Answer:
[tex] \frac{x - 2}{7} [/tex]
Step-by-step explanation:
[tex]f(x) = 7x + 2[/tex]
[tex]let \: \: f(x) = y[/tex]
[tex]7x + 2 = y[/tex]
[tex]7x = y - 2[/tex]
[tex]x = \frac{y - 2}{7} [/tex]
[tex] {f}^{ - 1} (x) = \frac{x - 2}{7} [/tex]
[tex]\large\text{view\:explanation\:for\:more\:details}[/tex]
Calculations ↓Remember , inverse functions do the opposite things in the opposite order.
Here's what happened to x here :
First , it's been multiplied by 7 .Then , 2 has been added to it .We can easily find the inverse of any function by following these steps :
Set the function equal to y as follows :f(x)=7x+2
y=7x+2
2. Now , switch y and x places :
x=7y+2
3. Solve for y .
First , subtract 2 on both sides :
x-2=7y
Divide by 7 on both sides :
[tex]\text{y=$\displaystyle\frac{x-2}{7}$}}[/tex]
We've found the inverse function of f(x)=7x+2.[tex]\tiny\text{hope\:helpful}[/tex]
After being involved in a car accident last month, Thomas' insurance company has increased his annual premium by
$398.37. Approximately what change will Thomas see on his future monthly statements as a result of the change?
Show work.
The approximate change that Thomas will see on his future monthly statements as a result of the change is; $33.1975
How to Calculate Monthly Insurance?We are told that Thomas' insurance company has increased his annual premium by $398.37.
Now, the premium above is the change in his annual premium. Thus, to find the change in his monthly premium, we just divide by 12 months to get;
Change in Monthly statements = $398.37/12
Change in Monthly statements = $33.1975
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Please help with work shown will give accommodations!!!
Answer:
(E) < BDE = 2x + y.
Step-by-step explanation:
As triangle ABC is isosceles the 2 base angles are equal.
Therefore m < BAC = x.
Consider triangle ABD:
m < BDE = m < BAC + m < ABD ( external angle of a triangle theorem)
So < BDE = x + x + y = 2x + y.
NO LINKS!!!! Exponential Growth and Decay Part 2
Problem 4
a = 10800 = initial populationb = 1 + r = 1 + (-0.025) = 0.975 is the decay factorThe template of [tex]y = a*b^x[/tex] becomes [tex]y = 10800*0.975^x[/tex] to represent the exponential function.
x = number of years since 2002y = populationWe want to know when the population reaches half of 10800, so we want to know when the population is 10800/2 = 5400
Plug in y = 5400 and solve for x.
[tex]y = 10800*0.975^x\\\\5400 = 10800*0.975^x\\\\0.975^x = 5400/10800\\\\0.975^x = 0.5\\\\\log(0.975^x) = \log(0.5)\\\\x\log(0.975) = \log(0.5)\\\\x = \log(0.5)/\log(0.975)\\\\x \approx 27.377851\\\\x \approx 28\\\\[/tex]
I rounded up to the nearest whole number because x = 27 leads to y = 5452, which is not 5400 or smaller.
Luckily, x = 28 leads to y = 5315 which gets over the hurdle of being 5400 or smaller.
Add 28 years onto the starting year 2002 and we get to 2002+28 = 2030
The population reaches half of its original amount in the year 2030.
Answers:The exponential function is [tex]y = 10800*0.975^x[/tex]It takes 28 years to get to half the population. This occurs in the year 2030============================================================
Problem 5
a = 28750 = starting value for the carb = 1 + r = 1 + (-0.12) = 0.88 = decay factorIf the car loses 12% of its value each year, then it keeps the remaining 88%
Plug those values into [tex]y = a*b^x[/tex].
We find the equation is [tex]y = 28750*0.88^x[/tex] where,
x = number of years since 2012y = car's valueReplace y with 10,000 and solve for x.
[tex]y = 28750*0.88^x\\\\10000 = 28750*0.88^x\\\\0.88^x = 10000/28750\\\\0.88^x \approx 0.347826\\\\\log(0.88^x) \approx \log(0.347826)\\\\x\log(0.88) \approx \log(0.347826)\\\\x \approx \log(0.347826)/\log(0.88)\\\\x \approx 8.261168\\\\x \approx 9\\\\[/tex]
Like in the previous problem, we round up so we clear the hurdle.
Adding 9 years onto 2012 gets us to 2012+9 = 2021
Answers: The function is [tex]y = 28750*0.88^x[/tex]It takes about 9 years, and it occurs in the year 2021Answer:
Exponential Function
General form of an exponential function: [tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept)b is the base (growth/decay factor) in decimal formx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
Question 4Given:
a = 10,800b = decrease of 2.5% = 0.975x = time (in years)y = populationAs the population is decreasing by 2.5% each year, the population will be 100% - 2.5% = 97.5% of the previous year. Therefore, the base is 0.975.
Final equation: [tex]\large \text{$ y=10800(0.975)^x $}[/tex]
Half of population: 10800 ÷ 2 = 5400
[tex]\large \begin{aligned}y & =5400\\\implies 10800(0.975)^x & =5400\\(0.975)^x & = \dfrac{5400}{10800}\\(0.975)^x & = 0.5\\\ln (0.975)^x & = \ln 0.5\\x \ln 0.975 & = \ln 0.5\\x & = \dfrac{\ln 0.5}{\ln 0.975}\\x & = 27.377785123\end{aligned}[/tex]
2002 + 27.37785... = 2029.37785...
Therefore, the population will reach half during 2029 (by 2030).
Question 5Given:
a = 28,750b = decrease of 12% = 0.88x = time (in years)y = value (in dollars)As the value is decreasing by 12% each year, the value will be 100% - 12% = 88% of the previous year. Therefore, the base is 0.88.
Final equation: [tex]\large \text {$ y=28750(0.88)^x $}[/tex]
Find when the car is worth $10,000:
[tex]\large \begin{aligned}y & = 10000\\\implies 28750(0.88)^x & = 10000\\(0.88)^x & = \frac{10000}{28750}\\(0.88)^x & = \frac{8}{23}\\\ln (0.88)^x & =\ln \left(\frac{8}{23}\right)\\x \ln (0.88) & =\ln \left(\frac{8}{23}\right)\\x & =\dfrac{\ln \left(\frac{8}{23}\right)}{\ln (0.88)}\\x & = 8.26116578\end{aligned}[/tex]
2012 + 8.26116578.. = 2020.26116578..
Therefore, the value of the car will reach $10,000 during 2020 (by 2021).
A total of 750 tickets were sold for the school play. They were either adult tickets or student tickets. There were 50 more student tickets sold than adult tickets.
How many adult tickets were sold?
1 adult tickets
х
5
?
Answer:
350 adult tickets were sold.
Step-by-step explanation:
Let's set up some values:
x = adult tickets
x + 50 = student tickets, since there were 50 more student tickets than adult tickets.
Now, let's set up our equation. If these two values add up to 750 tickets, then we can conclude the following:
(x) + (x + 50) = 750
2x + 50 = 750
2x = 700
x = 350 adult tickets. This means there were 400 student tickets sold.
A circular swimming pool has a radius of 8
feet. Which measurement is closest to the area
of the swimming pool in square feet?
Answer: 706.5
Step-by-step explanation:
no promisees that its right
Please help with this! I have to reflect over the x axis by the way
Answer:
T' = (-8, 8)
U' = (2, 8)
V' = (-8, 7)
Step-by-step explanation:
reflection over x axis means we change the sign of the y coordinate and nothing else
T = (-8, -8)
y coordinate = -8, change the sign to get 8
T' is thus (-8, 8)
U = (2, -8)
y coordinate = -8, y' = 8
U' = (2, 8)
V = (-8, -7)
y' = 7
V' = (-8, 7)
Find the 60th term of the following sequence.
8, 16, 24. ...
Answer:
Step-by-step explanation:
Remark
You want the 60th term of the arithmetic (?) sequence given.
Formula
L = a + (n - 1)*d
Givens
L = ?
a = 8
d = 8
n = 60
Solution
L = 8 + (60 - 1)*8
L = 8 + 60*8 - 8
L = 480
Answer
The 60th term is 480
Answer:
Step by step explanation :
As we know
[tex]\:\bf\boxed{an\:=\:a\:+\:(n\:-\:1)\:d}[/tex]
where,
an = the nth term in the sequence
n = the term
d = common difference
a = first term of the AP.
Here,
an = a60
n = 60
d = 16 - 8 = 8
a = 8
Now,
[tex]\:\mathsf{a60\:=\:8\:+\:(60\:-\:1)(8)}[/tex]
=> [tex]\:\mathsf{a60\:=\:8\:+\:(59)(8)}[/tex]
=> [tex]\:\mathsf{a60\:=\:8\:+\:472}[/tex]
=> [tex]\:\bf{a60\:=\:480}[/tex]
Therefore the 60th term of the AP is 480.
A salesman earns $4 commission on all the merchandise that he sells. Last month he sold $9000
worth of merchandise. How much commission (in dollars) did he earn last month?
Answer:
2250
Step-by-step explanation:
In this problem, you do 9000/4 because he earns $4 commissions, and that will give you 2250.
Laurie says that 2+3 x 2+3= 13. Ray says that 2+3 x 2+3= 11. Who is correct
Answer:
Ray
Step-by-step explanation:
Ray is correct . Have a nice day :)
The number of months a group of middle-aged men have been on a certain heart medication is normal
distributed with a mean of 8 months and a standard deviation of 2 months. Approximately what percentage
of the men have been taking the medication for between 6 to 8 months?
50%
16%
34%
68%
Answer:
34 %
Step-by-step explanation:
One standard deviation below ( 2 months) to the mean
covers approx 34.1 %
In this equation f(x) = 3x -15, what is y if x is 9?
*
Answer:
y = 12
Step-by-step explanation:
To solve this equation... The function is basically:
y = 3x - 15
So by substituting in x=9:
y = 27 - 15 = 12.
y = 12
Hope this helps.
Answer:
y = 12
Step-by-step explanation:
f(x) = y, so to find y, we jut need to substitute 9 for all the x-values in the equation:
f(9) = 3(9) - 15
Simplify:
f(9) = 27 - 15
f(9) = 12
Since f(x) = y
y = 12 when x is 9
Hope this helped!
Juanita must buy 50 plastic ducks for a game at the carnival. The ducks are sold in packages of 6. What is the LEAST number of packages Juanita should buy?
Answer:
9
Step-by-step explanation:
The least number of packages she should buy is 9 because 9 x 6 is 54 so she would have 4 extra ducks but she would still have enough for the carnival game
Can some one help me???
The unknown sides of the right angle triangle using trigonometric ratios are as follows;
PR = 13.2 units
RQ = 17.6 units
What is a right angle triangle?
A right angle triangle is a triangle that has one of its angles as 90 degrees.
The sides of the triangle can be found using trigonometric ratios.
Therefore,
sin 37° = opposite / hypotenuse
sin 37° = PR / 22
cross multiply
PR = 22 sin 37
PR = 22 × 0.60181502315
PR = 13.2399305093
PR = 13.2 units
cos 37 = adjacent / hypotenuse
cos 37 = RQ / 22
RQ = 22 cos 37
RQ = 17.569981221
RQ = 17.6 units
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What is the solution to the given inequality? 1/2-1/4x>-1/4
Answer:
x ≤ 3
Step-by-step explanation:
[tex]\dfrac{1}{2}-\dfrac{1}{4}x \geq -\dfrac{1}{4}[/tex]
Subtract 1/2 from both sides:
[tex]\implies \dfrac{1}{2}-\dfrac{1}{4}x-\dfrac{1}{2} \geq -\dfrac{1}{4}-\dfrac{1}{2}[/tex]
[tex]\implies -\dfrac{1}{4}x \geq -\dfrac{3}{4}[/tex]
Multiply both sides by 4:
[tex]\implies -\dfrac{1}{4}x \cdot 4 \geq -\dfrac{3}{4} \cdot 4[/tex]
[tex]\implies -x \geq -3[/tex]
Divide both sides by -1 (remembering to flip the sign):
[tex]\implies \dfrac{-x}{-1} \geq \dfrac{-3}{-1}[/tex]
[tex]\implies x \leq 3[/tex]
find x. not sure what it is
Answer:
x=29°
Step-by-step explanation:
angle measure of circular arc=180-122=58°
x=1/2×58=29°
What is the value of x in the equation 5x+ 3 = 4x?
A.-3
B.- 1/3
C.1/3
D.3
Answer:
-3
Step-by-step explanation:
5•-3=-15
4•-3=-12
-15+3=-12
9 boxes of cookies cost $38.07. How many boxes did Gina buy if she spent $16.927
please help me asap
Paul has a standard deck of cards. What is the probability that he will choose a 2?
Answer:
Step-by-step explanation:
The deck is divided into 4 different kinds of cards
clubsdiamondsHeartsSpadesEach kind of card has a 2
So there are 4 twos in a standard deck of cards.
Answer:
P(2) = 4/52P(2) = 1/13P(2) = 0.07692ctions: Write your answer in the box. Do not use spaces
What is the value of the following expression if x 22: "five times a number
decreased by 2"?
Answer:
5x - 2
Step-by-step explanation:
if x is your number its 5 lots of your number - 2
Decide if each data set might produce one or more gaps when represented by a histogram. For each data set that you think might produce gaps, briefly describe or give an example of how the values in the data set might do so.
a. The ages of students in a sixth-grade class.
b. The ages of people in an elementary school.
c. The ages of people eating in a family restaurant.
d. The ages of people who watch football.
e. The ages of runners in a marathon.
There would be a gap in the age of people in an elementary school.
Which option would produce one or more gaps ?
There is a gap in a histogram when there is no data point represented in the data point.
There would be no gap in the ages of students in the sixth grade because their ages would have a range. There would be a gap in the age of people in an elementary school because there would be the ages of the students then the ages of teachers.
The ages of people eating in a family restaurant would have no gap because all ages would be represented. There is no age limit on those that can run a marathon, thus, the age of runners would have no gap.
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Consider that x = 1.5 and y = 3. Which statement is true about x + y?
Answer:
x + y = 4.5
Step-by-step explanation:
x + y = 1.5 + 3 = 4.5
HELPPPPPPPPPPPPPPPPP
7) What is the area of the figure below?
12 cm
13 cm
20 cm
21 cm
Answer:
65,520
Step-by-step explanation:
12x13x20x21=64,520
The average cost of 2 storybooks was 2.45. One of the books cost 2.80. Find the cost of the other book
Answer:
The answer is simply 26,25/3 which gives that each book costed 8,75 dollars assuming of course that all books have the same price.
How would you solve this without a calculator?
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Exact Form:
[tex]1351+780\sqrt{3}[/tex]
Decimal Form:
2701.99962990
Thus, 2,701 is your answer
Y=4x+1 function rule table
Answer:
the table of the function is below
Step-by-step explanation:
The ratio of the surface areas of two spheres is 1:9.
a) What is the ratio of the lengths of their radil? What is the ratio of their volumes?
b) If the volume of the smaller sphere is 64 cubic inches, what is the volume of the larger sphere?
in3
Answer:
b
Step-by-step explanation:
Which statement about the graph of the quadratic function is NOT true?
Answer:
2nd option
Step-by-step explanation:
the graph has a minimum value of - 6 ( U ) not a maximum
Answer:
2nd option
Step-by-step explanation:
The graph has a minimum of -6, hence the 2nd option, which states the maximum is 3 is incorrectA rectangular prism and its net are shown below.
(All lengths are in feet.)
The volume of the rectangular prism is 180 ft³, From the net of the prism, A = 10 feet, B = 4 feet, C = 6 feet and D = 3 feet.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The volume of the rectangular prism = length * width * height = 10 * 6 * 3 = 180 ft³
From the net of the prism, A = 10 feet, B = 4 feet, C = 6 feet and D = 3 feet.
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Question 2 of 10
Which of the following geometric objects occupy one dimension?
Check all that apply.
A. Line
B. Triangle
C. Plane
D. Segment
E. Ray
F. Point
A. Line
D. Segment
E. Ray
Step-by-step explanation:Math dimensions include length, width, and height (in that order). The dimension that an object occupies is dependent on how many different measurements, aka dimensions, an object has.
0th Dimension
The first dimension is actually the zeroth dimension. This dimension includes objects that do not have any measurements. A point does not have a length because it only occupies one spot on a plane.
The 0th dimension includes:
Point1st Dimension
The next dimension, the 1st dimension, has only length. This means the object can travel across the x-axis, but it can only go in one direction.
The 1st dimension includes:
LineSegementRay2nd Dimension
For this question, the last dimension is the 2nd dimension. The 2nd dimension has both length and width. This means that the object occupies both the x and y-axis.
The 2nd dimension includes:
TrianglePlane3rd Dimension
The 3rd dimension is not included in the question or the answer choices but is still important. The 3rd dimension has length, width, and height. This occupies the x, y, and z-axis and cannot be graphed on a regular geometric plane. The 3rd dimension is graphed in a geometric space.
The 3rd dimension includes:
CubePrism