First, I should point out that g(x) should be written as g(x)=(x+2)/3, otherwise the problem is confusing.
[tex]f(x)=3x-2 \enspace g(x)=\frac{x+2}{3}[/tex]
(A) [tex]f(g(x))=3(\frac{x+2}{3})-2=x\\g(f(x))=\frac{3x-2+2}{3}=x[/tex]
(B) Since [tex]f(g(x))=x[/tex] and [tex]g(f(x))=x[/tex], it holds that
[tex]f(g(x))=g(f(x))[/tex] for all x. This means the composed functions are *identical*
A
f(g(x)) = f([tex]\frac{x+2}{3}[/tex]) = 3([tex]\frac{x+2}{3}[/tex]) - 2 = x + 2 - 2 = x
g(f(x)) = g(3x - 2) = [tex]\frac{3x-2+2}{3}[/tex] = [tex]\frac{3x}{3}[/tex] = x
B
Since both composite functions f(g(x)) and g(f(x)) equal x
This indicates that the functions f(x) and g(x) are inverse functions
A kennel has 16 employees to watch over 400 dogs. What is the ratio of dogs to employees?
400/16= 25
answer: it's a 16 to 25 ratio
one worker covers 25 dogs
25 : 1
the ratio of dogs : employees = 400 : 16
to simplify the ratio divide both parts by 16
400 : 16 = 25 : 1 ← in simplest form
(Fifty points.)
Two functions, P and Q, are described as follows:
Function P
y = 5x + 3
Function Q
The slope is 2 and the y-intercept is 4.
How much more is the slope of function P than the slope of function Q?
A. 3
B. 5
C. 7
D. 8
A
the equation of a line in ' slope-intercept form ' is
y = mx + c ( m is the slope and c the y-intercept )
y = 5x + 3 is in this form with slope m = 5
function Q has equation y = 2x + 4
the slope of function P is 3 more than function Q
−4x + 3y = 15, where x is time and y is velocity in kilometers per hour. Use this function to determine when a certain particle will reach 40km/hr.
26.25 hours = 26 hours 15 minutes
substitute y = 40 into the equation and solve for x
- 4x + 120 = 15 ( subtract 120 from both sides )
- 4x = - 105 ( divide both sides by - 4 )
x = 26.25 hours = 26 hours 15 minutes
determine the truth value of the statement when p is T, q is F, and r is F
( p ↔ q ) → ( ∼ p ∨ r )
Given P is T, q is F and r is F.
Let us find p ↔ q first.
↔ is called bi-conditional operator and is true when p and q both are matched.
Since here p is T and q is F, p↔q is F. ( Since p and q are not matching)
~p v r = ~T v F = F v F = F
Hence (p↔q)→(~pvr) = F → F = T (Since conditional operator → is false if and if first proposition is T and second proposition is F, for all other values it is T)
Solve the system Solve the system of equations of equations
{y= 2x+7 y = 25−x
A (19, 6)
B (6, 19)
C (-6, -19)
D (19, -6)
E none of these
B
since both equations express y in terms of x we can equate the right sides
2x + 7 = 25 - x ( add x to both sides )
3x + 7 = 25 ( subtract 7 from both sides )
3x = 18 ( divide both sides by 3 )
x = 6
substitute x = 6 into either of the 2 equations for y
y = 2x + 7 = ( 2 × 6 ) + 7 = 12 + 7 = 19
solution is (6, 19 )
**PLEASE HELP** Easy brainliest!
Enter a number that correctly completes the following statement.
The point (12, 5) is ______ units from the origin.
The Pythagorean theorem is used for finding the distance between two points. You can consider the line from the origin to (12, 5) to be the hypotenuse of a right triangle with sides 12 and 5 (parallel to the x- and y-axes, respectively). Then the relation between these and the hypotenuse length is
... d² = 12² + 5² = 144 + 25 = 169
... d = √169 = 13
The point (12, 5) is 13 units from the origin.
Okay...... so for this problem you need to use the Pythagorean Theorem. So...
12^2 + 5^2
144+25
169
this = square root of 13
so.... The point (12,5) is 13 units from the origin.
A car depreciated (decreased in value) by 25% during the first year. If the car was purchased for $28,000, what is the car worth today
Show your work
Answer:
$21,000
Step-by-step explanation:
The cost of car=$ 28,000
A car is depreciated by 25%
Now, the price of car=$28000(1-)[tex]\frac{25}{100}[/tex]
The price of the car= $28000([tex]\frac{100-25}{100}[/tex])
The price of the car= $28000([tex]\frac{75}{100}[/tex])
The price of the car= $280×75
The price of the car= $21,000
The car worth today $21,000
Hence the correct answer is $ 21,000
BRAINLIEST!!
A cleaning company charges x dollars per hour to clean floors and y dollars per hour to clean the rest of a house.
• When the company spends 2 hours to clean floors and 3 hours to clean the rest of a house, the total charge is $80.
• When the company spends 1 hour to clean floors and 4 hours to clean the rest of a house, the total charge is $100.
Which ordered pair represents the hourly charges to clean floors and to clean the rest of the house?
A) (2, 12)
B) (4, 24)
C) (12, 2)
D) (24, 4)
Set up the equations:
2x+3y=80
1x + 4y = 100
solve for x and y:
1x + 4y = 100
x = 100-4y
plug into first equation
2(100-4y)+3y=80
200-8y+3y=80
y=120/5=24
x = 100-4y=100-96=4
So the charges are (x,y)=(4,24)
So the correct answer (B)
A survey of 2,000 doctors showed that an average of 3 out of 5 doctors use brand X aspirin. How many doctors use brand X aspirin? (Hint: Solve for X)
Show your work
2000 times 0.60 = 1200 doctors
3/5=0.6
x= 2000* 3/5
x=2000*0.6
x=1200
so... 1200 doctors use brand X aspirin.
What is the y-coordinate of A'? (picture included)
y- coordinate 0f A' = 2
note that the coordinates of A(1, 2 ) and the centre of dilatation (4, 2) both have the same y- coordinate 2
This means they are both on the horizontal line y = 2
and so the y- coordinate of A' will also be 2
The graph of an equation is shown below:
Based on the graph, which of the following represents a solution to the equation?
(−2,−3)
(3, 1)
(1, 3)
(3, 2)
pleaseee help will give brainliest
(1, 3 )
to determine if the given points are a solution to the equation
They must lie on the given line to be a solution
the only one that is on the line is (1, 3 ) and is therefore the only solution
The Fall Festival charges $0.75 per ticket for the rides. Kendall bought 18 tickets for rides and spent a total of $33.50 at the festival. She only spent her money on ride tickets and admission into the festival. The price of admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Define your variables.
(b) Write a linear equation to calculate the cost for anyone who only pays for festival admission and rides
(c) Explain your answer to Part B. I NEED HELP ASAPl
Answer:
y = 0.75x+20
Step-by-step explanation:
Given that there is an admission ticket fixed and extra cost of 0.75 per ticket for the rides.
This means even if there is no ride used, enterer has to pay a fixed amount for admission.
Let us find out this admission cost from the given information
If y is the total cost and x no of rides
a) x is the no of rides and y the total cost
b) y = 0.75x+20 is the linear equation to calculate the cost for anyone who only pays for festival admission and rides
(c)
Total cost = Admission charges +0.75 * no of ride tickets.
then y = 0.75x+C
where C is the admission fee
Kendall bought 18 tickets i.e. x= 18 and y = 33.50
33.50 = 0.75(18)+C
33.50=13.50+C
C = 33.50-13.50 = 20.00
Hence admission fee = 20
A theater can seat 550 people. The number of rows is 3 less than the number of seats in each row. How many rows of seats are there?
The number of rows will be a divisor of 550 such that the quotient is 3 more.
... 550 = 1×550 = 2×275 ≈ 5×110 = 10×55 = 11×50 = 22×25
Factors 22 and 25 differ by 3.
The number of rows of seats is 22.
_____
The number of seats in a row is 25.
The theater has 22 rows of seats. To find this, we solve the equation x(x - 3) = 550, where x is the number of seats per row, leading to x = 25 seats per row and 22 rows after subtracting 3.
To find out how many rows of seats are in the theater with a seating capacity of 550, where the number of rows is 3 less than the number of seats in each row, we can set up an equation to solve for the number of rows. Let the number of seats per row be represented by x, and the number of rows will then be x - 3. Since the total number of seats in the theater is the product of the number of rows and the number of seats per row, we have the equation x(x - 3) = 550.
Now, we will factor this quadratic equation to find the value of x.:
x² - 3x - 550 = 0
Factoring this, we find that it breaks down into (x - 25)(x + 22) = 0. We can then find the value of x by setting each factor equal to zero:
x - 25 = 0: x = 25x + 22 = 0: x = -22 (negative values are not feasible for number of seats)We ignore the negative solution since we cannot have a negative number of seats. Hence, there are 25 seats in each row. To find the number of rows, we subtract 3 from the number of seats per row: 25 - 3 = 22 rows.
Therefore, the theater has 22 rows of seats.
Am i right geometry below
I believe so. :) correct me if i'm wrong.
What is the greatest integer k such that 2k is a factor of 67!?
67!/2 = k = 18 235 555 459 094 342 644 124 929 548 302 732 213 583 817 657 024 762 296 850 814 250 133 981 218 471 936 000 000 000 000 000
about 1.82×10⁹⁴
Answer:
k=64
Step-by-step explanation:
To find out the greatest integer such that 2^{k}is a factor if 67!
We divide the quotients by 2 and then finally add all the quotients.
67/2 = 33.5 --------> 33
33/2 = 16.5 ---------> 16
16/2 = 8 --------> 8
8/2= 4 ---------> 4
4/2 = 2--------> 2
2/2 = 1 ----------> 1
k= 33+16+8+4+2+1
= 64
Hence, 64 is the greatest integer such that 2^{k} is a factor of 67!.
Angle JKL
is a straight angle.
The measure of angle JKM is 120 degrees.
The measure of angle MKL is X degrees
What is the value of X?
The value for X, the measure of angle MKL, is not specifically given in the question. Since angle JKL is a straight angle of 180 degrees, X can be any value up to 180 degrees.
Explanation:In mathematics, a straight angle is defined as an angle of 180 degrees. In the scenario described with angle JKL, it is mentioned that this is a straight angle. Given that angle MKL is a part of the straight angle, its degree measure X is a component of those 180 degrees. The specific value of X is not given in the question, and it can be any number less than or equal to 180, provided the other part of the angle KJM is equal to 180- X.
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The measure of angle MKL is 60 degrees.
Finding the Measure of Angle MKL
To determine the value of X in this problem, we first need to understand that a straight angle measures 180 degrees. The problem states that angle JKL is a straight angle, so:
Angle JKL = 180 degrees
Next, we have the measure of angle JKM given as 120 degrees. Since angle JKL is made up of angle JKM and angle MKL, we can set up the following equation to find the measure of angle MKL, which is X:
Angle JKM + Angle MKL = Angle JKL
Substituting the known values:
120 degrees + X = 180 degrees
To find X, subtract 120 degrees from both sides:
X = 180 degrees - 120 degrees = 60 degrees
Therefore, the measure of angle MKL is 60 degrees.
Approximate the data using the line y = 0.25x + 3. Find the data point that has the residual with the greatest absolute value. Give that data point and its associated residual. Data point: (20, 6); Residual = -2.00 Data point: (15, 5); Residual = 6.75 Data point: (5, 3); Residual = -1.25 Data point: (10, 10); Residual = 4.50
Solution: We are given data points and associated residuals:
Data Point Residual Absolute value(Residual)
(20,6) -2.00 2.00
(15,5) 6.75 6.75
(5,3) -1.25 1.25
(10,10) 4.50 4.50
From the above absolute value(Residual) column, we clearly see the data point (15,5) has the residual with greatest absolute value of 6.75.
Therefore, the data point and its associated residual is:
(15,5) and 6.75
Answer:
Data Point: (10,10); Residual = 4.50
Megan is going on a long distance road trip. She drives for 13 miles before being able to travel at a constant speed using cruise control. The equation used to find her total distance traveled is shown below.
y = 59x + 13
If y is the total number of miles driven, and x is the number of hours driven after reaching 13 miles, which statement best describes the rate of change in the distance traveled?
A. For every 13 hours, she will drive 72 miles.
B. For every two hours, she will drive 59 miles.
C. For every hour, she will drive 59 miles.
D. For every hour, she will drive 72 miles.
The rate of change of y (miles traveled) with respect to x (time in hours) is 59, the coefficient of x. The appropriate choice is ...
... C. For every hour, she will drive 59 miles.
The equation y = 59x + 13 shows that Megan's rate of change in distance traveled is 59 miles for every hour driven at cruise control, after the first 13 miles. So, the correct answer is C. For every hour, she will drive 59 miles.
The equation y = 59x + 13 represents Megan's total distance traveled after driving the first 13 miles without cruise control. The variable y stands for the total number of miles driven, and x represents the number of hours driven at a constant speed using cruise control. To identify the rate of change in the distance traveled, we look at the coefficient of x in the equation, which is 59. This coefficient indicates how many miles are added to the initial 13 miles for every hour of driving at cruise control. Therefore, for every hour, Megan will drive 59 miles after the initial 13 miles are accounted for. It is important to note that the initial 13 miles are a fixed distance and do not change with time. Thus, the correct statement describing the rate of change in the distance traveled is C. For every hour, she will drive 59 miles after the first 13 miles.
I’m literally begging u for help, I need help with the last question in the pic I’m
Jeremy is opening a savings account earning simple interest. he plans to deposit his $50 birthday money and leave the account alone until he goes to college. he will earn $5 per year in interest.
I just need help with the last question plzzzz
If the second coordinate of the ordered pair represents the dollar amount in Jeremy's savings account, then adding 10 to it means that $10 has been added to Jeremy's account.
Find the coordinates of the midpoint of HX. H(5.5, -4.75) and X(3.75, -2.75)
( 4.625, - 3.75 )
the midpoint of (x₁, y₁ ) and (x₂, y₂ ) is
[[tex]\frac{1}{2}[/tex](x₁ + x₂ ), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]
here (x₁, y₁ ) = (5.5, - 4.75 ) and (x₂, y₂ ) = (3.75, - 2.75 )
[ [tex]\frac{1}{2}[/tex](5.5 + 3.75 ), [tex]\frac{1}{2}[/tex](- 4.75 - 2.75 ) ]
= (4.625, - 3.75 ) ← midpoint of HX
WILL GIVE BRAINLIEST ANSWER PLEASE HELP In a theater there are 12 seats on the first row and 16 seats in the second row. the number of seats in a row continues to increase by 4 with each additional row
a. write and iterative (explicit rule to model the sequence formed by the number of seats in each row. Show your work
b. use the rule to determine which row has 60 seats. Show your work
(a) [tex]a_{n}[/tex] = 4n + 8
(b) row 13 has 60 seats
(a)
the sequence of seats is an arithmetic sequence whose n th term is
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1 )d
where [tex]a_{1}[/tex] is the first term and d the common difference
here the sequence is 12, 16, ....
with [tex]a_{1}[/tex] = 12 and d = 16 - 12 = 4, thus
[tex]a_{n}[/tex] = 12 + 4( n - 1 ) = 12 + 4n - 4 = 4n + 8
(b)
calculate the number of rows n when 60 seats
solve 4n + 8 = 60 ( subtract 8 from both sides )
4n = 52 ( divide both sides by 4 )
n = 13 ← number of rows
Layla is saving up money for a trip. She already has $650 saved and plans to save an additional $150 each month for the trip.
Complete the equation that represents the total amount of money Layla has saved, s, after m months.
s=?
The equation that represents the total amount of money Layla has saved, s, after m months is s = 150m + 650.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Layla is saving up money for a trip. She already has $650 saved and plans to save an additional $150 each month for the trip.
The equation will be written as:-
S = 150m + 650
Here, 650 is how much she already saved and 150 is how much per month.
Therefore, the equation that represents the total amount of money Layla has saved, s, after m months is s = 150m + 650.
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If f(x) = x + 8 and g(x) = -4x - 3, find (f - g)(x)
Melissa put her cat, Herman, on a diet and kept track of his weight. At the end of 4 weeks, she recorded Herman's weight change as −4 1/2 ounces. She noticed that he had lost the same amount of weight each week. What is Herman's weight change each week of the diet? Enter your answer in the box.
-103
if he lost the same weight each week that means -412 (the weight he lost) ÷ 4 (number of weeks) = -103 (amount of weight lost in one week)
Answer: -1 1/8
Step-by-step explanation: When you have a problem like this, you have to divide.
So you turn the improper fraction into a mixed number which (4 1/2 turns into 9/2) and then you do KCF (Keep Change Flip). So you keep the 9/8, change division into multiplication, and since we are going to put the four over a 1 like this 4/1, we need to change it into 1/4. Then you multiply across. 9x1=9 and 2x4=8 so it would be 9/8. But it's an improper fraction right? So you do long division, and you get -1 1/8.
Solve x -2/3(3x - 4) + 3x = 5/6 is x -19/6, 11/6, 21/6, 29/6
Answer:
x=-11/12
Step-by-step explanation:
Given an equation for x
x -2/3(3x - 4) + 3x = 5/6
We are asked to find the value of x.
We use equation rules to solve
To get rid of denominator in fraction, let us multiply the whole equation by 6.
6x-4(3x-4) +18x = 5
Simplify:
-6x+18x+16 =5
12x = 5-16 = -11
x = -11/12
Answer:
- 11/6
Step-by-step explanation:
What is the product of -1.24 and 4.25?
Answer:
-5.27
Since when multiplying a positive and negative integer the answer will become negative
The product of -1.24 and 4.25 is -5.27, found by performing the mathematical operation of multiplication.
Explanation:Given the question, you are asked to calculate the product of -1.24 and 4.25.
Multiplying two numbers together is a basic mathematical operation. To find the product of these two numbers, you can simply multiply them together.Which in this case, -1.24 * 4.25 equals -5.27
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Given: ΔABC, AB ≅ BC, BE − median of ΔABC, m∠ABE = 40°30' Find: m∠ABC, m∠FEC
Answer:
Given: A Δ ABC in which , AB ≅ BC, BE − median of ΔABC, m∠ABE = 40°30'
To Find: ∠ABC, ∠ CE B,∠A E B
Solution: In Δ ABC , BE is the median.
So, AE= EC
Now, In Δ A E B and Δ CE B
AE = EC [ BE is median]
BE is common.
AB=BC [given]
Δ A E B ≅Δ CE B { SSS Congruency]⇒S→side
So, ∠ABE=∠C BE [ C PCT]
∴ ∠ABC=2×∠ABE=2×40°30'=81°
∠B EA =∠C E B [ C P CT]
Also,∠B A C = ∠BC A=k° [As AB =BC , if opposite sides are equal , then angle opposite to them are equal]
∠A+ ∠B+∠C=180°[ angle sum property of triangle]
k°+81°+k°=180°
2 k°=180°-81°
2 k°=99°
k°=99°/2
k°=49°30'[1°=60']
In Δ A E B, ∠ABE=40°30',∠A=49°30',∠A E B=?
∠ABE+∠A+∠A E B=180°[ angle sum property of triangle]
40°30'+49°30'+∠A E B=180°
90°+∠A E B=180°
∠A E B=180°-90°
∠A E B=90°
As, ∠B EA =∠C E B
So,∠C E B= 90°
So, BE is perpendicular bisector.
The measure of the angle ∠ABC and ∠BCA are both 69°45'. and ∠FEC measures 99°.
How to find the angles?∠ABE and ∠BEC are opposite angles formed by the intersecting lines AB and BE, and BC and BE respectively.
Therefore, they are congruent.
The sum of the interior angles of a triangle is always 180°. So, we can find ∠ABE by subtracting ∠BEC from 180°.
Since m∠ABE = 40°30', we have:
∠BEC = ∠ABE = 40°30'
Since AB ≅ BC, the two sides are congruent.
This means that ∠ABC and ∠BCA are also congruent angles. Let's call their measure x.
Using the fact that the sum of the angles in a triangle is 180°, we can set up an equation:
∠ABC + ∠BCA + ∠BAC = 180°
Since ∠BCA = ∠ABC = x, we can substitute these values in:
x + x + 40°30' = 180°
Adding the like terms:
2x + 40°30' = 180°
Subtracting 40°30' from both sides:
2x = 180° - 40°30'
2x = 139°30'
Dividing both sides by 2:
x = 69°45'
So, ∠ABC and ∠BCA are both 69°45'.
To find ∠FEC, we can use the fact that the sum of the angles in a triangle is 180°. Since ∠BEC = ∠ABE = 40°30', we can find ∠FEC:
∠FEC = 180° - ∠BEC - ∠BCE
Substituting the values we know:
∠FEC = 180° - 40°30' - 40°30'
Simplifying:
∠FEC = 180° - 81°
∠FEC = 99°
Therefore, ∠FEC measures 99°.
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Which pair of angles shares ray A.F as a common side? DAF and DAB EAF and CAE BAF and EAD BAF and FAD
Look for the adjacent letters A.F or F.A in the names of the pair of angles.
The appropriate choice is ...
... BAF and FAD
Answer:
BAF and FAD
Step-by-step explanation:
In order for an angle to have A.F as a side, it must have the letters A.F or FA in its name.
In DAF, the angle is made of rays AD and A.F. In DAB, the angle is made up of rays AD and AB. This is not the correct pair.
In EAF, the angle is made of rays AE and A.F. In CAE, the angle is made up of rays AC and AE. This is not the correct pair.
In BAF, the angle is made of rays AB and A.F. In EAD, the angle is made up of rays AE and AD. This is not the correct pair.
In BAF, the angle is made up of rays AB and A.F. In FAD, the angle is made up of rays A.F and AD. This is the correct pair.
Lars bought 3 jars of marbles. Each jar has 42 marbles, of which 13 are red. Lars can use the calculation below to find the total number of red marbles. 3×(13×42) How can Lars simplify the calculation using only the associative property of multiplication? Drag and drop the appropriate number or expression into each box. 13342 (3×13) (13×42) ×
I had a test and this was one of the questions and the answer it said was (3x1/3) x 42 so you dont have to figure it out. hope this helps anyone who needs it. :)
Steve sang a song so bad it made 10 students laugh. Each of those 10 students made 10 other students laugh. If Steve was laughing at himself too, how many students, including Steve, were laughing by the end?
Answer:
The correct answer is:
New students laughing at Steve
10 × 10 = 100
Add all the students laughing at Steve
10 + 100 = 110
Add Steve
110 + 1 = 111
There were 111 students in total laughing.
Step-by-step explanation:
Answer:
111
Step-by-step explanation: