Answers
Answer: We have to pick a graph that represents a function and its inverse function, or:
[tex]\begin{gathered} f(x)\rightarrow\text{ and }\rightarrow f^{-1}(x) \\ \end{gathered}[/tex]The inverse function switches the x and y variables, therefore the axes with it, the final result is two functions that are symmetrical about y = x line.
Example:
[tex]\begin{gathered} f(x)=\sqrt{x}\rightarrow\text{ Function} \\ \\ f^{-1}(x)=x^2\rightarrow\text{ Inverse Function} \end{gathered}[/tex]Graph:
Therefore the graph out of the options which has these properties is:
[tex]\text{ Graph\lparen C\rparen}[/tex]The answer, therefore, is Graph(C).
Related Questions
What is the radius of a circle whose circumference is 36pi?
Answers
The circumference of a circle of radius r is given by:
[tex]C=2\pi r[/tex]For this question we simply need to take C=36π and solve for r:
[tex]36\pi=2\pi r[/tex]If we divide both sides by 2π we get:
[tex]\begin{gathered} 36\pi=2\pi r \\ \frac{36\pi}{2\pi}=\frac{2\pi r}{2\pi}=\frac{2\pi}{2\pi}\cdot r \\ 18=r \end{gathered}[/tex]Then the answer is option A, 18.
Solve: 9/14 + 2/6 = ?
Answers
We have to solve the expression:
[tex]\frac{9}{14}+\frac{2}{6}[/tex]We have to find a common denominator for the fractions and then solve it.
We can start by simplifying the fractions that can be simplified, like 2/6.
[tex]\frac{9}{14}+\frac{2}{6}=\frac{9}{14}+\frac{1}{3}[/tex]Then, the common denominator between 14 and 3 is 14*3=42, so we end with:
[tex]\frac{9\cdot3}{14\cdot3}+\frac{1\cdot14}{3\cdot14}=\frac{27}{42}+\frac{14}{42}=\frac{27+14}{42}=\frac{41}{42}[/tex]Answer: 41/42
Suppose cluster sampling were being used to survey digital camera users, who amount to 77% of the population of the United States. Based on the table below, which city would be considered the best cluster?
Answers
The best cluster is Las Vegas, which has a percentage of 78% that is linearly close to 77%, the percentage of the whole population of the United States.
AnswerLas Vegas
This expression 12(1.0515)t models the population of elephants in a wildlife refuge after years since 1975 is the population of elephants increasing or decreasing?
Answers
The function for an exponential growth/decay is given as follows;
[tex]f(x)=a(1+r)^x[/tex]Where,
[tex]\begin{gathered} x=\text{Number of years} \\ a=\text{initial value} \\ r=\text{rate of growth} \end{gathered}[/tex]Observe that from the equation provided, the rate is 1.015. This means there is a growth. If there was a decay(decrease), the rate would be less than 1 because, the formula then would be;
[tex]f(x)=a(1-r)^x[/tex]ANSWER:
Therefore, the population of elephants is INCREASING.
Using the translation that maps (3,-4) to its image (1,0), what is the image of any point (x,y)?A. (x+2,y+4)B. (x−2,y−4)C. (x+2,y−4)D. (x−2,y+4)
Answers
Explanation
Given (3,-4), its image (1,0) can be produced below;
[tex]\left(3,-4\right)\Rightarrow\left(x−2,y+4\right)\Rightarrow\left(1,0\right)[/tex]Answer: Option D
Members of the football team hold a fundraising dinner to raise money for their annual trip. They must sell tickets to the event at a price that will earn them more money than the cost of food.Here's a formula for this scenario:t = n (p - c)wheret = total profit made from the eventn = number of tickets soldp = price charged for each dinnerC = cost for food per plate The team hopes to sell 100 tickets. The cost for food per plate is $1.75 and they hope to charge $11.75 for each dinner. How much profit should they receive from the event?Enter the correct answer.
Answers
t = n(p-c)
t=100(11.75 - 1.75)
t = 100(10)
t=$1000
total profit received = $1000
miguel saves the same amount of money into a bank account each week. the bank account started with some money in it. after 3 weeks, the bank account contained $250. after 10 weeks the bank account contained $600.write an equation that cqn be used to model tbe number of dollars, y,iguel saves in x weeks.exain what slope and y intercept of youre equation mean in the context of the aituation.enter your equation and your explanations in tbe space provided.
Answers
Answer:
An equation that can be used to model the number of dollars, y, Miguel saves in x weeks is;
[tex]y=50x+100[/tex]The slope of the equation in the context is the amount of money Miguel saves in the bank account each week. So, Miguel saves $50 each week.
The y-intercept of the equation in the context is the amount of money Miguel initially have in the bank account. So, the initial amount of money in the bank account is $100.
Explanation:
Given that Miguel saves the same amount of money into a bank account each week.
Let y represent the amount of money in the account after x weeks;
[tex]y=mx+b[/tex]After 3 weeks, the bank account contained $250;
[tex]\begin{gathered} 250=m(3)+b \\ 3m+b=250 \end{gathered}[/tex]After 10 weeks the bank account contained $600;
[tex]\begin{gathered} 600=m(10)+b \\ 10m+b=600 \end{gathered}[/tex]Solving for m and b;
subtract the first equation from the second.
[tex]\begin{gathered} 10m-3m+b-b=600-250 \\ 7m=350 \\ m=\frac{350}{7} \\ m=50 \end{gathered}[/tex]substituting the value of m into the first equation;
[tex]\begin{gathered} 3m+b=250 \\ 3(50)+b=250 \\ 150+b=250 \\ b=250-150 \\ b=100 \end{gathered}[/tex]Therefore, an equation that can be used to model the number of dollars, y, Miguel saves in x weeks is;
[tex]y=50x+100[/tex]From the equation above, the slope m of the equation is;
[tex]m=50[/tex]and the y-intercept b of the equation is;
[tex]b=100[/tex]The slope of the equation in the context is the amount of money Miguel saves in the bank account each week. So, Miguel saves $50 each week.
The y-intercept of the equation in the context is the amount of money Miguel initially have in the bank account. So, the initial amount of money in the bank account is $100.
The perimeter of a rectangular pool is 44 feet. The length is 8ft longer than the width. Find the dimensions.
Answers
Given:
A rectangular pool with the following measures,
Perimeter
Length = x + 8
Width = x
Let's determine the measure of its dimensions:
[tex]\text{ Perimeter = 2L + 2W}[/tex][tex]\text{ = 2(x + 8) + 2(x)}[/tex][tex]\text{ 44 = 2x + 16 + 2x}[/tex][tex]\text{ 44 = 4x + 16}[/tex][tex]\text{ 44 - 16 = 4x}[/tex][tex]\text{ 28 = 4x}[/tex][tex]\text{ }\frac{28}{4}\text{ = }\frac{4x\text{ }}{4}[/tex][tex]\text{ 7 = x}[/tex]Let's now determine its dimensions,
Length = x + 8 = 7 + 8 = 15 ft.
Width = x = 7 ft.
Therefore, the dimension of the rectangular pool is Length = 15 ft. and Width =7 ft.
This is a maze where you find the answer starting from where it says start, and as you find the answer you highlight it along the way! Pls help I’m really bad at this
Answers
The start figure has two chords in the circle.
By theorem of internal division of chords it follows:
[tex]\begin{gathered} 21x=18\times14 \\ x=\frac{18\times14}{21} \\ x=12 \end{gathered}[/tex]Hence the value of x is 12.
Use your number sense to find the values for x and y that satisfy the equations.4y = 8
Answers
y = 2
Explanation:The given equation is 4y
Divide both sides of the equation by 4
[tex]\begin{gathered} \frac{4y}{4}=\frac{8}{4} \\ \end{gathered}[/tex]y = 2
Also, since we are asked to use our number sense, we can find what we will multiply by 4 to give 8
Since 4 x 2 = 8, then y = 2
5. An expression is shown. 78 - 14 Between which two consecutive whole numbers does this value lie? Enter your numbers in the box. Between and
Answers
78 divide by 14
First, divide the numbers
78/14 = 5.57
5.57 lies between 5 and 6
What is the measure of the "Central Angle" for the 20% section?
Answers
The sum of all central angle is 360.
Determine 20% of 360 to obtain central angle for 20% section.
[tex]\begin{gathered} \frac{20}{100}\times360^{\circ}=36^{\circ}\cdot2 \\ =72^{\circ} \end{gathered}[/tex]So answer is 72 degrees.
The weekly revenue for a product is given by R(x)=307.8x−0.045x2, and the weekly cost is C(x)=10,000+153.9x−0.09x2+0.00003x3, where x is the number of units produced and sold.(a) How many units will give the maximum profit?(b) What is the maximum possible profit?
Answers
Answer:
The number of units that will give the maximum profit is;
[tex]1900\text{ units}[/tex]The maximum possible profit is;
[tex]\text{ \$}239,090[/tex]Explanation:
Given that the weekly revenue for a product is given by ;
[tex]R(x)=307.8x-0.045x^2[/tex]and the weekly cost is ;
[tex]C(x)=10,000+153.9x-0.09x^2+0.00003x^3[/tex]Recall that
Profit = Revenue - Cost
[tex]P(x)=R(x)-C(x)[/tex][tex]\begin{gathered} P(x)=307.8x-0.045x^2-(10,000+153.9x-0.09x^2+0.00003x^3) \\ P(x)=307.8x-0.045x^2-10,000-153.9x+0.09x^2-0.00003x^3 \\ P(x)=153.9x+0.045x^2-0.00003x^3-10,000 \end{gathered}[/tex]Using graph to derive the maximum point on the function;
Therefore, the maximum point is at the point;
[tex](1900,239090)[/tex]So;
The number of units that will give the maximum profit is;
[tex]1900\text{ units}[/tex]The maximum possible profit is;
[tex]\text{ \$}239,090[/tex]Rosa sells cosmetics. She is paid a commission of 3.16% of her first 1500 in sales during the week and 11% on all sales over 1500. What is her commission in a week during which she sells 2137.38 worth of cosmetics? Express your answer as a dollar amount and round to the nearest cent
Answers
ANSWER:
$ 117.51
STEP-BY-STEP EXPLANATION:
The commissions are divided into two payments, the first payment of the first $ 1500 with a commission of 3.16% and a second payment with a commission of 11% of all the remaining money of the first $ 1500.
Therefore, we calculate it as follows:
[tex]\begin{gathered} p_T=p_1+p_2 \\ p_1=1500\cdot\frac{3.16}{100}=47.4 \\ p_2=(2137.38-1500)\cdot\frac{11}{100}=637.38\cdot0.11=70.11 \\ p_T=47.4+70.11 \\ p_T=117.51 \end{gathered}[/tex]The total commission is $ 117.51
A product initially with a value of $21,800 has been depreciating at 8.1% p.a over 8 years. What is it's current value?
Answers
we get that:
[tex]v=21800\cdot(0.919)^8=11091.25[/tex]its current value is $11091.25
To which subsets of numbers does 1/3 belong?
Answers
1/3 is a rational number, which written as a decimal is an infinite period decimal.
the number line shown is divided into segments of equal length use the number line diagram to answer the following questions A. what is the length of each segment on the number line B.what number does point N represent C. what is the opposite of point N
Answers
A. We must divide the distance between the number of divisions
from 0 to 1 we have a distance of 1 and count 8 divisions
so
[tex]\frac{1}{8}=0.125[/tex]so the length of each segment is 1/8 or 0.125
B.
If sides AB and DC of a quadrilateral ABCD are parallel, which additional informationwould be sufficient to prove that quadrilateral ABCD is a parallelogram.ABACABDCACBDADABNone of the other answers are correct
Answers
We have a quadrilateral ABCD, where we know that AB || DC.
The other condition for the quadrilateral to be a parallelogram is that the other 2 sides of the parallelogram are congruent.
The other two sides are AC and BD, so the other condition needed is that AC and BD are congruent.
Answer: AC and BD are congruent.
[tex]AC\cong BD[/tex]If a1 = 8 and an = 3an-1 then find the value of a4.
Answers
a_4= 216
1) Given that we have the first term and the Recursive Formula, let's find the fourth term of that Sequence
2) Let's find the second, the third to find the fourth since a Recursive formula depends on the prior term.
[tex]\begin{gathered} a_1=8 \\ a_n=3a_{n-1} \\ a_2=3(8)\text{ =24} \\ a_3=3(24)=72 \\ a_4=3(72)\text{ =216} \end{gathered}[/tex]3) Hence, the sequence is 8, 24, 72, 216 and the fourth term is 216
Select the correct answer.6cis5pi/6Convert57to rectangular form.OA. 3V3 + 31O B. –313 + 3iO C. 373 – 3iOD. -3V3 – 31O E. 3 – 3731
Answers
Answer:
Choice B.
Explanation:
The equation can be rewritten as
[tex]6\text{cis}\frac{5\pi}{6}=6\cos \frac{5\pi}{6}+i\sin \frac{5\pi}{6}[/tex]Now since
[tex]6\cos \frac{5\pi}{6}=-3\sqrt[]{3}[/tex]and
[tex]6\sin \frac{5\pi}{6}=3[/tex]the expression becomes
[tex]-3\sqrt[]{3}+3i[/tex]Hence, choice B is the correct answer since it matches the answer we got above.
There are 396 students who are enrolled in an introductory engineering course. If there are four boys to every seven girls, how many boys are in the course?
Answers
Solution
For this case we know that the total of students are 396 so we can do this:
x + y = 396
Where:
x= number of girls
y = number of boys
Then we have the following condition:
4x = 7y
Then solving for x we got:
x = 7/4 y
Replacing in the first equation we got:
7/4 y + y = 396
11/4 y= 396
y= 396*4/11 = 144
And x= 7/4 * 144 = 252
Then the answer would be:
252 girls and 144 boys
The population of retired citizens in Memphis is 54000. If the population decreases at a rate of 5.9 % each year. What will the population of retirees be in 6 years?Write an exponential growth model for the future population P(x) where x is in years:
Answers
We will have the following:
First, we construct the exponential decay function, that is:
[tex]P(x)=54000(1-0.059)^x\Rightarrow P(x)=54000(0.941)^x[/tex]Now, we will determine the population after 6 years:
[tex]P(6)=54000(0.941)^6\Rightarrow P(6)=37491.38638[/tex]So, the population after 6 years will be of approximately 37491 people-
Solve the equation.– 2y - 15 = 4y + 15y=
Answers
Given the equation;
[tex]-2y-15\text{ = 4y+15}[/tex]You are to calculate the value of y. This is as shown below;
First collect the like terms;
[tex]\begin{gathered} -2y\text{ - 4y = 15+15} \\ \end{gathered}[/tex]Evaaluate the expression an find y;
[tex]\begin{gathered} -6y=30 \\ \end{gathered}[/tex]Divide both sides by -6;
[tex]\begin{gathered} \frac{-6y}{-6}=\frac{30}{-6} \\ y\text{ = -5} \end{gathered}[/tex]Hence the value of y is -5
Solve the inequality. State the solution in inequality notation. 4(x - 5) + 10 > 2(5x – 2) – 4x
Answers
We will solve as follows:
[tex]4(x-5)+10>2(5x-2)-4\Rightarrow4x-20+10>10x-4-4x[/tex][tex]\Rightarrow4x-10>6x-4\Rightarrow-2x>6\Rightarrow x<-3[/tex]So, the solution is x < -3.
***Breakdown:
*After we obtain:
[tex]4x-10>6x-4[/tex]We operate like terms, that is we separate the variables and integers in the different side [Operating as if it were a normal equation]:
[tex]\Rightarrow4x-6x>-4+10\Rightarrow-2x>6[/tex]After this, we know that by dividing and/or multiplying by negative values in the inequality the orientation of the inequality will shift [That is if it was "<" then it will become ">" and viceversa], that is:
[tex]\Rightarrow x<\frac{6}{-2}\Rightarrow x<-3[/tex]Zappo’s has marked down rain boots 25% during its spring sale. What is the sale price of a pair of boots with a regular price of $149.99?
Answers
Substract the 25% of the price to the regular price:
1. Find the 25% of the price: Multiply by 0.25 the price:
[tex]149,99\cdot0.25\approx37.50[/tex]2. Substract the result in step 1 (amount marked down) from the regular price:
[tex]149,99-37,50=112.49[/tex]Then, the sale price of the pair of boots is $112.49Use the system of equations below to solve for z.7x+3y+2z-4w=184w+5x-3y-2z=6-2w-3x+y+z=-52z+3w+4y-8x=11253
Answers
Equations:
[tex]\begin{gathered} 7x+3y+2z-4w=18\text{ \lparen1\rparen} \\ 5x-3y-2z+4w=6\text{ \lparen2\rparen} \\ -3x+y+z-2w=-5\text{ \lparen3\rparen} \\ -8x+4y+2z+3w=11\text{ \lparen4\rparen} \end{gathered}[/tex]Sum (1)+ (2):
[tex]\begin{gathered} 7x+3y+2z-4w=18\text{ }\operatorname{\lparen}\text{1}\operatorname{\rparen} \\ + \\ 5x-3y-2z+4w=6\text{ }\operatorname{\lparen}\text{2}\operatorname{\rparen} \\ 5x+7x+3y-3y+2z-2z-4w+4w=18+6 \\ 12x=24 \\ x=\frac{24}{12}=2 \end{gathered}[/tex]x=2
Now, we are going to sum (3)*2+(2).
[tex]\begin{gathered} 5x-3y-2z+4w=6\text{ }\operatorname{\lparen}\text{2}\operatorname{\rparen} \\ + \\ 2*(-3x+y+z-2w)=-5*2\text{ }\operatorname{\lparen}\text{3}\operatorname{\rparen} \\ 5x-6x-3y+2y-2z+2z+4w-4w=6-10 \\ -x-y=-4 \\ -2-y=-4 \\ y=-2+4=2 \end{gathered}[/tex]y=2.
Replacing y and x in (4) and (3):
[tex]\begin{gathered} -3(2)+2+z-2w=-5\text{ }\operatorname{\lparen}\text{3}\operatorname{\rparen} \\ -8(2)+4(2)+2z+3w=11\text{ }\operatorname{\lparen}\text{4}\operatorname{\rparen} \end{gathered}[/tex][tex]\begin{gathered} -6+2+z-2w=-5 \\ z-2w=-5+6-2 \\ z-2w=-1\text{ \lparen5\rparen} \end{gathered}[/tex][tex]\begin{gathered} -16+8+2z+3w=11 \\ 2z+3w=11+16-8 \\ 2z+3w=19\text{ \lparen6\rparen} \end{gathered}[/tex]Isolating w in (5) ans replacing in (6):
[tex]\begin{gathered} 2w=-1-z \\ w=\frac{-1-z}{2} \end{gathered}[/tex][tex]\begin{gathered} 2z+3(\frac{-1-z}{2})=19 \\ \frac{4z-3-3z}{2}=19 \\ z-3=19*2 \\ z=38-3=35 \end{gathered}[/tex]Answer: z=35.
the perimeter of a rectangle room is 60 feet. let x be the width of the room (in feet) and let y be the length of the room (in feet). select all of the questions below that could modle this situation
Answers
Given that,
The perimeter of a rectangle is 60.
The perimeter is generally defined as the length of the outline of the shape.
So, in rectangle having four sides, the perimeter would be sum of all the sides.
Length1 + length2 + length3 + length4 = perimeter
Here, length1 and length3 are equal, that are the lengths (y),
Similarly,
Length2 and length4 are equal, that is width (x).
Hence, the equation becomes,
x + y + x + y = perimeter
or
2x + 2y = 60
or
2 (x + y) = 60
Hence, the first two options are correct.
Solve x² + 6x + 7 = 0.x = -1 and x = -5 3+ √2-3+√2-3 ± √22
Answers
ANSWER
[tex]x=-3\pm\sqrt{2}[/tex]EXPLANATION
We want to solve for x in the equation:
[tex]x^2+6x+7=0[/tex]To do this, apply the quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]where a = 1, b = 6, c = 7
Therefore, substituting the values of a, b, and c into the formula and solve:
[tex]\begin{gathered} x=\frac{-6\pm\sqrt{6^2-4(1)(7)}}{2(1)}=\frac{-6\pm\sqrt{36-28}}{2} \\ \\ x=\frac{-6\pm\sqrt{8}}{2}=\frac{-6\pm2\sqrt{2}}{2} \\ \\ x=-3\pm\sqrt{2} \end{gathered}[/tex]That is the solution for x.
The blank of a line is the x-coordinate of the point where the line crosses the x-axis. It occurs when y = 0.
Answers
Answer
The x-intercept of a line is the x-coordinate of the point where the line crosses the x-axis. It occurs when y = 0.
Hope this Helps!!!
THREE OF THE STATEMENTS BELOW ARE FALSE, USE THE TYPING TOOL TO FIND AND CORRECT THE FALSE STATEMENTS IN THE WHITE BOXES. A D The hypotonuse is the longest side of the right triangle The Pythagorean theorom applies to all triangles. The hypotenuse is always adjacent to the 90° angle E The Pythagorean theorem states that 2a + 2b - 20 INTRO TO PYTHAGOREAN THEOREM The logs, a and b, will always be adjacent to the 90° angle The square of the hypotonuts is always equal to the sum of the squares of the two legs in a right triangle Statement is false. || Statement is falso. Statement is fake Correct the statement: Correct the statement: Correct the statement er notes
Answers
We are asked to correct the following statements:
A. "The hypotenuse is the longest side of the right triangle" The statement is true.
B. "The Pythagorean theorem applies to all triangles". The statement is false. The Pythagorean theorem applies to RIGHT triangles.
C. "The hypotenuse is always adjacent to the 90° angle". The statement is false. The hypotenuse is opposite to the 90° angle.
D. "The Pythagorean theorem states that 2a + 2b - 2c". The statement is false. The Pythagorean theorem states that:
[tex]a^2+b^2=c^2[/tex]E. "The logs, a and b, will always be adjacent to the 90° angle". The statement is true, since a and b represent the adjacent sides of the 90 degrees angle.
F.