Answer:
No, the bottle will not be empty
Determine by composition whether f(x) = 3x + 18 and g(x)=x-6 are inverses of each other.
O No, f(g(x)) + X
O No, f(g(x)) = x
O Yes, f(g(x)) = g(f(x)) = x
O Yes, f(g(x)) = g(f(x)) * x
Thus, (x) = 3x + 18 and g(x)=x-6 are not inverses of each other.
Two function are inverse if they do undo or cancel each other, which means
f and g are inverse if
f(g(x)) = x and g(f(x)) = x
Here, f(x) = 3x + 18 and g(x)=x-6
Lets check by substituting the values in the formula
⇒ f(g(x))
⇒ f(x-6)
⇒ (3x + 18) - 6
⇒ 3x - 12
⇒ x = 4
g(f(x))
⇒ g(3x + 18)
⇒ 3(x-6) + 18
⇒ 3x - 18 + 18
⇒ 3x
⇒ x = 1/3
What is composition maths?A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.
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Mel and 5 friends went to the go-kart track. Four people rented helmets for $3 each. The total cost to
rent the helmet and to ride the karts was $75. What was the cost to ride the karts for each person?
The cost of a ride for an individual person will be $10.5
It is given that Mel and 5 friends went to ride which makes the Total number of people for the Ride will be 6. Also, Four of them rented Helmets for the rides each helmet cost $3. It is also given that the total cost of helmets and rides is $75. From this we get :
Total people = 6, Helmet cost = 4*3 = $12, and Total cost = $75
Taking the cost of a ride as 'x' we get the equation representing this statement:
=> 4*3 + 6x = 75 => 6x = 63
=> x = 10.5
We get value of x = $75.
Hence, we get the cost of an individual ride $75.
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The function has a minimum or maximum. Looking for help with screenshot
Answer:
The function has a minimum of -1 at x = 3
The function is increasing on the interval: (3,∞)
The function is decreasing on the interval (-∞,3)
Step-by-step explanation:
Since our parabola opens upwards on the graph, the function has a minimum.
The minimum is the lowest x-value and y-value in the function.
From left to right, the function is moving downwards (decreasing) from x = -∞ to x = 3.
From left to right, the function is moving upwards (increasing) from x = 3 to x = ∞
Select the values that make the inequality -b < 8 true. Then write an equivalent inequality, in terms of b. (Numbers written in order from least to greatest going across.)
Answer:
true
Step-by-step explanation:
Answer: true
step by step explanation:
the middle term of the expansion
[tex] (ax + ay)^{n} [/tex]
is
[tex]14580x ^{3} y^{3} [/tex]
find the value of a and the value of n, where a, n are elements of N.
Answer:
Hello,
a=3
Step-by-step explanation:
Since the middle term is x^3y^3 ==> n=6
Coefficient of x^3y^3 is 20 (triangle de Pascal)
So a^6= 14580/20=729 ==> a=3
1/2 ( 2p + 9 ) = p + 5 solve equation
that is impossible to solve because both sides do not equal eachother
Another job is advertising leaflets printed on sheets of A4 paper
The sheets are the fold into thirds as shown
What are the measurements in millimetres of each fold leaflet?
The measurement of the fold leaflet shorter dimension stays same but the longer side becomes 99 mm.
What are referred as dimension?In mathematics, dimensions are the measurements of the size or distance between an object, region, or space in one direction. In layman's terms, it refers to the measurement of something's length, width, and height.
Dimensions are commonly expressed as follows:
LengthBreadthWidthHeight or DepthA leaflet is mainly folded into thirds just on long side, so the short side remains unchanged while the long dimension has become 1/3, or 297/3 = 99 mm.
The final dimensions are
210 mm × 99 mm
Therefore, the measurement of the sorter side of the fold leaflet remains same but longer side becomes 99 mm.
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The complete question is-
Another job is advertising leaflets printed on sheets of A4 paper (210 x 297 mm).
The sheets are then folded into thirds as shown.
What are the measurements in millimetres of each folded leaflet?
on july 1 2022 ivanhoe company pays 17,500 to sheridan company for a one year insurance company both companies have fiscal years ending in dec 31
Answer:
what is the question?
()()()()()()()()()()()()()()
Students were asked how they travel to
school. 37% of the students said they
travel by train.
Of these, 24% live more than seven miles
from their school. What percentage of the
students travel over seven miles to school
by train? Give your answer to 2 d.p.
the percentage of the students travel over seven miles to school by train is 9 %.
Let the total number of students be represented by variable x
now, 37 % of them travel by train.
So, we get that:
By train = 37 % of x
By train = 37 / 100 (x)
By train = 0.37 x
Now, 24 % of them lives 7 miles away from the school.
So, 7 miles away = 24 % of 0.37 x
= 24 / 100 ( 0.37 x )
= 0.24 ( 0.37 x)
= 0.09 x
In percentage:
= 9 %
Therefore, we get that, the percentage of the students travel over seven miles to school by train is 9 %.
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The median for the given set of six ordered data values is 29.5
7 12 23 __ 41 50 What is the missing value?
Answer: 36
Step-by-step explanation:
Median of an even number data set, you would add the two middle numbers divided by 2. Answer is 36. See attached solution
The dose of posaconazole in the treatment of oropharyngeal candidiasis is 100 mg twice a day on the first day and then 100 mg once a day for the next 13 days. Posaconazole oral suspension (posaconazole, 40 mg/mL) is available in 4-fluidounce bottles. How many bottles should be dispensed to meet the dosing requirements?
The number of 4-fluidounce bottles that should be dispensed to meet the dosing requirements for the treatment of oropharyngeal candidiasis is 37.5 bottles.
How is the number of bottles determined?To determine the number of 4-fluidounce bottles, we apply mathematical operations of addition, subtraction, division, and multiplication.
First, the total dosage is determined as 1,500 mg.
Since 40 mg/mL is available in 4-fluidounce bottles, the total dosage is divided by 40 mg/mL to determine the number of bottles required.
Data and Calculations:Dose of posaconazole for the first day = 100 mg twice
= 200 mg (100 mg x 2)
The total number of days for the dosage = 14
Dose for next 13 days = 1,300 mg (100 mg x 13)
Total dosage = 1,500 mg (200 mg + 1,300 mg)
40 mg/mL = 4-fluidounce bottle
1,500 mg = 37.5 bottles (1,500/40)
Thus, the number of 4-fluidounce bottles is 37.5 bottles.
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The width of a painting is 24 centimeters shorter than its length, x. The area of the painting is 4,081 square centimeters. Which equation could be used to find the dimensions of the painting?
We can't find dimension of the painting because length of painting is imaginary form.
WHAT IS A CUBOIDAL OBJECT ?
Six rectangles make up a cuboid, each of which is referred to as a face. The cuboid's six faces are denoted by the letters ABFE, DAEH, DCGH, CBFG, ABCD, and EFGH in the previous diagram.
A pair of opposing faces is formed by the top face ABCD and the bottom face EFGH. The opposing faces ABFE, DCGH, and DAEH, CBFG, have similar pairings. Adjacent faces are any two faces that are not opposite faces.
Consider the faces ABCD, ABFE, BCGF, CDHG, and ADHE that are close by.
CALCULATIONThe width of painting = x- 24
the length of painting = x
according to question
area of painting = 4081 [tex]cm^{2}[/tex]
i.e. [tex]x * (x - 24) = 4081[/tex]
[tex]x^{2} -24x-4081 = 0[/tex]
applying shridharacharya formula :
[tex]x = (-b ± √(b2 - 4ac)) / 2a.[/tex]
it has imaginary roots !!!
Roots: -12 + 62.745517768204i, -12 - 62.745517768204i
Root Pair: -12 ± √(3937)i
Factored: f(x) = (x + 12 + 62.745517768204i)(x + 12 - 62.745517768204i)
Discriminant: -15748
Vertex: (-12, 3937)
Sum of Roots (-b/a): -24
Product of Roots (c/a): 4081
∴ We can't find dimension of the painting because length of painting is imaginary form.
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ow:
(7-21)-(4+ 8) =
Answer:-26
Step-by-step explanation:
Answer:-14-12=-26
Step-by-step explanation: PEMDAS. You do the first parentheses which is 7-21, which will get you -14. Then you do the second parentheses, 4+8. That will get you 12. Then since there’s no multiplication/division, you go to addition/subtraction and since there’s a subtraction symbol in between the parentheses, that’s what you do. -14-12 which will get you -26.
Hope this helps!
Btw PEMDAS stands for (for those people who don’t know or don’t remember)
Parentheses
Exponents
Multiplication*
Division*
Addition’
Subtraction’
*do both together, whichever one comes first when reading it
’do both together, whichever one comes first when reading it
( m n ) (x) for x = −3
The value of the composite function (mn)(-3) is 9
How to determine the value of the composite function?The given parameters are:
m(x) = x
n(x) = -3
The composite function is given as
(mn)(x)
The above composite function is calculated as
(mn)(x) = m(x) * n(x)
Substitute -3 for x in the above function
So, the above function becomes
(mn)(-3) = m(-3) * n(-3)
So, the above function becomes
(mn)(-3) = -3 *-3
Evaluate the product in the above equation
So, we have
(mn)(-3) = 9
Hence, the value of the composite function (mn)(-3) is 9
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Complete question
If m(x) = x and n(x) = -3, calculate ( m n ) (x) for x = −3
The equationnnnnnnnnnnnnn
Answer:
Step-by-step explanation:
9 ( 3 + 4) - 8 / 4 =
( use BIDMAS)
first step is brackets:
9 (7) - 8 / 4 =
next step is division:
63 - (8 / 4) =
63 - 2 = 61
hope that helps :)
Answer:
35
Step-by-step explanation:
thx for the pionts loolllll
Order these decimals from least to greatest.
A) 12.205
B) 12.2
C) 12.25
PLEASEEE BE ACCURATE! FIRST PERSON WHO RESPONDS CORRECTLY GETS BRAINLIST!!
Shinji reads 25 pages of a book every night. 1. Write an equation that represents how many pages Shinji reads (ppp) in some number of nights (nnn).
The equation that represents how many pages Shinji reads is P(n) = 25n
How to write an equation that represents how many pages Shinji reads?The given parameters are:
25 pages = 1 night
Multiply both sides by n
So, we have:
25 * n = 1 * n nights
Express as a function
25 * n = P(n)
Rewrite as
P(n) = 25n
Hence, the equation that represents how many pages Shinji reads is P(n) = 25n
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Answer:
Step-by-step explanation:
Jonathan invests $4100 in two different accounts. The first account paid 4 %, the second account paid 13 % in interest. At the end of the first year he had earned $299 in interest. How much was in each account?
$ _____________ at 4 %
$ _____________ at 13 %
The amount invested in the account that paid 4% interest is $2,600
The amount invested in the account that paid 13% interest is $1,500.
What are the simultaneous equations that represent the equation?a + b = 4100 equation 1
0.04a + 0.13b = 299 equation 2
Where:
a = amount invested in the account that paid 4% interest
b = amount invested in the account that paid 13% interest
How much was invested in each account ?
The first step is to multiply equation 1 by 0,04
0.04a + 0.04b = 164 equation 3
Subtract equation 3 from equation 2
0.09b = 135
b = 135 / 0.09
b = $1500
a = 4100 - 1500 = $2,600
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one fifth times w equals negative one eight what is w
If one fifth times w equals negative one eight then w = -5/8
What is Rational numbers?
A rational number is any number that can be written as a fraction, where both the numerator (the top number) and the denominator (the bottom number) are integers, and the denominator is not equal to zero. In other words, a rational number can be expressed as p/q, where p and q are both integers and q ≠ 0.
given that one fifth times w equals negative one eight
we have to find the value of w
one fifth = 1/5
one fifth times w = (1/5)* w
negative one eighth = - 1/8
now according to the question
one fifth times w equals negative one eight
(1/5) *w = -1/8
now solve the equation , we get
w= (5) * (-1/8)
= -5/8
Hence ,if one fifth times w equals negative one eight then w = -5/8
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if i compare 0.10__0.01 what would the answer be?
The answer will be 0. 10 > 0. 01 . Option B
How to compare the valuesGiven the values as;
0.100.01Turn the values into proper fractions
a. 0. 10 = 10/ 100
Reduce to simpler terms
= 10/ 100
= 1/ 10
b. 0. 01 = 1/ 100
a = 1/ 100
b = 1/ 100
This means that both decimals are not of equal proportion and thus a is greater than (>) b
Thus, the answer will be 0. 10 > 0. 01 . Option B
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Graph the line with slope
-1/2
passing through the point (-1,-4)
Equation of the line with slope -1/2 passing through the point (-1,-4) is x + 2y = -9
Given,
the slope of the line = -1/2
the line passes through the point (-1,-4)
=> s = -1 and t = -4
The following equation can be used to find the line's equation:
( y - t ) = slope ( x - s )
We get by substituting the values in the equation
=> y + 4 = - 1/2 * ( x + 1 )
=> x + 2y = -1 - 8
=> x + 2y = -9
Therefore, by using the formula for equation of line, we get the equation of the line with slope -1/2 passing through the point (-1,-4) as x + 2y = -9
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How do division properties help you evaluate expressions?
Drag a word or number to the box to correctly complete the statement.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
When the Response area of a fraction is equal to −1 and the numerator is nonzero, the value of the fraction is equal to the
The division property of equality simply tells us that if we divide both sides of an equation by the same number, then the equation remains the same.
How to explain the information?It should be noted that when the denominator of a fraction is equal to 1, and the numerator is nonzero, the value of the fraction is equal to the numerator of the fraction.
Fractions simply means, numbers that are not whole.
If the numerator is nonzero, and the denominator is 1; then the fraction has a value of the numerator.
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Answer:
When the denominator of a fraction is equal to 1 and the numerator is nonzero, the value of the fraction is equal to the numerator of the fraction.
Step-by-step explanation:
I took a 2.12 math quiz in K12 and got it 100% Correct! Yes!
Answer this question please
The correct option is option B) which is that the statement is true for all real numbers.
According to the question we have been given the inequality equation as
|2s-7| ≥ -1
We know that for b<0,
if |a| ≥ b then all real numbers.
Here we have been given,
|a| = |2s-7|
b = -1 <0
As it is fulfilling the above condition and also all the absolute values are non-negative. Therefore the statement is true for all real numbers.
Hence the solution of the |2s-7| ≥ -1 is true for all real numbers that is option B) is the correct option.
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Jacob built a box with a volume of 90 cubic meters.
Choose all the boxes that Jacob could have built.
Answer:
A and D
Step-by-step explanation:
[tex]\sf \boxed{\text{\bf Volume of rectangular box = length * width * height}}[/tex]
A) Volume of the given box = 6 * 3 * 5
= 90 cubic meters.
D) Volume of the given box = 3 * 2 * 15
= 90 cubic meters
What number n is four times as close to 10 as it is to2?
Answer:
I think 3.
Step-by-step explanation:
3*4=12 near 10
Question
Simplify: (-12az² — 2z³) + (-2a³ +7a²z) − (−4a²z + 8az²),
Find the equation of the line that passes through the points
3) and (-1, 11)
Enter your answer in slope-intercept form, y=mx+b
Answer: y=-4x+7
Step-by-step explanation:
(1, 3) and (-1, 11)
m=(y2-y1)/(x2-x1) ==> Slope formula
m=(11-3)/(-1-1)
m=8/(-2)
m=-4
y=mx+b
3=-4(1)+b
3=-4+b
b=7
y=-4x+7
PLEASE HELP!!! 100 POINTS!
Solve the following system of equations for all three variables.
9x+y-3z=-9
10x-y+2z=8
-10x-y+4z=10
X = ___ , Y =___ , Z =___
Answer:
x = 0; y = -6; z = 1
Step-by-step explanation:
You want to find the solution to the system of equations ...
9x+y-3z=-910x-y+2z=8-10x-y+4z=10SolutionThis set of equations is conveniently solved using the matrix row-reduction features of a scientific or graphing calculator, spreadsheet, or any of a number of apps or on-line calculators.
The attachment shows the solution to be ...
(x, y, z) = (0, -6, 1)
__
Additional comment
Solving a system of three or more equations "by hand" often can be done by an ad hoc process. It can be done in systematic fashion using Gauss-Jordan reduction techniques, but that often gets messy. Similarly, Cramer's Rule can be used, but that math tends to involve more arithmetic operations than are really necessary.
Adding the first equation to the other two eliminates the y-variable and reduces the system to two equations in two unknowns.
(9x +y -3z) +(10x -y +2z) = (-9) +(8) . . . . adding [1] and [2]
19x -z = -1 . . . . simplified
(9x +y -3z) +(-10x -y +4z) = (-9) +(10) . . . . adding [1] and [3]
-x +z = 1 . . . . simplified
At this point, we could graph the two equations, or we can proceed algebraically.
Adding these two equations gives ...
(19x -z) +(-x +z) = (-1) +(1)
18x = 0 ⇒ x = 0
Using the second of the reduced equations, we find ...
-x +z = 1
0 +z = 1 ⇒ z = 1
And using the second of the original equations, gives us ...
10(0) -y +2(1) = 8
-y = 6 . . . . . subtract 2
y = -6 . . . . multiply by -1
Then the solution is (x, y, z) = (0, -6, 1), as above.
Read the following description of a relationship:
Each crate of ceramic tiles has 17 more hexagonal tiles than square tiles.
Let s represent the number of square tiles in a crate and h represent the number
of hexagonal tiles in the same crate.
Complete the table using the equation h = s + 17.
S
5
6
7
8
h
24
Submit
I don't know
The sum of 23/6 and five times a number is equal to 13/6 subtracted from six times the number. find the number
The missing number in the equation is 6.
Given,
The sum of 23/6 and five times a number = 13/6 subtracted from six times the number.
We can take the number as x.
Now, the equation is:
23/6 + 5x = 6x - 13/6
Cross multiply both sides:
(23 + (5x × 6)) / 6 = ((6x × 6) - 13) / 6
We get,
(23 + 30x) / 6 = (36x - 13) / 6
Cancel 6 from both sides:
Then,
23 + 30x = 36x - 13
Add 13 to both sides:
23 + 13 + 30x = 36x - 13 + 13
We get,
36 + 30x = 36x
Add -30x to both sides:
36 + 30x - 30x = 36x - 30x
Then,
36 = 6x
x = 36/6 = 6.
That is, the missing number in the equation is 6.
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