Both BODMAS and PEMDAS are valid and in use in various parts of the globe. In the UK, BODMAS is frequently utilized, whereas in the US, PEMDAS is. Brackets, Order, Division, Multiplication, Addition, and Subtraction are all referred to as BODMAS.
Which mathematical procedure comes first?The acronym PEMDAS, which stands for parenthesis, exponents, multiplication and division from left to right, as well as addition and subtraction from left to right, can be used to recall the order of operations. Start by using parenthesis first.
For the list of operations, we wish to create an expression.
9 to the second power raised then, determine the ratio between the outcome and z
First, raise 9 to the second power.
9 divided by two equals
Find the product of the result and z in step two.
Today, quotient refers to "division."
The outcome of step 1 is =[tex]9^2[/tex]
Therefore:
Indicator of and z
As a result, the statement that describes the specified order of operations is [tex]\frac{9^2}{z}[/tex]
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What is the longest line segment that can be drawn in a right rectangular prism that is 14 cm long, 13 cm wide, and 9 cm tall?
The longest line segment that can be drawn in a right rectangular prism is 21.1 cm.
Let us assume the right rectangular prism be labelled as shown in figure. Now the longest possible line here is the diagonal between two most far points like A and G. So, finding the length of AG from triangle AGC.
But, prior to this calculation, we need to find AC. It will be calculated from the traingle ABC.
So, AC² = AB² + BC²
AC² = 14² + 13²
AC² = 196 + 169
AC² = 365
AC = 19.1 cm
Now, finding length of AG.
AG² = AC² + GC²
AG² = 365 + 9²
AG² = 365 + 81
AG² = 446 cm
AG = ✓446
AG = 21.1 cm
Thus, the diagonal AG is 21.1 cm.
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Six ounces of orange juice contain 75 calories. About how many calories are in fourteen ounces of orange juice ? Part A. Write a proportion, make sure to include units. Let x= the unknown calories. Part B. Solve for X
Answer:
175 calories
Step-by-step explanation:
75 / 6 = 12.5
12.5 x 14 = 175
x = 12.5 x 14
Abdoulaye spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 5925 feet. Abdoulaye initially measures an angle of elevation of 16
∘
∘
to the plane at point
�
A. At some later time, he measures an angle of elevation of 31
∘
∘
to the plane at point
�
B. Find the distance the plane traveled from point
�
A to point
�
B. Round your answer to the nearest tenth of a foot if necessary.
The distance the plane traveled from point A to point B is 10,802.1 feet.
What are trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given the height of the plane = 5925 feet
let the distance between A to B be x and distance from B to the position of the plane is y as shown in the image,
angle of elevation from point A = 16°
the angle of elevation from point B = 31°
using trigonometric functions,
tanα = perpendicular/base
base = x + y
perpendicular = 5925 feet
tan(16) = 5925/(x + y)
x + y = 5925/tan(16)
y = 5925/tan(16) - x.........(1)
and tan(32) = 5925/y
y = 5925/tan(32)
substitute the value of y from equation 1
5925/tan(16) - x = 5925/tan(32)
5925/tan(16) - 5925/tan(32) = x
x = 10,802.1 feet
Hence the distance covered by points A to B is 10,802.1 feet.
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Explain the difference between the graphs of inverse variation functions When k > O and when k < 0.
Answer:
Step-by-step explanation:
Inverse variation functions have the form y = k / x, where k is a constant.
When k > 0, the graph of the inverse variation function is a hyperbola that opens upwards or downwards, depending on the sign of k. When k > 0, the hyperbola opens upwards and the two branches of the hyperbola move away from the x-axis as x increases. This means that as x increases, the value of y decreases. When x approaches 0 from the right, y approaches positive infinity, and when x approaches 0 from the left, y approaches negative infinity.
On the other hand, when k < 0, the graph of the inverse variation function is a hyperbola that opens upwards or downwards, depending on the sign of k. When k < 0, the hyperbola opens downwards and the two branches of the hyperbola move toward the x-axis as x increases. This means that as x increases, the value of y increases. When x approaches 0 from the right or left, y approaches negative infinity.
In both cases, the inverse variation function is undefined for x = 0, as division by zero is undefined.
a man has two shirts and nine ties asuuming that they all match how many diferent shirtt and tie combination can he wear
The man can wear 27 different shirt and tie combinations.
Therefore the answer is 27.
The number of different shirt and tie combinations that a man can wear can be calculated by multiplying the number of choices for each item.
Number of choices for shirts = 3
Number of choices for ties = 9
Since the man has three different shirts and nine different ties, and each shirt can be paired with any one of the nine ties, the number of combinations is:
Combinations = 3 * 9 = 27
So the man can wear 27 different shirt and tie combinations.
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In the diagram below of triangle ABC, D is the midpoint of AC and E is the
midpoint of BC. If m/CB A = 16 + 6x, and m/CED = 48 - 2x, what is the
measure of ZC BA?
Answer: 40 degrees
Step-by-step explanation:
m/CBA = m/CED
16 + 6x = 48 - 2x; add 2x on both sides and subtract 16 on both
8x = 32; divide 8 on both sides to isolate the x
x = 4
m/CBA = 16+6(4) = 40
what is 28 divided by the square root of 2
Answer:
14√2
Step-by-step explanation:
28/√2
Since you can't have a square root as the denominator of a fraction, we must multiply the denominator and the numerator to get rid of the square root.
Hence,
28 x √2 , √2 x √2
Your problem would now be:
28√2 / 2
Reduce the fraction by canceling out the common factor of 2
ANS = 14√2
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The population of India was 1,324,671,354 in 2016. Round the population to the nearest million people.
Answer:
1,325,000,000 people
Step-by-step explanation:
Million = 1,000,000
Number = 1,324,671,354
The 1st 4 is in the millionth place. 6 > 4 so round 4 up to 5.
Rounded = 1,325,000,000 people
Draw a dilation of the figure around the origin using the given scale factor.
k=1/4
After dilation with the scale factor 1/4 is A'(0, 1), B'(1, 1) and C'(-1, -1).
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, the scale factor is k= 1/4.
From the given figure, vertices of triangle ABC are
A(0, 4), B(4, 4) and C(-4, -4)
After dilation with the scale factor 1/4, we get
A(0, 4)→1/4 (0, 4) =A'(0, 1)
B(4, 4)→1/4 (4, 4) =B'(1, 1)
C(-4, -4)→1/4 (-4, -4) =C'(-1, -1)
Therefore, after dilation with the scale factor 1/4 is A'(0, 1), B'(1, 1) and C'(-1, -1).
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Books in the clearance section at Reading Central Bookmart cost $5.00 for paperbacks and $9.00 for hardbacks. Which inequality best describes the number of paperback books, p, and the number of hardback books, h, that can be purchased for $45.00 or less?
A.
5p + 9h < 45
B.
5p + 9h < 45
C.
9p + 5h > 45
D.
9p + 5h < 45
The inequality best describes the number of paperback books 'p' and the number of hardback books 'h' that can be purchased for $45.00 or less
is 5p + 9h ≤ 45.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Two types of books paperbacks are represented by 'p', and hardbacks are represented by 'h'.
Also, we can only buy two types of books for $45 or less.
Therefore, The inequality representing the context is,
5p + 9h ≤ 45. (As the cost van be $45 or less not only less)
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648 divided by 19 in long division
a rectangular table top is three times as it is wide. it's width is 2 meters. what is the area of the table top
12m² is the area of the table top in rectangle .
What is a rectangle, exactly?
The parallel sides of a rectangle are equal to one another, and each of its four vertices is 90 degrees, making it a form of quadrilateral. As a result, it is sometimes referred to as an equiangular quadrilateral.
The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.
area = length x width
We know that the width is 2 meters, and since the length is three times the width, the length would be 6 meters.
Therefore, the area of the table = 2 x 6 = 12 m2.
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Two apple trees are going next to each other the oldest tree has a 36 ft Shadow the smaller Creek has a 12-in shadow and there is 8 ft tall how tall is the older tree
The old tree in 54 feet height.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that Two apple trees are going next to each other
the oldest tree has a 36 ft Shadow
the smaller Creek has a 12-in shadow and the tree is 8 ft tall.
We need to find the height of the older tree.
Let x be the height of older tree.
36/x=8/12
36×12=8x
432=8x
Divide both sides by 8
54=x
Hence, the old tree in 54 feet height.
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answer question a and b please
The graph for the functions is attached.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.
Given
A: graph of y = f(x)
since the graph is in form of a parabola so the function is a quadratic function,
f(x) = ax² + bx + c
the vertex of the graph is at (2, 0)
here in the given curve, the value of the y-axis is 0,
and y = f(x) - 3
in the equation y = f(x) - 3
the shape of the curve will be the same but only change in the vertex of the curve, the new vertex for the curve is (2, -3)
for x = 0 y = -3.
B: given y =g(x)
the graph shows the negative cubic function,
g(x) = -x³
and y = g(x + 4)
= -(x + 4)²
the graph will shift towards 4 units left.
Hence the graph is attached for both equations.
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8. Express the area of the figure as a monomial.
p2q4 and p2q4
The area of the figure as a monomial with the sides [tex]p^{2} q^{4}[/tex] and [tex]p^{2} q^{4}[/tex] is [tex]p^{4} q^{8}[/tex].
As per the given data we to express the area of the figure as a monomial.
Figure attached at the end of solution.
What is monomial?A polynomial with only one term is called a monomial. An algebraic expression known as a monomial has only one term but might have more than one variable and a higher degree.
As the sides are equal we use the area of the square formula.
Area of the square formula:
The formula for the area of a square is side × side
Simple multiplication is the answer to the equation.
Area of the given figure:
= [tex]p^{2} q^{4} \times p^{2} q^{4}[/tex]
= [tex]p^{4} q^{8}[/tex]
[tex]p^{4} q^{8}[/tex] is a monomial as it is expressed as a single term.
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Convert 1.05 • 10^-8 to standard form.
Answer:
0.0000000105
Step-by-step explanation:
Simply move the decimal 8 places to the left, since it is a negative exponent.
Drag each expression to show whether the expression is equivalent to 24x−48 24 x - 48 , 36x+12 36 x + 12 , or neither.
the expression 24x - 48 is equivalent to 36x + 12
The label 24x - 48 applies to the expression because it is the same as itself. The value obtained by multiplying 24 by x and then taking 48 out is represented by this expression.
The label "36x + 12" applies to the expression because it is the same as itself. The value generated by multiplying 36 by x and then adding 12 is represented by this expression.
Since the formulations in both situations have distinct coefficients for x and various constant terms, they are not comparable to one another. Since both expressions are equal to one another, the term "neither" does not apply to them.
Therefore, the expression 24x - 48 is equivalent to 36x + 12
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Two model cars, A and B, are in a race.
They start together on the starting line.
Assume each car travels at a constant speed.
Car A takes 30 seconds to complete each lap of the track.
Car B takes a whole number of seconds to complete each lap of the track.
The two cars next cross the starting line together 150 seconds after the start of the race.
Find the four possible times that car B could take to complete one lap.
Step 1: Calculate the number of laps the cars have completed. To calculate the number of laps the cars have completed, divide the total time (150 seconds) by the time it takes car A to complete one lap (30 seconds), which gives us a total of 5 laps.
Step 2: Calculate the possible times for car B. To calculate the possible times for car B, we need to find out how many times car B must complete a lap in order to keep up with car A. Since car A takes 30 seconds to complete one lap and the cars have completed 5 laps in 150 seconds, car B must take the same amount of time as car A, i.e. 30 seconds, in order to keep up with car A. Therefore, the possible times for car B are 30, 60, 90, and 120 seconds.
Therefore, the four possible times that car B could take to complete one lap are 30, 60, 90, and 120 seconds.
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Solve for z zz. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. − 4 z + 31 ≥ 17 z + 23 −4z+31≥17z+23
[tex]-4z+31\geqslant 17z+23\implies 31\geqslant 13z+23\implies 8\geqslant 13z\implies \cfrac{8}{13}\geqslant z[/tex]
The function f is defined by f (x) = 50.3%. The function g is defined by g(x) = a. b
Here are graphs of f and g.
g
X
1. How does a compare to 50? Explain how you know.
2. How does b compare to 3? Explain how you know.
On solving the provided question, we can say that Point (1,1) must be on the graph of f if point (x,1) is on the graph of f. (x).
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
Given that y=f(x) and g(x)=f (x)
Flipping the graph of y=f(x) across the y axis, as shown in the image, will give you the graph of g(x)=f(x).
For instance, the point (2,2) must be on the graph of f if point (2,2) is on the graph of f(x) (x).
Point (3,1) must be on the graph of f if point (3,1) is on the graph of f(x) (x).
Point (1,1) must be on the graph of f if point (1,1) is on the graph of f(x) (x).
Point (1,1) must be on the graph of f if point (x,1) is on the graph of f. (x).
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A recipe for biscuits calls for 1/4 teaspoon baking powder per 1 2/3 cups of flour. What is the unit rate for baking powder and flour?
The ratio of baking powder to flour is 1/192 teaspoon of baking powder for every teaspoon of flour.
The amount of baking powder per unit of flour is the unit rate for baking powder and flour. The amount of flour in this situation equals 1 2/3 cups. We must change the baking powder measurement to the same unit as the flour measurement in order to calculate the unit rate.
For every 1 2/3 cups of flour, 1/4 teaspoon of baking powder should be used as follows:
1/4 teaspoon / (1 2/3 cups)
By changing the numerator and denominator of the fraction on the right side to a standard unit, such as teaspoons, we may make it simpler. 1 2/3 cups equal 48 teaspoons, so:
1/4 teaspoon / (1 2/3 cups) = 1/4 teaspoon / (48 teaspoons)
The ratio of baking powder to teaspoons is as follows:
1/4 teaspoon / (48 teaspoons) = 1/192 teaspoon per teaspoon
So The ratio of baking powder to flour is 1/192 teaspoon of baking powder for every teaspoon of flour.
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Select the values that are solutions to the inequality x2 + 3x – 4 > 0. –6 –2 0 5
The values that are solutions to inequality are -6 and 5.
Options A and D are the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
x² + 3x - 4 > 0
Now,
Substituting x = -6, -2, 0, 5
(-6)² + 3(-6) - 4 > 0
36 - 18 - 4 > 0
36 - 22 > 0
14 > 0
True.
x² + 3x - 4 > 0
(-2)² + 3 x (-2) - 4 > 0
4 - 6 - 4 > 0
-6 > 0
This is not true.
x² + 3x - 4 > 0
0 + 3 x 0 - 4 > 0
0 + 0 - 4 > 0
-4 > 0
This is not true.
x² + 3x - 4 > 0
5² + 3 x 5 - 4 > 0
25 + 15 - 4 > 0
40 - 4 > 0
36 > 0
This is true.
Thus,
-6 and 5 are the solutions to inequality.
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Mrs. Klein went to Target in search of a good deal on laundry detergent (Owen is one messy boy!). She found Tide was $15.99 with 20% off. Gain was $17.55 with 25% off. She has a target red card and gets 5% off her total purchase.
The product which cost less is Tide which has a cost value of $15.99 with 20% off.
What is Cost?This is referred to as the expenditure required to create and sell products and services, or to acquire assets.
Tide was $15.99 with 20% off which when calculated = 20/100 × $15.99 = $3.198.
Gain was $17.55 with 25% off which when calculated = 25/100 × $17.55 = $4.388.
Therefore the cheaper alternative will be Tide detergent.
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The full question:
Mrs. Klein went to Target in search of a good deal on laundry detergent (Owen is one messy boy!). She found Tide was $15.99 with 20% off. Gain was $17.55 with 25% off. She has a target red card and gets 5% off her total purchase. which one of the products costs less?
The notation "f(x)" (f of x) is another way of representing y-values in a function
True
False
need help is it true or false
Describe the transformations that maps figure RSTU onto figure R1 S1 T1 U1
Problems had to do with translation and units
Figure RSTU is transformed into Figure R1 S T 1 U1 by moving down two units and reflecting on the y axis.
what is transformation ?Deformations are four alternative approaches that can be utilized to change a point, line, or mathematical figure's orientation and/or shape. Both the Pre-Image, who describes the shape of the object there at initial state, and the Photograph, which describes the final state and location of the object following change, are words. Translations, reflection, and dilations are the three types of transformations that can be differentiated. A function can undergo two different types mathematical transformations: vertical (it affects the y-values) and sideways (affects the x-values). Its function's equation is provided below, and it comprises the share the information variables (a, b, h, and k). modifying the log. observation. even by square root, invert.
given
From the figure RSTU to R'S'T'U' R moved from P(5,2) to P(-3,0), translating 8 units to the left.
Hence, 5-(-3)= 8 = 2-0 = 0.
Down two units.
as well as reflection on the y axis.
Figure RSTU is transformed into Figure R1 S T 1 U1 by moving down two units and reflecting on the y axis.
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A string with a linear density of 2 kg/m and a tension of 100 N is fixed at both ends. Determine the frequency of the first harmonic of the string.
Step-by-step explanation:
The frequency of the first harmonic of a string fixed at both ends can be determined using the formula:
f = (1 / 2L) * √(T / μ)
where f is the frequency, L is the length of the string, T is the tension, and μ is the linear mass density. Plugging in the given values:
f = (1 / 2 * L) * √(100 N / 2 kg/m)
= (1 / 2 * L) * √(50 N/m)
So, the frequency of the first harmonic depends on the length of the string, which is not specified in the problem.
Answer:
Step-by-step explanation:
The frequency of the first harmonic of a string fixed at both ends can be calculated using the formula:
f = (1 / 2L) * (T / μ)^(1/2)
where:
f = frequency
L = length of the string
T = tension
μ = linear density of the string
Plugging in the values:
f = (1 / 2 * L) * (100 N / 2 kg/m)^(1/2)
f = (1 / 2L) * (10 N/kg)^(1/2)
We don't have the length of the string, L, so we can't calculate the frequency.
What is the measure of angle R?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
m∠R =
The measure of the angles of the triangles are 90° , 67.380° and 22.620°
What is the law of sines?The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.
Law of Sines :
a / sin A = b / sin B = c / sin C
Given data ,
Let the triangle be represented as ΔPQR
Now , the measure of ∠PQR = 90°
The measure of side PR = 13 cm
The measure of side PQ = 5 cm
The measure of side QR = 12 cm
From the law of sines , we get
a / sin A = b / sin B = c / sin C
Substituting the value sin the equation , we get
12 / sin P = 13 / sin 90°
From the trigonometric relations , sin 90° = 1
So , Multiply by sin P on both sides of the equation , we get
sin P = 12/13
Taking inverse on both sides of the equation , we get
sin⁻¹ ( 12/13 ) = 67.380°
Therefore , the measure of ∠QPR = 67.380°
And , the measure of ∠PRQ = 180 - ( 90° + 67.380° )
The measure of ∠PRQ = 22.620°
Hence , the angles of triangles is solved
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3. A cube has volume 9261 cubic centimetres. Determine the area of one face of the cube.
Show your work. (2 marks)
volume =
3
9261cm
find
surface
area
of this
alde
If the volume of cube is 9261 cubic centimeters, then the surface area of the cube is 2646 square centimeters.
It is given that a cube has volume 9261 cubic centimeters. Let the length of the side of cube is 'a' centimeters.
The formula of volume of a cube is [tex]a^{3}[/tex]
9261 cubic centimeters = [tex]a^{3}[/tex]
a = [tex]\sqrt{9261}[/tex]
a = [tex]\sqrt{21\times21\times21}[/tex]
a = 21 cm
The surface area of cube = [tex]6a^{2}[/tex]
The surface area of cube = [tex]6\times21^{2}[/tex]
The surface area of cube = 2646 square centimeters.
Also the area of one face of the cube = [tex]a^{2}[/tex]
The area of one face of the cube is 441 square centimeters.
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A car sales person makes $7.00 per hour plus $100.00 for every car sold. Which expression represents the amount in dollars the salesperson makes, before taxes, if x cars are sold in 40 hours?
The expression that represents the amount in dollars the salesperson makes, before taxes, would be equal to 7x + 100 = 40.
What is an expression?Expression in maths is defined as the collection of 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 symbol that can also be used to indicate the logical syntax's order of operations and other features.
Given that car sales person makes $7.00 per hour plus $100.00 for every car sold.
Therefore, we have,
7x + 100 = 40
The expression that represents the amount in dollars the salesperson makes, 7x + 100 = 40.
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list the elements of the Sets (1) (AnB)' UC (ii) (AUC) 'n B (iii) (AUBUC)'
Answer:
(i) The complement of the intersection of Sets A and B, denoted by (A∩B)', is the set of all elements that are not in the intersection of Sets A and B. It can be found by taking the union of the complements of Sets A and B, denoted by A' and B'. Hence, (AnB)' = A' U B'.
(ii) The complement of the union of Sets A and C, denoted by (A U C)', is the set of all elements that are not in the union of Sets A and C. It can be found by taking the intersection of the complements of Sets A and C. Hence, (A U C)' = A' ∩ C'.
(iii) The complement of the union of Sets A, B, and C, denoted by (A U B U C)', is the set of all elements that are not in the union of Sets A, B, and C. It can be found by taking the intersection of the complements of Sets A, B, and C. Hence, (A U B U C)' = A' ∩ B' ∩ C'.