87,700 43
College Degree G 56,200 97,700 74
College Degree H 50,400 87,000 73
College Degree I 48,800 97,800 100
College Degree J 60,800 105,000 73
College Degree K 47,500 91,500 93
College Degree L 41,500 88,300 113
College Degree M 49,300 87,100 77
College Degree N 50,900 90,300 77
College Degree O 46,400 88,300 90
College Degree P 63,900 105,000 64
College Degree Q 93,000 159,000 71
College Degree R 50,700 99,600 96
College Degree S 56,700 91,300 61
College Degree T 50,000 93,400 87
(a) using a class width of 10, construct a histogram for the percentage increase in the starting salary. A histogram with 8 class labels along the horizontal axis is given. The horizontal axis is labeled: % increase. The vertical axis is labeled: frequency. Centered over the leftmost label, 40-49. 9, a bar is drawn 1 unit tall. Moving to the right, information about the remaining bars (beginning with class label) is listed. 50-59. 9: 1 unit tall 60-69. 9: 3 units tall 70-79. 9: 3 units tall 80-89. 9: 7 units tall 90-99. 9: 4 units tall 100-109. 9: no bar 110-119. 9: 1 unit tall a histogram with 8 class labels along the horizontal axis is given. The horizontal axis is labeled: % increase. The vertical axis is labeled: frequency. Centered over the leftmost label, 40-49. 9, a bar is drawn 7 units tall. Moving to the right, information about the remaining bars (beginning with class label) is listed. 50-59. 9: 4 units tall 60-69. 9: no bar 70-79. 9: 1 unit tall 80-89. 9: 1 unit tall 90-99. 9: 1 unit tall 100-109. 9: 3 units tall 110-119. 9: 3 units tall a histogram with 8 class labels along the horizontal axis is given. The horizontal axis is labeled: % increase. The vertical axis is labeled: frequency. There is no bar centered over the leftmost label, 40-49. 9. Moving to the right, information about the remaining bars (beginning with class label) is listed. 50-59. 9: 1 unit tall 60-69. 9: 4 units tall 70-79. 9: 3 units tall 80-89. 9: 7 units tall 90-99. 9: 3 units tall 100-109. 9: 1 unit tall 110-119. 9: 1 unit tall a histogram with 8 class labels along the horizontal axis is given. The horizontal axis is labeled: % increase. The vertical axis is labeled: frequency. Centered over the leftmost label, 40-49. 9, a bar is drawn 1 unit tall. Moving to the right, information about the remaining bars (beginning with class label) is listed. 50-59. 9: no bar 60-69. 9: 4 units tall 70-79. 9: 7 units tall 80-89. 9: 3 units tall 90-99. 9: 3 units tall 100-109. 9: 1 unit tall 110-119. 9: 1 unit tall (b) comment on the shape of the distribution. The histogram is ---select---. (c) develop a stem-and-leaf display for the percentage increase in the starting salary. (enter numbers from smallest to largest separated by spaces. Enter none for stems with no values. ) Leaf Unit = 1
4 5 6 7 8 9 10 11
The histogram of the magazine ranks the best paying college degrees in a country is illustrated below.
A histogram is a graphical representation of data that displays the frequency distribution of a set of continuous or discrete data
To construct a histogram, we would first need to determine the range of the data. In this case, the range would be the difference between the highest and lowest starting salaries or mid-career salaries. We would then divide the range into several intervals or "bins" of equal width.
For example, if we use a bin width of $10,000, the first bin would be $40,000-$49,999, the second bin would be $50,000-$59,999, and so on.
We would then count the number of degrees that fall into each bin and plot the counts as bars on a graph, with the bin ranges on the x-axis and the frequency counts on the y-axis. The resulting graph would be a histogram, showing the distribution of the data.
It is important to label the axes of the histogram and include a title that accurately reflects the data being presented.
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Complete Question:
Suppose a magazine ranks the best paying college degrees in a country. The following data show the median starting salary, the mid- career salary, and the percentage increase from starting salary to mid-career salary for the 20 college degrees with the highest mid- career salary.
Degree Starting Salary | Mid-Career Salary | % Increase
College Degree A 59,400 104,000 75 College Degree B 56,400 101,000 79 College Degree C 54,800 101,000 84 College Degree D 64,800 104,000 60 College Degree E 53,500 93,400 75 College Degree F 61,200 87,700 43 College Degree G 56,200 97,700 74 College Degree H 50,400 87,000 73 College Degree I 48,800 97,800 100 College Degree J 60,800 107,000 76 College Degree K 47,500 91,500
Frequency 40-49.9
Using a class width of 10, construct a histogram for the percentage increase in the starting salary.
HELP DUE TONIGHT!!!
Answer:
1. $1900
2. $9
Step-by-step explanation:
Part a:
‘If she doesn’t sell any copies of History is Fun’ means x = 0:
[tex]y = 1900 + 9(0)[/tex]
∴ y = Melissa’s total pay = $1900
Part b:
Rearranging the equation:
[tex]y = 9x + 1900[/tex]
∴m = slope of equation = positive 9
c = y-intercept = 1900
The shape of the graph would be increasing or ascending. And since the Number of copies (x) can never be negative, this means that the amount of pay CANNOT be less than $1900. The amount of $1900 is her minimum pay
The value of m for this equation indicates the change in Melissa’s total pay for every copy she sells.
∴Change in Melissa’s total pay = 9 dollars
Linette and Ruth breed poodles as a hobby. They sold half of the puppies and half a puppy from the latest litter to the local pet shop. Then they sold half of the puppies that were left in the litter and half a puppy to the poodle palace. Then they decided to give the one remaining puppy to their friend Grace. How many puppies were originally in the litter
There were originally 10 puppies in the litter, as of the given condition.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
We can represent the number of original puppies as "x", and the sequence of events can be represented as:
Sold half of the puppies, so they have x/2 left - 1 sold to the local pet shop.
Sold half of the remaining puppies, so they have (x/2 - 1)/2 left sold to poodle palace.
One puppy was given to Grace, so they have ((x/2 - 1)/2- 1 = x - 2 / 4 - 1 remaining.
Since they are left with x - 2 / 4 - 1 puppies in the end, we can set this equal to 1 (the remaining puppy given to Grace), and solve for x:
x - 2 / 4 - 1 = 1
x - 2 = {1 + 1} * 4
x = 8 + 2
x = 10
Therefore, there were originally 10 puppies in the litter.
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Two numbers are co-prime if they do not have any prime factors in common.
List all possible numbers that are co-primes with the following numbers that are < 50:
(a) 390
(b) 210
(c) 49335
On solving the provided question, we can say that Here, 21 and 22 only share a single element, which is 1. Since they are co-prime factor, their HCF equals 1.
what is prime factor?Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.
21 and 22:
1, 3, 7, and 21 are the factors of 21.
1, 2, 11, and 22 are the factors of 22.
Here, 21 and 22 only share a single element, which is 1. Since they are co-prime, their HCF equals 1.
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Two different investment companies offer college savings plans, one at 8. 4% compounded continuously and the other at 8. 6% compounded quarterly. Which is the better investment?
The 8.4% compounded quarterly is the better investment because it gives a good return.
Compound interest is “interest-on-interest”, or the ability of a financial instrument to generate earnings on its earnings. Compound interest, can be calculated using the formula :
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
where A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
(i)S = P
S = P(1.0854) (1.0854)
AP(1) = 1.0846 - 1
AP(1)= 0.08546 or 8.546%
(ii)r = 0.084/4
AP(2) = (1 + 0.084/4)⁴ -1
AP(2) = 1.08688 - 1
AP(2) = 8.668%
The 8.4% compounded quarterly investment is therefore preferable.
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Find the mode of each group of numbers:
62,63,67,66,66,63,62,68,69,65,67,63,64,68,65,62,69,63,61,60,63,65
The mode of the data set given is 63.
What is the Mode of a dataset?Statistics uses the terms mean, median, and mode to describe central tendency. They each provide information about what value in a data set is conventional or representative of the data set in their own unique ways.
The number that appears the most frequently in a piece of data is the mode. Count the occurrences of each number in the data collection. The figure with the largest total is the mode. More than one mode is acceptable. Additionally, there is no mode if all numbers appear exactly once.
Given that:
62,63,67,66,66,63,62,68,69,65,67,63,64,
By rearrangement, we have:
62, 62, 63, 63, 63, 64, 65, 66, 66, 67, 67, 68, 69
Therefore, the highest occurring number(mode) is 63.
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Yen takes her pomeranian kiwii to the dog park once inside the fence kiwii runs across the filed in 10 seconds his path is shown on the graph belowwhat is the average velocity 4 to 8 seconds
The average velocity from 4 to 8 seconds is given as follows:
v = [position at 8 seconds - position at 4 seconds]/4.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
The change in the distance from 4 to 8 seconds is given as follows:
position at 8 seconds - position at 4 seconds
The change in the time from 4 to 8 seconds is given as follows:
8 - 4 = 4 seconds.
Hence the velocity is of:
v = [position at 8 seconds - position at 4 seconds]/4.
Missing InformationThe problem is incomplete, hence the general procedure to obtain the average velocity was presented.
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Please help (will mark as brainlest)
Answer:
TRIANGLE PROBLEM:
area : 6a^4
perimeter : 12a^2
SIMPLIFY problem:
-40c^2+26a^2+30ac
EVALUATE & FACTOR:
(q^2 - p) ( p^2 - q)
and the solved form is 240
hope it helps :)
Step-by-step explanation:
lol im an rsm kid too. but i hope these are right,
first i'm gonna start with 263 c.
AREA = 4a^2 * 3a^2 divided by 2.
12a^4 divided by 2 = 6a^4.
AREA = 6a^4
Perimeter you can find with the pythag. th.
(4a^2) ^2 + (3a^2 ) ^2 = c^2
16a^4 + 9a^4 = c^2
, the missing side is 5a^2
therefore the perimeter is 4a^2 + 3a^2 + 5a^2 = 12a^2
ok next, im gonna do 266
the answer is -40c^2+26a^2+30ac
make sure to check this w/ symbo or mthway
ok last one!!
factored form is (q^2 - p) ( p^2 - q)
and the solved form is 240
write the equations from word form.
The transformed functions is
a) The absolute value function reflected across the x axis and shifted up 2 units is y₁ = -| x₁ | + 2
b) The absolute value function that is shifted left 3 units and is compressed by a third is y₂ = ( 1/3 ) | x₂ + 3 |
c) The absolute value function reflected across the x axis stretched vertically by 5 units shifted left 4 units and up 6 units is y₃ = -5 | x₃ + 4 | + 6
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
a) The absolute value function reflected across the x axis and shifted up 2 units is y₁
The absolute value function is y₁ = | x₁ |
when reflected over x axis , the new function is
y₁ = - | x |
when shifted up 2 units ,
y₁ = -| x₁ | + 2
b)The absolute value function that is shifted left 3 units and is compressed by a third is y₂
The absolute value function is y₂ = | x₂ |
when shifted left 3 units ,
y₂ = | x₂ + 3 |
when compressed by a third , the new function is
y₂ = ( 1/3 ) | x₂ + 3 |
c)The absolute value function reflected across the x axis stretched vertically by 5 units shifted left 4 units and up 6 units is y₃
The absolute value function is y₃ = | x₃ |
when reflected across the x axis ,
y₃ = - | x₃ |
when stretched vertically by 5 units ,
y₃ = - 5 | x₃ |
when shifted 4 units left ,
y₃ = - 5 | x₃ + 4 |
when shifted 6 units up ,
y₃ = -5 | x₃ + 4 | + 6
Hence , the transformation of functions are solved
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How so i graph this ans what is thr solution.
The system of equations has a unique solution. The solution of the system of equations is (-3,4).
What is the system of equations?
Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
Given equations are
y = x + 7 ......(i)
y = -7/3x - 3 ......(ii)
Putting x = 0 in equations (i) and (ii):
y = 0 + 7
y = 7
y = -7/3 × 0 - 3
y = -3
Putting x = 3 in equations (i) and (ii):
y = 3 + 7
y =10
y = -7/3 × 3 - 3
y = -10
Putting x = -3 in equations (i) and (ii):
y = -3 + 7
y = 4
y = -7/3 × (-3) - 3
y = 4
The points in equation (i) are (0,7), (3,10), (-3,4)
The points in equation (ii) are (0,-4), (3,-10), (-3,4)
Plot the points and join the points:
The intersection of the equation is (-3,4).
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What is the area of this compound figure? PLEASE HELP
The area of the composite figure is equal to 254 m² square metres.
How to calculate for the area of the figureThe composite figure can be observed to be a vertical rectangle, a square and an horizontal rectangle, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:
area of the vertical rectangle = 19 m × 7 m
area of the vertical rectangle = 133 m²
area of the square = 5 m × 5 m
area of the square = 25 m²
area of the horizontal rectangle = 16 m × 6 m
area of the horizontal rectangle = 96 m²
total area of the composite figure = 133 m² + 25 m² + 96 m²
total area of the composite figure = 254 m²
Therefore, the area of the composite figure is equal to 254 m² square metres.
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what happens to the equation of f(x) = 1/x, if it's translated 4 units up and to the right 3 units
What is the frequency of the function f(z)?
f(z)=-2 sin (2) +3
Express the answer in fraction form
Enter your answer in the box.
Consider the function f(x) = (x - 3)².
a. How could you restrict the domain of f(x) so that its inverse will be a function?
b. Graph f(x) with its restricted domain and then graph its inverse on the same set of axes.
c. Find the equation of the inverse of f(x) with its restricted domain.
The inverse of f(x) has no restriction on the domain.
The graph of the inverse function is given below.
The inverse equation is [tex]f^{-1}[/tex](x) = x² + 3.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = (x - 3)²
The inverse of f(x).
Step 1:
Make f(x) = y
y = (x - 3)²
Step 2:
Interchange x and y
x = (y - 3)²
Step 3:
Solve for y.
square root on both sides.
x² = y - 3
y = x² + 3
So,
[tex]f^{-1}[/tex](x) = x² + 3.
a)
[tex]f^{-1}[/tex](x) = x² + 3
we see that for any values of x, [tex]f^{-1}[/tex](x) is a function.
So,
There is no restriction on the domain.
b)
The graph is given below.
c)
The inverse equation is
[tex]f^{-1}[/tex](x) = x² + 3.
Thus,
The inverse of f(x) has no restriction on the domain.
The inverse equation is [tex]f^{-1}[/tex](x) = x² + 3.
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What is the length of the radius of the above sphere if the volume is 14,130 in3?
Solve this equation and you will have the solution:
4 • 3.14 • r3 ÷ 3 = 14,130
Your last step when solving this equation is to find the cube root of a both sides!
The length of the radius of the sphere is 15 in.
What is a sphere?It is a three-dimensional figure and has a diameter and a radius and the volume of a sphere is 4/3πr³.
We have,
Volume of the sphere = 14130 in³
So,
4/3πr³ = 14130 _____(1)
Solve for r.
4/3 x 3.14 x r³ = 14130
keep r on one side and the rest on the other side.
r³ = 14130 x 3 / 4 x 3.14
Cube root on both sides.
r³ = 3375
∛r³ = ∛3375
[ 15 x 15 x 15 = 3375 ]
So,
r = 15
Thus,
The radius of the sphere is 15 in.
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Your school is going to start offering afterschool clubs they will be nine clubs to choose from to have clubs at least 23 students we will need to sign up for each one what is the least number of students that must sign up to have all nine clubs
At least number of students who must have signed up to have all nine clubs is equal to 207.
Number of clubs school going to start after school = 9 clubs
At least number of students need to sign up in each one of the club is equal to 23 students.
At least number of students need to sign up to have all in nine clubs is equal to :
At least number of student in 1 club > 23
⇒ At least number of student in 9 club > 23 × 9
At least number of student in 9 club > 207
Therefore, at least number of students need to signed up to have in all nine given clubs are 207 students.
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