Answer:
23
Step-by-step explanation:
Given : [tex]f(x) = log_3(x + 4)[/tex]
To Find: [tex]f^{-1}(3)[/tex]
Solution:
[tex]y = log_3(x + 4)[/tex]
Replace y with x and x with y
[tex]x = log_3(y + 4)[/tex]
[tex]3^x = y + 4[/tex]
[tex]3^x-4 = y [/tex]
So, [tex]f^{-1}(x)=3^x-4[/tex]
Now substitute x= 3
[tex]f^{-1}(3)=3^(3)-4 [/tex]
[tex]f^{-1}(3)=27-4 [/tex]
[tex]f^{-1}(3)=23[/tex]
Hence the value of [tex]f^{-1}(3)[/tex] is 23
If M9=119,what is the sum of the measures 0f 11 and 16?
238
299
122
119
Sally Leadfoot was pulled over on her way from Syracuse to Ithaca by an officer claiming she was speeding. The speed limit is 65 mph and Sally has traveled 97 km in 102 minutes. How fast was Sally's average speed in mph? In a complete sentence, explain whether or not Sally deserves a ticket?
Answer:
35.5 mph
Step-by-step explanation:
We are given that Sally Leadfoot was pulled over on her way from Syracuse to Ithaca by an officer claiming she was speeding.
Speed limit =65 mph
Sally traveled distance 97 km in 102 minutes
We have to find the Sally's average speed in mph
Time =102 minutes
We know that 1 hour =60 minutes
[tex]102 minutes=\frac{102}{60}=1.7 [/tex]hours
We know that 1 km=0.621371
97 km=[tex]0.621371 \times 97=60.272987[/tex]miles
Average speed =[tex]\frac{60.272987}{1.7}=35.45 mph[/tex]
Average speed of Sally's =35.5 mph
Hence, average speed of Sally is less than 65 mph .Therefore, she was not fast speeding and she deserves a ticket.
What is the simplified form of 15 x to the eighth power over 24 y to the fifth power divided by 4 x to the fourth power over 8 squared
A) 4 y cubed over 5 x to the fourth power
B) 4 y to the fourth power over 5 x cubed
C) 5 x to the fourth power over 4 y cubed
D) 5 x cubed over 4 y to the fourth power
From the table below, determine whether the data shows an exponential function. Explain why or why not.
x: 3, 1, -1, -3
y: 1, 2, 3, 4
(A) No; the domain values are at regular intervals and the range values have a common sum 1.
(B) No; the domain values are not at regular intervals.
(C) Yes; the domain values are at regular intervals and the range values have a common factor 2.
(D) Yes; the domain values are at regular intervals and the range values have a common sum 1.
Answer:
a
Step-by-step explanation:
Cassandra is trying to think of a good way to keep her financial records. She makes a lot of purchases, using cash, debit cards, and credit cards about equally. When she gets home every day, she tends to be very tired and doesn’t like to do a lot of organized thinking. She tends to lose individual pieces of paper if she doesn’t file them immediately. What might be a good method for Cassandra to use? a. Recording all of her daily expenditures in an organizational computer program. b. Keeping and collecting receipts for everything she buys. c. Tracking and collecting her bank and credit statements every month. d. Carrying a notebook and immediately recording all of her transactions in it.
Answer:
d. Carrying a notebook and immediately recording all of her transactions in it.
Step-by-step explanation:
The correct answer is option D.
What is bank statement?A bank statement is a document that is typically sent by the bank to the account holder every month, summarizing all the transactions of an account during the month.
Bank statements contain bank account information, such as account number and a detailed list of deposits and withdrawals.
Cassandra's best option would probably be carrying a notebook and immediately recording all of her transactions in it.
Since she does not like to do a lot of heavy thinking when she gets home, and tends to lose pieces of paper, this method is ideal because it would allow her to consolidate all her purchase records in one notebook, eliminating the need to carry receipts, and recording them immediately will make it so she can relax when she gets home.
Perhaps once a month, she can compile all of her notebook activity into a computer program and reconcile it to her bank statements.
Hence, the correct option is D.
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Find the number of ways to purchase 5 different kinds of drinks from a selection of 13 drinks.
The sum of the reciprocals of two consecutive integers is startfraction 11 over 30 endfraction 11 30. find the two integers.
The consecutive integers are 5 and 6.
What are integers?Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."
Given:
The sum of the reciprocals of two consecutive integers is 11/30.
Let the integers be n and n+1.
Then,
1/n + 1/n+1 = 11/30
{n + 1 + n}/n(n+ 1) = 11/30
30(2n+1 ) = 11(n²+n)
60n + 30 = 11n² + 11n
11n² - 49n - 30 = 0
(11n +6) (n-5) = 0
Only taking,
n = 5.
So, 5 and 6.
Therefore, 5 and 6 are the integers.
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You record a temperature of 0.75 °C. Is this a positive or negative temperature?
The function H(t)=-16t+48t+12 shows the height H(t), in feet, of a cannon ball afte t seconds. A second cannon ball moves in the air along a path represented by g(t)=10+15.2t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: create a table using integers 0 through 3 for the 2 functions. Between wat 2 seconds is the solution to H(t)=g(t) located? How do you know?
Part B: Explain what the solution from Part A means in the context of the problem.
How to quickly convert degrees to radians?
Use cavalieri's Principle to calculate the exact of an oblique cylinder with a radius of 10 meters and a height of 11 meters.
Answer: Volume of cylinder is 1152.38 m³.
Step-by-step explanation:
Since we have given that
Radius of cylinder = 10 m
Height of cylinder = 11 m
Using Cavalieri's principle , volume of an oblique cylinder is equal to volume of cone.
So, Volume of an oblique cylinder is given by
[tex]V=\frac{1}{3}\pi r^2h\\\\V=\frac{1}{3}\frac{22}{7}\times 10\times 10\times 11\\\\V=1152.38\ m^3[/tex]
Hence, Volume of cylinder is 1152.38 m³.
Solve this inequality: 8z + 3 – 2z < 51
4 (x+2)=2 (x+3)+2 (x-1) answer?
[tex]4(x+2)=2(x+3)+2(x-1)\\\\use\ the\ distributive\ property:\ a(b\pm c)=ab\pm ac\\\\(4)(x)+(4)(2)=(2)(x)+(2)(3)+(2)(x)-(2)(1)\\\\4x+8=2x+6+2x-2\ \ \ \ |simplify\\\\4x+8=(2x+2x)+(6-2)\\\\4x+8=4x+4\ \ \ \ |-4x\\\\8=4\ FALSE!!!\\\\Answer:\ NO\ SOLUTION\ (x\in\O)[/tex]
Find the length and width of a rectangle that has perimeter 24 meters and a maximum area.
Let the length of the rectangle = x
since the perimeter is 24m then the width of rectangle is (12-x)m.
the area of
rectangle is:
A=x*(12-x)
A=-x^2+12x
x=-12/-2 =6:
Since the length is 6m the width will be: 12-6=6m
We conclude
that this rectangle has the maximum area when its shape is square of side 6m.
We find the value of area for x=6m :
Area = 6^2 =36M^2
How tall is the tower ?
x = 50 * tan(60) = 50sqrt(3) =86.6 feet
tower is 93.6 feet tall
Which statement is true the graph of y=log(x-4) is the graph of y=log(x) translated 4 units down
The true statement is: The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of y = (log(x) translated 4 units up.
Let's analyze each statement:
1. The graph of [tex]\(y - \log(x-4)\)[/tex] is the graph of [tex]\(y - \log(x)\)[/tex] translated 4 units down.
This statement is incorrect. The function [tex]\(y - \log(x-4)\)[/tex] is the result of shifting the graph of [tex]\(y = \log(x)\) 4[/tex] units to the right, not down.
2. The graph of [tex]\(y = \log(x) - 4\)[/tex] is the graph of [tex]\(y = \log(x)\)[/tex] translated 4 units down.
This statement is incorrect. The function [tex]\(y = \log(x) - 4\)[/tex] represents a vertical translation of 4 units down from the graph of [tex]\(y = \log(x)\)[/tex], not left.
3. The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of [tex]\(y = \log(x)\)[/tex] translated 4 units up.
This statement is true. Adding a constant term to a function vertically shifts the graph of the function by that amount. So, adding 4 to [tex]\(y = \log(x)\)[/tex] shifts it 4 units up.
4. The graph of [tex]\(y = \log(x+4)\)[/tex] is the graph of [tex]\(y = \log_2(x)\)[/tex] translated 4 units right.
This statement is incorrect. The function [tex]\(y = \log(x+4)\)[/tex] represents a horizontal translation of 4 units to the left from the graph of [tex]\(y = \log(x)\).[/tex]
Therefore, the true statement is: The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of y = (log(x) translated 4 units up.
Question
Which statement is true?
The graph of Y - log(x-4) is the graph of y-log,(x) translated 4 units down.
The graph of Y = log: (x)-4 is the graph of y = log. (x) translated 4 units left.
The graph of y = log,(x)+4 is the graph of Y=log.(x) translated 4 units up.
The graph of y = log. (x+4) is the graph of y = log2 (x) translated 4 units right.
How do you know when the function is in simplified form?
Final answer:
A function is in simplified form when all unnecessary terms have been eliminated, subscripts are used appropriately, and it uses the most compact and standard notation possible. Always verify the reasonableness of the simplified function.
Explanation:
To determine when a function is in simplified form, several steps should be followed:
Eliminate terms wherever possible to simplify the algebra.Use the simplified subscript in the final formula.Do not write the subscript if it is one, as it is understood to be implied.Condense constant quantities within parentheses, replacing them with a single symbol, for example, 'a', to make the equation look simpler.When an equation contains more than one unknown, use an additional equation to solve the problem.In cases where several unknowns must be determined, keep physical principles in mind and possibly use multiple equations to find the required variable.Condense formulas for chemical structures by using subscripts to denote multiple identical elements, making notation more compact.When you have eliminated all unnecessary terms and used standard conventions for simplification mentioned above, the function is considered to be in its simplest form. It is always good practice to check the answer to see if it is reasonable and does not violate any known principles or constraints.
Lemon drops and jelly beans are mixed to make a 100 pound mix. if the lemon drops cost $1.90 per pound and jelly beans cost $1.20 per pound, how many pounds of lemon drops are need to make the mix cost $1.48 per pound. formulate an equation and then solve it to find how many pounds of lemon drops are needed. show all of your work
L = lemon drops
J = jelly beans
L +J = 100
L=100-J
1.90L + 1.20J=1.48*100
1.90(100-j) +1.20J =148
190-1.90J+1.20J=148
190-0.7J=148
-0.7J=-42
J = 60
L=100-60 = 40
40 pounds of Lemon Drops are needed
Final answer:
40 pounds of lemon drops are needed.
Explanation:
To find out how many pounds of lemon drops are needed to make a 100-pound mix that costs $1.48 per pound, we can set up a system of equations. Let L represent the number of pounds of lemon drops and J represent the number of pounds of jelly beans.
Since the total weight of the mix is 100 pounds:
L + J = 100
Given the cost of lemon drops is $1.90 per pound and jelly beans cost $1.20 per pound, and the entire mix should cost $1.48 per pound:
1.90L + 1.20J = 100 * 1.48
We already have that L + J = 100, so J can be expressed as 100 - L. Substituting J in the second equation we get:
1.90L + 1.20(100 - L) = 148
Solving for L:
1.90L + 120 - 1.20L = 148
0.70L = 28
L = 28 / 0.70
L = 40
Therefore, 40 pounds of lemon drops are needed for the mix.
Perform the indicated operation. 5/17 ∙ 3/8
How many window coverings are necessary to span 50 windows if each window covering is 15 windows long? 3 4 5 6?
To cover 50 windows with coverings that are 15 windows long, at least 4 window coverings are needed to span all the windows.
Explanation:The question asks how many window coverings are necessary to span 50 windows, given that each window covering is 15 windows long. To find out how many window coverings are required, you divide the total number of windows by the length of one window covering. So, we do 50 ÷ 15 which equals approximately 3.33. Since you can't have a fraction of a window covering, you'll need at least 4 full window coverings to span all 50 windows.
Consider the function given by the graph.
What are these values?
f(–2 ) =__
f(0) = __
f(4) = __
Answer:
f(-2 ) =2
f(0) = 3
f(4) = -1
Step-by-step explanation:
Clearly by looking at the graph of the given function f(x) we could observe that the function f(x) is increasing in the interval (-∞,0] and then decreasing in the interval (0,∞).
Also, the function is discontinuous at x=0.
( Since, there is a break in a graph and also the left and right hand limit of the function are not equal at x=0)
Hence, from the graph we could directly say that:
f(-2 ) =2
f(0) = 3
f(4) = -1
The values of the function values are:
f(-2 ) =2, f(0) = 3 and f(4) = -1
The value of f(-2)On the graph, the value of the function when x = -2 is 2
Hence, the value of f(-2) is 2
The value of f(0)On the graph, the values of the function when x = 0 are 1 and 3.
However, the line that has a closed circle (i.e f(0) = 3) will take precedence over the line that has an open circle (i.e f(0) = 1)
Hence, the value of f(0) is 3
The value of f(4)On the graph, the value of the function when x = 4 is -1
Hence, the value of f(4) is -1
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In one town, 79% of adults have health insurance. what is the probability that 4 adults selected at random from the town all have health insurance? round to the nearest thousandth if necessary.
Answer:
0.039 on gradpoint
Step-by-step explanation:
I got it right on the test
Given f(x) and g(x) = f(x) + k, look at the graph below and determine the value of k. k = _______ Graph of f of x and g of x. f of x equals 1 over 3 x minus 3 and g of x equals 1 over 3 x plus 1 Numerical Answers Expected!
Answer:
The value of k is 4.
Step-by-step explanation:
Given,
f of x equals 1 over 3 x minus 3,
[tex]\implies f(x)=\frac{1}{3}x-3[/tex]
Also, g of x equals 1 over 3 x plus 1,
[tex]\implies g(x)=\frac{1}{3}x+1[/tex]
Since, g(x) = f(x) + k,
By substituting the values,
[tex]\frac{1}{3}x+1=\frac{1}{3}x-3+k[/tex]
[tex]1=k-3[/tex]
[tex]\implies k = 1+3 = 4[/tex]
Hence, the value of k is 4.
Determine the number of elements in the Sample Space for each of the following:
1. Tossing a coin three times
2. The order that the top 5 students will receive their diplomas.
3. Tossing a pair of dice.
Which polynomial can be simplified to a difference of squares? 10a2 + 3a – 3a – 16 16a2 – 4a + 4a – 1 25a2 + 6a – 6a + 36 24a2 – 9a + 9a + 4
Answer:
2.[tex]16a^2-4a+4a-1[/tex]
Step-by-step explanation:
We have to find the polynomial can be simplified to a difference of squares.
1.[tex]10a^2+3a-3a-16[/tex]
Combine like terms
[tex]10a^2-16[/tex]
10 in [tex]10a^2[/tex] is not a perfect square number because when a number end with one zero then the number is not perfect square number.
Therefore, it can not be simplified to a difference of squares.
2.[tex]16a^2-4a+4a-1[/tex]
[tex]16a^2-1[/tex]
Combine like terms
[tex](4a)^2-(1)^2[/tex]
Hence, the polynomial can be simplified as difference of squares.
3.[tex]25a^2+6a-6a+36[/tex]
Combine like terms
[tex]25a^2+36[/tex]
[tex](5a)^2+(6)^2[/tex]
Hence, the polynomial can not be simplified as difference of squares because the polynomial can be simplified as sum of squares.
4.[tex]24a^2-9a+9a+4[/tex]
Combine like terms
[tex]24a^2+4[/tex]
[tex]24a^2+(2)^2[/tex]
[tex]24=2\times 2\times 3\times 2[/tex]
24 is not a perfect square number because when factorize 24 then 2 and 3 are not paired.
Hence, the polynomial can not be simplified as difference of squares.
what is 0.004% of 6800 round to the nearest hundredth
Which of the following is a like radical to
Find the slope and the y- intercept then rewrite the equation in slope intercept form 2x+3y=6
The perimeter of a square is 56 cm what is the approximate length of its diagonal
perimeter = 4s
56=4s
s=56/4 = 14
diagonal = sqrt (s^2 x 2)= sqrt(14^2 x 2) = sqrt(392) = 19.7989 cm
round answer as needed
Answer:
The approximate length of diagonal is:
19.796 cm.
Step-by-step explanation:
We are given the perimeter of a square as 56 cm.
Let 's' be the side of the square.
We know that the perimeter of square is given as:
[tex]Perimeter=4\times s\\\\56=4s\\\\s=\dfrac{56}{4}\\\\s=14[/tex]
Hence, the side of square is 14 cm.
Now, the length of a diagonal(D) is given as:[tex]D=\sqrt{2}s[/tex]
( Since it could be proved with the help of Pythagorean Theorem )
Hence, as s=14 cm
Hence, the length of diagonal is:
[tex]D=\sqrt{2}\times 12\\\\D=1.414\times 14\\\\D=19.796\ cm[/tex]
Hence, the approximate length of diagonal is:
19.796 cm.
What is the slope of the line shown below?