Let's find the inverse function:
1. replace f(x) with y
[tex]y=\frac{2x-9}{3}[/tex]2. Replace every x with a y and every y with an x:
[tex]x=\frac{2y-9}{3}[/tex]3. solve for y:
[tex]y=\frac{3x+9}{2}[/tex]4. replace y with f^-1(x)
[tex]f^{-1}(x)=\frac{3x+9}{2}[/tex]Now:
[tex]f^{-1}(3)=\frac{3(3)+9}{2}=\frac{9+9}{2}=\frac{18}{2}=9[/tex]since the functions are equal for x = 3 we can conclude that they have the same result
[tex]f(3)=f^{-1}(3)[/tex]Find the equation of the line with slope m=1/5 that contains the point (-10,-5)
The point-slop form for a line is
[tex]y-y_0=m(x-x_0),[/tex]so, we only need to subsitute and solve for y or put it in the general form
[tex]\begin{gathered} y-(-5)=\frac{1}{5}(x-(-10))_{} \\ y+5=\frac{1}{5}x+2 \\ y=\frac{1}{5}x-3 \end{gathered}[/tex]Another way to write this equation is
[tex]\begin{gathered} y=\frac{1}{5}x-3 \\ y+3=\frac{1}{5}x \\ 5y+15=x \\ x-5y-15=0 \end{gathered}[/tex]you working at a theater where you at every evaluating attendance at several events from the first event to the second event, attendance drop from 250 to 230 the percent decrease to the nearest percent
Question: You're working at a theater where you are evaluating attendance at several events. From the first event
to the second event, attendance dropped from 250 to 230. Find the percent decrease to the nearest percent.
Answer:
8%
Explanation:
To be able to find the percentage decrease, the 1st step is to find the difference between old attendance value and the new attendance value;
[tex]250-230=20[/tex]We'll then divide this value by the old attendance value;
[tex]\frac{20}{250}=0.08[/tex]The final step will be to convert the decimal number to a percentage by multiplying by 100;
[tex]0.08\ast100=8[/tex]Due NOW HELP BRAINIEST IF RIGHT
Angles X and Y are supplementary. Angle X measures 115.75° and angle Y measures (m − 8)°. Find m∠Y.
136.5°
128.5°
72.25°
64.25°
The value of m is 72.25° and value of ∠Y = 64.25
if two angles are supplementary, sum of their values will be equal to 180°
∴∠ X + ∠Y = 180°
∠X = 115.75°
∠Y = (m-8)°
∴ 115.75 + ∠ Y = 180°
∠Y = 64.5°
m-8 = 64.5°
m = 72.25°
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The value of [tex]m\angle Y[/tex] is [tex]64.25^o[/tex].
In the give question,
Angles [tex]X[/tex] and [tex]Y[/tex] are supplementary.
Angle [tex]X[/tex] measures [tex]115.75^o[/tex] and angle [tex]Y[/tex] measures [tex](m-8)^o[/tex].
We have to find [tex]m\angle Y[/tex].
We firstly learn about supplementary angel.
Angles that add up to [tex]180[/tex] degrees are referred to as supplementary angles.
As given that [tex]X[/tex] and [tex]Y[/tex] are supplementary so the sum of angle [tex]X[/tex] and [tex]Y[/tex] equals to [tex]180^o[/tex].
[tex]\angle X+\angle Y=180^o[/tex]
As we know that [tex]\angle X=115.75^o, \angle Y=(m-8)^o[/tex]
Now putting the value
[tex]115.75^o+(m-8)^o=180^o[/tex]
Now simplifying the expression.
[tex]115.75^o+m^o-8^o=180^o[/tex]
[tex]107.75^o+m^o=180^o[/tex]
Subtract [tex]107.75^o[/tex] on both side
[tex]107.75^o+m^o-107.75^o=180^o-107.75^o[/tex]
[tex]m^o=72.25^o[/tex]
We have to find the value of [tex]m\angle Y[/tex].
The given value of [tex]Y[/tex] is
[tex]m\angle Y=(m-8)^o[/tex]
Now putting the value of [tex]m[/tex]
[tex]m\angle Y=(72.25-8)^o[/tex]
[tex]m\angle Y=64.25^o[/tex]
Hence, the value of [tex]m\angle Y[/tex] is [tex]64.25^o[/tex].
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Michael deposited $2,500 in a savings account that pays 1.6% simple interest. He kept the money in the account for 5 years without any deposits or
withdrawals. How much was in the account after 5 years?
There was
in the account after 5 years.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2500\\ r=rate\to 1.6\%\to \frac{1.6}{100}\dotfill &0.016\\ t=years\dotfill &5 \end{cases} \\\\\\ A=2500[1+(0.016)(5)] \implies A=2500(1.08)\implies A = 2700[/tex]
A triangle has a base length of 10 inches and a height of 4 inches
The area of a triangle is 20 inches².
The area of a triangle:
The area of a triangle is equal to half the product of the base and its height.
The formula for the area of a triangle = 1/2 × base × height
Here the base = 10 inches
height = 4 inches
Area = 1/2 × 10 × 4
= 10×2
= 20 inches²
Therefore the area of a triangle is 20 inches².
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Last year, Greg had $30,000 to invest. He invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 7% simple interest per year. After one year, he received a total of $2790 in interest. How much did he invest in each account?
According to the question, Greg had $30,000 to invest. He invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 7% simple interest per year. After one year, he received a total of $2790 in interest. Then we write the following equations:
First account (10%): 0.1 x = a (money gained in one year, where x is the amount invested)
Second account (7%) : 0.07 (30.000 - x) = b (money gained in one year, where 30.000 - x is the amount invested inthe seond account).
a + b = 2790 (total amount of money gained due to interest).
Replacing the two first equations in the third one, we obtain the following expression:
0.1 x + 0.07 (30.000 - x) = 2790
(0.1 - 0.07)x + 2100 = 2790
0.03 x = 690, solving for x:
x = $23.000 (the amount of money invested in the first account) and
($30.000 - x) = $7.000 is the amount of money invested in the second account.
What inequality represents the sentence, the sum of the quotient of a number and 3 and 6 is no more than-12?
We need to split the sentence.
First part, the sum of:
• quotiene of a number and 3
,• and 6
The above could be writen as:
[tex]\begin{gathered} \frac{n}{3}+6 \\ \text{Where n is some number.} \end{gathered}[/tex]The sum above is no more than -12, so the sum is less than -12:
[tex]\frac{n}{3}+6<-12[/tex]The first option is the correct answer.
4x + 5y = 19 8x - 6y = -10
Given the system of equations :
[tex]\begin{gathered} 4x+5y=19\rightarrow(1) \\ 8x-6y=-10\rightarrow(2) \end{gathered}[/tex]Multiply the first equation by -2:
[tex]\begin{gathered} -2\cdot4x+(-2)\cdot5y=-2\cdot19 \\ -8x-10y=-38\rightarrow(3) \end{gathered}[/tex]Add the equations (2) and (3) to eliminate x :
[tex]\begin{gathered} 8x-8x-6y-10y=-10-38 \\ -16y=-48 \\ \\ y=\frac{-48}{-16}=3 \end{gathered}[/tex]Substitute with y in equation (1) to find x :
[tex]\begin{gathered} 4x+5\cdot3=19 \\ 4x+15=19 \\ 4x=19-15 \\ 4x=4 \\ \\ x=\frac{4}{4}=1 \end{gathered}[/tex]So, the solution of the system is :
[tex]\begin{gathered} x=1 \\ y=3 \\ (x,y)=(1,3) \end{gathered}[/tex]The approximate volume in milliliters, y, for a volume of x fluid ounces is equal to 29.57 times the value of x. Which table represents this relationship?
The table which represents the relationship is:
Fluid ounces, x Volume y ( in millimeters)
1 29.57
2 59.14
3 88.71
4 188.28
In mathematics, a relation describes how two distinct sets of information related to one another. If more than two non-empty sets are taken into consideration, a connection between their elements will indicate that more than two sets are being evaluated.
Let y be the volume of fluid x in millimeters.
Now, y is equal to 29.57 times the value of x.
Therefore,
y = 29.57 × x
y = 29.75x
So, when x = 1:
y = 29.75(1) = 29.57
When x = 2,
y = 29.57(2) = 59.14
When x = 3,
y = 29.57(3) = 88.71
When x = 4,
y = 29.57(4) = 118.28
Therefore, the table that represents the relationship is:
Fluid ounces, x Volume y ( in millimeters)
1 29.57
2 59.14
3 88.71
4 188.28
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Express 5√27 in the form n√3, where n is a positive integer.
Answer:
n = 15Step-by-step explanation:
See the steps below:
[tex]5\sqrt{27} =[/tex][tex]5\sqrt{3^2*3} =[/tex][tex]5*3\sqrt{3} =[/tex][tex]15\sqrt{3}[/tex]The value of n is 15.
Using the following image, if JL=120, what are X,JK, And KL
Given: A-line segment JL=120 units,
[tex]\begin{gathered} JK=4x+6 \\ KL=7x+15 \end{gathered}[/tex]Required: To determine the value of x, JK, and KL.
Explanation: From the given figure, we can write
[tex]JK+KL=JL[/tex]We are now putting the values-
[tex]\begin{gathered} 4x+6+7x+15=120 \\ 11x=120-21 \\ 11x=99 \\ \end{gathered}[/tex]Hence
[tex]x=9[/tex]Now
[tex]\begin{gathered} JK=4x+6 \\ =4\times9+6 \\ =42\text{ units} \end{gathered}[/tex]And
[tex]\begin{gathered} KL=7x+15 \\ =7\times9+15 \\ =78\text{ units} \end{gathered}[/tex]Final Answer: The value of
[tex]\begin{gathered} x=9 \\ JK=42\text{ units} \\ KL=78\text{ units} \end{gathered}[/tex]triangle ABC has side lengths 10 14 and 26 do the silence form a Pythagorean triple explain
Solution:
Given the side lengths of a triangle ABC;
[tex]a=10,b=14,c=26[/tex]The side lengths form a Pythagorean triple if ithe square of the longest side is equal to the sum of squares of the remaining two sides.
Thus;
[tex]\begin{gathered} 10^2+14^2=100+196 \\ \\ 10^2+14^2=296 \\ \\ 296\ne29^2 \\ \\ \text{ Thus;} \\ \\ 10^2+14^2\ne26^2 \end{gathered}[/tex]Hence, they do not form a Pythagorean triple.
CORRECT OPTION: (B) No, they do not form a Pythagorean triple.
[tex]10^{2}+14^{2}\ne26^{2}[/tex]
An aquarium is 26 inches long, 14 inches wide and 24 inches high. The volume of water in the aquarium is 5824 cubic inches. How deep is the water?
The depth of the water is 16 inches.
What is the depth?The depth represents the vertical distance from the bottom of the aquarium to the top of the water level.
The depth can be found by dividing the volume of the water by the area of the aquarium.
The length of an aquarium = 26 inches
The width of the aquarium = 14 inches
The height of the aquarium = 24 inches
The Capacity of the aquarium = 8,736 cubic inches (26 x 14 x 24)
The volume of water in the aquarium = 5,824 cubic inches
The area of the aquarium = 364 squared inches (26 x 14)
The depth of the water in the aquarium = Volume of Water/Area of aquarium
= 16 inches (5,824/364)
Thus, we can conclude that the water is 16 inches deep.
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Write a quadratic equation with a integer coefficients with roots x= 1/2 and x=-4
The quadratic equation with roots a and b is given by:
[tex]x^2-(a+b)x+ab=0[/tex]Here a=1/2 and b=-4.
So the equation is given by:
[tex]\begin{gathered} x^2-(\frac{1}{2}-4)x+(\frac{1}{2})(-4)=0 \\ x^2+\frac{7}{2}x-2=0 \\ 2x^2+7x-4=0 \end{gathered}[/tex]The quadratic equation is as shown above.
One number is 8 more than another. Their product is -16.
Answer:
The two numbers are 4 and -4
Step-by-step explanation:
Turn the words into equations: let's assign one number to be x and the other to be y
x+8=y
x*y=-16
To solve, substitute the value of y in the first equation into y in the second equation.
This gives x*(x+8)=-16
Simplifying gives x^2+8x=-16
x^2+8x+16=0
(x+4)^2=0
x=-4
plug this value of x back into the first equation, -4+8=y, y is 4
Now to make sure the answer is correct: 4 is 8 more than -4, and 4*-4 does equal 16
Solve for x (Simplify your answer. Type an integer or a decimal. Round to 3 decimal places if needed.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex]e^{ln3x}=e^{ln(x+6)}[/tex]STEP 2: Simplify the expression
[tex]\begin{gathered} e^{\ln \left(3x\right)}=e^{\ln \left(x+6\right)} \\ Apply\text{ exponent rules} \\ \ln \left(3x\right)=\ln \left(x+6\right) \\ By\text{ simplification,} \\ x=3 \end{gathered}[/tex]Hence, x = 3
Can u Please help me review this question by solvingPart B and C
Part B
Given:
P(5, 16), Q(8, 4), R(28, 7), S(10, 16)
u in trigonometric form:
[tex]\begin{gathered} u\text{ = \lparen8-5, 4-16\rparen} \\ =\text{ \lparen3, -12\rparen} \end{gathered}[/tex]The trigonometric form of a vector v is:
[tex]v(cos\theta,\text{ sin}\theta)[/tex]Solving for u:
[tex]\begin{gathered} u\text{ = }\sqrt{3^2\text{ + \lparen-12\rparen}^2} \\ =\text{ 12.37} \end{gathered}[/tex]Solving for the angle:
[tex]undefined[/tex]Change this to slope-intercept form. Keep in mind this is in standard form currently.
[tex]\frac{3}{8} x+\frac{2}{3} y=5[/tex]
well, is not exactly in standard form, but close enough.
well, let's take a peek at the denominators, hmmmm 8 and 3, well let's get their LCD hmmm that'd be 24 pretty much, so, let's multiply both sides by the LCD of the denominators, that way we do away with the denominators
[tex]\cfrac{3}{8}x+\cfrac{2}{3}y=5\implies \cfrac{3x}{8}+\cfrac{2y}{3}=5\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{24}}{24\left( \cfrac{3x}{8}+\cfrac{2y}{3} \right)~~ = ~~24(5)} \\\\\\ 9x ~~ + ~~ 16y ~~ = ~~ 120\implies 16y=-9x+120\implies y=\cfrac{-9x+120}{16}[/tex]
[tex]y=\cfrac{-9x}{16}+\cfrac{120}{16}\implies \implies y=-\cfrac{9}{16}x+\cfrac{15}{2} \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
I need help with part A bit if u can help me with every I will give you 5 stars ⭐️ this is my homework
SOLUTION
From the diagram of the box plot
A. The IQR for the male's data is approximately 14 - 5 = 9
B. The median for female is 7
The median for male is estimated 10
Difference 10 - 7 = 3.
C. The mean would be better to compare males with females because from the box plot diagram, more males saw the movie than females.
D. The possible reason for the outlier in the data set could be due to more females attending the movie than normal.
help i don’t know how to do this math problem
Answer:
Given that,
Total surface are=102 m square.
To find the side length of A,
Let the side length of A be a,
we get,
[tex]\text{Total surface area}=102[/tex][tex]18+A+A+6+6+18=102[/tex][tex]48+2A=102[/tex][tex]2A=102-48[/tex][tex]2A=54[/tex][tex]A=27[/tex]One side of the A is 3, we get that
A=product of one side and a
we get,
[tex]A=3\times a[/tex]Substitute for A=27 we get,
[tex]27=3\times a[/tex][tex]a=\frac{27}{3}[/tex][tex]a=9[/tex]The required side length of A is 9 m
if the parent function is ^3sqrt(x), describe the translation of the function y=^3(x+4)-3
Given:
The parent function is
[tex]y=\sqrt[3]{x}[/tex]The translation function is
[tex]y=\sqrt[3]{x+4}-3[/tex]Required:
We need to find the translation.
Explanation:
Let f(x) be the parent function.
The translation function of the form f(x+h)+k.
The value of 'h' controls how much the graph shifts to the left or right
Comparing f(x+h)+k, we get h =4 anf k=-3.
The value of h is positive so the graph shift left by 4 units.
The value for 'k' controls how much the graph shifts up or down
The value of k is negative so the graph shifts down by 3 units.
Final answer:
Four units left and 3 units down.
Write two linear functions, f(x) and g(x). For example, f(x)=
3x-7-and glx) = -2x+5. Then see whether f(x)= (-g(x)) is equivalent to f(x) + g(x) hint : To find -g(x), just change the signs of all the terms in g(x). Discuss whether you think your results would apply to every function.
The most appropriate choice for functions will be given by -
f (x) - (-g(x)) = f(x) + g(x) holds for f(x)=3x-7-and g(x) = -2x+5.
f (x) - (-g(x)) = f(x) + g(x) holds for every functions
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
For f(x) - (-g(x))
-g(x) = -(-2x + 5)
= 2x - 5
f (x) - (-g(x)) = (3x - 7) - (2x - 5)
3x - 7 - 2x + 5
x - 2
For f(x) + g(x)
f(x) + g(x) = (3x - 7) + (-2x + 5)
= 3x - 7 - 2x + 5
= x - 2
So f (x) - (-g(x)) = f(x) + g(x) holds here
Since addition and subtractions can be done on functions,
f (x) - (-g(x)) = f(x) + g(x) holds for every functions.
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The following data show the average hourly wage( in dollars) of customer service representative for a random sample of U.S states 17.94 20.43 21.28 20.41 17.04
Answer:
Explanation:
Given:
The average hourly wage: 17.94 20.43 21.28 20.41 17.04
To find:
a) sample mean, b) sample standard deviation
To determine the sample mean, we will apply the formula:
[tex]\begin{gathered} Smaple\text{ mean = }\frac{1}{n}\sum_\text{ x} \\ \\ n\text{ = number of dataset = 5} \\ Sample\text{ mean = }\frac{1}{5}(17.94+20.43+21.28+20.41+17.04) \end{gathered}[/tex][tex]\begin{gathered} Sample\text{ mean = }\frac{1}{5}(97.1) \\ \\ Sample\text{ mean = 19.42} \end{gathered}[/tex]To get the median, we need to re-arrange the numbers either in ascending or descending order
In ascending order: 17.04, 17.94, 20.41, 20.43, 21.28
The middle number is 20.41. Hence, the median is 20.41
To determine the sample variance, we will apply the formula:
[tex][/tex]Can you help me with this test I got I can give you all the info you need.
Given data:
The given radius is JK=JM=3.
The given length is LM=2.
The tangent is always perpendicular to the radius, the expression for the Pythagoras theorem is,
[tex]\begin{gathered} (JK)^2+(KL)^2=(JL)^2 \\ (JK)^2+(KL)^2=(JM++ML)^2 \end{gathered}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} (3)^2+(KL)^2=(3+2)^2 \\ 9+(KL)^2=25 \\ (KL)^2=16 \\ KL=4 \end{gathered}[/tex]Thus, the first option is correct.
Change 64 square metres into square millimetres.
Give your answer in standard form.
Answer:
64,000,000
Step-by-step explanation:
im smart
What was the new balance to start the
next bank statement?
$913.40
$672.40
$554.54
Answer:
Assuming that the amount shown is an addition to the bank account, you add all those and get 2140.34 dollars to start the next statement.
Step-by-step explanation:
Assuming that the amount shown is an addition to the bank account, you add all those and get 2140.34 dollars to start the next statement.
Percy rides his bike 11.2 miles in 1.4 hours at a constant rate write an equation to represent the proportional relationship between the number of hours Percy rides x and the distance in miles y that he travels
The proportional relationship representing the situation is given by
y = 8x.
Two numerical sequences, typically experimental data, are said to be proportionate or directly proportional if the ratio of their associated parts is constant, which is known as the coefficient of proportionality of proportionality constant. Two sequences are termed inversely proportionate if the product of their respective elements is constant, also known as the proportionality coefficient.
This concept is usually extended to related changeable quantities, sometimes known as variables. This is not the standard definition of variable in arithmetic, because two separate concepts have the same name for historical reasons.
Given that Percy rides his bicycle for 11.2 miles in 1.4 hours.
Let the constant of proportionality be k.
Therefore the proportional relationship is represented as:
y = k x
Now therefore putting the values we get:
11.2 = k × 1.2
or, k = 8
Hence the relationship will look like :
y = 8 x
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write the equation if the following graph (0,2) (4,1)
Step 1: Problem
write the equation if the following graph (0,2) (4,1)
Step 2: Concept
Firstly, find the slope m
Secondly, the intercept c at the vertical axis.
The equation of a line is
y = mx + c
Step 3: Method
[tex]\begin{gathered} \text{Slope m = }\frac{y_2-y_1}{x_2-x_1} \\ (\text{ 0, 2 ) and ( 4, 1 )} \\ x_1=0 \\ y_1\text{ = 2} \\ x_2\text{ = 4} \\ y_2\text{ = 1} \\ m\text{ = }\frac{1\text{ - 2}}{4\text{ - 0}} \\ m\text{ = }\frac{-1}{4} \\ \\ \text{Intercept c = 2} \end{gathered}[/tex]Step 4: Final answer
Substitute m and c in the equation below to find the equation of the line.
y = mx + c
[tex]y\text{ = }\frac{-1}{4}x\text{ + 2}[/tex]Roberto is charged 0.04% compound interest per day on his credit card purchase of $1200. Find the amount of interest owning after 30 days.
Given:
Assuming 360days in a year and proceeding
[tex]P=\text{ \$1200 ; r=0.04\% ; }t=\frac{1}{12}\text{ years ; n=36}0[/tex][tex]A=P(1+\frac{r}{n})^{nt}[/tex][tex]A=1200(1+\frac{0.04}{360})^{360\times\frac{1}{12}}[/tex][tex]A=1200(1.0001)^{30}[/tex][tex]A=1200(1.003)[/tex][tex]A=1203.60[/tex]Amount of interest owning after 30days is $3.60
How do I solve one-variable inequalities with fractions and parentheses?
Given:
[tex]6x\text{ + }\frac{1}{4}(4x\text{ + 8) > 12}[/tex]First, let's open the bracket:
[tex]\begin{gathered} 6x\text{ + }\frac{1}{4}\times\text{ 4x + }\frac{1}{4}\times8\text{ > 12} \\ 6x\text{ + x + 2 > 12} \end{gathered}[/tex]Collect like terms:
[tex]\begin{gathered} 6x+x\text{ > 12 - 2} \\ 7x\text{ > 10} \end{gathered}[/tex]Divide both sides by 7:
[tex]\begin{gathered} \frac{7x}{7}\text{ > }\frac{10}{7} \\ x\text{ > }\frac{10}{7} \end{gathered}[/tex]Solution:
x > 10/7
