Let [tex]f^{-1}(x)[/tex] be the inverse of
[tex]f(x) = 3 \log_3 (x + 3) + 1[/tex]
Then by definition of inverse function,
[tex]f\left( f^{-1}(x) \right) = 3 \log_3 \left(f^{-1}(x) + 3\right) + 1 = x[/tex]
Solve for the inverse :
[tex]3 \log_3 \left(f^{-1}(x) + 3\right) + 1 = x[/tex]
[tex]3 \log_3 \left(f^{-1}(x) + 3\right) = x - 1[/tex]
[tex]\log_3 \left(f^{-1}(x) + 3\right) = \dfrac{x - 1}3[/tex]
[tex]3^{\log_3 \left(f^{-1}(x) + 3\right)} = 3^{\frac{x-1}3}[/tex]
[tex]f^{-1}(x) + 3 = 3^{\frac{x-1}3}[/tex]
[tex]f^{-1}(x) = 3^{\frac{x-1}3} - 3[/tex]
What is the answer to the following question?
Answer:
SAS similarity
Step-by-step explanation:
You have two side ratios and the angle between the sides with those ratios. The appropriate similarity theorem is SAS.
The length of a rectangular garden is 3 feet more than 2 times the width. The perimeter of the garden is 48 feet. Find the length and width of the garden .
Answer:
length 17 feet
width 7 feet
Step-by-step explanation:
Let w represent the width. Then the length is 2w+3, and the perimeter is ...
P = 2(L +W)
48 = 2((2w+3) +w) = 6w +6
42 = 6w
7 = w . . . . . . . . width
(2w+3) = 17 . . . length
The length of the garden is 17 feet; its width is 7 feet.
A pair of dice is rolled. Determine the probability of a result with: i. one die showing a 4 and the other a 5?
Answer:
2/11
Reasoning, there are 36 possible (and equally likely) combinations that we can obtain from two dice. Of these 11 (1,5 2,5 3,5 4,5 5,5 6,5 5,6 5,4 5,3 5,2 5,1) would allow us to ‘know’ that “one dice (not necessarily the first) has shown a 5”. Of these 11 possibilities only two also contain a 4. So the probability is 2/11
Step-by-step explanation: have a good day
A woman walks x km north, then (x+7) km east. She is now 13km from her starting point. Find x.
Alan has $400 in his checking account. He withdraws $50 each week. The amount remaining in his account, f(x), after x weeks is
represented by a function. What is the range of the function?
Answer:
{0, 50, 100, 150, ..., 350, 400}
Step-by-step explanation:
The range of Alan's balance will be multiples of 50 that are between (and including) 0 and 400.
{0, 50, 100, 150, ..., 350, 400}
_____
The expression for f(x) is ...
f(x) = initial balance - (rate of withdrawal) × (time period)
f(x) = 400 -50x
This is a continuous linear function defined for all x, and capable of producing f(x) values between -∞ and +∞. The range of this function is "all real numbers."
However, as applied to this problem, the domain of x is the set of integers from 0 to 8. The corresponding range is multiples of 50 from 0 to 8, that is, values 0, 50, ..., 350, 400.
a storage tank is 60% filled with chemical solution. The storage tank holds 1,280 liters of chemical solution. How many liters of chemical solution are needed to fill the storage tank to the top?
Answer:
Step-by-step explanation:
write a proportion and cross multiply to solve for x
[tex]\frac{60}{100} = \frac{x}{1280}[/tex]
100x=76,800
x=768
60% full is 768 L. If the tank can hold 1,280 Liters, you need 512 more to fill it.
Alternatively...if the tank is 60% full, we need 40% more to fill it
[tex]\frac{40}{100} =\frac{x}{1280}[/tex]
100x=51,200
x=512 L
Mrs. Heath baked 56 cookies. She put an equal number of cookies into 7 bags. How many cookies did she put in each bag?
Answer:
8
Step-by-step explanation:
you have to divide 56 by 7 and you will get 8.
Answer:
8
Step-by-step explanation:
You're dividing the 56 cookies into 7 bags, so you write 56 ÷ 7 = 8
Karma took a 50 question math test, but only 40 questions were correct. What was the percentage of correct answers?
Answer:
85 percent
Step-by-step explanation:
I need help on my homework.
Answer:
[tex] \frac{3}{4} > \frac{ - 2 + 2x}{4} \\ \\ (4 \times) \frac{3}{4} > \frac{ - 2 + 2x}{4} ( \times 4) \\ \\ 3 > - 2 + 2x \\ \\ 3 + 2 > - 2 + 2 + 2x \\ \\ 5 > 2x \\ \\ 5 \div 2 > 2x \div 2 \\ \\ \frac{5}{2} > x \\ \\ x < \frac{5}{2} [/tex]
I hope I helped you^_^
What is ten times as great as 450?
Answer: The answer is 4,500.
Explanation: 450 x 10 = 4,500.
Ten times as great as 450 is 4500.
We need to find what is ten times as great as 450.
What is multiplication?When we multiply two numbers, the answer is called product. The number of objects in each group is called multiplicand, and the number of such equal groups is called the multiplier.
Multiplication step:
Multiply the multiplicand by each of the numbers of the multiplier, moving from right to left. The units of the product are written below the line.The tens place of each product is added to the next product.Now, ten times as great as 450=10×450=4500
Therefore, ten times as great as 450 is 4500.
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Mrs. Montgomery earns a 6.5% commission on her total sales. Last month, she had sales of $55,780. How much commission did Mrs. Montgomery earn last month?
Answer:
3625.7
Step-by-step explanation:
hope that will help goodbye
Solve for B.
15B +9C =6
Answer:b=5
Step-by-step explanation:
The value of B for the given expression is B = (2 - 3C) / 5.
What is an expression?An expression in mathematics is a grouping of one or more numbers, variables, and arithmetic operations (such as addition, subtraction, multiplication, division, and exponentiation) that illustrates a relationship or calculation.
Parentheses, braces, and other grouping symbols that specify the sequence in which operations should be carried out are also permitted in expressions.
To solve for B, we need to isolate B on one side of the equation.
15B + 9C = 6
Subtract 9C from both sides:
15B = 6 - 9C
Divide both sides by 15:
B = (6 - 9C) / 15
Simplifying the right side gives:
B = (2 - 3C) / 5
Therefore, B = (2 - 3C) / 5.
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Write as the opposite of a square root. -3√5
Answer:
3x5² is the opposite of ur uestion
The value of -3√5 as the opposite of the square root is -75.
What is square root?The factor of a number that, when multiplied by itself, yields the original number is known as the square root of the number. Special exponents include squares and square roots. Think about the number 9. When the number 3 is multiplied by itself, the result is 9.
Given:
-3√5
The opposite of the square root is the square, so,
-3√5 = -3 × 5²
-3√5 = - 3 × 25
-3√5 = - 75
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Two tanks hold a total of 61 gallons of a toxic solvent. One tank holds 4 gallons more than twice the amount in the other. How many gallons does each tank hold?
Answer:
tank 1 : 19 gallons
tank 2 : 42 gallons
Step-by-step explanation:
tank 1 : x
tank 2 : 2x+4 ( 4 more than twice the other )
x + ( 2x + 4 ) = 61
3x + 4 = 61 [ add x + 2x = 3x ]
3x = 57 [ subtract 4 on both sides ]
x = 19 [divide 3 on both sides ]
tank 1 : 19 gallons
tank 2 : 42 gallons
The width of a rectangle is 7ft less than the length. The area of the rectangle is 228 square feet. Find the length and width
Set up figure, side length x, and width x-7. Set equation up
[tex]228 = (x)(x - 7) \\ 228 = {x}^{2} - 7x \\ {x}^{2} - 7x - 228 = 0 \\ (x - 19)(x + 12) = 0 \\ x = - 12 \\ x = 19[/tex]
Since the value x, cannot be negative, x is equal to 19. Therefore the length is 19, width 12 (19-7)
Find the circumference of a circle with a radius of 8 mm.
Answer:
C=50.27mm
Step-by-step explanation:
C=2πr=2·π·8≈50.26548mm
Bidmass
Working out equations
Answer:
16
Step-by-step explanation:
5+15-8/4=
5+15-4=
16
Answer:
10/2+15-8/4= 18
Step-by-step explanation:
glad to help
3 more day till christmas
find the rate of change
input 1 2 3 4 5
output 11 13 15 17 19
Answer:
2
Step-by-step explanation:
x-values in the table increase by 1, while y-values increase by 2. The rate of change is ...
m = slope = rate of change = (change in y)/(change in x) = 2/1 = 2
The rate of change is 2.
Answer:2
Step-by-step explanation:
2. Mark works as a consultant for a computer firm. His weekly income is $425. His
monthly expenses are $1,266. How much does he have left for variable expenses?
(Hint: There are four pay periods in one month.)
Hi there, I hope you understand my answer and that it is correct :)
So, First we multiply $425 by 4 because there are approximately 4 weeks in every month, so as shown [tex]425*4=1,700[/tex]
____________________________________________________________
Next We subtract the answer, which we got to be 1,700 from 1266.
[tex]1700 - 1266=434[/tex]
____________________________________________________________
Answer : $434 left to spend :)
According to the telegram which of the following description of the data are true
Answer:ITS THE SECOND ONE
Step-by-step
Subtract:
(3x^3– 10x^2+ 13x) – (5x^3+ 4x² – 9x)
A. 8x^3 + 14x^2 - 22x
B. 8x^3 - 6x^2 + 4x
C. 2x^3 - 6x^2 - 4x
D. -2x^3 - 14x^2 + 22x
Answer:
D
Step-by-step explanation:
(3x³ - 10x² + 13x) - (5x³ + 4x² - 9x)
3x³ - 10x² + 13x - 5x³ - 4x² + 9x Change all terms after the subtraction sign to
the opposite sign (definition of Subtraction)
(3x³ - 5x³) + (-10x² - 4x²) + (13x + 9x) Group like terms together
-2x³ - 14x² + 22x
Schedule of Cash Payments
Shakti Power Inc. was organized on February 28. Projected selling and administrative expenses for each of the first three months of operations are as follows:
March
$68,000
April
77,000
May
88,000
Depreciation, insurance, and property taxes represent $5,000 of the estimated monthly expenses. The annual insurance premium was paid on February 28, and property taxes for the year will be paid in Online file. Open the spreadsheet, perform the required analysis, and input your answers in the question below.m
dAnswer:
fffff
Step-by-step explanation:ff m
One month Chris rented 7 movies and 9 video games for a total of $71. The next month he rented 5 movies and 3 video games for a total of $31. Find the rental cost for each movie and each video game.
candy is 5 years older than one-third Liam's age .if candy is 16,how old is Liam
Answer:
33
Step-by-step explanation:
16-5=11
11×3=33
so yeah
Answer:
18
Step-by-step explanation:
is (33,10), (35,8), and (36,10) a function
Answer: yes it’s a function because the x values aren’t repeating
What is the third number in this sequence?
Step-by-step explanation:
x = the first number of the sequence
x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) = 519
6x + 1 + 2 + 3 + 4 + 5 = 519
6x = 504
x = 84
so, the third number is x+2 = 84 + 2 = 86
0.1/0.5=X/10 what is x
0.1/0.5 is the same as 1/5
1/5 = X/10
we times both sides by 10 to get x on its own
1/5 x 10 = 10/5 = 2 ( which equals X/10 x 10)
X/10 x 10 = X
2 = X
Someone help please
It is 4pi/7, or b. Just want to help ;)
please help! will mark brainliest.
Answer:
16
Step-by-step explanation:
The two triangles are similar. Find the values of the unknown variables
Answer:
x = 84 y = 59°
Step-by-step explanation:
x = (40/30)×63
x = 84
∆ABC = ∆PQR
so y = 59°
Answer:
1.) 47
2.) 28
Step-by-step explanation:
you just had to use the sin equation for both