Select the correct answer.
Which statement describes the solutions of this equation?
(X/3) + (x-1/x+4) = (x+3/x+4) help please
Answers
The statement describes the solutions of this equation is
The Equation have two valid solution and No Extraneous solution.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
x/3 + (x-1)/ (x+ 4)= (x+3)/ (x+4)
Now, simplifying the above Expression
(x² + 4x + 3x - 3) / 3(x+4) = (x+3)/ (x+4)
(x² + 4x + 3x - 3) / 3 = (x+3)
x² + 7x -3 = 3(x+3)
x² + 7x -3 - 3x - 9 = 0
x² + 4x - 12 = 0
Solving the above Quadratic Equation
x² + 6x- 2x - 12 = 0
x(x+6)- 2(x+6)= 0
(x-2)(x+6)= 0
x= 2, -6.
So, the Equation have two valid solution and No Extraneous solution.
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Related Questions
Find the image of the given point
under the given translation.
P(12, 8)
T(x, y) = (x-8, y - 12)
Answers
P(12,8)
Move 8 units to the left (X) and 12 units down(Y).
P'(12-8, 8-12)
P'(4, -4)
If you don't how to do translation try plotting (12,8).
Find the distance the point P(3, 1, 7), is to the plane through the three points
Q(5, 0, 3), R(0, -1, 7), and S(7, 5, 0).
Answers
The distance between the point P and the plane through the points Q, R, and S is 60/23.
How did we get the value?The distance of a point P(x1, y1, z1) from a plane that passes through the points Q(x2, y2, z2), R(x3, y3, z3), and S(x4, y4, z4) can be found using the following formula:
d = |(A * x1 + B * y1 + C * z1 + D) / sqrt(A^2 + B^2 + C^2)|
Where A, B, and C are the coefficients of the plane's normal vector and D is the constant term in the equation of the plane. The normal vector can be found by taking the cross product of the vectors Q-R and Q-S:
n = (Q-R) x (Q-S)
The coefficients of the normal vector can be found using the following equations:
A = n1
B = n2
C = n3
D = -(A * x2 + B * y2 + C * z2)
Substituting the values of Q, R, and S, we have:
Q-R = (5-0, 0-(-1), 3-7) = (5, 1, -4)
Q-S = (7-5, 5-0, 0-3) = (2, 5, -3)
The cross product of Q-R and Q-S is:
n = (1 * -3 - 5 * -4, -3 * 5 - 2 * -4, -2 * 1 - 5 * 5) = (-23, 29, 17)
So,
A = -23
B = 29
C = 17
D = -(A * x2 + B * y2 + C * z2) = -(-23 * 5 + 29 * 0 + 17 * 3) = -109
Finally, substituting the values of x1, y1, and z1:
d = |(A * x1 + B * y1 + C * z1 + D) / √(A^2 + B^2 + C^2)|
= |(-23 * 3 + 29 * 1 + 17 * 7 + -109) / √(-23^2 + 29^2 + 17^2)|
= |(-69 + 29 + 119 -109) / √(-23^2 + 29^2 + 17^2)|
= |60 / √(-23^2 + 29^2 + 17^2)|
= |60 / √(529)|
= 60 / 23
So the distance between the point P and the plane through the points Q, R, and S is 60/23.
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Suppose that 71% of the surface of the Earth is covered in water, and a random number generator uses latitude and longitude to select a random location on the Earth. If 7 such locations are generated, what is the probability that the first 5 locations are in water and the last 2 locations are on land?
A. 0.0010
B. 0.0152
C. 0.0910
D. 0.9090
Answers
Answer:
0.0152 is the probability that the first 5 locations are in water and the last 2 locations are on land.
Add Decimals-Instruction - Level E
June makes slime using 1.5 liters of white glue and 0.72 liter of a starch and water mixture.
Find the total volume of the slime.
Are there enough hundredths to make a tenth?
➡ There are ? hundredths. That is
enough to make a tenth.
✓is
is not
Answers
➡ There are 22 hundredths. That is enough to make a tenth.
What is the arithmetic operations?
Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms,[disputed – discuss] which are highly important to the field of mathematical logic today.
The four basic mathematical operations are Addition, subtraction, multiplication, and division.
To find the total volume of the slime, we need to add 1.5 and 0.72:
1.5 + 0.72 = 2.22
There are 22 hundredths, which is enough to make a tenth.
Hence, the answer is:
➡ There are 22 hundredths. That is enough to make a tenth.
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The length of the dashed line in the circle
Answers
The length of the dotted line would be 7.922 ft.
What is the diameter of the circle?
The diameter of a circle is the distance across the circle through its center. It is equal to twice the length of the radius, which is the distance from the center of the circle to any point on the circle.
In mathematical terms, if d represents the diameter of a circle, and r represents its radius, we have the formula:
d = 2r
In the given circle, for finding the inner diameter we have to remove the thickness of the circle from outer diameter, we get
q = 17.708 - 4.893 - 4.893
By solving this, we get
q = 7.922
Hence, the length of the dotted line would be 7.922 ft.
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10 inches in 6 hours
80 inches in 2 days
Answers
The relation is a direct variation
How to determine if the relation is a direct variationFrom the question, we have the following parameters that can be used in our computation:
10 inches in 6 hours
80 inches in 2 days
Convert 2 days to hours
So, we have the following representation
10 inches in 6 hours
80 inches in 72 hours
For the relation to be a direct variation, the following must be equal
6/10 = 72/80
Evaluate
0.6 = 0.6
Hence, the relation is a direct variation
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Complete question
Determine if the following relation represents a direct variation
10 inches in 6 hours
80 inches in 2 days
what is statistics?
Answers
Statistics is referred to as a discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
What is Data?This is referred to as information that has been translated into a form that is efficient for movement or processing.
Statistics involves using information that has been translated into a form that is efficient for movement or processing through different tools such as mean standard deviation etc.They help to provide more details about a set of data which makes it use very important.
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How many solutions does the system have? { � = 5 � + 1 � = − 2 � − 8 ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ y=5x+1 y=−2x−8
Answers
The given system of linear equations has a unique solution.
What are linear equations?A linear equation is an algebraic equation in which each term has an exponent of 1 and when graphed, the result is always a straight line.
Given that, a system of linear equations, y = 5x+1 and y = -2x-8, we are asked to find how many solutions do they have,
The rule for a system of linear equations, a₁x+b₁y+c₁ = 0 and a₂x+b₂y+c₂ = 0 are :-
When the system has a unique solution :-a₁ / a₂ ≠ b₁ / b₂, and the lines intersect at one only point.
When the system has a no solution :-a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂, and the lines are parallel.
When the system has infinite solution :-a₁ / a₂ = b₁ / b₂ = c₁ / c₂, and the lines overlaps.
Checking for the given equations,
y = 5x+1 and y = -2x-8
Converting into standard form of the linear equations,
5x-y +1 = 0 and 2x+y+8 = 0
5/2 ≠ -1
The equation is following the rule of unique solution, also the graph is intersecting at one point, [graph is attached]
Hence, the given system of linear equations has a unique solution.
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Answer:
One solution
Step-by-step explanation:
A sample, sized 5, was taken with the following measurements: 5, 10, 2, 7, and 6.
What is the point estimate of the population mean?
Answers
The point estimate of the population mean is 6
What is the point estimate of the population mean?From the question, we have the following parameters that can be used in our computation:
Measurements: 5, 10, 2, 7, and 6.
Sample size = 5
The point estimate of the population mean is the sample size of the mean
Using the above as a guide, we have the following:
Sample mean = Sum/Count
substitute the known values in the above equation, so, we have the following representation
Sample mean = (5 + 10 + 2 + 7 + 6)/5
Evaluate
Sample mean = 6
Hence, the estimate is 6
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PLSSSS HELP ME ASAP I DONT UNDERSTAND THIS
Jon filled up the tank of his semitruck with 240 gallons of fuel and set out to deliver a shipment of vegetables. His truck uses an average of 0.15 gallons of fuel for each mile he drives. You can use a function to approximate the amount of fuel in Jon's tank after he drives x miles.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)^x.
Answers
The equation for the function is [tex]y=-0.15x+240[/tex].
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, occasionally referred to as a "linear equation of two variables."
It is given that the amount of fuel filled up in Jon's semi truck is 240 gallons.
It is also given that for 1 mile the truck uses 0.15 gallons of fuel.
So, for "x" miles, the truck uses 0.15*x gallons of fuel.
So, the remaining fuel in the tank will be 240-0.15x.
Let the remaining fuel be "y".
This can be written as:
[tex]y=240-0.15x\\y=-0.15x+240[/tex].
Therefore the remaining fuel in the tank after Jon drives x miles will be a linear equation [tex]y=-0.15x+240[/tex]
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Write the sentence as an equation.
242 fewer than the quantity 193 times n equals 131
Answers
I think this is it
252-(193×n) =131
The price (in S) of a cookbook is determined by the number of cookbooks x demanded by consumers and supplied by the publisher.
Supply: p=0.003.x
Demand: p= -0.008x+330
(a) Solve the system of equations defined by the supply and demand models.
(b) What is the equilibrium price?
(c) What is the equilibrium quantity?
Answers
The system of equations defined by the supply and demand models solved for equilibrium price is $9 and equilibrium quantity is 3000 units
How to solve system of equation?Supply:
p=0.003x
x = p/0.003
x = 1/0.003p
Demand:
p= -0.008x+330
-0.008x = p - 330
x = (p - 330)/-0.008
Equilibrium price
Equate supply and demand price
0.003x = -0.008x+330
0.003x + 0.008x = 330
0.011x = 330
x = 330/0.11
x = 3,000
Substitute into
p=0.003x
p = 0.003(3000)
p = $9
Consequently, the equilibrium quantity and price is 3000 units and $9
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6.88 + 3w= 17.98 find w
Answers
Answer:
3w= 17.98-6.88
3w=11.1
w =3.7
Step-by-step explanation:
After subtracting divide both side by 3
Answer:
w = 3.70
Step-by-step explanation:
Given that,
6.88 + 3w= 17.98 ..........(1)
Now subtracting both sides by 6.88 in equation (1), We have
6.88 + 3w - 6.88 = 17.98 - 6.88
or, 3w + 0 = 11.1
or, 3w = 11.1
Again dividing both sides by 3 in the above equation, We have
[tex]\frac{3w}{3}=\frac{11.1}{3} = 3.70[/tex]
Hence the required answer is w = 3.70
help help help help help help help help help help help help help help help
What is the number of sides of a regular polygon in which each interior angle has a measure of 165°?
Answers
Answer:
the answer is 24 sides
explanation
5.3A Find Two Numbers Whose Product and Sum is as Indicated
Answers
Due to length restrictions, we kindly invite to read the explanation of this question for further details about two numbers related to a given sum and a given product.
How to find a set of two real numbers
In this problem we find 48 case of two numbers that must be found and whose sum and product are given. Mathematically speaking, the expressions describing the problem:
x₁ + x₂ = b
x₁ · x₂ = c
Whose solution can be found by numerical methods.
Now we proceed to determine the values for each cases:
(x₁, x₂) = (6, 1)(x₁, x₂) = (4, 9)(x₁, x₂) = (3, - 2)(x₁, x₂) = (- 4, - 9)(x₁, x₂) = (- 8, 2)(x₁, x₂) = (2, - 2)(x₁, x₂) = (4, - 2)(x₁, x₂) = (- 4, 3)(x₁, x₂) = (- 5, - 4)(x₁, x₂) = (5, - 3)(x₁, x₂) = (6, 2)(x₁, x₂) = (- 2, - 3)(x₁, x₂) = (- 2, - 7)(x₁, x₂) = (2, 8)(x₁, x₂) = (11, - 2)(x₁, x₂) = (5, - 4)(x₁, x₂) = (- 8, 1)(x₁, x₂) = (8, - 3)(x₁, x₂) = (7, 8)(x₁, x₂) = (8, 8)(x₁, x₂) = (6, 4)(x₁, x₂) = (6, 9)(x₁, x₂) = (3 - 2√2, 3 + 2√2)(x₁, x₂) = (9, - 4)(x₁, x₂) = (8, - 7)(x₁, x₂) = (- 4, - 9)(x₁, x₂) = (8, - 2)(x₁, x₂) = (- 9, - 9)(x₁, x₂) = (- 15, 3)(x₁, x₂) = (7, - 6)(x₁, x₂) = (- 7, - 7)(x₁, x₂) = (- 8, - 8)(x₁, x₂) = (12, - 3)(x₁, x₂) = (- 3, - 8)(x₁, x₂) = (4, - 3)(x₁, x₂) = (- 12 - √119, - 12 + √119)(x₁, x₂) = (7, - 4)(x₁, x₂) = (- 6, - 9)(x₁, x₂) = (5, 7)(x₁, x₂) = (- 8, 4)(x₁, x₂) = (- 7, 6)(x₁, x₂) = (5 / 2 + √73 / 2, 5 / 2 - √73 / 2)(x₁, x₂) = (5, 6)(x₁, x₂) = (- 10, 4)(x₁, x₂) = (- 9, 4)(x₁, x₂) = (- 9, 7)(x₁, x₂) = (6, 8)(x₁, x₂) = (- 7, 3)To learn more on real numbers: https://brainly.com/question/24908711
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Please help will mark Brainly
Answers
Answer:
P=10x^2+38y
Step-by-step explanation:
its the answer
which is a true statement about two numerical sets of data that have negative association
Answers
Answer:
Option D.
Step-by-step explanation:
Negative correlation also called an " inverse correlation " is a relation between 2 variables where-by they behave in opposite manner. When one variable moves ---> in an increasing /\ direction, the other variable moves in a decreasing \/ direction.
Thus, Option D.
Find the area of a rectangle with side lengths 5/8ft. and 1/3 ft.
A. 5/11
B. 1 11/12
C. 6/11
D. 5/24
Answers
The area of a rectangle with side lengths 5/8ft. and 1/3 ft is: D. 5/24 ft².
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width or base of a rectangle.L represents the length or height of a rectangle.Substituting the given points into the area of rectangle formula, we have the following;
Area of rectangle = 5/8 × 1/3
Area of rectangle = 5/24 square feet.
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Circle the pair of like fractions 4/6and5/6and1/2and3/4and1/3and2/6 and1/10and2/100
Answers
The required pair of the like fraction among the given fraction is given as 1/3 and 2/6.
What is the fraction?A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.
Here,
For pairs of fraction area given we have to determine that fair of like fraction,
So we have to simplify the fraction given in the pair,
1. 4/6 and 5/6 = 2/3 and 5/6which not like pair of fraction, Similarly pairs [1/2 and 3/4] and [1/10and2/100] are not like fractions.
Now,
3. pair 1/3and2/6 is like fractions because 1/3 = 2/6 (=1/3)
Thus, the required pair of the like fraction among the given fraction is given as 1/3 and 2/6.
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Write 15*15*15*15 using an exponent
Answers
Answer:
15^4
Step-by-step explanation:
An exponent refers to the number of times a number is multiplied by itself,
so 15 multiplied 3 more times by itself (15 * 15 * 15 * 15) its 15^4.
[tex]15^{4} .[/tex]
Step-by-step explanation:1. General concept about exponents.When working with positive non fractional exponents, we state that a number A elevated to the n power is that number A in a multiplication of itself n times. For example, when we write [tex]7^{3}[/tex] we're stating that the seven is being multiplied 3 times: [tex]7*7*7[/tex].
2. Use the rule to rewrite the expression.As you may see, the expression "15*15*15*15" is just the number 15 being multiplied by itself four times. Hence, we could say that the number 15 to the power of 4. Thus, we can rewrite it as:
[tex]15^{4} .[/tex]
6 3/14 divided by 250 + 5 2/7 divided by 250
Answers
Answer:
The solution is 23/500 or 0,046
Step-by-step explanation:
6 3/14÷250+5 2/7÷250
= 6 3/14×1/250+5 2/7×1/250
= (87/14×1/250)+(37/7×1/250)
= (87/3500)+(37/1750)
= 87+37(2)/3500
= 87+74/3500
= 161/3500
= 161÷7/3500÷7
= 23/500
= 0,046
The sum of the digits in a two-digit number is 14. If you reverse
and double the original number, and then add the result to the
original number, the sum is 222. Find the original number. Please help me.
Answers
Answer:
The original number is 86.
Step-by-step explanation:
The only two-digit numbers whose digits sum to 14 are:
5968778695If we reverse and double the original number:
59 reversed is 95 → 95 × 2 = 19068 reversed is 86 → 86 × 2 = 17277 reversed is 77 → 77 × 2 = 15486 reversed is 68 → 68 × 2 = 13695 reversed is 59 → 59 × 2 = 118If we add the result of reversing and doubling the original number to the original number:
59 + 190 = 24968 + 172 = 24077 + 154 = 23186 + 136 = 22295 + 118 = 213As the sum of adding the result of reversing and doubling the original number to the original number is 222, the original number must be 86.
How do we rewrite 10^ -1 without using negative exponents?
Answers
Answer:
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
Suki wants to pour 25 milliliters
of water, 35 milliliters of oil,
and 45 milliliters of syrup into
the same beaker for a science
experiment. The beaker holds up to 100 milliliters. Will the beaker hold all three liquids? Explain why or why not.
Answers
Therefore, the beaker will not be able to hold all three liquids, and Suki will need to adjust the amount of one or more of the liquids in order for them to fit into the beaker.
If x=3. what is y=?
Y=
X: -3 0 3 6
Y: -5 -4 -3 -3
Answers
Answer:
Step-by-step explanation:
y = -3
The accompanying data represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0 liter engine.
(a)
Compute the z-score corresponding to the individual who obtained miles per gallon. Interpret this result.
(b)
Determine the quartiles.
(c)
Compute and interpret the interquartile range, IQR.
(d)
Determine the lower and upper fences. Are there any outliers?
Answers
a) The value of z-score is -0.299.
c) The IQR value is measure of spread of data, IQR = 4.25.
d) There is outliers since observations are not less than 30.375 and greater than 47.375.
What is z- score?The z-score is an example of a standardised score. The standard deviation of a data point's divergence from the mean of the distribution is calculated using a z-score.
Given:
Sample Data = 31.5, 36.0, 37.8, 38.5, 40.1, 42.2, 34.2, 36.2, 38.1, 38.7, 40.6, 42.5, 34.7, 37.3, 38.2, 39.5, 41.4, 43.4, 35.6, 37.6, 38.4, 39.6, 41.7, 49.3
(a) The value of z-score is calculated as follows,
μ = [tex]\sum _{i=1}^n[/tex]/ n = 933.1 /24 = 38.88
σ = 3.61
So, z = X - μ / σ
= 37.8 - 38.88/3.61
= − 0.299
(b) Quartile:
Q₁ = ( n+1/4)th value
= (24+1/4)th
= 6.25th
= 36.2 + 0.25 x ( 37.3 − 36.2 )
= 36.47
and, M = ( n+1/2)th value
= (24+1/2)th
= (24+1/4)th
= 12.5 t h
= 38.4 + 38.5/2
= 38.45
Q₃ = 3( n+1/4)th
= 3(24+1/4)th
= 18.75 t h
= 40.6 + 0.75 x ( 41.4 − 40.6 )
= 41.2
(c) Interquartile range
= Q ₃ − Q ₁
= 41.2 − 36.47
= 4.25
(d) Lower fences = Q₁− 1.5 ( I Q R )
= 36.75 − 1.5 ( 4.25 )
= 30.375
Upper fences = Q ₃+1.5
= 41 + 1.5( 4.25 )
= 47.375
Hence, there is outliers since observations are not less than 30.375 and greater than 47.375.
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Find the dimensions of a rectangular Persian rug whose perimeter is 22 ft and whose area is 10 ft squared
Answers
rectangular Persian rug's measurements are 10 ft in length and 1 ft in width.
How to calculated dimensions of a rectangular Persian rug?Let's say that the Persian rug is rectangular, with length "l" and width "w".
The total of a rectangle's four sides is known as the perimeter, and it can be calculated as follows:
Perimeter = 2l + 2w
Given that the distance around it is 22 feet, we can write:
2l + 2w = 22
When we simplify this equation, we obtain:
l + w = 11
A rectangle's area is determined by the product of its length and breadth, which may be written as follows:
l x w = area
Given that the space is 10 square feet, we can write:
l x w = 10
Two equations with two variables are now available:
L+W = 11, and L x W = 10.
To find l and w, we can utilise substitution or elimination. For instance, we can solve for w from the first equation in terms of l:
w = 11 - l
Using this expression as w's replacement in the second equation, we obtain:
l x (11 - l) = 10
The result of expanding and rearrangement is a quadratic equation:
l² - 11l + 10 = 0
Using the quadratic formula or factoring, we can solve this quadratic problem. Factoring results in:
(l - 10)(l - 1) = 0
so either l = 10 or l = 1 is true.
w = 1 if l = 10, otherwise. w equals 10 if l = 1.
As w is always smaller than l, we have
The rectangular Persian rug's measurements are 10 ft in length and 1 ft in width.
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write 76 in the base-nine system
Answers
The base-nine system of 76 base 10 is 84
What is 76 base 10 in the base-nine system?We will divide 76 by 9 and write down the remainder
9 | 76 R
9 | 8 | 4
9 |8 | 8
The remainder is then written from the bottom value giving us 84
Consequently, base 10 numbers can be converted to base 9 by dividing by 9 and writing the remainder in the reverse order of bottom to top.
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Charles and some friends ate at the Winterfield Café. Their bill was $50.00$ They paid $60.00. What percentage gratuity did they pay?
Answers
The percentage of gratuity paid is 20%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Amount for the bill = $50
Amount paid = $60
The amount of gratuity.
= 60 - 50
= $10
Now,
The percentage of gratuity.
= 10/50 x 100
= 20%
Thus,
The percentage of gratuity is 20%.
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verify the
identity algebraically.
Answers
Step-by-step explanation:
[tex] \frac{1}{ \sin(x ) } - \frac{1}{ \csc(x) } = \csc(x) - \sin(x) [/tex]
[tex] \frac{ \csc(x) - \sin(x) }{ \csc(x) \sin(x) } [/tex]
[tex] \csc(x) - \sin(x) = \csc(x) - \sin(x) [/tex]
