The inverse of the function f(x) = 1/5x is found by switching the roles of y and x, then solving for y. This results in the inverse function f^-1(x) = 5x, which undoes the effect of the original function.
Explanation:The inverse of a function, in this case f(x) = 1/5x, is the function that will reverse the effect of the original function. In this case, to find the inverse function of f(x), you swap the roles of y and x in the original function and solve for y.
So, f(x) = 1/5x becomes x = 1/5y. Multiply both sides by 5 to get rid of the denominator on the y-side, which results in 5x = y. Thus, the inverse function is f^-1(x) = 5x.
It's indeed an inverse function as it reverses the effect of the initial function f(x).
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Penelope invested $6650 into theee investment accounts, earning 8%, 12.5%, and 7.5% simple interest per year. If the annual interest earned totaled $671.25 and the amount invested at 12.5% was $300 more than twice the amount invested at 8%, find the amount invested into each account.
Answer: $1500 was invested in the account earning 8%.
$3300 was invested in the account earning 12.5%.
$1850 was was invested in the account earning 7.5%.
Step-by-step explanation:
Let x represent the amount invested in the account earning 8%.
Let y represent the amount invested in the account earning 12.5%.
Let z represent the amount invested in the account earning 7.5%.
Penelope invested $6650 into theee investment accounts, earning 8%, 12.5%, and 7.5% simple interest per year. It means that
x + y + z = 6650- - - - - - - - - - -1
Interest earned from the $x investment is
8/100 × x = 0.08x
Interest earned from the $y investment is
12.5/100 × x = 0.125y
Interest earned from the $z investment is
7.5/100 × x = 0.075z
If the annual interest earned totaled $671.25, it means that
0.08x + 0.125y + 0.075z = 671.25- - - - - - - 2
The amount invested at 12.5% was $300 more than twice the amount invested at 8%. It means that
y = 2x + 300
Substituting y = 2x + 300 into equation 1 and equation 2, it becomes
x + 2x + 300 + z = 6650
3x + z = 6650 - 300
3x + z = 6350- - - - - - - - - 4
0.08x + 0.125(2x + 300) + 0.075z = 671.25
0.08x + 0.25x + 37.5 + 0.075z = 671.25
0.33x + 0.075z = 671.25 - 37.5
0.33x + 0.075z = 633.75- - - - - - - 5
From equation 4, z = 6350 - 3x
Substituting z = 6350 - 3x into equation 5, it becomes
0.33x + 0.075(6350 - 3x) = 633.75
0.33x + 476.25 - 0.225x = 633.75
0.33x - 0.225x = 633.75 - 476.25
0.105x = 157.5
x = 157.5/0.105
x = 1500
y = 2x + 300
y = 2(1500) + 300
y = 3300
Substituting x = 1500 and y = 3300 into equation 1, it becomes
1500 + 3300 + z = 6650
z = 6650 - 4800
z = 1850
Brahm has $250 in his bank account. This is $75 more than his brother, basil has in his bank account. Find the amount of money in basil’s account with an addition problem.
Answer:175
Step-by-step explanation:
250-75 is 75 I believe this is correct
round 462 to the nearest 100.
Answer:
462 to the nearest hundred is 500
So your answer is 500
Step-by-step explanation:
Mark as brainliest please
Answer:
500
Step-by-step explanation:
In ΔRST, the measure of ∠T=90°, the measure of ∠R=64°, and RS = 5.8 feet. Find the length of ST to the nearest tenth of a foot.
Answer:
The length of ST to the nearest tenth of a foot is 5.2 ft
Step-by-step explanation:
Here we have
∡T = 90°
∡R = 64°
RS = 5.8 ft
To answer the question, we have apply sine rule as follows;
[tex]\frac{a}{Sin\alpha } = \frac{b}{sin\beta } = \frac{c}{sin\gamma}[/tex]
Therefore, for triangle RST, we will have;
[tex]\frac{RS}{SinT } = \frac{ST}{sinR } = \frac{RT}{sinS}[/tex]
Therefore;
[tex]\frac{5.8}{Sin90 } = \frac{ST}{sin64 }[/tex] from which
[tex]{ST}{ } = \frac{5.8 \times sin64}{Sin90 } = 5.213 \, ft[/tex]
Therefore, the length of ST to the nearest tenth of a foot = 5.2 ft.
Answer: 53 degrees
Step-by-step explanation:
Question 7
4 pts
Assuming that the Earth is a sphere of radius 4000 miles, find the
distance between the following two cities whose latitudes are given.
You may assume that these cities are on the same basic longitude.
Cincinnati, Ohio (39° 8' 46" N) and Huntsville, Alabama (34° 43'41"N)
Next >
Answer:
308.4miles
Step-by-step explanation:
Given that radius of earth= 4000miles
Change in latitude = 39° 8' 46" - 34° 43'41"
= 4° 25' 5"
= 4+25/60+5/3600
4+0.4166+0.00138
θ = 4.417°
Converting to radian = 4.417°×π÷180
= 4.417×0.0174
= 0.07710
Distance between the cities = rθ
S = 4000×0.07710
S= 308.4miles
Final answer:
The distance between Cincinnati, Ohio and Huntsville, Alabama is calculated by first converting their latitudes to radians, finding the difference, and then using the arc length formula on a sphere (assuming both cities are on the same longitude). The estimated distance is approximately 308 miles.
Explanation:
The question is asking to calculate the distance between Cincinnati, Ohio and Huntsville, Alabama, assuming the Earth is a sphere with a radius of 4000 miles and that both cities are on the same longitude. To calculate the distance, we first convert the latitudinal degrees to radians and then use the formula for arc length on a sphere, which is:
Arc Length = radius times (latitude1 - latitude2)
Firstly, convert the latitudes from degrees, minutes, and seconds to decimal degrees:
Cincinnati, Ohio: 39 degrees, 8 minutes, 46 seconds N = 39 + (8/60) + (46/3600) = 39.1461° NHuntsville, Alabama: 34 degrees, 43 minutes, 41 seconds N = 34 + (43/60) + (41/3600) = 34.7281° NThen, convert the decimal degrees to radians:
Cincinnati: 39.1461° times (π/180) = 0.6832 radHuntsville: 34.7281° times (π/180) = 0.6062 radCalculate the difference in latitude in radians:
Difference in latitude = 0.6832 rad - 0.6062 rad = 0.077 rad
Finally, use the arc length formula:
Arc length = 4000 miles times 0.077 rad = 308 miles
Therefore, the distance between Cincinnati, Ohio, and Huntsville, Alabama, is approximately 308 miles.
what 1256.64 rounded to the nearest tenth
Answer: The answer to this question is 1256.6
Answer:
1256.6
Step-by-step explanation:
Work out the area of a rectangle with base=32mm and perimeter=78mm
Answer:
224
Step-by-step explanation:
[tex]A = P[/tex] [tex]\frac{l}{2}[/tex]﹣[tex]l^{2}[/tex] = [tex]78[/tex] · [tex]\frac{32}{2}[/tex]﹣[tex]32^{2}[/tex] [tex]= 224[/tex]
if the points are connected what polygon is formed
PLEASE ANSWER ASAP!
Five tickets to a carnival cost $45. How much would seven tickets cost?
Answer: it will cost 63
Step-by-step explanation:
Since 5 times 9 is 45, I’ve assumed that the tickets cost 9 dollars, hence 7 times 9 equals 63
What does x equal ? Please help meeeeee
Answer:
19.66 or 19.7 units
Step-by-step explanation:
[tex]sin \: 24 \degree = \frac{8}{x} \\ \\ 0.4067366431 = \frac{8}{x} \\ \\ x = \frac{8}{0.4067366431} \\ x = 19.6687467 \\ x \approx 19.7 \: units \\ [/tex]
y=x^2-6x+7 from algebra nation
Answer:
Step-by-step explanation:
We
I had to give u a screenshot...here u go.
Which decimal is equivalent to 5/6 ?
A. 0.83
B. 0.83
C. 0.833
D. 0.56
One month Jane rented 5 movies and video games for a total of .$34 The next month she rented 2 movies and video games for a total of .$73 Find the rental cost for each movie and each video game.
Answer: each movie costs $6.80, each game costs $29.7
Step-by-step explanation:
First to find the movie cost i divided 34/5, and it gave me an answer of 6.80, then i multiplied 6.80 by 2 because it said you bought 2 movies along with 2 video games, 6.80 times 2 is 13.6. afterwards i subtracted, 73-13.6, my answer was 59.4, later i divided that by 2, and each game is $29.7, and each movie is $6.80
find the measure to the nearest degree
1. tan A= 1.6643
2. sin A= 0.8480
3. cos A= 0.3420
4. cos U= 0.4695
Answer:
1. tan A= 1.6643
A = tan^-1(1.6643)
A = 59° , 239°
2. sin A= 0.8480
A = sin^-1(0.8480)
A = 58°, 122°
3. cos A= 0.3420
A = cos^-1(0.342)
A = 1° , 359°
4. cos U= 0.4695
U = cos^-1(0.4695)
U = 62°, 298°
Answer:
Please see the attached pictures for the full solution.
Suppose triangle ABC is dilated with center (0,0) and scale factor 0.25, and the resulting image is then reflected in the x-axis to make triangle PQR. What are the coordinates of point P?
Coordinate of P, after the sequence of transformation is
(-1.25, -1)
How to find the coordinate of P
To find the coordinate of P we first establish that P is in corresponding position with A
Coordinate of A is (-5, 4)
Dilation by 0.25 will result to (-5 * 0.25, 4 * 0.25) → (-1.25, 1)
Reflection over the x-axis is done as follows
(-1.25, 1) → (-1.25, -1)
A laptop is in the shape of a rectangular prism. The laptop has a length of 14 inches, a width of 10 inches, and a height of 1 inch. What is the volume of the laptop?
Answer:
140 inches
Step-by-step explanation:
The formula for volume or a rectangular prism is v=lwh
Length = 14
Width= 10
Height= 1
Multiplying them together gives you the volume which is 140
What is the answer plz help
Answer:
y = 5x + 4
Step-by-step explanation:
The slope always goes before the x and your y-intercept is plus or minus depending on weather it is positive or negative. Your parent function or standard equations) is y = mx + b, so just plug your variable into there.
PLZ HELPP!!!!
Alexia set up the tent below in case it rained during the barbecue.Which equation shows how to determine the volume of the tent?Mark this and return
Answer: its A
Step-by-step explanation:i did the test
Answer:
Its A
Step-by-step explanation:
thx byye
Keesha bought 11 binders and notebooks
from the store and spent $45. Binders cost
$6 each and notebooks cost $2.50 each. Which
two equations can be used to find the number
of binders, b, and notebooks, 11, she purchased?
Answer:
sssssssss
Step-by-step explanation:
Given,
Keesha bought = x binder.
Let Keesha bought (11-x) notebook.
Total money spent = $45
Cost of each binder = $ 6
Cost of each notebook = $ 2.50
Now,
Equation
$ 6 × x + $ 2.50 × (11-x) = $ 45
$ 6 x + $27.5 - $ 2.50 x= $ 45
$ 3.50 x = $ 17.5
x = 5
Number of binder = 5.
Number of cover = 11-5 = 6.
Final answer:
The two equations to determine the number of binders (b) and notebooks (n) Keesha purchased are: b + n = 11 and 6b + 2.50n = 45. These equations are based on the total number of items and the total cost of the items.
Explanation:
To determine the number of binders and notebooks Keesha purchased, we need to set up two equations based on the given information. The first equation will represent the total number of items purchased, and the second will represent the total cost of those items.
Equation 1 (total number of items):
b + n = 11
Equation 2 (total cost):
$6 × b + $2.50 × n = $45
In the above equations, b represents the number of binders and n represents the number of notebooks. These two equations can be used to solve for the variables b and n using methods such as substitution or elimination.
The table shows the scores for three teams over five games.
Team A
Team B
Team C
56
65
45
48
32
30
29
60
45
48
32
45
59
28
82
Which team has the mode with the highest score?
Select from the drop-down menu to correctly complete the statement.
has the mode with the highest score.
PLEASE HELP!
Answer:
Team A-
Modes are alike numbers.
Team A had two 48s
Team B had two 32s
and Team C had three 45s
48 is the highest number
Step-by-step explanation:
i answerd it right on e d g e n u i t y
What is the radius and diameter of the following circle?
14 cm
Radius
cm
Diameter
cm
Answer:
Radius = 7cm
Diameter = 14cm
Step-by-step explanation:
Radius is a straight line that connects the center of a circle to a point on the circumference (outside of the circle).
Diameter is a straight line that goes through the center of a circle and connects two points on the circumference (outside of the circle).
The line shown goes across the entire circle, so it is the diameter
Diameter = 14 m
The radius of a circle is half the length of the diameter.
r = [tex]\frac{d}{2}[/tex]
r = [tex]\frac{14}{2}[/tex]
r = 7 cm
This is why the radius is 7cm, and the diameter is 14cm.
Hope this helped!
what is 100 percent if 27 is 45%
Answer:
YOUR WRONG 27 IS NOT 45%
Step-by-step explanation:
[tex]\frac{27}{100}[/tex]=27%
100%=1 whole
Answer:
It is 60
Step-by-step explanation:
A better way to rephrase the problem is:
"what is 100 percent of something if 27 is 45% of something. ?"
so
100% * X = ?
given: 27 = 45% * X
Solve for X,
27/ 45% = X
X = 27 / 0.45 = 60
so. 100% * X = 100% * 60 = 1 * 60 = 60
01) Solve for x the equation 5x - 3=12*
O
x=1
O
x=3
O x=5
O x=7
x=3
Step-by-step explanation:
five time three is fifteen minus three is twelve.
x=3 is the solution to the equation 5x - 3 = 12.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
To solve for x in equation 5x - 3 = 12, we need to isolate x on one side of the equation.
First, we can add 3 to both sides of the equation:
5x - 3 + 3 = 12 + 3
Simplifying the left-hand side:
5x = 15
Next, we can divide both sides of the equation by 5:
5x/5 = 15/5
Simplifying the left-hand side:
x = 3
Therefore, the solution to the equation 5x - 3 = 12 is x = 3.
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George has two different savings accounts. Savings Account A currently has $140 after one year. It earned 12% interest during that year. Savings Account B currently has $160 after one year. It earned 20% interest during that year. How much money in total did George have in the accounts at the beginning of the year?
Answer:
A= 125$ B=134
Step-by-step explanation:
Graph the circle which is centered at (-5,1) and has a radius of 4 units
Suppose wellington pours 1/8 gallons from the remaining juice into a glass. He pours the same amount into more glasses until the pitcher is empty. How many glasses of juice will Wellington pour?
Answer: 7 glasses
Step-by-step explanation:
Hi, to answer this question, first, we have to subtract the amount of juice poured (1/8) to the amount of remaining juice before he poured some (1).
1-1/8 = 7/8 remaining juice
Since he pours the same amount into more glasses until the pitcher is empty, we have to divide the remaining juice (7/8) by the amount poured in each glass (1/8).
7/8 ÷ 1/8 = 7 glasses
Feel free to ask for more if needed or if you did not understand something.
Marble Slab Creamery is creating a cone-shaped paper wrapper for its new green Baby Yoda waffle cone. The wrapper should have a radius of 5 cm and a slant height of 10 cm. One location wants to offer the cones a weekend earlier, so they plan to make the cone-shaped wrappers for first 25 waffle cones sold that Saturday. About how many square cm of wrapper paper will they need? (Round up to the nearest cm.)
Answer:
3927 cm² wrapping paper will be required.
Step-by-step explanation:
Lateral surface area of a cone shaped wrapper = πrl
where, r = radius of the waffle cone
and l = slant height of the cone
It has been given in the question, radius 'r' = 5cm
and lateral height 'l' = 10 cm
Lateral surface area of the cone = π(5)(10)
= 50π
= 157.08 cm²
If they plan to make 25 waffles then wrapper paper required
= 25×157.08
= 3927 cm²
Therefore, 3927 cm² wrapping paper will be required.
the mean of 8 numbers is 12. Five of the numbers are 6, 8, 5, 10 and 28. The remaining 3 numbers are each equal to k. Find
(i) The sum of the 8 numbers
(ii) The value of k
Answer:
(i) 96
(ii) k = 13
Step-by-step explanation:
(i)
numbers averaged x Average of the numbers = Total of all of the numbers
8 x 12 = 96
(ii)
6 + 8 + 5 + 10 + 28 + 3k = 8 x 12
57 + 3k = 96
3k = 39
k = 13
Please help!!!
find the median, first quartile, third quartile, and interquartile range of the data.
12, 31, 9, 20, 36, 5, 22
and
63, 68, 58, 77, 50, 49, 63, 73
Answer:
Part 1) 12, 31, 9, 20, 36, 5, 22
Sort the data:
5, 9, 12, 20, 22, 31, 36
Median: 20
First Quartile: 9
Third Quartile: 31
IQR: 31 - 9 = 22
and
Part 2) 63, 68, 58, 77, 50, 49, 63, 73
Sort the data:
49, 50, 58, 63, 63, 68, 73, 77
Median: (63÷63)/2 = 63
First Quartile: (50+58)/2 = 54
Third Quartile: (68+73)/2 = 70.5
IQR: 70.5 - 54 = 16.5
if point a is located at -8 on a number line and point b is located at 3 on the same number line, what is the distance between a and b?
Answer:
11
Step-by-step explanation:
-8 is 8 spaces away from 0 and 3 is 3 spaces away from zero so you add 8 and 3 and get 11.