Answer:
Step-by-step explanation:
For this case we must determine the inverse of the following function:
[tex]f(x)=3x-2[/tex]
Step 1:
We would write
[tex]y=f(x)[/tex] or [tex]y=3x-2[/tex]
Step 2:
We clear x:
[tex]y+2=3x[/tex]
[tex]\frac{y+2}{3}=x[/tex]
Step 3:
"x" and "y" are exchanged:
[tex]y=\frac{x+2}{3}[/tex]
The inverse is:
[tex]f^{-1}(x)=\frac{x+2}{3}[/tex]
Enter the value for x that makes the equation √x-7=-4
Answer:
Your answer is 9
Step-by-step explanation:
√9=3
3-7=-4
The length of one rectangle in a quilt is 6 inches. Its width is 3 inches. About how many of these rectangles do you need to cover an area of 7,500 square inches?
Step-by-step explanation:
Area=2(L+W)
A=2(6+3)
A=2(9)
A=18in²
therefore, 7500/18
=416.66in²
find the area of sector AOB given that angle AOB is 60°and radius of the circle 7cm
Answer:
25.67cm²
Step-by-step explanation:
the area of sector= 60/360 × 22/7× 7²=
1/6 × 154 = 25.67 cm²
Answer:
25.67
Step-by-step explanation:
An account is compounded continuously at 4.5% interest. What was the initial amount deposited if after 8 years it is worth $1720?
9514 1404 393
Answer:
$1200.00
Step-by-step explanation:
The balance is given by the formula ...
A = Pe^(rt) . . . . . principal P invested at annual rate r for t years
Using your numbers, we can find P to be ...
P = Ae^(-rt) = $1720·e^(-0.045·8) = $1720·e^-0.36
P ≈ $1200.00
help please i cant do this LOL
Answer and Step-by-step explanation:
Answer is in picture.
First you need to translate (or move) to the right 1 unit, the translate (or move) downwards 5 units.
Then, reflect the points over the y-axis (reflecting is like when you see your reflection in a mirror, how your hand lines up with the hand in the mirror)
#teamtrees #PAW (Plant And Water)
Portia has purchased a new aquarium for her fish. It is in the shape of a hexagonal prism. 3a) How much water can Portia’s new aquarium hold? * 1 point a) 166.28 cubic inches b) 790.28 cubic inches c) 956.56 cubic inches d) 3120 cubic inches e) 6240 cubic inches
Answer:
D. 3120
Step-by-step explanation:
How many sides does a hexagon have? Six. Let's begin our equation with 6. The area of a triangle formula would be: 1/2 bh. And a hexagon is just six triangles put together. Now our equation is: 6 (1/2 bh) What's bh then? B (base)= 8in. The base is usually always at the bottom. Now we take 10 and add it into the equation. Next we would multiply this by 13. Our equation is now: 6(1/2*8*10)*13. What do you get then? 3120.
For Part B: Portia's new fish require complete darkness for 12 hours a day. Rather than buying a blackout curtain for her room, she decides to make an aquarium cover out of a tropical print, with a blackout liner. How much tropical print fabric will she need to purchase in order to cover the top and sides of the aquarium?
Now, we're dealing with surface area. What is surface area, anyway? Surface area is the sum of all faces. There are 2 hexagonal faces and 6 sides.
What is 6*1/2 *8? 24! Now what's 10*24? That's right, 240!
8*13=104
6(104)=624
624+240=864
find 11/25 of a liter
Answer:
0.44l
Step-by-step explanation:
a litre=1l
11/25 of it=11/25×1l
=0.44l
Answer:
A litre=1 l
Or, 1/25×1
=0.44.
In the number 3,941,608,572, which digit is in the hundred millions place?
Answer:
9
Step-by-step explanation:
A hundred millions is: 100,000,000
looking at the number the number in the place hundred millions place is 9, so the answer is 9.
Answer:900,000,000
The digit is 9
Step-by-step explanation:
In the following table y is proportional to x.
What is the constant of proportionality?
A. 5/14
B. 5/7
C. 7/5
D.20/7
When 12 radios were left, how many hours had gone by?
Hellpp
solve this: - 6 n = 30
Answer:
-6n=30
so find value of n
n=30÷(-6)
n=-5
so, value of n = -5
Answer:
-6 n = 30
or,n=30÷(-6)
or,n=-5
simplify 3a/a^2-9a+18-2/a-6
Answer:
A or C
Step-by-step explanation:
Rob can complete his bus route in 4 hours. Joan can complete her bus route in 3 hours. If they both left the terminal at 3:00 am and after each completed route returned to the terminal, determine the next time they would leave the terminal at the same time.
Answer:
3:00 pm
Step-by-step explanation:
Given
[tex]Rob = 4\ hrs[/tex]
[tex]Joan = 3\ hrs[/tex]
[tex]Start\ Time = 3:00\ am[/tex]
Required
The next time they leave at the same time
To do this, we first list out the multiples of 4 and 3 (i.e. their time of completing each route)
So, we have:
[tex]Rob: 4, 8, 12, 16, 20...[/tex]
[tex]Joan: 3,6,9,12,15,18....[/tex]
The least common multiple in the above is:
[tex]Least = 12hrs[/tex]
This means that they will meet at the terminal after 12 hours
So, their meeting time is:
[tex]Time = 3:00am + 12\ hrs[/tex]
[tex]Time = 3:00\ pm[/tex]
The graph above shows the cost, in dollars, of apples as
a function of the number of pounds of apples purchased
at a particular grocery store. The equation above defines
the cost C, in dollars, for p pounds of pears at the same
store. Which of the following statements accurately
compares the cost per pound of apples and the cost per
pound of pears at this store?
A. Apples cost approximately $0.07 less per pound
than pears do.
B. Apples cost approximately $0.04 less per pound
than pears do.
C. Apples cost approximately $0.73 less per pound
than pears do.
D. Apples cost approximately $0.62 more per pound
than pears do.
The accurate statement is A. Apples cost approximately $0.07 less per pound.
Cost of Apples per pound using the given graph:The constant of proportionality would give us the cost of per pound. From the graph, when number of pounds (p) = 3, cost in dollars (C) = 4.
Constant of proportionality = C/p = 4/3
Therefore, Cost of apples per pound = 4/3 = $1.33 (approximated)
Cost of Pears per pound using the given equation:[tex]C = \frac{7}{5} p[/tex]
The constant of proportionality of the equation function will give us the cost per pound for pears.
From the equation, the we can deduce that [tex]\frac{7}{5}[/tex] represents the cost of pears per pound (constant of proportionality).
Thus:
Cost of pears per pound = 7/5 = $1.40
The difference between the cost per pound of pears and the cost per pound of apples would be:
$1.40 - $1.33 = $0.07
Therefore, we can conclude that apples cost approximately $0.07 less per pound.
Learn more about constant of proportionality here:
https://brainly.com/question/11703625
5) Find the measure of the unknown
angle in the triangle
O 100°
O 105
106
0 112
PLEASE HELP
A bag contains 10 marbles: 2 are green, 2 are red, and 6 are blue. Yolanda chooses a marble at random, and without putting it back, choose another one at random. What is the probability that both marbles she chooses are green? Write your answer as fraction in simplest form.
Answer:
2/10 = 1/5
Step-by-step explanation:
Which Which value of x makes this equation true? -3x+10=5x-8
value of x makes this equation true? -3x+10=5x-8
Answer:
9/4
Step-by-step explanation:
-3x+10=5x-8
or, -3x-5x = -8-10
or, -8x=-18
or, 8x=18 (i.e. - is cancelled)
or, x=18/8
i.e. x=9/4
Hence, the value of x is 9/4
Answer:
The value of x is 9/4
Step-by-step explanation:
-3x+ 10 = 5x - 8
Add 3x both side
-3x + 3x + 10 = 5x + 3x - 8
10 = 8x - 8
Now, Add 8 both side
10 + 8 = 8x - 8 + 8
18 = 8x
8x = 18
Now, Divide by 8 from both side
8x/8 = 18/8
x = 9/4
Thus, The value of x is 9/4
FOR VERIFICATION ONLY:-3x + 10 = 5x - 8
-3(9/4) + 10 = 5(9/4) - 8
-27/4 + 10 = 45/4 - 8
-27 + 4 × 10/4 = 45 - 8 × 4/4
-27 + 40/4 = 45 - 32/4
13/4 = 13/4
Hence, L.HS = R.H.S
-TheUnknownScientist
What is the correct ratio?
D)32/40
Hope it helps you
Answer:
[tex]\frac{24}{40}[/tex]
Step-by-step explanation:
Sin = [tex]\frac{opposite}{hypotenuse}[/tex] (relative to the angle asked for)
The opposite of Angle Z is 24
The hypotenuse no matter what would always be 40; therefore,
Sin(Z) = [tex]\frac{24}{40}[/tex]
Hope this helps!
please help this is overdue and i get my grades tmr
Answer:
162 sq
Step-by-step explanation:
6 x 9 x 3 = 162
unless im wrong :/
Answer:
The surface area is 198 square centimeters.
Step-by-step explanation:
A = 2 · (wl + hl + hw)
2 · (6 · 9 + 3 · 9 + 3 · 6)
198
Find the radius of convergence and the interval of convergence.
[tex]\displaystyle \sum \limit_{n=1}^\infty \frac{x^\text{n}}{2^\text{n}(n+1)^2}[/tex]
Answer:
Radius of Convergence: 2
Interval of Convergence: [-2, 2]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Exponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex]Exponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Calculus
Series Convergence Tests
P-Series: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{1}{n^p}[/tex]Direct Comparison Test (DCT)Alternating Series Test (AST)Ratio Test: [tex]\displaystyle \lim_{n \to \infty} \bigg| \frac{a_{n + 1}}{a_n} \bigg|[/tex]Radius of Convergence (ROC)
Ratio TestInterval boundInterval of Convergence (IOC)
Testing endpointsStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{x^n}{2^n(n + 1)^2}[/tex]
Step 2: Find ROC
Apply Ratio Test
[Series] Set up [Ratio Test]: [tex]\displaystyle \lim_{n \to \infty} \bigg|\frac{x^{n + 1}}{2^{n + 1}(n + 2)^2} \cdot \frac{2^n(n + 1)^2}{x^n} \bigg|[/tex][Ratio Test] Rewrite exponentials [Exponential Rule - Multiplying]: [tex]\displaystyle \lim_{n \to \infty} \bigg|\frac{x^n \cdot x}{2^n \cdot 2(n + 2)^2} \cdot \frac{2^n(n + 1)^2}{x^n} \bigg|[/tex][Ratio Test] Simplify: [tex]\displaystyle \lim_{n \to \infty} \bigg| \frac{x}{2(n + 2)^2} \cdot (n + 1)^2 \bigg|[/tex][Ratio Test] Multiply: [tex]\displaystyle \lim_{n \to \infty} \bigg| \frac{x(n + 1)^2}{2(n + 2)^2} \bigg|[/tex][Ratio Test] Evaluate limit: [tex]\displaystyle \bigg| \frac{x}{2} \bigg| < 1[/tex][Ratio Test] Isolate x: [tex]\displaystyle |x| < 2[/tex]Our ROC is 2.
Step 3: Find IOC
Test endpoints
[ROC] Find interval bound: [tex]\displaystyle -2 < x < 2[/tex]x = -2
Substitute in x [Series]: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{(-2)^n}{2^n(n + 1)^2}[/tex][Series] Rewrite [Exponential Rules - Multiplying]: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{(-1)^n2^n}{2^n(n + 1)^2}[/tex][Series] Simplify: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{(-1)^n}{(n + 1)^2}[/tex]Test convergence of modified series: Alternating Series Test
[AST] Condition 1 [Limit Test]: [tex]\displaystyle \lim_{n \to \infty} \frac{1}{(n + 1)^2} = 0 \ \checkmark[/tex][AST] Condition 2 [aₙ vs bₙ comparison]: [tex]\displaystyle \frac{1}{(n + 2)^2} \le \frac{1}{(n + 1)^2} \ \checkmark[/tex]At x = -2, the series is convergent.
∴ Current IOC is -2 ≤ x < 2 or [-2, 2); 2 undetermined
x = 2
Substitute in x [Series]: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{2^n}{2^n(n + 1)^2}[/tex][Series] Simplify: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{1}{(n + 1)^2}[/tex]Test convergence of modified series: Direct Comparison Test
[DCT] Condition 1 [Define comparing series]: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{1}{n^2}[/tex][DCT] Condition 1 [Test convergence of comparing series]: [tex]\displaystyle p = 2 > 1, \ \sum \limit_{n = 1}^\infty \frac{1}{n^2} \ \text{convergent by p-series}[/tex][DCT] Condition 2 [aₙ vs bₙ comparison]: [tex]\displaystyle \frac{1}{(n + 1)^2} \le \frac{1}{n^2} \ \checkmark[/tex]At x = 2, the series is convergent.
∴ IOC for [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{x^n}{2^n(n + 1)^2}[/tex] is -2 ≤ x ≤ 2 or [-2, 2]
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Taylor Polynomials and Approximations - Power Series (BC Only)
Book: College Calculus 10e
Michelle and Pierre both want to buy guitars, Michelle has already saved $60, and
plans to save $5 per week until she can buy the guitar, Pierre has $25, and plans to save
$12 per week. How many weeks will pass before Michelle and Pierre have the same
amount of money?
Answer:
on the 5th week they would both have the same amount of money they would both have a total of 85$
Step-by-step explanation:
The number of weeks will pass before Michelle and Pierre have the same amount of money will be 5.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
Let x be the number of the weeks and y be the total amount.
Michelle and Pierre both want to buy guitars, Michelle has already saved $60, and plans to save $5 per week until she can buy the guitar, Pierre has $25, and plans to save $12 per week.
Then the equations will be
y = 5x + 60 ....1
y = 12x + 25 ....2
Subtract equation 1 from equation 2. Then we have
7x – 35 = 0
7x = 35
x = 5 weeks
Then the number of weeks will pass before Michelle and Pierre have the same amount of money will be 5.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
Suppose that a regression line for some data transformed with logarithms predicts that when x equals 7. logi) will equal 1.755. What does the regression line predict y will equal when xequals 7? Round your answer to the nearest whole number A. 57 O OB. 12 Oc. 2 O D. 30
Answer:
A: 57
Step-by-step explanation:
We are told that;
When x = 7, log y = 1.755
Since we want to find the value of y when x = 7, and the log function is in base 10, we will just use anti log to solve for y in the equation.
Thus;
Log₁₀y = 1.755
y = 10^(1.755)
y = 56.89
Approximating to a whole number gives;
y = 57
Determine the rate of change of the function given by the table.
A) 2
B) 1
C) -1
D) -2
Pls anyone I need answer of this urgent PLEASE
Answer:
Q.#1 is a
Q.#2 is d
Step-by-step explanation:
hope this helps:)
I need the answer fast pls
Answer:
B
Step-by-step explanation:
It's B because that's the only answer that talks about the highest temperature, which is mentioned in the question
What linear equation is represented by the table?
Please hurry!
Best answer gets Brainliest!!!!
A) Y= 2x
B) y= 4x
C) y= 4x -2
D) y= 2x - 2
Answer:
y = 4x - 2
Step-by-step explanation:
linear equation - y = mx + b
where m = slope and b = y intercept
The y intercept is the y value of the coordinate where x = 0
Looking at the table, we notice that when x = 0, y = -2
Which means that the y intercept ( b ) = -2
Slope = change in y over change in x
As y goes up 4 x goes up 1
Thus, slope ( m ) = 4
Now we plug in the identified slope and y intercept into " y = mx + b "
we get that the equation is y = 4x - 2
Solve for x.
4x - 14
x + 85
x = [?]
Answer:
x = 33
Step-by-step explanation:
4x - 14 = x + 85
3x = 99
x = 99/3
x = 33
Complete the function table
Answer:
8, 6, 3, 2, 1
Step-by-step explanation:
g(x) = -x + 3
using g(x),
g(-5) = (-1 x -5) + 3
= 5 + 3
= 8
g(-3) = (-1 x -3) + 3
= 3 + 3
= 6
g(0) = 0 + 3
= 3
g(1) = -1 + 3
= 2
g(2) = -2 + 3
= 1
Please solve!
l = 48.1 m, w = 51.62 m, h = 3.42 m
Answer:
Volume? Surface area?
Step-by-step explanation:
Volume=8491.59
Surface area=5647.93
Paula needs to replace the floor in her family room since her cat peed in several places. She wants to put down both vinyl flooring and carpet in the room. The carpet she selected costs $2 per sq. foot. The vinyl floor covering costs $1 per sq. foot. She has $500 to spend on materials and must cover an area of 300 sq. feet. How much carpet and vinyl flooring will she buy to meet her requirements?
Answer:
c = amount of carpet flooring; v = amount of vinyl flooring2c + 1v = $500v = 100 sq. ft.c + v = 300c = 200 sq. ft.
Step-by-step explanation:
the anwser