Answer:
f⁻¹(x) = (x + 10)/2
General Formulas and Concepts:
Algebra I
Equality PropertiesInverse FunctionsStep-by-step explanation:
Step 1: Define
f(x) = 2x - 10
Step 2: Rewrite
Redefine: y = 2x - 10Swap x/y: x = 2y - 10Step 3: Find Inverse
Solve for the new y.
Add 10 to both sides: x + 10 = 2yDivide 2 on both sides: (x + 10)/2 = yRewrite: y = (x + 10)/2Redefine: f⁻¹(x) = (x + 10)/2Answer:
[tex]let \: the \: {f}^{ - 1}(x) \: be \: m \\ m = \frac{1}{2x - 10} \\ m(2x - 10) = 1 \\ 2x - 10 = \frac{1}{m} \\ x = \frac{1}{2m} + 5 \\ therefore \\ {f}^{ - 1} (x) = \frac{1}{2x} + 5[/tex]
12 years ago, Catherine deposited $200 in a savings account that pays 7.25% simple
interest What is the balance in Catherinesco
Answer:
$374
Step-by-step explanation:
First you need to find how much money does the back pay per year
$200*7.25
=1450
1450/100
=14.5
Secondly you need to find how much does Catherine have in 12 years
14.5*12 years
=$174
Lastly add the money she already had 12 years ago to how much the bank payed in that 12 years
$200+$174
=$374
Write a Play
Write a short play about the
adventures of characters x, y, m, b,
as they travel around the coordinate
plane. Have your characters meet
many friends and relatives along the
way. The purpose of your play is
to educate the audience about the
mathematics in this topic through
action, dialogue, staging, and props.
Answer:
math is a difficult subject
Wendy drew a square. She then erased it and drew a second square whose sides were 3 times the sides of the first square. The area of the second square is k% greater than the area of the first square. What is k?
Answer:
x times x is x^2 for first area. second area is 3 times that so 3x times 3x you get 9x^2 for the second area. 9 - 1 times 100% would then be 800% larger.
y-x^2=5 written in function notation
Answer:
f(x) = x² + 5
General Formulas and Concepts:
Algebra I
Equality PropertiesFunction NotationStep-by-step explanation:
Step 1: Define
y - x² = 5
Step 2: Rewrite
Add x² to both sides: y = x² + 5Rewrite y: f(x) = x² + 5For each ångle pair, tell whether they are congruent or supplementary
Answer:
1&3 are supplementary
3&6 are congruent
4&5 are supplementary
2&3 are congruent
1&6 are supplementary (not sure about this one)
Step-by-step explanation:
Brianna has a container with a volume of 1.5 L she estimates the volume to be 2.1 m what is the percent error
===================================================
Work Shown:
Subtract the values to get 2.1-1.5 = 0.6
Brianna is off by 0.6 liters
Divide that error by the true value 1.5 to get 0.6/1.5 = 0.40
Then move the decimal point 2 spots to the right to arrive at 40%
Therefore, the percent error is 40%
------------------
The formula you can apply is:
[tex]P = \frac{|G-T|}{T}*100\%[/tex]
where
P = percent error
G = guess value (in this case it is 2.1)
T = true value (which is 1.5 in this case)
If we were to apply the formula, then we get:
[tex]P = \frac{|G-T|}{T}*100\%\\\\P = \frac{|2.1-1.5|}{1.5}*100\%\\\\P = \frac{|0.6|}{1.5}*100\%\\\\P = \frac{0.6}{1.5}*100\%\\\\P = 0.40*100\%\\\\P = 40\%\\\\[/tex]
A 1/2-mile long train enters a 2-mile long tunnel traveling at a speed of 10 mi/h. How many minutes pass from the time the front of the first train car enters the tunnel until the rear of the last train car exits the tunnel?
Answer:
15 minStep-by-step explanation:
The distance required is the length of the tunnel added to the length of the train
d = 1/2 + 2 = 5/2 miless = 10 mile/hour = 10/60 mile/min= 1/6 mile/minTime is:
t = d/st = 5/2 : 1/6 = 5/2*6= 15 min
1,Find the eighth term of the geometric sequence whose 1st term is 5 and whose 4th term is
1/25.
Answer:
Solution will be 1/15625
Step-by-step explanation:
Substitute the value of first term for ar^(4-1) for the third term with 1/25 on RHS, make r the subject (which is the common ratio)
you'll get r as 1/5
Now for the eighth term, replace the "4" in the formula with "8" and a with "5" and observe the magic.
When the area of a square is increasing four times as fast as the diagonals, what is the length of a side of the square
Answer:
Length of a side of a square = 2√2 units
Step-by-step explanation:
Let the length of a square is 'x' units.
Therefore, Area of the square A = (Side)²
= x² square units
And by Pythagoras theorem,
(Diagonal)²= (Side 1)² + (Side 2)²
= x² + x²
= 2x²
Diagonal 'p' = x√2 units
It is given in the question that area of the square is increasing four times as fast as the diagonals.
[tex]\frac{d(A)}{dt}=4(\frac{dp}{dt} )[/tex] -------(1)
[tex]\frac{d(A)}{dt}=\frac{d(x^2)}{dt}[/tex]
[tex]\frac{d(A)}{dt}=2x\frac{d(x)}{dt}[/tex]
Similarly, [tex]\frac{d(p)}{dt}=\frac{d(x\sqrt{2})}{dt}[/tex]
[tex]=\sqrt{2}\frac{dx}{dt}[/tex]
Now by placing the value of [tex]\frac{d(A)}{dt}[/tex] and [tex]\frac{d(p)}{dt}[/tex] in equation (1),
[tex]2x\frac{dx}{dt}=4\sqrt{2}\frac{dx}{dt}[/tex]
[tex](2x - 4\sqrt{2})\frac{dx}{dt}=0[/tex]
Since, [tex]\frac{dx}{dt}\neq 0[/tex]
[tex](2x - 4\sqrt{2})=0[/tex]
x = 2√2
Therefore, length of a side of the square is 2√2.
Find the value of x that makes mll n.
150°
(3x-15)
Answer:
[tex]3x - 15 = 150 \\ 3x = 165 \\ x = 55[/tex]
55° is the right answer.pls help me. I have to state whether each graph is a function?.
Answer:
Step-by-step explanation:
1 no.. not continuous
2no.. not continuous
3 yes , over a certain range it is
4no b/c it fails the vertical line test.. there is more than one point on the x axis
5no multiple point on the x axis and not continuous
6 yes, over a certain range
Someone please tell me the answer
Answer:
30 times three
Step-by-step explanation:
because all the bottom number are multiplying buy three.
Graph this function using intercepts: 27x–15y=1,350. Provide x and y intercepts
I really don't know how to do it myself and when I try to solve using a website they can't even do it
Answer:
graph attached
Step-by-step explanation:
27x - 15y = 1350
15y = 27x -1350
y = 27/15 x - 1350/15
y = 9/5 x - 90
y = mx + b y intercept (b) = -90
y=0 x = 90 * 5/9 = 50 x intercept
Step-by-step explanation:
Given function
27x – 15y = 1350Easy way to find x- and y-intercepts and graph the line:
x-intercept found when y = 0
27x - 15*0 = 135027x = 1350x = 1350/27x = 50y-intercept found when x = 0
27*0 - 15y = 1350-15y = 1350y = -1350/15y = - 90So the points are:
(0, -90) and (50, 0)Plot these two points on a coordinate plane and connect with a line
What is an equation of the line that passes through the point (-6, -3) and is
parallel to the line 5x – 3y = 9?
Answer:
Submit Answer
9514 1404 393
Answer:
5x -3y = -21
Step-by-step explanation:
The parallel line will have the same x- and y-coefficients, but a constant suitable for the given point.
5x -3y = constant
5(-6) -3(-3) = constant = -30 +9 = -21
The equation of the line is ...
5x -3y = -21
Maximus is playing a game. When he rolls the dice he wins if he gets an even number and loses if he gets an odd number. Which of the following statements is FALSE?
a. The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution
b. Rolling an even number is considered a success
c. The count of rolling an even number can be approximated with a normal distribution
d. The count of rolling an odd number can be approximated with a normal distribution
Answer:
a. The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution.
Step-by-step explanation:
Whenever we roll a fair dice, the possible outcomes are { 1, 2, 3, 4, 5, 6}. In this three numbers are even numbers, i.e. {2, 4, 6}.
The probability of getting an even number is [tex]$p (\text{even}) =\frac{3}{6} = \frac{1}{2}$[/tex]
Since each of the rolls is independent and each probability of getting even remains the same.
Using the central limit theorem, the sampling distribution of a large sample, usually more than 30 can be approximated by the normal distribution. A single roll of an even or odd number cannot be approximated by a normal distribution, it follows the Binomial distribution.
If number of rolls are large, then a normal approximation can be used.
Answer:
The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution.
Step-by-step explanation:
At 1:00 P.M., oil begins leaking from a tank at a rate of (6 0.77t) gallons per hour. (Round your answers to three decimal places.) (a) How much oil is lost from 1:00 P.M. to 4:00 P.M.
Answer:
[tex]Amount = 8.31[/tex]
Step-by-step explanation:
Given
[tex]Rate = 6 + 0.77t[/tex]
Required
Determine the gallons of oil lost between 1pm to 4pm
[tex]Rate = 6 + 0.77t[/tex]
Where t represents number of hours
First, we need to calculate the duration between 1pm and 4m.
[tex]t = 4pm - 1pm[/tex]
[tex]t = 3\ hours[/tex]
Substitute 3 for t in [tex]Rate = 6 + 0.77t[/tex]
[tex]Amount = 6 + 0.77 * 3[/tex]
[tex]Amount = 6 + 2.31[/tex]
[tex]Amount = 8.31[/tex]
Hence, 8.31 gallons of oil has been lost
The function F(x) varies inversely with x and f(x) = 25 when x = 6 what is f(x) when x= 18
Answer:
8.333
Step-by-step explanation:
F(x) α 1/ x
F(x) = k/x
F(x) = 25 ; x = 6
Lets use the information above to obtain the value of k
25 = k/6
k = 25 * 6 = 150
k = 150
Therefore, the value of f(x) when x = 18 will be :
Using the relation :
F(x) = k/x
k = 150, x = 18
F(x) = 150 / 18
F(x) = 8.333
Which list shows the numbers in order from least to greatest?
479, 4.79, 4.709
479, 4.709, 4,79
4.709, 479, 4.79
4.79, 479, 4.709
4.79, 4.709, 479
At the Italian deli, the sandwich maker cut 4 2/3 lb of turkey and 9 3/5 of roast beef. How many more pounds of roast beef were cut?
Answer:
4 14/15 more pounds of roast beef
Step-by-step explanation:
subtract 4 2/3 from 9 3/5
9 3/5 - 4 2/3= 4 14/15
So your answer is 4 14/15
Please help!!!!!!!!
Answer:
He rode 20 miles in 2 hours
I need help anyone can anyone help
Answer:
14
Step-by-step explanation:
The perimeter is the sum of the sides, so we have
2x+x+15+4x-7=57
= 7x+8
Subtracting 8 from both sides, we get
7x= 49
Dividing 7 from both sides, we get
x=7
Our sides are then 2x=14, x+15=22, and 4x-7=21. 14 is our answer
Answer:
The shortest length of the triangle is: 14
Hence, option B is correct.
Step-by-step explanation:
Given the triangle with the lengths
[tex]x+15[/tex][tex]4x-7[/tex][tex]2x[/tex]Given that the perimeter of triangle = P = 57
We know that the perimeter of a triangle is the sum of the lengths of the sides of a triangle.
so
[tex]P = (x+15)+(4x-7)+(2x)[/tex]
substitute P = 57
[tex]57 = (x+15)+(4x-7)+(2x)[/tex]
switch sides
[tex]\left(x+15\right)+\left(4x-7\right)+\left(2x\right)=57[/tex]
[tex]x+15+4x-7+2x=57[/tex]
Group like terms
[tex]x+4x+2x+15-7=57[/tex]
Add similar elements
[tex]7x+15-7=57[/tex]
[tex]7x=49[/tex]
divide both sides by 7
[tex]\frac{7x}{7}=\frac{49}{7}[/tex]
simplify
[tex]x=7[/tex]
Now, measuring the lengths by substituting x = 7
[tex]x+15 = 7+15 = 22[/tex][tex]4x-7 = 4(7)-7 = 28 - 7 = 21[/tex][tex]2x = 2(7) = 14[/tex]Therefore, the shortest length of the triangle is: 14
Hence, option B is correct.
A three digit number is selected at random from the set of all three digit numbers. The probability that the selected number has all the three digits the same is:__________.A.1/9B. 1/10C. 1/50D. 1/100
Answer:
1 /100
Step-by-step explanation:
Probability = (number of required outcomes / number of total possible outcomes)
Total possible outcomes = count of all 3 digit numbers ={100, 101,... 999} = 900
Required outcome = count of Three digit numbers with all 3 digits being the same = {111,222,333,444,555,666,777,888,999} = 9
Hence, probability that selected number has all 3 digits being the same :
9 / 900 = 1 /100
Evaluate 24 = (8-2).
Answer:
24 ÷ ( 8 - 2 )
= 24 ÷ 6
= 4
so, 4 is the answer
Answer:
on your question it says “=“ but on the picture it says “÷”
so for 24=(8-12) it would be 30
and for 24÷ (8-12) it would be -6
Step-by-step explanation:
Hope this helps, have a good day
Is 17/23 a irrational number
Answer:
NO.
Step-by-step explanation:
An irrational number cannot be written as a fraction.
Estimate the amount of the tip by rounding the bill to the nearest dollar before calculating.
20% tip on a bill of $36.04
The amount of the tip is approximately $
$7.00
O $7.20
0 $7.25
$7.50
Answer:
36.04
The amount of the tip is approximately $
$7.00
O $7.20
0 $7.25
$7.50
Step-by-step explanation:
What fraction more of the coupon books did Jabar sell than Guto?
Answer:
1/20
Step-by-step explanation:
Take 1/12 and 2/15 and find a common denomitator of 180 then multiply the tops to get 24/180 for 1/2 and 15/180 for 2/15 and then subtract to get 9/180
Finally simify to get 1/20
Beads are dropped to create a conical pile such that the ratio of its radius to the height of the pile is constant at 2:3 and the volume is increasing at a rate of 5 cm^3/s. Find the rate of change of height at h = 15cm.
Answer:
[tex]\displaystyle \frac{dh}{dt} = \frac{1}{20 \pi} \ cm/s[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Equality PropertiesGeometry
Volume of a Cone: [tex]\displaystyle V = \frac{1}{3} \pi r^2h[/tex]Calculus
Derivatives
Derivative Notation
Differentiating with respect to time
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{r}{h} = \frac{2}{3} \\\frac{dV}{dt} = 5 \ cm^3/s\\h = 15 \ cm[/tex]
Step 2: Rewrite Cone Volume Formula
Find the volume of the cone with respect to height.
Define ratio: [tex]\displaystyle \frac{r}{h} = \frac{2}{3}[/tex]Isolate r: [tex]\displaystyle r = \frac{2}{3} h[/tex]Substitute in r [VC]: [tex]\displaystyle V = \frac{1}{3} \pi (\frac{2}{3}h)^2h[/tex]Exponents: [tex]\displaystyle V = \frac{1}{3} \pi (\frac{4}{9}h^2)h[/tex]Multiply: [tex]\displaystyle V = \frac{4}{27} \pi h^3[/tex]Step 3: Differentiate
Basic Power Rule: [tex]\displaystyle \frac{dV}{dt} = \frac{4}{27} \pi \cdot 3 \cdot h^{3-1} \cdot \frac{dh}{dt}[/tex]Simplify: [tex]\displaystyle \frac{dV}{dt} = \frac{4}{9} \pi h^{2} \frac{dh}{dt}[/tex]Step 4: Find Height Rate
Find dh/dt.
Substitute in known variables: [tex]\displaystyle 5 \ cm^3/s = \frac{4}{9} \pi (15 \ cm)^{2} \frac{dh}{dt}[/tex]Isolate dh/dt: [tex]\displaystyle \frac{5 \ cm^3/s}{\frac{4}{9} \pi (15 \ cm)^{2} } = \frac{dh}{dt}[/tex]Rewrite: [tex]\displaystyle \frac{dh}{dt} = \frac{5 \ cm^3/s}{\frac{4}{9} \pi (15 \ cm)^{2} }[/tex]Evaluate Exponents: [tex]\displaystyle \frac{dh}{dt} = \frac{5 \ cm^3/s}{\frac{4}{9} \pi (225 \ cm^2) }[/tex]Evaluate Multiplication: [tex]\displaystyle \frac{dh}{dt} = \frac{5 \ cm^3/s}{100 \pi cm^2 }[/tex]Simplify: [tex]\displaystyle \frac{dh}{dt} = \frac{1}{20 \pi} \ cm/s[/tex]If Z is a standard normal variable find the probability. The probability that Z lies between -0.558 and 0.558
Answer:
0.4245
Step-by-step explanation:
The probability that Z lies between -0.558 and 0.558 can be written as;
P(-0.558 < z < 0.558) = P(z < 0.558) - P(z < -0.558)
Using z - distribution table, we have;
P(z < 0.558) = 0.7122
P(z < -0.558) = 0.2877
Thus;
P(z < 0.558) - P(z < -0.558) = 0.7122 - 0.2877 = 0.4245
What's 7.3 and 23 as a precent and what's 2/5 as a precent
Answer:
730% 23% and 40%
Step-by-step explanation:
.......
Ema’s family has completed 60% of a trip. They have traveled 45 miles. How far is the trip?
Answer:
72 miles
Step-by-step explanation:
60% times 45 = 27
27 + 45 = 72
Answer is 72 miles
Answer:
Ema's Family would drive 72 miles
Step-by-step explanation:
Hope this helps :)
And I hope this is correct