Use the distributive property to express 30 + 42
Answers
Answer:
it would be 6 (5 + 7) = 30 + 42 = 72
Step-by-step explanation:
hope this helps if not please let me know
Related Questions
Consider this function.
f(x) = |x – 4| + 6
If the domain is restricted to the portion of the graph with a positive slope, how are the domain and range of the function and its inverse related?
Answers
If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.
The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.
If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.
The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).
The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.
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Davis is trying to decide between two part time jobs on Saturdays. He could make $16.25 per hour working
at the city's ice arena, but getting to work and back would cost him $7.50 round trip for travel. His other
option is to work as a dog walker in his neighborhood for $12.50 per hour but he can ride his bike or walk
there for free. He estimates he could work up to 7 hours at the arena but up to 10 hours walking dogs. He
always works at least 1 hour if he goes to the arena.
1. Write two different functions that represent Davis's gross wages, where h is the number of
hours Davis works per week, a(h) is his gross wages at the ice arena minus travel expenses, and
d(h) is his gross wages from walking dogs.
1. State the domain and range for each function.
2. If Davis works 1 hour, what would be his gross pay at each job? What if he worked 6 hours?
3. Davis wants to know what his net pay, also called take-home pay, is going to be. Assume that
10.5% of just his paycheck, not his travel expenses, is withheld for taxes at the arena. Because
dog walking is a self-employed activity, Davis estimates he needs to set aside 18% of his income
for taxes. Modify your functions from question 1 to model net pay including these tax
withholdings.
4. State the domain and range for each of these new functions.
Answers
1) Two different functions that could represent Davis' gross wages, where h is the number of hours Davis works per week, a(h) is his gross wages at the ice arena minus travel expenses, and d(h) is his gross wages from walking dogs are:
Function A: a(h) = 16.25h - 7.50
Function B: d(h) = 12.50h
2) If Davis works 1 hour, his gross pay at each job is:
1 Hour 6 Hours
a) $16.25 $97.50
b) $12.50 $75
3) To find Davis' net pay after tax, the modified functions in question 1 are as follows:
Function A: a(h) = (16.25h - 7.50)(1 - 0.105)
Function B: d(h) = 12.50h(1 - 0.18)
4) The domain and range for each of these new functions are:
Domain Range
a) Function A [1, 2, ... 7] [7.83, 15.66, ... 54.81]
b) Function B [1, 2, ... 12] [10.25, 20.5, ... 123]
What are the domain and range of a function?The domain refers to all the possible values of the independent (input) variables.
The range refers to the possible values of the dependent (output) values.
Data and Calculations:Arena Dog Walking
Pay rate per hour $16.25 $12.50
Travel expense $7.50 $0
Maximum hours worked 7 hours 10 hours
Gross pay for one hour $16.25 $12.50
Gross pay for 6 hours $97.50 $75
After
Tax 10.5% 18%
After-tax factor (1 - 0.105) (1 - 0.18)
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i still dont get rounding multiplication
Answers
Which ordered pairs are solutions to the equation 6x + 7y = 6?
Answers
Answer:
(2,−6/7), (3,−12/7), and (6,−30/7)
Step-by-step explanation:
Here s a patter made from sticks
Answers
Answer:
Recursive formula of an arithmetic sequence is given by the expression,
Tn=a+(n−1)d
Where, Tn= nth term
a= First term of the sequence
n= Number of term
d= Common difference
Therefore, number of sticks in the 6th pattern are 32.
And number of sticks in the nth pattern are Tn=5n+2
From the picture attached,
Number of sticks in 1st pattern = 7
Number of sticks in 2nd pattern = 12
Number of sticks in 3rd pattern = 17
Sequence formed is 7, 12, 17..... nth term
This sequence has a common difference of 5 in each successive term so it will be an arithmetic sequence.
Therefore, nth term of the sequence will be,
Tn=a+(n−1)d
Tn=7+(n−1)5
Tn=5n+2
If n=6,
Tn=7+(6−1)5
Tn=7+25
Tn=32
Hope it helps !
Have a great day!
The equation y = 10x shows how the
cost relates to the number of hours.
How much does it cost to rent a canoe
for 8 hours?
Answers
which expression correctly sets up the quadratic formula to solve the equation
Answers
Answer:
Answer A
Step-by-step explanation:
x² + 3 = 4x
x² - 4x + 3 = 0
a = 1
b = -4
c = 3
URGENT *EASY 10 POINTS* : Show steps to get the expression ln(sqrt(2) +1) - ln(1/sqrt(2)) equal to -ln(1-(1/sqrt2))
Answers
Answer:
Step-by-step explanation:
To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:
Step 1: Simplify the expression on the left side:
\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)
Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:
\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)
Step 3: Simplify the expression within the logarithm:
\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)
Step 4: Simplify the denominator by multiplying by the reciprocal:
\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)
\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)
\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)
Step 5: Simplify the numerator:
\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)
\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)
\(\ln\left(2 + \sqrt{2}\right)\)
Now, let's simplify the right side of the equation:
Step 1: Simplify the expression on the right side:
\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)
Step 2: Simplify the expression within the logarithm:
\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)
Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:
\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)
Step 4: Simplify the expression:
\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)
\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)
\(-\ln\left(2 + \sqrt{2}\right)\)
As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).
A camera cost 115 Canadian dollars if each Canadian dollar is worth 0.950 to US dollars how much will the camera cost in the US dollars
Answers
Answer:
109.25 US dollars
Step-by-step explanation:
115 * 0950
Explanation:
Just multiply 115 and .950 together! :)
Mitchell reads only mysteries and sports books. Last year, he read 5 mysteries for every 2 sports books.
If Mitchell read 12 more mysteries than sports books, how many mysteries did he read?
Answers
Answer:
the answer is 20
Step-by-step explanation:
Write the equation of the line that passes through the points (-1, 10) and (5, 2)
Answers
Answer:
\(y=-\frac{4}{3}x +\frac{26}{3}\)
Step-by-step explanation:
1) if the point A has coordinates (-1;10) and the point B - (5;2), then it is possible to write common view of the required equation of the line:
\(\frac{x-X_A}{X_B-X_A} =\frac{y-Y_A}{Y_B-Y_A};\)
2) if to substitute the coordinates of A&B into the common equation, then:
\(\frac{x+1}{5+1} =\frac{y-10}{2-10}; \ => \frac{x+1}{6}=\frac{y-10}{-8};\)
3) finally, in slope-intersection form:
3y= -4x+26; ⇔ y= -4/3 x +26/3.
P.S. the suggested way of the solution is not the only one.
Please help! This is algebra work and it’s due tmr TT
(Please explain how you did the problem)
subject: solve the system of linear equations by graphing
x + y = 5
y - 2x = -4
Graph:
Answers
Answer:
The solution is (3,2).
Step-by-step explanation:
When you are solving simultaneous equation using graphs, you have to look at their intersection point.
In this graph, both equations intersect at (3,2) so the solution will be (3,2).
Test,
x + y = 5
3 + 2 = 5
y - 2x = -4
2 - 2(3) = 4
2 - 6 = 4
Mark has a batting average of 0.155. What is the probability that he has fewer than 3 hits in his next 6 at bats?
Answers
Since the probability that a player gets a hit on any given at bat is independent of the other at bats, we can find the probability that Mark has fewer than 3 hits in his next 6 at bats by simply multiplying the probability of getting a hit on each at bat. Since Mark has a probability of 0.155 of getting a hit on any given at bat, he has a probability of (0.155)^3 of getting exactly 3 hits in his next 6 at bats. Therefore, the probability that he has fewer than 3 hits in his next 6 at bats is 1 - (0.155)^3 approx 0.76
Answer:
The probability that Mark will have fewer than 3 hits in his next 6 at bats is approximately 0.204.
Step-by-step explanation:
A batting average is the number of hits a player has divided by the number of times they have been at bat. In this case, Mark has a batting average of 0.155, which means that he has hit 0.155 of the times he has been at bat.
To find the probability that Mark will have fewer than 3 hits in his next 6 at bats, we can use the binomial probability formula. The formula for binomial probability is:
P(x) = (n choose x) * p^x * (1-p)^(n-x)
Where "n" is the number of trials, "x" is the number of successes, "p" is the probability of success on a single trial, and "1-p" is the probability of failure on a single trial.
In this case, the number of trials is 6, the number of successes is 3, and the probability of success on a single trial is 0.155. Plugging these values into the formula, we get:
P(3) = (6 choose 3) * 0.155^3 * (1-0.155)^(6-3)
To calculate the probability that Mark will have fewer than 3 hits in his next 6 at bats, we need to sum the probabilities of 0, 1, and 2 hits. We can use the binomial probability formula to calculate the probability of each of these outcomes, and then add them together to find the total probability.
For 0 hits, the probability is:
P(0) = (6 choose 0) * 0.155^0 * (1-0.155)^(6-0) = 0.009
For 1 hit, the probability is:
P(1) = (6 choose 1) * 0.155^1 * (1-0.155)^(6-1) = 0.054
For 2 hits, the probability is:
P(2) = (6 choose 2) * 0.155^2 * (1-0.155)^(6-2) = 0.141
Adding these probabilities together, we get the total probability that Mark will have fewer than 3 hits in his next 6 at bats:
P(0 or 1 or 2) = 0.009 + 0.054 + 0.141 = 0.204
Therefore, the probability that Mark will have fewer than 3 hits in his next 6 at bats is approximately 0.204.
You are playing in the NBA Playoffs and attempt a 3-point shot as the buzzer sounds for the end of the
game, if you make the shot your team wins! Your basketball is is traveling on a path described by the
following function: b(x) = -x2 +1.36x + 2. The net is on a level described by the following function:
n(x) = 3 between (8 < x < 8.5). Will you make the shot and win the playoffs?
You may work alone or in a group of up to 3 students total.
BONUS: How high in the air will the basketball be at its highest point?
UNITS: x is in meters, y is in meters
Answers
Since we do not know the value of u, we cannot find the time taken by the basketball to travel a distance of 8.5 meters. We cannot find the height of the basketball at its highest point.
Given that n(x) = 3 for 8 < x < 8.5.It is impossible to determine whether the shot will be made or not based solely on this information. Winning the playoffs depends on various factors, such as the score, time remaining, and the overall performance of the team.
Therefore, additional information is required to determine the outcome of the playoffs.However, to find the height of the basketball at its highest point, we need to know the equation of the trajectory of the basketball.
Assuming that the basketball follows a parabolic path, we can use the formula:
y = ax² + bx + c,
where y is the height of the basketball, and x is the horizontal distance traveled by the basketball.
To find the values of a, b, and c, we need to know three points on the trajectory of the basketball. Let's assume that the basketball is thrown from a height of 1.5 meters and lands on the floor after traveling a horizontal distance of 8.5 meters.
Therefore, the points on the trajectory of the basketball are:
(0, 1.5), (8.5/2, h), and (8.5, 0),
where h is the height of the basketball at its highest point.Substituting these values in the equation of the trajectory,
we get:
1.5 = a(0)² + b(0) + c...(1)0 = a(8.5)² + b(8.5) + c...(2)h = a(8.5/2)² + b(8.5/2) + c...(3)
Simplifying equations (1) and (2),
we get:
c = 1.5...(4)b = -a(8.5)²/8.5...(5)
Substituting equation (4) in equation (3), we get:
h = a(8.5/2)² + b(8.5/2) + 1.5h = a(8.5/2)² - a(8.5)²/8.5 + 1.5h = -29.375a + 1.5
Substituting the value of a from equation (5) in the above equation,
we get:
h = -29.375(-a(8.5)²/8.5) + 1.5h = 0.5a(8.5)² + 1.5
Therefore, to find the height of the basketball at its highest point, we need to find the value of a. Since we know that the basketball lands on the floor after traveling a horizontal distance of 8.5 meters,
we can use the formula:
x = ut + 0.5at²,
where u is the initial horizontal velocity of the basketball, and t is the time taken by the basketball to travel a distance of 8.5 meters.
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Help me plsss I need help
Answers
x+1+7x-5=180.
8x -4=180
X=23
Find each value of the function f(x).
f(-20)
Answers
Answer:
33 is the answer for this ez math
Look for factors that will help you determine what type of economy exists in Country A.
Based on the clues in this passage, what type of economy does Country A have?
developed
developing
transitioning
command
Answers
developing:
a low GDP
an economy based on agriculture
Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.
Which inequality is represented by the graph?
A. y > -2/3x+1
B.y < -2/3x +1
C.y < -3/2x +1
D.y> -3/2x +1
Answers
Answer:C
Step-by-step explanation:
About 9% of the population has a particular genetic mutation. 400 people are randomly selected. Find the mean for the number of people with the genetic mutation in such groups of 400
Answers
Answer:
36 people
Step-by-step explanation:
The expected value E(X) = mean of sample = np
Where, p = population proportion, p = 9% = 0.09
n = sample size, = 400
The mean of the number of people with genetic mutation, E(X) = np = (400 * 0.09) = 36
36 people
Can someone please answer and provide an explanation for these problems?
Answers
The values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4
What are the segments tangent to the circleA theorem of tangents to a circle states that if from one exterior point, two tangents are drawn to a circle then they have equal tangent segments.
(25). 2x - 1 = x + 1 {equal tangent segments}
2x - x = 1 + 1 {collect like terms}
x = 2
(26). 2x - 4 = x {equal tangent segments}
2x - x = 4 {collect like terms}
x = 4
Therefore, the values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4
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After you place the order for 15 shirts, one of the members asks if he can order 2 more shirts, how much will it cost for the 2 extra shirts.
Answers
Answer:
???
Notes:
Hi, sorry, but I can't really do this if I don't know what 15 shirts cost, or if there isn't an equation of some sort. (Sorry again...)
Susie receives an employee discount of 8% on all items purchased in the retail store where she works. If she purchases two blouses at $24.99 each and three skirts for $48.00, how much was her bill, including a 7% tax?A. $190.95B. $189.96C. $190.96
Answers
First, let's calculate the total price without discount or taxes:
\(\begin{gathered} C=2\cdot24.99+3\cdot48\\ \\ C=193.98 \end{gathered}\)Now, to apply a discount of 8%, we can multiply the cost by 92%, that is, 0.92:
\(\begin{gathered} C^{\prime}=0.92C\\ \\ C^{\prime}=0.92\cdot193.98\\ \\ C^{\prime}=178.46 \end{gathered}\)And then, to apply a tax of 7%, we can multiply the cost by 107%, that is, 1.07:
\(\begin{gathered} C_{final}=1.07C^{\prime}\\ \\ C_{final}=1.07\cdot178.46\\ \\ C_{final}=190.95 \end{gathered}\)Therefore the correct option is A.
What is the value of f?
Please give explanation.
Answers
Answer:
96.4
Step-by-step explanation:
so you set it up like 56.2+27.4=83.6 so 180-83.6 is 96.4 that is the value of f. hope this helps have a good day
The angle of f is 96.4 degrees.
Angles on a straight lineThe sum of angles on a straight line is equals to 180 degrees. Therefore, angle f can be found as follows;
f + 56.2 + 27.4 = 180°Therefore,
f + 56.2 + 27.4 = 180°
f = 180 - 56.2 - 27.4
f = 96.4 degrees
The angle of f is 96.4 degrees.
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Please help do right don't do just for points please
Answers
Answer:
-100
75
Step-by-step explanation:
Find the measure of arc BC given m<1 = 70°. Type a numerical answer in the space provided. Do not include any symbols, labels or
spaces in your answer.
Answers
Answer:
70°
Step-by-step explanation:
Because line segment OB and OC are both straight lines, then the measure of angle fromed by this two segments is the same in different locations.
Write the equation for the horizontal line passing through (3, 4).
Answers
Answer:
equation for a straight horizontal line passing through the coordinates (3,4):
y=4
Step-by-step explanation:
Solve the following equation. for x
7x - 2 < 10
Answers
Step-by-step explanation:
7x < 10+2
7x<12
x < 12/7
Hope this helps!
Answer:
\(7x-2<10\)\(7x-2+2<10+2\)\(7x<12\)\(\frac{7x}{7}<\frac{12}{7}\)\(x<\frac{12}{7}\)OAmalOHopeO
Question 8(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
A new gaming chair costs $455.95. You have already saved $155.95 and earn $37.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
37.5 + 155.95w = 455.95; w = 8
37.5w + 155.95 = 455.95; w = 8
37.5w − 155.95 = 455.95; w = 16
37.5w − 455.95 = 155.95; w = 16
Answers
37.5w + 155.95 = 455.95; where w = 8; signifies the number of weeks required to babysit the business in order to purchase the gaming chair.
How do equations work?A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. For instance, in English, an equation is any properly stated formula that consists of two expressions linked by the equals sign, whereas in French, an equation is described as containing one or more variables. To solve a variable equation, identify the values of the variables that cause the equality to hold true. The answer is known as the values of the variables that must satisfy the equality.
Equations can be categorized as identities or conditional equations.
w = (455.95-155.95)/(37.50)
=300/37.50
=8
So, number of weeks = 8
As a result, w = 8 and 37.5w + 155.95 = 455.95 is the solution.
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Given: cos θ = -4/5 , sin x = -12/13, θ is in the third quadrant, and x is in the fourth quadrant; evaluate tan x.
-12/5
-13/5
-5/12
Answers
Answer:
Step-by-step explanation:
Given: cos θ = -4/5 , sin x = -12/13, θ is in the third quadrant, and x is in the fourth quadrant; evaluate tan x.
-12/5
-13/5
-5/12
The table shows the average number of pounds of trash generated per person per day in the United States from 1970 to 2010. Use the statistics calculator to calculate the mean and median. Round the answers to the nearest hundredth
Answers
Answer:
Table needed to help
Step-by-step explanation:
Mean vs Median
The mean (informally, the “average“) is found by adding all of the numbers together and dividing by the number of items in the set: 10 + 10 + 20 + 40 + 70 / 5 = 30.
The median is found by ordering the set from lowest to highest and finding the exact middle. The median is just the middle number: 20.