f−1(x)=x−32
Explanation:Follow the steps:
f(x)=2x+3
1- replace f(x) with y →y=2x+3
2- simply switch x and so the equation looks like x=2y+3
3- use algebra to solve for y. (isolate y)
x=2y+3
x−3=2y
x−32=y
This is the inverse function and is written as
f−1(x)=x−32
For the compound inequality x + 2 ≥ a AND x - 7 ≤ b, find values of a and b for which the only solution is x = 1.
Mr. Brown needs 2 1/2 meters of materials to make a dress. How many similar dresses can be made from 35 meters of material?
cory earns 52.50 in 7 hours. find the unit rate
divide 52.5o by 7
52.50 / 7 = 7.50 per hour
In monopoly one rolls a pair of dice. Find the probability of getting a sum of 12.
Final answer:
The probability of rolling a 12 with two six-sided dice is 1/36, since there is only one combination (6+6) that yields a sum of 12 out of 36 possible outcomes.
Explanation:
The question requires calculating the probability of getting a specific sum when rolling a pair of six-sided dice, which is a common problem in probability theory. To find the probability of getting a sum of 12, we first need to understand that each die has 6 faces, and therefore, there are a total of 6 x 6 = 36 possible outcomes when rolling two dice.
Now, only one combination yields a sum of 12: when both dice show a six (6 + 6). Therefore, there is only one favorable outcome that gives the sum of 12. The probability of this outcome is then 1 (favorable outcome) divided by 36 (total possible outcomes), which gives us a probability of 1/36.
To put it mathematically, we apply the fundamental principle of probability which states that the probability of an event is equal to the number of ways the event can happen divided by the total number of possible outcomes. Hence:
Probability of rolling a sum of 12 = Number of ways to get a sum of 12 / Total number of possible outcomes = 1/36.
Julio works at an electronics store where he earns $11 an hour. Last week, he received a $120 bonus. How many hours did he work if he earned $505 total last week?
If 1/64=4^2s-1 times 16^2s+2 what is the value of s?
Answer: s=-1
Explanation:
We can re-write the equation as follows:
[tex]\frac{1}{64}=(4^{2s-1})(16^{2s+2})[/tex]
Let's rewrite the terms on the left and on the right as follows:
[tex]2^{-6} = ((2^2)^{2s-1})((2^4)^{2s+2})[/tex]
So we have
[tex]2^{-6} = (2^{2(2s-1)})(2^{4(2s+2)})[/tex]
Now we can use the following rule:
[tex]x^{a+b}=x^a x^b[/tex]
to rewrite the term on the right:
[tex](2^{2(2s-1)})(2^{4(2s+2)})=2^{2(2s-1)+4(2s+2)}[/tex]
So now we have
[tex]2^{-6}=2^{2(2s-1)+4(2s+2)}[/tex]
and since the bases are the same, we can just equalize the exponents:
[tex]-6=2(2s-1)+4(2s+2)[/tex]
[tex]-6=4s-2+8s+8\\-12 = 12 s\\s=-1[/tex]
Which is more valuable $20000 received now or $5000 per year for 4 years?
Please me
Estimate 127+290
A car starts from rest and accelerates uniformly at 3.0 m/s2 toward the north. a second car starts from rest 6.0 s later at the same point and accelerates uniformly at 5.0 m/s2 toward the north. how long after the second car starts does it overtake the first car?
Answer:
the answer is t = 20.625
Step-by-step explanation:
To begin, you would need to find the displacement of the first car and the equation to find that is d = 1/2at^2. So you would plug in what you have from the problem into the equation: d = (1/2)3(6)^2 and d is equal to 54 m. THIS IS YOUR DISPLACEMENT FOR THE FIRST CAR.
Next, you need to find the velocity of the car and the equation would be v = at. Plug in what you know from the problem: v = 3(6) which is 18. THIS IS YOUR INITIAL VELOCITY.
Next, we need to find out the distance of the 2nd car and we would use d = 1/2at^2. Plug in what you now from the problem: d = (1/2)5t^2 which would be d = 2.5t^2.
Next, you would equal these two equations together: 2.5t^2 = 1.5t^2 + 18t +54. All these values are from when we solved them from above, and once you solve it you will get 20.625. (SOLVE FOR T)
A doctors office schedules 15-minute appointments and half hour appointments for week days. The doctor limits these appointments to, at most, 30 hours per week. Write an inequality to represent the number of 15-minute appointments x and the number of half-hour appointments y the doctor may have in a week
Radio listeners were asked to call in and pick their two favorite rodents the listeners had 4 choices woodchuck prairie dog beaver and chipmunk what is the complete list of the possible pair of rodents
The complete list of possible pairs of rodents from the choices woodchuck, prairie dog, beaver, and chipmunk includes six combinations, showcasing an application of combinatorics in mathematics to determine all possible selections.
Explanation:The question involves determining the complete list of possible pairs of rodents that radio listeners could choose from four options: woodchuck, prairie dog, beaver, and chipmunk. This is a matter of combinatorics, a branch of mathematics focused on counting, arrangement, and combination of sets of elements. Since each listener picks two favorites and the order in which they pick them does not matter (choosing a beaver and a woodchuck is the same as choosing a woodchuck and a beaver), we use combinations to find the total number of possible pairs.
Woodchuck and Prairie DogWoodchuck and BeaverWoodchuck and ChipmunkPrairie Dog and BeaverPrairie Dog and ChipmunkBeaver and ChipmunkMathematically, the number of ways to choose 2 favorites out of 4 is given by the combination formula C(n, r) = n! / r!(n-r)!, where n is the total number of options and r is the number being chosen. Here, n=4 and r=2, resulting in C(4, 2) = 4! / 2!(4-2)! = 6, which matches our list of 6 possible pairs.
What's the answer to this question please help me it's hard for me
A wooden board is 1.848 meters long. What is the value of the 4 in the number? Write your answer as a decimal and as a fraction.
An overdraft balance occurs when the available balance in a bank account is below zero. Yvonne has an overdraft balance at the beginning of the year. The function graphed models Yvonne's account balance, y, in dollars, x weeks after the beginning of the year.
Select True or False to describe each statement.
True False
The x-intercept represents Yvonne's account balance at the beginning of the year.
The slope represents the amount Yvonne deposits to her account each week.
Yvonne no longer has an overdraft balance 4 weeks after the beginning of the year.
Graph of a line on a coordinate plane. The horizontal x axis ranges from 0 to 9 in increments of 1. The vertical y axis ranges from negative 100 to 100 in increments of twenty five. A line passes through the points begin ordered pair 0 comma negative 1 hundred end ordered pair and begin ordered pair 4 comma 0 end ordered pair and begin ordered pair 8 comma 1 hundred end ordered pair.
Answer:
False; True; True.
Step-by-step explanation:
In this situation, the y-intercept would represent the amount of money in her account at x=0 weeks, or the beginning of the year. This is not the x-intercept, so the first statement is false.
The slope is the rate of change. This would describe how her account changes every week, so this represents the amount of money she deposits into her account each week. This means the second statement is true.
The line goes through the point (4, 0). Since x is the number of weeks, this would represent the amount in her account after 4 weeks. Since the y-value is 0, this means she no longer has an overdraft balance after 4 weeks. This means the second statement is true.
Following are the response to the given points:
The y-intercept, it would represent the number of funds in her account at x=0 weeks, or the start of the year. As this is not the x-intercept, the first assertion is untrue.The rate of increase is represented by the slope. This would illustrate how her account varies, That's the sum of money she puts into her account each week. This point is crossed by the line (4, 0), since x is indeed a couple of weeks, this is the amount in the account following 4 weeks. Since y-value=0, she no longer has an overflow balance after 4 weeks.Therefore, the final answer is "false, true, and true".
Learn more:
Help I need to turn these into two equations???
John can travel 368 miles on one tank of gas. His gas tank holds 16 gallons. What is the unit rate for miles per gallon?
12 students share 3 pizzas equally what fraction of the pizza each student gets
Final answer:
Each student gets 1/4 of a pizza when 12 students share 3 pizzas equally. This is because 3 pizzas divided by 12 students results in each student receiving 1/4 of a pizza.
Explanation:
To determine the fraction of the pizza each student gets when 12 students share 3 pizzas equally, you'd divide the total number of pizzas by the number of students. Here's the step-by-step breakdown:
First, understand that each pizza can be considered as '1 whole' unit. So, 3 pizzas would be '3 whole' units.To share these '3 whole' units equally among 12 students, we need to divide 3 by 12.This calculation would look like this: 3 ÷ 12, which simplifies to 1 ÷ 4 when reduced to the lowest terms, as you are essentially dividing each pizza into four equal parts for every group of three students.Therefore, each student gets 1/4 of a pizza.Understanding fractions can be similar to figuring out slices of pie or the number of quarters in a dollar.
Given that X varies proportionally to Y and y=27 when x =3, find the constant of proportionality.
the store has 53 cases of apples and oranges in a storm if there are 28 cases of apples how many cases of oranges are there in the store room
Maria’s dog weighs six times as much as a rabbit. together the pets weight 56 pounds what does Maria’s dog weigh?
- 24 = 6a - 15 - 5a solve for the answer of the question
A cylinder has a volume of 360 in^3. If the height and radius are multiplied by 2.5, what will the resulting volume be?
A) 5525 in^3
B) 2880 in^3
C) 5400 in^3
D) 3600 in^3
A firm advertises for workers to address envelopes. Priscilla says she will work 100 hours. Herb will work for 80 hours. If each can address 10,000 envelopes in the time they work, how long would it take them to address 10,000 envelopes if they work together?
Priscilla and Herb can address 10,000 envelopes together in approximately 44.44 hours, when we combine their individual work rates of 100 and 125 envelopes per hour respectively.
Explanation:Priscilla and Herb are addressing envelopes for a firm, and we need to determine how long it would take them to address 10,000 envelopes if they work together. Priscilla can address 10,000 envelopes in 100 hours, and Herb can do the same in 80 hours.
To solve this, we can calculate each person's work rate and then combine these work rates to get the rate at which they complete the task together.
First, we calculate their work rates:
Priscilla's rate: 10,000 envelopes / 100 hours = 100 envelopes per hourHerb's rate: 10,000 envelopes / 80 hours = 125 envelopes per hourWorking together, their combined rate would be:
Combined rate = Priscilla's rate + Herb's rate
Combined rate = 100 envelopes/hour + 125 envelopes/hour
Combined rate = 225 envelopes per hour
To address 10,000 envelopes at this combined rate, we can divide the total number of envelopes by their combined rate:
Time to address 10,000 envelopes together = 10,000 envelopes / 225 envelopes/hour
Time to address 10,000 envelopes together = approximately 44.44 hours
This diagram of airport runway intersections shows two parallel runways. A taxiway crosses both runways. How are 6 and 2 related?
corresponding angles
alternate interior angles
same-side interior angles
none of these
There are 9 members on a board of directors. If they must select a chairperson, a secretary, and a treasure, how many different slates of candidates are possible?
Help me solve this equation please. y/9 + 5 = 0
y/9 +5 =0
subtract 5 from each side
y/9 = -5
multiply both sides by 9
y = -5 * 9
y = -45
#MathHelp HelpPlease
It's important to understand and apply various mathematical concepts taught in high school, including basic algebra, arithmetic, and vector representation. Success also often comes from group work and discussions, which can provide new perspectives.
Explanation:In mathematics, figuring for yourself and collaborative group activities are essential aspects of learning. When we talk about basic algebra and arithmetic, it means we are dealing with mathematical operations such as addition, subtraction, multiplication, division, and solving equations. The principles given in a chapter can be applied to various questions. For instance, if you understand the concept of 'solving for x', you can apply it in different scenarios and questions.
Similarly, when vectors are represented with an arrow above them, this is one of the common notations in mathematics, specifically in vector algebra. It is also important to note that working in groups and participating in discussions can bring another perspective and help understand the subject better.
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The function d(x) = 1375 − 110x represents the distance (in miles) a high-speed
train is from its destination after x hours. (Section 3.3)
a. How far is the train from its destination after 8 hours?
b. How long does the train travel before reaching its destination?
If the function d(x) = 1375 − 110x represents the distance (in miles) a high-speed train is from its destination after x hours:
a) The train is 495 miles from its destination after 8 hours
b) It will take the train 12.5 hours to travel before reaching its destination
The given function is:
d(x) = 1375 - 110x
Where d(x) is the distance (in miles) a high-speed train is from its destination after x hours.
a) How far is the train from its destination after 8 hours?
To find how far the train is from its destination after 8 hours, substitute x = 8 into d(x) = 1375 - 110x
d(8) = 1375 - 110(8)
d(8) = 1375 - 880
d(8) = 495
The train is 495 miles from its destination after 8 hours
b) How long does the train travel before reaching its destination?
Note that:
d(x) = 1375 - 110x
From the equation above, the speed at which the train is traveling is 110 miles/hr
The distance of the destination = 1375
The time it will take to reach the destination will be calculated as:
Time = Distance / speed
Time = 1375 / 110
Time = 12.5
It will take the train 12.5 hours to travel before reaching its destination
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What is the equation of the circle passing through the point (−5, −2) whose center is at (−2,3)?
The equation of the circle passing through the point (−5, −2) and center at (−2, 3) is [tex]\bold{( x +2 )^2 + ( y - 3 )^2 = 34}[/tex]
What is the general equation of the circle?The general equation of the circle whose center at (h, k) and radius r is,
[tex]( x - h )^2 + ( y - k )^2 = r^2[/tex]
For given example,
the circle passing through the point (−5, −2) whose center is at (−2, 3).
The radius of the circle is the distance between point (-5, -2) and the center (-2, 3).
Using distance formula the radius of a circle would be,
⇒ [tex]r=\sqrt{(-2-3)^2 + (-5-(-2))^2}[/tex]
⇒ [tex]r=\sqrt{(-5)^2+(-3)^2}[/tex]
⇒ [tex]r=\sqrt{25+9}[/tex]
⇒ [tex]r=\sqrt{34}[/tex] units
Let center (h, k) = (-2, 3)
Using the general form of the circle,
⇒ [tex]( x - h )^2 + ( y - k )^2 = r^2[/tex]
⇒ [tex]( x - (-2) )^2 + ( y - 3 )^2 = (\sqrt{34})^2[/tex]
⇒ [tex]( x +2 )^2 + ( y - 3 )^2 = 34[/tex]
Therefore, the equation of the circle passing through the point (−5, −2) whose center is at (−2,3) would be [tex]\bold{( x +2 )^2 + ( y - 3 )^2 = 34}[/tex]
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W4-21w2-100 how do you factor this