Answers
Answer:
The first one is c the second is b
Related Questions
What is the outlier in this data set 23,31,28,73,19
Answers
If f(x) = 2/3x - 6, find f^-1. Justify your answer using the composition of functions f(f^-1(x))=f^-1(f(x))
Answers
Answer:
[tex]f^{-1}(x)= \frac{3}{2}(x+6)[/tex]
[tex]f(f^{-1}(x)) = f^{-1}(f(x))= x[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \frac{2}{3}x - 6[/tex]
Required
Determine [tex]f^{-1}(x)[/tex]
[tex]f(x) = \frac{2}{3}x - 6[/tex]
Represent f(x) as y
[tex]y=\frac{2}{3}x - 6[/tex]
Swap the positions of x and y
[tex]x=\frac{2}{3}y - 6[/tex]
Add 6 to both sides
[tex]x+6=\frac{2}{3}y - 6+6[/tex]
[tex]x+6=\frac{2}{3}y[/tex]
Multiply both sides by 3
[tex]3(x+6)=\frac{2}{3}y * 3[/tex]
[tex]3(x+6)=2y[/tex]
Divide both sides by 2
[tex]\frac{3}{2}(x+6)=\frac{2y}{2}[/tex]
[tex]\frac{3}{2}(x+6)=y[/tex]
[tex]y= \frac{3}{2}(x+6)[/tex]
Replace y with [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x)= \frac{3}{2}(x+6)[/tex]
Justify the result:
First, we solve for [tex]f(f^{-1}(x))[/tex]
[tex]f(x) = \frac{2}{3}x - 6[/tex]
[tex]f(x) = \frac{2}{3}x - 6[/tex] becomes
[tex]f(f^{-1}(x)) = \frac{2}{3}x - 6[/tex]
Substitute [tex]\frac{3}{2}(x + 6)[/tex] for x
[tex]f(f^{-1}(x)) = \frac{2}{3}(\frac{3}{2}(x + 6)) - 6[/tex]
[tex]f(f^{-1}(x)) = \frac{2*3}{3*2}(x + 6)- 6[/tex]
[tex]f(f^{-1}(x)) = \frac{6}{6}(x + 6)- 6[/tex]
[tex]f(f^{-1}(x)) = 1*(x + 6)- 6[/tex]
[tex]f(f^{-1}(x)) = x + 6- 6[/tex]
[tex]f(f^{-1}(x)) = x[/tex]
Next, we solve [tex]f^{-1}(f(x))[/tex]
[tex]f^{-1}(x)= \frac{3}{2}(x+6)[/tex]
[tex]f^{-1}(x)= \frac{3}{2}(x+6)[/tex] becomes
[tex]f^{-1}(f(x))= \frac{3}{2}(x+6)[/tex]
Substitute [tex]\frac{2}{3}x - 6[/tex] for x
[tex]f^{-1}(f(x))= \frac{3}{2}(\frac{2}{3}x) - 6+6[/tex]
[tex]f^{-1}(f(x))= \frac{3}{2}(\frac{2}{3}x)[/tex]
[tex]f^{-1}(f(x))= \frac{2*3}{3*2}x[/tex]
[tex]f^{-1}(f(x))= \frac{6}{6}x[/tex]
[tex]f^{-1}(f(x))= 1*x[/tex]
[tex]f^{-1}(f(x))= x[/tex]
Hence:
[tex]f(f^{-1}(x)) = f^{-1}(f(x))= x[/tex]
En un Gran Premio de Fórmula 1, diez pilotos han obtenido estos tiempos en la clasificación. ¿Cuál es el orden de salida?
Answers
Answer:
WHat did he say
Step-by-step explanation:
The cost to fill a car’s tank with gas and get a car wash is a linear function of the capacity of the tank. The costs of a fill-up and a car wash for three different customers are shown in the table. Write an equation for the function in slope-intercept form. Then, find the cost of a fill-up and a car wash for a customer with a truck whose tank size is 30 gallons.
Answers
Answer:
ok so firstly you need a graph to decipher what the answer will be
Step-by-step explanation:
So due to that error i am unable to complete the problem because you did not provide enough information
5 The temperature on Janice's birthday is -10.6°C. Which absolute value equation BEST describes how many degrees below 0°C the temperature is on Janice's birthday?
A) l–10.6l = 10
B) l–10.6l = –10.6
C) l–10.6l = –10
D) l-10.6l = 10.6
Answers
X is carrying out a series of experiments which involve using increasing amounts of a chemical. In the first experiment he uses 6g of the chemical and in the second experiment he uses 7.8g of the chemical.
(i) Given that the amounts of the chemical used form an arithmetic progression, find the total amount of chemical used in the first 30 experiments. [4]
(ii) Instead it is given that the amounts of the chemical used form a geometric progression. X has a total of 1800g of the chemical available. Show that N, the greatest number of experiments possible, satisfies the inequality
1.3N ≤ 91.
and use logarithms to calculate the value of N.
Answers
Answer:
a) 963g
b) 17
Step-by-step explanation:
i) Now we must first find the common difference of the AP
d = 7.8 -6 = 1.8
Now the sum of the AP gives the total amount of chemical used for 30 experiments
Sn = n/2 [2a + (n-1)d]
n= 30, a = 6, d= 1.8
Sn = 30/2[2(6) + (30-1) (1.8)]
Sn = 15[12 + 52.2]
Sn = 963g
ii)For the G.P the common ration is (r)= 7.8/6 = 1.3
Since r>1, sum of GP = a (r^n -1)/r-1
If sum = 1800g
1800= 6(1.3^n -1)/1.3 - 1
1800 = 6(1.3^n -1)/0.3
1800 * 0.3 = 6(1.3^n -1)
540 = 6(1.3^n -1)
540/6 = (1.3^n -1)
90 = 1.3^n -1
90 + 1 = 1.3^n
1.3^n = 91
log 1.3^n = log 91
nlog1.3 = log 91
n = log91/log 1.3
n = 1.959/0.114
n = 17
Answer:
a) 963g
b) 17
Step-by-step explanation:
i) Now we must first find the common difference of the AP
d = 7.8 -6 = 1.8
Now the sum of the AP gives the total amount of chemical used for 30 experiments
Sn = n/2 [2a + (n-1)d]
n= 30, a = 6, d= 1.8
Sn = 30/2[2(6) + (30-1) (1.8)]
Sn = 15[12 + 52.2]
Sn = 963g
ii)For the G.P the common ration is (r)= 7.8/6 = 1.3
Since r>1, sum of GP = a (r^n -1)/r-1
If sum = 1800g
1800= 6(1.3^n -1)/1.3 - 1
1800 = 6(1.3^n -1)/0.3
1800 * 0.3 = 6(1.3^n -1)
540 = 6(1.3^n -1)
540/6 = (1.3^n -1)
90 = 1.3^n -1
90 + 1 = 1.3^n
1.3^n = 91
log 1.3^n = log 91
nlog1.3 = log 91
n = log91/log 1.3
n = 1.959/0.114
n = 17
solve the system of function by graphing. Then classify the system.
f(x) = x + 4
g(x) = -5x + 10
Answers
Answer:
Step-by-step explanation:
what is the slope and intercept of this equashion y = -9x + 3
Answers
Answer:
slope is -9
y intercept is 3
Step-by-step explanation:
its in the equation
We are told that the two players, taken together, scored a total of 49 points. What is the probability that player A scored first?
Answers
Answer:
1/2 or 50% probability
Step-by-step explanation:
There are just two players, player A and player B. Since it is between this two players, for player A to score first we would have:
AB where player A is the first player to score, we wouldn't have BA since player would not be the first here
Probability = number of favorable outcomes/total number of outcomes
Therefore probability of A being the first player = number of A/total number of players
=1/2 = 0.50
There is therefore a 50% chance of A being the first player
How do you turn a percentage into a fraction?
Answers
Answer:
write the percent divided by 100
Step-by-step explanation:
1) write the percent divided by 100.
2) if the percent is not a whole number, multiply both top and bottom by 10 for every number after the decimal point.
3) reduce (simplify) the fraction.
1. Jessica starts at an elevation of 40 feet and descends 60 feet. Use the
number line to find Jessica's current elevation. Then complete the equation.
-80-70-60-50-40-30-20-10 0 10 20 30 40 50 60 70 80 90 100 110 120
---
40 + (-60) =
Answers
Answer:
Jessicas current elevation is -20 feet.
Step-by-step explanation:
Start and 40 on the number line and make a straight line to -20 on the number line with dots at 40 and -20 on the number line
The drama club is selling short-sleeved shirts for $5 Let x represent the number of short-sleeved shirts
each, and long-sleeved shirts for $10 each. They hope to ordered and let y represent the number of long-sleeve
sell all of the shirts they ordered, to earn a total of
shirts ordered.
$1,750. After the first week of the fundraiser, they sold How many short-sleeved shirts were ordered?
3
of the short-sleeved shirts and 15 of the long-sleeved
How many long-sleeved shirts were ordered?
shirts, for a total of 100 shirts.
This system of equations models the situation.
5x + 10y = 1,750
**+ y = 100
Answers
This data is Inaccurate Data
Equations of the system are When The situation is described is modeled by the following system of equations: Step first 5x + 10y = 1,750 Step second x + y = 100Where are
x = number of short-sleeved shirts y = number of long-sleeved shirtsDivide first by 5:
Then third step will be x + 2y = 350Multiplye secondly by -2:
-2x - 2y = -200
Add with the third one -x = 150 x = -150 Then, The value of x should not be negative. also, This happens because the problem is inaccurately stated. Not even selling 100 of the $10 shirts we can get to $1,750. If the total shirts sold was 200, then it secondly x + y = 200 And then x = 50, y=150 was an acceptable solution.Learn more:
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A right triangle has a base equal to 13 inches and a height equal to 18 inches. Find the area of the trlangle.
Answers
Answer:
117
Step-by-step explanation:
The formula for a triangle is base times hight divided by two. So, 13 x 18 = 234, and 234/2 = 117
ngl i kinda wanna boo anyone down :)
Answers
Answer:yo it’s me leo remember me my acount got deleted
Step-by-step explanation:
question down below thanks
Answers
Expand brackets
6x-6-4x=6x-10
Collect like terms 2x-6=6x-10
Move all terms to the left side
2x-6-6x+10=0
Collect like terms
-4x+4=0
Move +4 to the other side as a negative number
-4x=-4
Divide both sides by -4
Therefore, x is equal to 1
Which property of equality should be used with the equation c+5=78 to solve?
Answers
Answer:
the subtraction property of equality
Step-by-step explanation:
We use the "subtraction property of equality" to solve for the unknown in the equation:
c + 5 = 78
subtract 5 from both sides:
c + 5 - 5 = 78 - 5
c = 73
Two lemon creams plus four fudge cookies have 450 calories. Four lemon creams plus two fudge cookies have 420 calories. How many calories are in each cookie?
Answers
Answer:
Each fudge cookie has 80 calories.
Each lemon cream has 65 calories.
Step-by-step explanation:
We will let [tex]\ell[/tex] represent the calories in lemon creams and [tex]f[/tex] represent the calories in fudge cookies.
Two lemon creams and four fudge cookies together have 450 calories. So, we can write the following equation:
[tex]2\ell+4f=450[/tex]
And four lemon creams plus two fudge cookies together have 420 calories. So, we can write the following equation:
[tex]4\ell+2f=420[/tex]
We now have a system of equations. We can solve this by elimination.
For the first equation, we can multiply both sides by -2. This way, the [tex]\ell[/tex] will cancel when we add the two equations together.
So, the first equation becomes:
[tex]-4\ell-8f=-900[/tex]
Add this to the second equation. Hence:
[tex](-4\ell+4\ell)+(-8f+2f)=(-900+420)[/tex]
Simplify:
[tex]-6f=-480[/tex]
Divide both sides by -6. Hence:
[tex]f=80[/tex]
So, there are 80 calories in one cookie.
We can use the first equation again to find the amount of calories in one cream. We have:
[tex]2\ell+4f=450[/tex]
Substituting 80 for [tex]f[/tex] yields:
[tex]2\ell+320=450[/tex]
Then it follows that:
[tex]\ell=65[/tex]
So, there are 65 calories in each lemon cream.
Answer:
567
Step-by-step explanation:
Which expression represents
"thirty-eight less than the sum of forty and nineteen"?
A 38 – 40 + 19
® 38 - (40 – 19)
19+ (40 – 38)
D (40+ 19) – 38
Answers
Answer:
(40+ 19) – 38
Step-by-step explanation:
We need to find the expression for "thirty-eight less than the sum of forty and nineteen".
Sum of forty and nineteen = 40 + 19
38 less than the above is 40 + 19 - 38
Overall expression is :
(40 + 19) - 38
Hence, the correct option is (d) "(40+ 19) – 38".
The product of three and a number equals the sum of 16 and a number. find the number
Answers
Answer:
n = 8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
Set up the equation.
3n = n + 16
Step 2: Solve for n
Subtract n on both sides: 2n = 16Divide 2 on both sides: n = 8Find the number if 12/13 of it is 24 plz help
Answers
Step-by-step explanation:
12/13 of a number = 24
13/13 of a number = 24 * (13/12) = 26
Hence the number is 26.
Answer:
26
Step-by-step explanation:
Let n be the number. Then:
12n/13=24
n=13/12 x 24
=26 ..............
what is the interior angle sum of 31-gon
Answers
Sum of Interior Angles = (Number of Sides -2) • 180 degrees
Sum of Interior Angles = 29 * 180
Sum of Interior Angles = 5,220
The interior angle sum of 31-gon is A = 5220°
What is the sum of the interior angles of a polygon?
The sum of the interior angles of a polygon is given by the formula
Sum of Interior angles of a polygon with n sides is
nθ = 180 ( n - 2 )
where n is the number of sides
θ = angle in degrees
Given data ,
Let the interior angle sum of the polygon be = A
Now , the value of A is calculated by
The number of sides of the polygon n = 31
So , the interior angle sum of the 31-gon is given by the equation
Sum of Interior angles of a polygon with n sides is
nθ = 180 ( n - 2 )
where n is the number of sides , so
Substituting the values in the equation , we get
The value of nθ = 180 ( n - 2 )
The value of nθ = 180 ( 31 - 2 )
The value of nθ = 180 x 29
The value of nθ = 5220°
Therefore , the value of A is 5220°
Hence , The interior angle sum of 31-gon is A = 5220°
To learn more about interior angle sum of a polygon click :
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The table shows the price for different numbers of board games:
Number of Board Games Price (in dollars)
2 7
4 14
5 17.50
9 31.50
Does this table of numbers represent a proportional relationship? (5 points)
a
Yes, because 3.5 times the price is the number of board games
b
Yes, because the price is 3.5 times the number of board games
c
No, because the price of 4 board games should be $9 and not $14
d
No, because the price of 9 board games should be $40.50 and not $31.50
Answers
Answer:
We conclude that the price is 3.5 times the number of board games.
Hence, option B is true.
Step-by-step explanation:
We know that when y varies directly with x, the equation is
y ∝ x
y = kx
k = y/x
where 'k' is called the proportionality constant.
From the table,
For the point (2, 7)
k = y/x
= 7/2
= 3.5
For the point (4, 14)
k = y/x
= 14 / 4
= 7/2
= 3.5
For the point (5, 17.50)
k = y/x
= 17.5 / 5
= 3.5
For the point (9, 31.50)
k = y/x
= 31.50 / 9
= 3.5
From the above calculations, we computed that the value of the proportionality constant remains the same.
Thus, the table of numbers represents a proportional relationship.
Therefore, the equation becomes
y = kx
The price of 2 board game
y = 3.5 (2)
= 7
The price of 4 board game
y = 3.5 (4)
= 14
Therefore, we conclude that the price is 3.5 times the number of board games.
Hence, option B is true.
Help me please I need this
Answers
Answer:
i think the answer is -13
Step-by-step explanation:
b-6= -7-6
=-13
your correct answer is 13
I am sure it's correct... just go for it
Tait earns $89,000 this year. He gets a cost of living raise to compensate for yearly inflation of 396. What will his raise be next year?
Answers
Step-by-step explanation:
His raise is 3% of 89.000
.03*89.000=$2.670
His new salary is ( to get the number you need to add 89.000+2.670={$91.67})
Tait's raise in the coming year will be $2,670
Question meant to say that the inflation is 3%.
Inflation refers to the general rise in the price of goods and services in a country. It therefore makes a currency weaker because that currency will only be able to buy less than it could before.
The raise will have to be 3% as well to ensure that inflation does not affect Tait
The raise is based on his salary so can be found by:
= Amount Tait earns x Inflation rate
= 89,000 x 3%
= $2,670
In conclusion, the raise is $2,670
Find out more at https://brainly.com/question/1234186.
Describe another pattern you see in this set of numbers 20,24,28,32, and 36
Answers
(06.01)
What is the value of the expression 62 +33? Someone HELP meee
Answers
Answer:
21
Step-by-step explanation:
Trust me its correct
Mark me brainliest
Question 3 (Fill-In-The-Blank Worth 2 points)
(06.01)
What is the value of the expression 62 + 33?
Numerical Answers Expected!
Answer for Blank 1:
21
Answer:
95.
Step-by-step explanation:
62 + 33 do 60+30 then add 5
Duela de 1a 1 1/2 x 10 x 3, $ 120.00 m2
Answers
¡Hola!
¿Qué puede significar una duela de 1 a 1 1/2 x10x3 $ 120.00m2?
Este ejercicio es para que puedas acomodar la información para que quien la lea tenga una forma de entenderla claramente así:
1. Primero podríamos decir que una duela es una tabla de madera que se curva y contornea los barriles o también las tablas de los pisos.
2. Lo siguiente es para confirmar que la mesa es de excelente calidad, es decir, Primera o.
3. 1, puede hacer referencia a una unidad.
4. 1/2 x10x3 este puede ser su volumen en centímetros 1 / 2cm de alto, 10cm de largo y 3cm de ancho.
5. Por último, el precio de la duela, 120.000 dólares el metro cuadrado.
Entonces podemos organizar todo esto:
Duela de Primero, 1 unidad; 1/2 cm de alto, 10cm de largo y 3cm de ancho, con un precio de $ 120.00 el metro cuadrado.
¡Espero haber ayudado!
the greatest number that divide 60 and 84 without leaving a reminder
Answers
Step-by-step explanation:
HCF of 60 and 84 = 6
So the required greatest number that divides 60 and 84 without leaving remainder is 6.
4 divided by 60 is 15
4 divided by 84 is 21
Drag and drop each pair of lines into the correct category to indicate whether the pair of lines are parallel, perpendicular, or neither.
1/7x + y = 9; y = -7x
y = 3x - 3; 12x - 4y = 12
7y = 2x + 1; 14x + 4y = 12
x - 4y = 18; y = x + 4
3x - 4y = -1; 3y = -4x + 5
Parallel Perpendicular Neither
Answers
Answer:
Step-by-step explanation:
(1). [tex]\frac{1}{7}[/tex] x + y = 9 and y = - 7x ( Neither ) ; lines intersect.
(2). y = 3x - 3; 12x - 4y = 12 ( Neither ) ; Lines are overlapped or both equation are of the same line.
(3). 7y = 2x + 1; 14x + 4y = 12 ( Perpendicular ) ; [tex]m_{1}[/tex] = [tex]\frac{2}{7}[/tex] and [tex]m_{2}[/tex] = - [tex]\frac{7}{2}[/tex] , slopes are opposite reciprocals.
(4). x - 4y = 18; y = x + 4 ( Neither ) ; lines intersect.
(5). 3x - 4y = - 1; 3y = - 4x + 5 ( Perpendicular ) ; [tex]m_{1}[/tex] = [tex]\frac{3}{4}[/tex] and [tex]m_{2}[/tex] = - [tex]\frac{4}{3}[/tex] , slopes are opposite reciprocals.
please help!!!! find x and y
Answers
9514 1404 393
Answer:
(x, y) = (10, 2)
Step-by-step explanation:
The upper angle marked with an expression in x and y is supplementary to the angle marked 70°. The lower angle marked with an expression in x and y is an alternate interior angle with respect to the one marked 70°, is equal to that. This gives the two equations in x and y:
6x +10y +30 = 110
4x +10y +10 = 70
Subtracting the second equation from the first gives ...
2x +20 = 40
x +10 = 20 . . . . . divide by 2
x = 10 . . . . . . . . . subtract 10
Substituting into the second equation gives ...
4(10) +10y +10 = 70
4 + y + 1 = 7 . . . . . . . . divide by 10
y = 2 . . . . . . . . . . . . . . subtract 5
The values of x and y are 10 and 2, respectively.
Answer:
9514 1404 393
Step-by-step explanation: