In algebra, the notation "FG" refers to the composition of two functions, "F" and "G", where the output of "G" is used as the input for "F" and the notation is represented as "F(G(x))".
The composition of functions is a way to combine two functions to create a new function. The output of the first function "G" is used as the input for the second function "F". This process is represented by the notation "F(G(x))", where "x" is the input for both functions. The function "F" is applied to the output of the function "G". This composition of functions is useful for modeling complex systems and can simplify mathematical expressions.
It also allows for the creation of more complex functions by combining simpler functions. However, not all functions can be composed and the order of the functions also matters. It's important to note that the order of the functions in composition matters and can change the result of composition.
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Where would the point (-1,3) be if it wa rotated 270 degree counterclockwie about the point (1,0) ?
The point (-1,3) would be located at the point (3,-1) after a 270 degree counterclockwise rotation about the point (1,0).
To rotate a point in a 2D space, we can use the rotation matrix formula:
[x'] = [cos(Ф) -sin(Ф)][x]
[y'] [sin(Ф) cos(Ф)][y]
Where x' and y' are the coordinates of the point after rotation, x and y are the coordinates of the point before rotation, and theta is the angle of rotation in radians.
In this case, the point to be rotated is (-1,3) and the point of rotation is (1,0). The angle of rotation is 270 degrees, which is equivalent to 3/2π radians.
Plugging in the values:
[x'] = [cos(3/2π) -sin(3/2π)][-1]
[y'] [sin(3/2π) cos(3/2π)][3]
[x'] = [0 1][-1]
[y'] [-1 0][3]
x' = 3 and y' = -1
Therefore, the point (-1,3) is located at the point (3,-1) after a 270 degree counterclockwise rotation about the point (1,0).
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Triangle PQR is similar to Triangle XYZ. If PQ = n + 2, QR = n - 2, and XY = n^2 - 4,
what is the value of YZ, in terms of n?
Note that if Triangle PQR is similar to Triangle XYZ, and If PQ = n + 2, QR = n - 2, and XY = n²- 4, then the value of YZ, in terms of n is: (n-2)²
What is the justification for the above expression?
Where triangle PQR is similar to triangle XYZ, then;
PQ/QR =XY/YZ
Given
PQ = n + 2,
QR = n - 2 and
XY=n² - 4,
Substitute
n+2/n-2 = n²-4/YZ
n+2/n-2 = (n+2)(n-2)/YZ
1/n-2 = n-2/YZ
Cross multiply
YZ = (n-2)(n-2)
YZ = (n-2)²
Hence the value of YZ in terms of n is (n-2)²
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Express the product (√2 – √3) (√2 – √3) in simplest form.
Answer:
The expression (√2 – √3) (√2 – √3) simplifies to 2 - 2√6 + 3, which can be further simplified to 3 - 2√6.
b divided by 9 = 18
giving 15 points for correct
Answer:
B = 162
Step-by-step explanation:
B/9 = 18
(9) B/9 = 18(9)
B = 162
Answer:
b = 162
Step-by-step explanation:
Given statement,
→ b divided by 9 = 18
Forming the equation,
→ b/9 = 18
Now the value of b will be,
→ b/9 = 18
→ b = 18 × 9
→ [ b = 162 ]
Hence, value of b is 162.
y - 3x = 1
2y - x = 12
Answer:
x = 2, y = 7
Step-by-step explanation:
y - 3x = 1 |*2
2y - x = 12
2y - 6x = 2
2y - x = 12 | - Ist equation
2y-x-2y+6x = 12-2
5x = 10
x = 2
Insert x to first equation:
y - 3*2 = 1
y = 7
Madelyn earns $159.25 for 7 hours of work. If she makes a constant hourly wage, which table represents the relationship between the number of hours she works and her total earnings?
Answer: She makes around $22 dollars per hour.
Step-by-step explanation:
You can divide her wage by the amount of hours she works.
Aria conducted a scientific experiment. For a certain time, the temperature of a
compound rose 1 1/4 degrees every 1 2/3 hours. What was the rate, in degrees per hour,
that the temperature of the compound rose?
The rate at which the temperature of the compound rose was 0.75 degrees per hour.
What is tempreture?Temperature is a measure of how hot or cold an object or environment is. It is measured in degrees on the Celsius, Fahrenheit, or Kelvin scales. Different objects and environments have different temperatures. For example, the temperature of the human body is usually around 37°C (98.6°F). The temperature of boiling water is 100°C (212°F). The temperature of a winter day can be much colder than the temperature of a summer day.
To solve this problem, divide 1 1/4 degrees by 1 2/3 hours, which equals 0.75 degrees per hour. Therefore, the rate at which the temperature of the compound rose was 0.75 degrees per hour.
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In Triangle RMC, RM = 19. MC = 27. and CMR = 27°. What is the area of RMC? Round to the nearest tenth.
the area of the triangle RMC will be 116.44 unit²
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle. There are different types of triangles such as isosceles, right-angled, equilateral etc.
The sum of all angles of triangle = 180
In Triangle RMC, RM = 19. MC = 27. and CMR = 27°.
Area is = A*B*sin(M)/2
= 19*27*sin(27)/2
=116.44856
Hence the area of the triangle RMC will be 116.44 unit²
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5. Solve for angle x.
*
27 m
18 m
Therefore , the solution of the given problem of angle comes out to be
x= 48.19° .
What is an angle defined as?An angle is a shape in Euclidean geometry comprised of two rays, known as the sides of the loop, that diverge at the apex of both the angle and the vertex, which is situated in the middle. It is possible for two rays to combine to generate an angle inside the plane they are located in. An angle also comes from the collision of two planes. They are known as dihedral angles. There are many options for arranging two line ray with end points in two dimensions to form an angle.
Here,
Given : A right angle triangle,
Where we have to find the value of x angle
thus,
Using trigonometric ratios:
=> Cos x = 18/27
=> Cos x = 6/9
=> Cos x = 2/3
=> x = Cos⁻¹ (2/3)
=> x = 48.19°
Therefore , the solution of the given problem of angle comes out to be
x= 48.19° .
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Write the fraction that repreent the colored part of each hape. Then, anwer and urround the larger fraction of each pair
The fraction that represents the colored part of each shape is i) ½ ii) 8/9 iii) ½ iv) ¼ v) 3/7 vi) ¼ vii) 1 viii) 4/9 ix) ½ x) 1/2.
Fractions refer to the parts of a whole. A fraction is a ratio between specified parts of a figure to all parts of a figure. The numerator indicates the parts of the whole and the denominator indicates the total number of equal parts. In the given shapes, as everything is equally divided, the fraction of shaded region is equal to the number of shaded parts divided by the number of total parts.
i) The number of shaded regions = 2
The total number of regions = 4
Fraction = 2/4 = 1/2
ii) The number of shaded regions = 8
The total number of regions = 9
Fraction = 8/9
iii) The number of shaded regions = 4
The total number of regions = 8
Fraction = 4/8 = ½
iv) The number of shaded regions = 1
The total number of regions = 4
Fraction = 1/4
v) The number of shaded regions = 3
The total number of regions = 7
Fraction = 3/7
vi) The number of shaded regions = 3
The total number of regions = 12
Fraction = 3/12 = 1/4
vii) The number of shaded regions = 10
The total number of regions = 10
Fraction = 10/10 = 1
viii) The number of shaded regions = 4
The total number of regions = 9
Fraction = 4/9
ix) The number of shaded regions = 4
The total number of regions = 8
Fraction = 4/8 = 1/2
x) The number of shaded regions = 1
The total number of regions = 2
Fraction = 1/2
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Small MOTOR cooter can trouble uing 1 gallon of gaoline. Complete the table to find the number of mile the chool don’t control for other amount of gaoline
According to the Science and Technology Desk Reference, a US fuel gallon weighs 6.1 pounds. The weight of gasoline may be slightly influenced by the quality of the fuel.
This year, high demand for crude oil and limited supply drove up gas prices. There are other international forces at play even though the Federal Reserve has increased interest rates five times so far in 2022 and plans to do so again soon to push prices down.
|0.1 | 11.8|\s| 1 | 118|\s|10 | 1180|
When you can travel 118 miles on 1 gallon, that is equivalent to a ratio of 1:18.
Just solve for the remaining ratios, 0.1: 11.8; 10: 1180.
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The complete question is
The table shows the distance a small motor scooter can travel using one gallon of gasoline. complete the table to find the number of miles the scooter can travel for other amounts of gasoline.
| Gallons | Miles |
| 0.1 | *Ans* |
| 1 | 118 |
| 10 | *Ans* |
Ben and Jerry together scored 78 points. If Ben scored 29 points, how many points did Jerry score?
Answer: 49
Step-by-step explanation:
78 subtracted by 29 equals 49
Answer:
Step-by-step explanation:
78-29
49
Jerry scored 49 points
Kevin bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $350 less than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 7% per year, and for the laptop it was 9.5% per year. The total finance charges for one year were $305. How much did each computer cost before finance charges?
The cost of the desktop is $2083.8 and the cost of the laptop is $1783.8.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Kevin bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $350 less than the desktop. He paid for the computers using two different financing plans. For the desktop, the interest rate was 7% per year, and for the laptop, it was 9.5% per year.
The cost will be calculated as:-
305 = 0.06x + 0.095( x + 300 )
305 = 0.06x + 0.095x + 28.5
276.5 = 0.155x
x = $1783.8
Desktop cost = x + 300
Desktop cost = 1783.8 + 300= $2083.8
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What is the formula for finding the base of an isosceles triangle?.
The formula for finding the base of an isosceles triangle is Base = 2 x (Area) / (Height)
An isosceles triangle is a particular kind of triangle in which the lengths of the two sides are equal. This indicates that the two base angles' lengths are similar (congruent means that they are of the same measure). The third side is referred to as the base, and its opposite angle is referred to as the vertex angle. The legs are the two sides that are of equal length.
The formula for finding the base of an isosceles triangle is - Base = 2 * (Area) / (Height). Where the Area is the total area of the triangle, and "Height" is the height of the triangle as measured from the base to the apex (or the point opposite the base).
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What is 8 and 4/8 as a simplified number? And what is 4 and 1/6 + 7 and 1/6, and also try and simplify the number if possible.
a hot airballoon rises 120 feet every 3 seconds. which equation represents the relationship bettween time and height
y = 30x
y = 40x
y = 120x
y = 3x + 120
Answer:
y = 40x
Step-by-step explanation:
there is 2 worker, one can make a house in 2 days, while the other one make a house in 3 days, how much days it take them to make a house
Answer:
5 days to make a house for both of them
Answer: 6/5 days
Step-by-step explanation:
If a worker can make a house in 2days, it can make 1/2 of the house in 1 day.
Similarly, the other worker can make 1/3 of the house in 1 day.
So, in 1 day, together, they will make 1/2 + 1/3 = 5/6 of the house.
So, it will take them 6/5 days to complete the house together.
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What is inequality algebraically |x+9|<7
The inequality |x+9|<7 can be written as -16<x<-2.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
we have the inequality:|x+9|<7
By Definition of Absolute Value.
-(x+9)<7 and x+9<7
-x-9<7
-x<16
x>-16..(1)
and
x+9<7
x<-2...(2)
-16<x<-2
Hence, the inequality |x+9|<7 can be written as -16<x<-2.
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Combine the two congruent trapezoid at the right to make new polygon. Draw your new polygon and claify them
A parallelogram is a four-sided shape with two sets of parallel lines and two pairs of congruent sides. It is formed by combining two congruent trapezoids, which results in a quadrilateral with two pairs of opposite sides that are parallel and equal in length. All four angles of the parallelogram are also equal.
1. Draw the two congruent trapezoids.
2. Line up the two trapezoids, making sure that the corresponding sides are parallel and the same length.
3. Connect the two trapezoids with lines to form the parallelogram.
4. Check that the angles of the parallelogram are all equal, and that the two pairs of opposite sides are parallel and the same length.
A parallelogram is a four-sided shape with two sets of parallel lines and two pairs of congruent sides. To make a parallelogram, two congruent trapezoids are combined. This can be done by lining up the two trapezoids, making sure that the corresponding sides are parallel and the same length. Then, the two trapezoids can be connected with lines to form the parallelogram. It is important to check that the angles of the parallelogram are all equal, and that the two pairs of opposite sides are parallel and the same length. If these criteria are met, then the shape is a parallelogram.
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Write an expression that passes through (6,-3) and is parallel to the line y=-2/3 x+. 5
The equation of the line that passes through (6,-3) and is parallel to the line y = -2/3 x + 5 is y = - 2 / 3 x + 1.
How to write equation of a line?The equation of a line can be represented in slope-intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptTherefore, the equation of the line passes through (6,-3) and is parallel to y = -2/3 x + 5.
Parallel lines have the same slopes.
Therefore, the slope of the line is - 2 / 3.
Hence, let's find the y-intercept of the line using (6, -3).
Therefore,
y = - 2 / 3 x + b
-3 = - 2 / 3 (6) + b
-3 = -12 / 3 + b
b = -3 + 4
b = 1
Therefore, the equation of the line is y = - 2 / 3 x + 1.
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How many solutions are there for 3x 4y 12 explain?.
There are two solutions to the given equation 3x + 4y = 12.
Finding two solutions for the equation 3x + 4y = 12
Putting the value of x = 0 in equation 3x + 4y = 12
⇒3(0) + 4y = 12
⇒ 4y = 12
⇒y = 3
Thus, (0, 3) is a solution to the equation 3x + 4y = 12
Putting the value of y = 0 in the equation 3x + 4y = 12
Thus,
⇒3x + 4(0) = 12
⇒3x = 12
⇒x = 4
Thus, (4, 0) is a solution to equation 3x + 4y = 12
Therefore, (0, 3) and (4, 0) are two solutions to the equation 3x + 4y = 12.
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PLEASE HURRY, LIMITED TIME !!!!!
Question- A circle has an area of A=36π and a center of (-4,0). What is the standard form equation of this circle?
Answers:
A. (x+4)^2 + y^2 = 36
B. (x-9)^2 + (y-2)^2 = 9
C. (x+4)^2 + y^2 = 72
D. (x+4)^2 + y^2 = 6
The standard form equation of the circle which has an area A=36π and a center of (-4,0), (x+4)² + y² = 36. So Option A is correct
What is a circle?In mathematics, the circle is a two dimensional rounded figure which has no corner edges.
Area = [tex]\pi r^{2}[/tex]
Perimeter = [tex]2\pi r^{}[/tex]
Standard form = (x - a)² + (y - b)² = r²
Given that,
A circle has an area of A=36π
And a center of (-4,0)
The area of a circle for radius r is,
Area = [tex]\pi r^{2}[/tex]
[tex]\pi r^{2}[/tex] = 36π
[tex]r^{2}[/tex] = 36
r = 6
here,
a = -4
b = 0
Now,
Standard equation,
(x -(-4))² + (y - 0)² = 6²
(x+4)² + y² = 36
Hence, The standard form is (x+4)² + y² = 36
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How much water do you add to make each concentration? 25% sugar syrup using 15 grams of sugar pls help.
Answer:
25% sugar syrup means in a mixture of 100g sugar syrup, sugar should be 25g
so, when sugar is 25g , mixture is 100g
when sugar is 1g, mixture is 100/25 = 4g
when sugar is 15g, mixture is 15*4 =60g
So, amount of water to be added=60-15= 45g
Step-by-step explanation:
El producto de
97
×
8
97×897, time, 8 e igual a
776
776776. Ua el dato anterior para reolver como un decimal. 9. 7
×
0. 08
=
9. 7×0. 08=9, point, 7, time, 0, point, 08, equal
La fórmula para multiplicar dos números decimales es la misma que para multiplicar números enteros.
Primero, muestra los números en forma de dígitos y coloca un punto decimal entre los números. Luego, multiplica los dígitos del número de la izquierda a la derecha, como si fueran números enteros. Después, añade los resultados, teniendo en cuenta la regla de los puntos decimales. Por último, contar el número de dígitos que hay después del punto decimal, y coloca el punto decimal en el resultado.
En este caso, se multiplican los números 9.7 y 0.08. Primero, se muestran los números en forma de dígitos: 9.7 y 0.08. Luego, se multiplican los dígitos de la izquierda a la derecha, como si
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PLSSS HELP TURLY KNOW THISSS
Answer:
13
Step-by-step explanation:
Since a = 3, 10 x 3 = 30
5c = 5 x 2 = 10
2c = 2 x 2
Now we have 30 - 3 - 10 - 4
30 - 3 = 27 - 10 = 17 - 4 = 13
13 is our total
Answer:
[tex] \sf \: 10a - 3 - 5c - 2c = 13[/tex]
Step-by-step explanation:
Given expression,
→ 10a - 3 - 5c - 2c
Now we have to use,
→ a = 3
→ c = 2
Let's solve the expression,
→ 10a - 3 - 5c - 2c
→ 10(3) - 3 - 5(2) - 2(2)
→ 30 - 3 - 10 - 4
→ 30 - 3 - 14
→ 30 - 17
→ 13 => final value
Therefore, the answer is 13.
How do you find the class range of Class 9?.
Class range of 9 can be calculated, this can be shown through below illustrations :Determining the following marks on a test 15 students took: 45, 68, 82, 79, 67, 55, 75, 55, 85, 89, 90, 78, 45, 66, and 49.
To know the maximum and minimum values in the data set, which are 90 and 45, respectively.
Mention the maximum and minimum values. The difference between the maximum and minimum values in a distribution, also called the range, is considered by max - min = 45.
Mention the number of classes, say n = 9, to measure class width i.e. class width = 45 / 9 = 5.
The class width formula gives back the appropriate class width to distribute this data into 9 classes, that is 5.
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Answer:
Step-by-step explanation:
Class range of 9 can be calculated, this can be shown through below illustrations:Determining the following marks on a test 15 students took: 45, 68, 82, 79, 67, 55, 75, 55, 85, 89, 90, 78, 45, 66, and 49.
To know the maximum and minimum values in the data set, which are 90 and 45, respectively.
Mention the maximum and minimum values. The difference between the maximum and minimum values in a distribution, also called the range, is considered by max - min = 45.
Mention the number of classes, say n = 9, to measure class width i.e. class width = 45 / 9 = 5.
The class width formula gives back the appropriate class width to distribute this data into 9 classes, that is 5.
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In the figure below, ‖hl and ‖jk. Find the values of z and x.
Answer:
Step-by-step explanation:
z°=180°-79°=91°
(3x+13)°=79°, so x=22°
Prepaid off-peak call cost = R41,67 (rounded off) + R1.30 x airtime used. O 1 Time (in min) Prepaid costs Contract costs 0 41,67 108,42 10 54,67 108,42 20 30 67.67 80.67 108.42 C 40 50 93,67 107 108,42 108.42 60 B D 10214 . Use your completed table to draw a graph of the airtime in minutes versus the prepaid contract call costs on different sets of axes.
Answer: I can provide you with the data in tabular format if you want to create the graph with the provided data.
Airtime (min) | Prepaid costs | Contract costs
0 | 41.67 | 108.42
10 | 54.67 | 108.42
20 | 67.67 | 108.42
30 | 80.67 | 108.42
40 | 93.67 | 108.42
50 | 102.14 | 108.42
60 | 114.64 | 108.42
This table shows the airtime (in minutes) used, and the corresponding costs for both prepaid and contract call plans. The prepaid costs are calculated using the formula: R41.67 + R1.30 x airtime used, whereas the contract costs are fixed at R108.42.
It's worth noting that the costs for the contract call plan is fixed and doesn't change with the airtime used, while for the prepaid plan the costs increase as the airtime increases.
Step-by-step explanation:
The corporate team-building event will cost $44 if it has 11 attendees. If there are 12 attendees, how
much will the corporate team-building event cost? Solve using unit rates.
Answer: 12 attendees can attend the corporate team-building event, with a budget of $48.
How to calculate event cost?
step1:
First you have to find the unit rate. So for every 11attendees it costs $44, divide them both by the GCF which is 7. 44÷11=4
11÷11=1
So for every 1 attendee it is $4.
Now to figure out how much it would cost for12attendees, figure out what you have to do to 1 to get 12. Multiply it by 12
And whatever you do to one number you have to do for the other.
Step2:
so $4*12= $48
So for every 12 attendees it costs $48.
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12 attendees can attend the corporate team-building event, with a budget of $48.
How to calculate event cost?step1:
First you have to find the unit rate. So for every 11attendees it costs $44, divide them both by the GCF which is 7. 44÷11=4
11÷11=1
So for every 1 attendee it is $4.
Now to figure out how much it would cost for12attendees, figure out what you have to do to 1 to get 12. Multiply it by 12
And whatever you do to one number you have to do for the other.
Step2:
so $4*12= $48
So for every 12 attendees it costs $48.
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what is the difference of (-2x+9) and (3x-4)
Answer:
-5x + 13
Step-by-step explanation:
Difference = subtraction
[tex](-2x+9) - (3x-4)\\-2x - 3x + 9 + 4\\-5x + 13[/tex]
