Evaluate each of the following expressions. (NO denominators are equal to 0.) |x-y/y-x|
Answers
The absolute value of - \(\frac{(y-x)}{(x-y)}\) is always equal to 1.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
The expression \(\frac{x-y}{y-x}\) can be simplified using the properties of absolute value and algebraic manipulation.
First, note that the denominator of the expression is y-x. Since we are given that none of the denominators are equal to 0, we can assume that y is not equal to x.
Next, we can apply the definition of absolute value, which is:
|a| = a, if a is positive or zero
|a| = -a, if a is negative
In the expression \(\frac{x-y}{y-x}\) , the fraction \(\frac{x-y}{y-x}\) could be positive or negative, depending on whether x is greater than or less than y.
If \(\frac{x-y}{y-x}\) is positive or zero, then \(\frac{x-y}{y-x}\) simplifies to \(\frac{x-y}{y-x}\) , since the absolute value of a non-negative number is itself.
If \(\frac{x-y}{y-x}\) is negative, then \(\frac{x-y}{y-x}\) simplifies to - \(\frac{(y-x)}{(x-y)}\) since the absolute value of a negative number is its opposite.
However, we can simplify the expression further by noting that \(\frac{x-y}{y-x}\) is equal to - \(\frac{(y-x)}{(x-y)}\) , since swapping the numerator and denominator of a fraction changes its sign.
Therefore, \(\frac{x-y}{y-x}\) simplifies to |-1| = 1, since - \(\frac{(y-x)}{(x-y)}\) is always negative, regardless of the values of x and y. This means that the absolute value of - \(\frac{(y-x)}{(x-y)}\) is always equal to 1.
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Related Questions
1. -3(2x + 1) - 4x + 45
Answers
- 3 (2x + 1) - 4x + 45
= - 6x - 3 - 4x + 45
= - 6x - 4x - 3 + 45
= - 10x + 42
Hope it helps ⚜
Answer:
\(\large\boxed{\boxed{\underline{\underline{\maltese{\pink{\pmb{\sf{\: Solution : \:-10x + 42}}}}}}}}\)
Step-by-step explanation:
\(\sf{-3(2x + 1) - 4x + 45}\\\\\sf{Multiply \: the \: numbers : -3(2x + 1)}\\\\\sf{=( -3 * 2x) +( -3*1 )- 4x + 45}\\\sf{= -6x - 3 - 4x + 45}\\\\\sf{Rearrange \: the \: terms \: and \: do \: the \: operations} \\\\\sf{= -6x - 4x - 3 + 45}\\=\large{\boxed{\tt{ -10x + 42}}}\\\)
_______
Hope it helps!
\(\mathfrak{Lucazz}\)
marlon is picking out some movies to rent, and he has narrowed down his selections to 4 documentaries, 4 mysteries, 5 comedies, and 4 children's movies. how many different combinations of 9 movies can he rent if he wants all 4 children's movies?
Answers
1287 different combinations of 9 movies can he rent if he wants all 4 children's movies as "Marlon is picking out some movies to rent, and he has narrowed down his selections to 4 documentaries, 4 mysteries, 5 comedies, and 4 children's movies. She want all 4 children's movie".
What is combination?Combinations are ways to choose items from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each set. The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant." Combining these two words means "Selection of things," where the order of the items is irrelevant. If n>k, nCk = n!/k!(n-k)!
Here,
4C4=1
4+4+5+4=17-4=13
9-4=5
13C5
1287*1=1287
1287 different combinations of 9 movies can he rent if he wants all 4 children's movies. If he wants to rent all 4 children's movies, there are 1287 different combinations of 9 movies "Marlon has chosen four documentaries, four mysteries, five comedies, and four children's movies from his list of potential rentals. She desires all 4 of the kid's movies ".
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Year 9 Non-realationship question
Could you help me to do just question 12b please?
Answers
The equation of the parabola shown in the 12b is y = x² - 4 if the vertex of the parabola is (0, -4).
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
It is given that:
The graph of a parabola is shown in the 12b question:
As we know, the standard form of the parabola is:
y = a(x - h)² + k
(h, k) is the vertex of the parabola:
From the graph: h = 0, k = -4
y = ax² - 4
Plug (2, 0) in the above equation:
0 = 4a - 4
a = 1
y = x² - 4
Thus, the equation of the parabola shown in the 12b is y = x² - 4 if the vertex of the parabola is (0, -4).
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The number of pennies in a jar of coins is 4 more than 5 times the number of dimes in the jar Let p = the number of pennies in the jar. Let d = the number of dimes in the jar. Which equation represents this situation?
Answers
The equation that represents this situation is p = 4 + 5d
What are algebraic expressions?Algebraic expressions are known as mathematical expressions made up of:
VariablesConstants AdditionSubtractionMultiplicationSome other algebraic operationsFrom the information given, we have that:
p is the number of pennies in the jard is the number of dimes in the jarThe number of pennies in a jar of coins is 4 more than 5 times the number of dimes in the jarThe equation this represents is:
p = 4 + 5d
Thus, the equation that represents this situation is p = 4 + 5d
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someone please help asap.. what even is this. ill give brainliest
Given: line AC is perpendicular to line BC
Prove: the slopes of lines AC and BC is -1
Complete the Proof.
first blank: angle addition; definition of perpendicular lines; definition of congruent angles; definition of a straight angle.
second blank: addition property of equality; subtraction property of equality; transitive property of equality; substitution property of equality.
third blank: transitive property of equality; substitution property of equality; definition of slope; corresponding sides of similar triangles are proportional.
fourth blank: multiplication property of equality; substitution property of equality; addition property of equality; transitive property of equality.
Answers
Congruency property relates to two or more triangles with similar dimensions, and internal angles. So that the required statements to complete the proof are:
1. definition of a straight angle.
2. subtraction property of equality
3. corresponding sides of similar triangles are proportional
4. transitive property of equality.
The intersection of two or more lines forms a number of angles which depends on the number of lines involved. These angles formed may have similar or different properties.
When two or more triangles have similar lengths of sides and measure internal angles, it can be said that they are congruent. Thus they have some common properties.
Therefore, the appropriate statements to answer the given question are stated below:
Definition of a straight angle.Subtraction property of equality.Corresponding sides of similar triangles are proportional.Transitive property of equality.For more clarifications on the properties of congruent triangles, visit: https://brainly.com/question/15835221
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Which expression is a perfect cube?
Answers
Answer:
Step-by-step explanation:
Only is a perfect cube
I will give barinliest please help
Answers
Answer:
Step-by-step explanation:
In order:
50.24,
12.56,
3.14,
200.96,
113.04,
38.465,
153.86,
28.26,
19.625
If there is no joint variability between two variables, then the r value will be?
Answers
Answer:
If r=0, there is absolutely no relationship between the two variables.
Step-by-step explanation:
Adjacent angles and their uncommon sides are opposite rays
Answers
Adjacent angles are angles that share a common vertex and a common side but do not overlap. The uncommon sides of adjacent angles are opposite rays.
Adjacent angles are two angles that share a common vertex and a common side, but their interiors do not overlap. In other words, they are side by side. For example, if we have two adjacent angles, angle A and angle B, they would share a common vertex, say point O, and a common side, say line segment OA. The interior of angle A does not overlap with the interior of angle B.
The uncommon sides of adjacent angles are the sides that are not shared by the angles. In our example, the uncommon sides would be line segment OB for angle A and line segment OB for angle B. These uncommon sides are opposite rays. Opposite rays are two rays that have the same initial point but extend in opposite directions, forming a straight line. So, line segment OB extends indefinitely in one direction and line segment OB extends indefinitely in the opposite direction, forming a straight line.
Understanding this concept is useful in geometry because it allows us to identify and analyze adjacent angles in various geometric figures. It helps us establish relationships between angles and apply angle properties to solve problems. Recognizing that the uncommon sides of adjacent angles are opposite rays provides a foundation for reasoning about angles and their relationships within geometric systems.
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Diego and Amit were trying to solve the equation: x^2-8x=1x 2 −8x=1x, squared, minus, 8, x, equals, 1 Diego said, "I can solve by completing the square. If I add 161616 to each side, I can rewrite the equation as (x-4)^2=17(x−4) 2 =17left parenthesis, x, minus, 4, right parenthesis, squared, equals, 17." Amit said, "I'll subtract 111 from each side and rewrite the equation as x^2-8x-1=0x 2 −8x−1=0x, squared, minus, 8, x, minus, 1, equals, 0. Then I'll use the quadratic formula with a=1a=1a, equals, 1, b=-8b=−8b, equals, minus, 8, and c=-1c=−1c, equals, minus, 1." Whose solution strategy would work? Choose 1 answer: Choose 1 answer: (Choice A) A Only Diego's (Choice B) B Only Amit's (Choice C) C Both (Choice D) D Neither
Answers
Answer:
Both.
Step-by-step explanation:
Answer:
both
Step-by-step explanation:
guy above me is right
mike earns a 3 1/2% commission on sales of 90,000 what was his commission pay?
Answers
Answer:
3150
Step-by-step explanation:
(3.5×90000)/100
=3150
6. You have 220 feet of fencing material to enclose a rectangular area for your pet animals. Let x = the length of the rectangular enclosure. (a) [7 points] Set up the function A(x) that represent the enclosed area. (b) [7 points] What should be the dimensions of the enclosed area? (c) [2 points] What is the maximum area of the enclosed area?
Answers
Answer:
I will start with (c)
(c) What is the maximum area of the enclosed area?
the maximum area of a rectangle is always given by a square figure
since the square has 4 equal sides, each side will be 220 / 4 = 55 ft long
maximum area = 55 x 55 = 3,025 ft²
(b) What should be the dimensions of the enclosed area?
the dimensions would be 55 ft in length by 55 ft in width
(a) Set up the function A(x) that represent the enclosed area.
perimeter of the rectangle = 220
we have 4 equal sides, so
A(x) = x²
Zachary earns $5 per hour, and he makes a $20 bonus.
His equation is shown in red on the graph, y = 5x + 20.
Maisy earns $7.50 per hour, and she makes a $5 bonus.
Her equation is shown in blue on the graph, y = 7.50x +
5.
After how many hours do they earn the same amount of
money? Where do you see this on the graph? Share
your answer with the class when you are finished, then
read other people's responses.
Answers
Answer:
5x?
Step-by-step explanation:
Because Zachary earns $5 per hour, and he makes a $20 bonus.
His equation is shown in red on the graph, y = 5x + 20.
Maisy earns $7.50 per hour, and she makes a $5 bonus.
Her equation is shown in blue on the graph, y = 7.50x +
5.
After how many hours do they earn the same amount of
money? Where do you see this on the graph? Share
your answer with the class when you are finished, then
read other people's responses.
Simplify the trigonometric expression below by writing the simplified form in terms of cos x. Enclose arguments of functions in parentheses. For example, sin (2x). tan x+cotx/csc x = ____
Answers
The simplified form of the expression is sec x.
Substituting these identities into the expression, we get:
(tan x + cot x) / csc x
= (sin x / cos x + cos x / sin x) / (1 / sin x)
To simplify further, we can combine the fractions by taking the common denominator:
= [(sin^2 x + cos^2 x) / (cos x * sin x)] / (1 / sin x)
Using the Pythagorean identity sin^2 x + cos^2 x = 1, we have:
= [1 / (cos x * sin x)] / (1 / sin x)
Next, we can simplify by multiplying the numerator and denominator by sin x:
= [1 / (cos x * sin x)] * (sin x / 1)
= 1 / cos x
The simplified form of the expression is sec x.
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A normally distributed process has specifications of LSL = 75 and USL = 85 on the output. A random sample of 25 parts indicates that the process is centered in the middle of the specification band (i.e. sample mean = 80) and the sample standard deviation is s = 1.5. Obtain the estimate of Cp. Is this process capable? (Note that if Cp ≥ 1.0, a process is capable) Suppose you produce 100 parts per day. How many defective parts do you expect per day?
Answers
The normally distributed process has specifications of LSL = 75 and USL = 85 has a Cp of 2.22 , this process is capable and 0.08 defective parts can be expected per day.
To obtain the estimate of Cp, we first need to calculate the process capability index (Cpk) using the formula:
Cpk = min[(USL - mean) / (3 * standard deviation), (mean - LSL) / (3 * standard deviation)]
In this case, the sample mean is 80 and the sample standard deviation is 1.5, so:
Cpk = min[(85 - 80) / (3 * 1.5), (80 - 75) / (3 * 1.5)]
= min[1.11, 1.11]
= 1.11
To obtain Cp, we simply multiply Cpk by 2, since Cp = 2 * Cpk when the process is centered:
Cp = 2 * Cpk
= 2 * 1.11
= 2.22
Since Cp is greater than 1.0, this process is capable.
To calculate the expected number of defective parts per day, we need to know the proportion of parts that are defective.
Assuming that the process is centered, the proportion of parts that are defective can be estimated using the area under the normal distribution curve beyond the specification limits.
Since the process is normally distributed with mean 80 and standard deviation 1.5, we can use a standard normal distribution table to find the area beyond the limits:
Area beyond USL = P(Z > (USL - mean) / standard deviation) = P(Z > (85 - 80) / 1.5) = P(Z > 3.33) = 0.0004
Area beyond LSL = P(Z < (LSL - mean) / standard deviation) = P(Z < (75 - 80) / 1.5) = P(Z < -3.33) = 0.0004
So the proportion of parts that are defective is:
Proportion defective = 0.0004 + 0.0004 = 0.0008
To find the expected number of defective parts per day, we multiply this proportion by the number of parts produced per day:
Expected number of defective parts per day = 0.0008 * 100 = 0.08
So we would expect to see approximately 0.08 defective parts per day.
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ABCD is a quadrilateral.
Work out angle x.
В.
B
8 cm
A
X
6 cm
D
FIND x (
ABCD IS A QUADRILATERAL)
29%
13 cm
C
Answers
(Use law of sines)
A/Sin a = B/Sin b
10/Sin 29 = 13/Sin x
Sin(x)=(13sin(29))/10
Sin(x)= 0.63
(x=39)
Session 4: Editing Basics:Question 5
Color connotations and emotions associated with
colors are set in stone.
Select one:
Time Left: 1 hr, 25 mins Stop Assessm
O False
O True
Answers
Answer:
True
Step-by-step explanation:
Y
2
0
A
с
B
o'
D
Which point is located at
(11.2)
Answers
The point that is located at the ordered pair (4, -2) is given as follows:
Point B.
How to define the ordered pair?The general format of an ordered pair is given as follows:
(x,y).
In which the coordinates are given as follows:
x is the x-coordinate.y is the y-coordinate.On the coordinate plane, we have that:
x is the horizontal coordinate.y is the vertical coordinate.Hence the coordinates for this problem are given as follows:
A(-2, 4), B(4, -2), C(-4, 2) and D(2, -4).
Missing InformationThe graph is given by the image presented at the end of the answer.
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I need help plz on this problem
Answers
3(x - 4) + 9 = 18
Step by step (and explanation)
Answers
Answer:
= 7
Step-by-step explanation:
3(x−4)+9=18
3 − 1 2 + 9 = 1 8
3 − 3 = 1 8
3 = 1 8+3
3 = 21
x= 21/3
x=7
Shawn has a coupon that reduced their total bill from 31.58 to 26.58.what percentage of the original bill did they save with the coupon?
Answers
Answer: 15.83%
Step-by-step explanation: To find the percentage of the original bill saved with the coupon, you need to find how much of the original bill is reduced by. 31.58 - 26.58 = 5. And 5 is what percentage of 31.58. So you do 5/31.58 and multiply by 100% to get the answer in percent.
Five balls, A, B, C, D, and E, weigh 30g, 50g, 50g, 50g, and 80g each. Which ball weighs 30g?
Answers
Ball A weighs 30g, as stated in the problem
We have,
The problem states that there are five balls, labeled A, B, C, D, and E, and provides their respective weights:
A weighs 30g, B weighs 50g, C weighs 50g, D weighs 50g, and E weighs 80g.
There is only one ball that weighs 30g in this problem, which is ball A.
The other balls weigh different amounts - ball B, C, and D all weigh 50g, and ball E weighs 80g.
It is possible that the question is asking which ball does not weigh 30g, in which case the answer would be any of the balls except for ball A.
However, based on the wording of the original question, it specifically asks which ball weighs 30g, making ball A the correct answer.
Therefore,
The ball that weighs 30g is Ball A.
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The length of each side of a square is 6 feet more than the length of a side of a regular Octagon. The perimeter of the square is equal to the octagon. Find the length of the square and the length of a side of the octagon.
Please show work, I will give brainliest.
Answers
9514 1404 393
Answer:
square: 12 ft sidesoctagon: 6 ft sidesStep-by-step explanation:
This problem can be worked in your head.
If the perimeters of the square and regular octagon are the same, the side length of the 4-sided square must be the same as the length of 2 sides of the 8-sided octagon. Since the side of the square is 6 ft more than the side of the octagon, each side of the octagon must be 6 ft, and each side of the square must be 12 ft.
__
We can let s represent the side length of the octagon. Then we have ...
8s = perimeter of octagon
4(s +6) = perimeter of square
These are equal, so ...
4(s +6) = 8s
s +6 = 2s . . . . . . divide by 4
6 = s . . . . . . . . . . subtract s
The octagon has 6-ft sides; the square has 12-ft sides.
Jenny has $2.40 deducted from her monthly allowance every time she forgets to do a chore. If she forgets three times in a month, What will be the change in Jennys total allowance? A $7.20 B $5.40 C -$6.40 D -$7.20
Answers
Answer:
D -$7.20
Step-by-step explanation:
If she takes (substance) $2.40 every times she forgets to do a chores you have to substance but first you have to multiply because she forgets 3 times 2.40 × 3 is 7.20but since she taking it away it would be negativeso your answer is -$7.20
I hope this helps
$7.20 will be Jennys total allowance.
What is Unitary Method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary Method
First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
Jenny has $2.40 deducted from her monthly allowance every time she forgets to do a chore.
If she forgets three times in a month.
Thus, Jennys total allowance will be
=2.40 x 3
=$7.20
Hence, $7.20 will be Jennys total allowance.
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In a sporting event, the championship is won by the first team to win four games. The lengths of the championship games are given in the table. Let X denote the number of games that it takes to complete a championship, and Y denote the number of games that it took to complete a randomly selected championship from among those considered in the table. Use this information to answer parts (a) and (b) below Click the icon to view the frequency table for the number of games required to complete previous championship series Determine the mean and standard deviation of the random variable Y. The mean is ___games(Round to three decimal places as needed.) The standard deviation is ___ games (Round to three decimal places as needed.)
Answers
The mean of the random variable Y is 5.71.
The standard deviation of the random variable Y is 1.13.
Given a table that shows the lengths of the championship games, the frequency, and the relative frequency.
Mean can be found as:
Mean = [(4)(19) + (5)(22) + (6)(24) + (7)(32) ] / [9 + 22 + 24 + 32]
= 554/97
= 5.71
Standard deviation can be found as:
Standard deviation = √[(19)(4)² + (22)(5)² + (24)(6)² + (32)(7)²] - ((554)² / 97) ] / 96
= √1.26997
= 1.13
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The missing table is given below:
Number of games Frequency Relative frequency
4 19 0.196
5 22 0.227
6 24 0.247
7 32 0.330
need help with this question
Answers
The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.
What is an explicit formula?
The explicit equations for L-functions are the relationships that Riemann introduced for the Riemann zeta function between sums over an L-complex function's number zeroes and sums over prime powers.
Here, we have
Given: the sequence 14,16,18,….
First term a₁ = 14
Common difference d = 16 - 14 = 2
Now, plug the values into the above formula and simplify.
aₙ = a₁ + d( n - 1 )
aₙ = 14 + 2( n - 1 )
aₙ = 14 + 2n - 2
aₙ = 14 - 2 + 2n
aₙ = 2n + 12
Hence, the explicit formula is aₙ = 2n + 12.
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Can someone help me with this?
Answers
Answer:
\( \sqrt{30} \)
A.
Write a recursive formula for the sequence 8, 10, 12, 14, 16,. Then find the next term.
a = a,-1 + 2, where a, 8; 18
b.
a.
+ 2, where a
18; 8
c.
a, = a -1 -2, where a, 8; 18
d. A, = a. -1
2, where a, = = 2; -2
= a. - 1
Answers
The recursive formula for the sequence is a(n) = a(n - 1) + 2 and the next term is 18
Writing a recursive formula for the sequenceFrom the question, we have the following parameters that can be used in our computation:
8, 10, 12, 14, 16,.
In the above sequence, we have
First term, a(1) = 8
And we have the common difference to be
d = 2
So, we have
a(n) = a(n - 1) + 2
The next term of the sequence is
Next = 16 + 2
Evaluate
Next = 18
Hence, the recursive formula for the sequence is a(n) = a(n - 1) + 2
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Identify the volume of the composite figure. Round to the nearest tenth. Need help ASAP. Need all of the steps please
Answers
The volume of the composite figure is equal to 860.6 cubic meters to the nearest tenth
How to calculate for the volume of the figureThe composite figure is a cuboid with a cylinderical open space within, so the volume is derived by subtracting the volume of the cylinderical open space from the volume of the cuboid as follows:
Volume of cuboid = length × width × height
Volume of the cuboid = 10m × 10m × 12m
Volume of the cuboid = 1200m³
Volume of cylinder is calculated using:
V = π × r² × h
Volume of the cylinder = 22/7 × (3m)² × 12m
Volume of the cylinder = 339.4m³
Volume of the composite figure = 1200m³ - 339.4m³
Volume of the composite figure = 860.6 m³
Therefore, the volume of the composite figure is equal to 860.6 cubic meters to the nearest tenth
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help asap if you can pls!!!!!!
Answers
The following statements can be concluded if ∠ABC and ∠CBD are a linear pair:
B. ∠ABC and ∠CBD are supplementary.
D. ∠ABC and ∠CBD are adjacent angles.
What is the linear pair theorem?In Mathematics, the linear pair theorem states that the measure of two angles would add up to 180° provided that they both form a linear pair. This ultimately implies that, the measure of the sum of two adjacent angles would be equal to 180° when two parallel lines are cut through by a transversal.
According to the linear pair theorem, ∠ABC and ∠CBD are supplementary angles because BDC forms a line segment. Therefore, we have the following:
∠ABC + ∠CBD = 180° (supplementary angles)
m∠ABC ≅ m∠CBD (adjacent angles)
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