Simplify square root of 540 Radical way
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6. Which ordered pair is a solution to this system of equations below ? *7х + 5y = 59Зх — 9y = 159О(( -17, -12)О (-17, 12)О(17, -12)(17,12)
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Answer:
(17, -12)
Explanation:
The system of equations is
7x +5y = 59
3x - 9y = 159
An ordered pair satisfies the system if it satisfies both equations. So, for each option we need to replace the ordered pair on the given equations.
For (x, y) = (-17, -12)
7x +5y = 59
7(-17) + 5(-12) = 59
-119 - 60 = 59
-179 = 59
The equality is not satisfied, so (-17, -12) is not a solution to this system
For (x, y) = (-17, 12)
7x +5y = 59
7(-17) + 5(12) = 59
-119 + 60 = 59
-59 = 59
The equality is not satisfied, so (-17, 12) is not a solution to this system
For (x, y) = (17, -12)
7x +5y = 59
7(17) + 5(-12) = 59
119 - 60 = 59
59 = 59
3x - 9y = 159
3(17) - 9(-12) = 159
51 + 108 = 159
159 = 159
Since both equations are satisfied, so (17, -12) is a solution to the system of equations
Therefore, the answer is (17, -12)
Evaluate.
(2a−1/3)÷b/15 when a=−3/5 and b=−6.75
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The simplified mixed number upon evaluation is [tex]3\frac{11}{27}[/tex].
What is a mixed number?Mixed numbers, also known as mixed fractions, are made up of a whole number and a proper fraction (a fraction whose numerator is less than its denominator). There are a few features that mixed numbers and decimals have in common. A decimal number is made up of a whole number and a fractional element separated by a decimal point. A mixed number is made up of a whole number and a proper fraction, but they are not separated by a decimal point.Given:
a = −3/5 and b = −6.75
We have to determine the value of (2a−1/3) ÷ b/15.
Substituting the values of a and b in the expression, we get
(2(−3/5)−1/3) ÷ (−6.75)/15
⇒ (-6/5 - 1/3) ÷ (-0.45)
⇒ (-23/15) ÷ (-0.45)
⇒ 23/15 × 100/45
⇒ 92/27
⇒ [tex]3\frac{11}{27}[/tex]
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a groundskeeper needs grass seed to cover a circular field 290 ft in diameter. a store sell 50 lb bags of grass seed. 1 lb of grass seed covers about 400 square feet of field. what is the smallest number of bags the groundskeeper must buy to cover the circular field?
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The diameter of circular field is 290ft .
The area of circular field is
[tex]A=\Pi(r^2)^{}[/tex][tex]A=\Pi(145)^2=66018.5ft^2[/tex]It is given that 1 lb of grass seed covers about 400 square feet of field.
The smallest number of bags he should buy is
[tex]\frac{66018.5}{400}=165\text{ bags}[/tex]Ay help a guy out, won’t you? I’m very lost I only got until November 12th.
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The quadratic equations solved using the square root property is;
a. x = -3 and 7
b. x = 3 and -11
How to solve the quadratic equationsGiven the quadratic equation as;
(x -2)² - 11 = 14
To determine the roots, we have to take the following steps;
expand the bracket
(x-2)(x-2) - 11 = 14
x² -2x -2x + 4 - 11 =1 4
collect like terms
x² - 2x - 2x + 4 -11 - 14 = 0
Add or subtract like terms
x² - 4x - 21 = 0
Factorize the equation
x² - 7x + 3x - 21 = 0
factorize further
x(x - 7) + 3(x - 7) = 0
Then. x = - 3, x = 7
x² + 8x + 16 = 49
collect like terms
x² + 8x + 16 - 49 = 0
x² + 8x - 33 = 0
Factorize further
x² + 11x - 3x - 33 = 0
x( x + 11) - 3(x + 11) = 0
Then, x = 3 and x = -11
Hence, the values are -3 and 7 and 3 and -11 respectively.
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What is the inverse of the function h(x) = 3 over 4 x+12
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To answer this question we will set the equation y=f(x), then we will solve the equation for x, and finally, we will exchange x and y.
Setting y=f(x) we get:
[tex]y=\frac{3}{4}x+12.[/tex]Subtracting 12 from the above equation we get:
[tex]\begin{gathered} y-12=\frac{3}{4}x+12-12, \\ y-12=\frac{3}{4}x\text{.} \end{gathered}[/tex]Multiplying the above equation by 4/3 we get:
[tex]\begin{gathered} (y-12)\times\frac{4}{3}=\frac{3}{4}x\times\frac{4}{3}, \\ x=\frac{4}{3}y-16. \end{gathered}[/tex]Exchanging x and y in the above equation we get:
[tex]y=\frac{4}{3}x-16.[/tex]Therefore the inverse function of h(x) is:
[tex]h^{-1}(x)=\frac{4}{3}x-16.[/tex]Answer:
[tex]h^{-1}(x)=\frac{4}{3}x-16.[/tex]Yesterday, Charmaine went on a bike ride. Her average speed was 10 miles per hour. Today, she went on another ride, this time averaging 13 miles per hour. In
the two days, she biked for a combined total time of 12 hours.
Let x be the number of hours she biked yesterday. Write an expression for the combined total number of miles she biked in the two days.
total number of miles biked
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Use your calculator to find tan−1(5) to the nearest degree.
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79 degree
Explanation:
When typing tan^-1 (5), click on the function that allows you to access the tan^-1 (generaly above the tan option),
A washer and a dryer cost $905 combined. The washer costs $55 more than the dryer. What is the cost of the dryer?sXХ5?
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Solution:
Given:
Let the washer be represented by w.
Let the dryer be represented by d.
Hence,
[tex]\begin{gathered} A\text{ w}asher\text{ and a dryer cost \$}905 \\ This\text{ means;} \\ w+d=905.........................(1) \\ \\ \\ The\text{ washer costs \$55 more than the dryer} \\ w=d+55..........................(2) \end{gathered}[/tex]Substituting the equation (2) into equation (1);
[tex]\begin{gathered} d+55+d=905 \\ 2d+55=905 \\ 2d=905-55 \\ 2d=850 \\ d=\frac{850}{2} \\ d=425 \\ \\ \\ Hence,\text{ } \\ w=d+55 \\ w=425+55 \\ w=480 \end{gathered}[/tex]Hence, the cost of the dryer is $425 and the cost of the washer is $480.
Therefore, the cost of the dryer is $425.
As she climbs a hill, a cyclist slows down from 40 km/h to 10 km/h in 10 seconds. What is her deceleration?
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Deceleration is the term used to describe a decrease in speed as the body moves away from the beginning place. The opposite of acceleration is deceleration. It is written as. Negative acceleration is another name for deceleration.
As she climbs a slope, a bicycle slows from 40 km/h to 10 km/h in 10 seconds. How quickly does she brake?
When motion changes, the term acceleration is used to describe it. It is customary to refer to accelerating as going faster and decelerating as going slower.
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x^2+16x+64 factor polynomial completely if polynomial is prime state this
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(x + 8)(x + 8)
Explanation:[tex]x^2\text{ + 16x + 64}[/tex]factors of 64 whose sum gives 16: +8 and +8
[tex]\begin{gathered} 8\text{ + 8 = 16} \\ 8(8)\text{ = 64} \\ x^2\text{ + 8x + 8x + 64} \end{gathered}[/tex]factorise:
[tex]\begin{gathered} x(x\text{ + 8) + 8(x + 8)} \\ (x\text{ + 8)(x + 8)} \\ \\ A\text{ polynomial is only prime if it not factorisable with an whole number.} \\ \text{This is a reducible polynomial (factorisable). Hence, not a prime} \end{gathered}[/tex]Hence, the factorised form:
(x + 8)(x + 8)
A linear function f(x) contains the coordinates (-9,4) and (6,4). Joy says f(x) is a horizontal line, and Lu says f(x) is a vertical line. Which student correctly described the function? Explain.
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The student whose name is Joy has described the function correctly as the line is horizontal line.
What are the coordinates ?
Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.
The given coordinates of the linear function f(x) are (-9, 4) and (6,4).
The y-coordinates for both of these points will be the same if we plot them on the graph.
Additionally, if the y-coordinates on the graph are the same, then the line connecting these points is horizontal in nature.
So , we can conclude that , Joy is saying correct by saying it is a horizontal line.
Therefore , the student whose name is Joy has described the function correctly as the line is horizontal line.
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Find the x-intercept and y-intercept of the graph of − 2 x + 3 y = − 6 . Then graph.
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The x and y intercepts of the graph - 2x + 3y = - 6 are (3, 0) and (0, -2).
What are the x and y intercepts?We know to find the x-intercept of a graph we have to substitute y = 0 in the given equation and to find the y-intercept we have to substitute x = 0 in the given equation.
The graph of the equation is - 2x + 3y = - 6.
Now at y = 0, the equation becomes
- 2x + 3(0) = -6.
- 2x = - 6.
2x = 6.
x = 3.
Now at x = 0, the equation becomes
- 2(0) + 3y = - 6.
3y = - 6.
y = - 2.
∴ The x and y intercepts of the graph are (3, 0) and (0, -2).
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PROBLEM: Equivalent Expressions Create three different expressions that are each equal to 20. Each expression should include only these three numbers: 4. -2. and 10.
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Given the numbers: 4, -2, and 10.
We want to create three different expressions that are each equal to 20.
First Expression
[tex](4-2)\times10=20[/tex]Second Expression
[tex]\begin{gathered} (4\times10)+(-2\times10) \\ =40+(-20) \\ =40-20 \\ =20 \end{gathered}[/tex]Third Expression
[tex]\begin{gathered} 10\lbrack4+(-2)\rbrack \\ =10\lbrack4-2\rbrack \\ =10\times2 \\ =20 \end{gathered}[/tex]Using factoring, what are the solutions to the polynomial below? 2x ^ 3 + 4x ^ 2 - 30x = 0
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We can start solving the solution to the polynomial given by factoring out 2x, getting:
[tex]2x(x^2+2x-15)=0[/tex]The expression inside the parenthesis is a quadratic equation. By methods of factoring, we can rewrite this as:
[tex]\begin{gathered} 2x((x+5)(x-3))=0 \\ 2x(x+5)(x-3)=0 \end{gathered}[/tex]Solving for the value of x that satisfies the polynomial given, we have:
[tex]\begin{gathered} 2x=0,x+5=0,x-3=0 \\ x=0,x=-5,x=3 \end{gathered}[/tex]Hence, the solutions to the polynomial given are x = -5, 0, 3.
Answer: x = -5, 0, 3
please help me find the y-intercept in the graph!
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Answer:
(0,9)
Step-by-step explanation:
simplify the product using a table [tex]( - 3h - 4)(4h - 3)[/tex]
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1) Simplifying this product, using the distributive property
(-3h -4)(4h-3)
-12h²+9h-16h+12
-12h²-7h +12
2) Inserting the table, or better making a similar one, multiplying the row by the column number:
_____|4h | -3 |
-3h | -12h² | 9h |
------------------------------
-4 | -16h | 12
------------------------------
-12h² +9h -16h +12
-12h² -7h +12
3) So the answer is -12h²-7h +12
what is the answer to the equation 14=-2-6-3
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14 = -2c - 6 - 3c
14 + 6 = -2c - 3c
20 = -5c
c = 20/-5
c = -4
A student entering a doctoral program in educational psychology is required to select three courses from the list of courses provided as part of his or herprogram(a) List all possible three-course selections.(6) Comment on the likelihood that EPR 669, EPR 634, and EPR 679 will be selectedClick the icon to view the course list(a) Select all the possible three-course selections below.A. 669,644, 679C. 669,634, 644DE 669.669, 634G. 669, 679, 6561669,634, 656K. 669, 669M. 634, 644,679(b) There is a chance that these courses will be selected.(Simplify your answer)B. 634, 644, 656D. 669. 644, 656OF 634, 679,656DH. 669,634, 679J. 656, 612, 656OL. 644,679, 656N. 644, 656, 644
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(a) We need to find the number of combinations of selecting 3 courses of a group of 5 courses.
The number of combinations of n things chosen r at a time is found using:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]Substituting with n = 5 and r = 3, we get:
[tex]_nC_r=\frac{n!}{r!(n-r)!}=\frac{5!}{3!(5-3)!}=\frac{5\cdot4\cdot3!}{3!2!}=\frac{5\cdot4}{2\cdot1}=10[/tex]The 10 possible combinations are:
• 669, 644, 679
,• 669, 634, 644
,• 669, 679, 656
,• 669, 634, 656
,• 634, 644, 679
,• 634, 644, 656
,• 669, 644, 656
,• 634, 679, 656
,• 669, 634, 679
,• 644, 679, 656
(b) There is a 1 in 10 chance that these courses will be selected
A 22-foot-tall structure standing next to a 5-foot shed casts a shadow. If the shed's shadow is 40 feet
long, how long is the structure's shadow?
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Answer:
176 feet of shadow
Step-by-step explanation:
Since 5 feet cast 40 feet, that means that 1 foot casts 8 feet. 22*8 = 176.
Can somebody answer on 2 and 4 I’m lost
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The measure of the angles are given below.
What is an angle?
An angle is a symbol in Euclidean space made up of two arcs that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of 2 dimensions ultimately creates angles. We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves. Angle can also refer to the length of a rotation or an angle. This metric represents the relationship between a circular arc's length and radius. The arc is centered when there is a geometric angle.
Answer 2
angle 1 = angle 6 = angle 9 = angle 14 = 97°
angle 4 = angle 7 = angle 12 = angle 15 = 114°
angle 2 = angle 5 = angle 10 = angle 13 = 180° - 97° = 83°
angle 3 = angle 8 = angle 11 = angle 16 = 180° - 114° = 66°
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Which are the intercept points and vertex point for the function ƒ(x) = x^2 + 5x + 6?
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Answer:
The intercept points are:
[tex]\begin{gathered} (-3,0) \\ (-2,0) \end{gathered}[/tex]The vertex is:
[tex](-\frac{5}{2},-\frac{1}{4})[/tex]Step-by-step explanation:
To find the intercept points, we equal the function to zero and solve for x, as following:
[tex]\begin{gathered} x^2+5x+6=0 \\ \rightarrow(x+3)(x+2)=0 \\ \\ \rightarrow x+3=0\Rightarrow x_1=-3 \\ \\ \rightarrow x+2=0\Rightarrow x_2=-2 \end{gathered}[/tex]Now, we know that the intercept points have an x-value of -3 and -2. Since we're talking about intercepts, the y-values will be 0.
Therefore, we can conlcude that the intercept points are:
[tex]\begin{gathered} (-3,0) \\ (-2,0) \end{gathered}[/tex]The vertex of any given quadratic function in the form:
[tex]f(x)=ax^2+bx+c[/tex]is:
[tex](-\frac{b}{2a},f(-\frac{b}{2a}))[/tex]This way, for the given function, we'll have that the vertex point is:
[tex](-\frac{5}{2},-\frac{1}{4})[/tex]Eleni's landscaping company placed two orders. The first order was for 13 bushes and 4 trees and totaled $487. The second order was for 6 bushes and 2 trees and totaled $232. What is the price of one tree?
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The required cost of the bushes is $23 and the cost of the tree is $45.
What is arithmetic?
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Let the prices of bushes are x and prices of tress are y,
According to the question,
13x + 4y = 487 - - - - - -(1)
6x +2y = 232 - - - - - - -(2)
From equation 2
y = 116 - 3x - - - - -(3)
Put this y in equation 1
13x + 4(116 - 3x) = 487
13x + 464 - 12x = 487
x = 487 - 464
x = 23
Now put this x in equation 3
y = 116 - 3(23)
y = 116 - 69
y = 45
Thus, the required cost of the bushes is $23 and the cost of the tree is $45.
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Differentiate. y 5 ody (AX (52 O dy 5 (4x - 52
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ANSWER
[tex]\frac{dy}{dx}\text{ = }\frac{-5}{(4x-5)^2}[/tex]EXPLANATION
We want to differentiate y given:
[tex]y\text{ = }\frac{x}{4x\text{ - 5}}[/tex]To differentiate fractions as this, we first spllit the numerator and denominator as:
U = x
V = 4x - 5
Now, differentiate them separately.
dU/dx = 1
dV/dx = 4
Now, use formula:
[tex]\frac{dy}{dx}\text{ =}\frac{V\frac{du}{dx}\text{ - U}\frac{dV}{dx}}{V^2}[/tex]So, let us put those values in there:
[tex]\begin{gathered} \frac{dy}{dx}\text{ = }\frac{(4x\text{ - 5) }\cdot\text{ 1 - (x }\cdot\text{ 4)}}{(4x-5)^2} \\ \frac{dy}{dx}\text{ = }\frac{4x\text{ - 5 - 4x}}{(4x-5)^2} \\ \frac{dy}{dx}\text{ = }\frac{-5}{(4x-5)^2} \end{gathered}[/tex]That is the answer
do these pairs of values (x and y) represent two quantities that are proportional? x. y3. 125. 206. 249. 36
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Info given
We have the following info given
x. y
3. 12
5. 20
6. 24
9. 36
Solution
In order to see if the two quantites are prportional we can check the following:
k=y/x
If we analyze the first pair of values we have:
k= 12/3=4
And for the next pairs we have:
k= 20/5=4
k= 24/6=4
k=36/9=4
So then as we can see the value of k is the same so then we can say that x and y are proportional since for each unit that x increase y increase 4 units
helpppppppppppppppppppppppppp
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Answer:
yes
Step-by-step explanation:
The final answer would be -126<-105
What is the effect on the graph of f(x) = x2 when it is transformed toh(x) = 12 – 13?
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downloading about 35%
Use the figure to find the measures of the numbered angles. Explain your reasoning
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The measures of the numbered angles are as follows:
3.
m∠1 139°m∠2 = 41°m∠3 = 139° m∠4 = 139° m∠5 = 41°m∠6 = 139°m∠7 = 41°4.
m∠1 = 117° m∠2 = 63°m∠3 = 117°m∠4 = 63° m∠5 = 117° m∠6 = 63° m∠7 = 63° How to find measures of angles?When parallel lines are cut by a transversal line, angle relationships are formed such as alternate angles, corresponding angles, linear angles, vertically opposite angles etc.
Therefore, line a and b are parallel to each other. The transversal line t cut the parallel lines.
Hence,
3.
m∠1 = 180 - 41 = 139° (angles on a straight line)
m∠2 = 41° (vertically opposite angles)
Vertically opposite angles are congruent.
m∠3 = 139° (vertically opposite angles)
m∠4 = 180 - 41 = 139° (same interior angles)
Same interior angles are supplementary.
m∠5 = 41° (same interior angles)
m∠6 = 139° (vertically opposite angles)
m∠7 = 41° (vertically opposite angles)
4.
m∠1 = 117° (alternate exterior angles)
Alternate exterior angles are congruent
m∠2 = 180 - 117 = 63° (sum of angles on a straight line)
m∠3 = 117° (vertically opposite angles)
m∠4 = 63° (vertically opposite angles)
m∠5 = 117° (vertically opposite angles)
m∠6 = 180 - 117 = 63° (sum of angles on a straight line)
m∠7 = 63° (vertically opposite angles)
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Kindly help me with this question.
1. Given that f(x) = 2x-1, g(x) =(1/3) x 2 find:
i)(f o g(x)) ii) (g o f(x)) iii) (f o f(x)) iv) ( g o g(x)) v)confirm that f -1
(f(x))=x
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Graph one complete cycle of y = -sec(2)+3. and list out your critical values points. Include asymptotes, if any.
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Solution:
Given:
[tex]y=-sec(\frac{x}{4})+3[/tex]The graph of the above equation is shown below:
The critical values points are
[tex][/tex]Elsa, Chau, and Felipe served a total of 100 orders Monday at the school cafeteria. Chau served 3 times as many orders as Felipe. Felipe served 5 more orders than Elsa. How many orders did they each serve?
Answers
Answer:
Chau served 63 orders.
Elsa served 16 orders.
Felipe served 21 orders.
Step-by-step explanation:
Given information:
Elsa, Chau, and Felipe served a total of 100 orders.Chau served 3 times as many orders as Felipe. Felipe served 5 more orders than Elsa.Define the variables:
Let e = number of ordered Elsa served.Let c = number of ordered Chau served.Let f = number of ordered Felipe served.Create a system of equations from the given information and defined variables:
[tex]\begin{cases}e+c+f=100\\c=3f\\e=f-5\end{cases}[/tex]
Substitute the second and third equations into the first equation and solve for f:
[tex]\implies e+c+f=100[/tex]
[tex]\implies (f-5)+3f+f=100[/tex]
[tex]\implies 5f-5=100[/tex]
[tex]\implies 5f=105[/tex]
[tex]\implies f=21[/tex]
Substitute the found value of f into the second equation and solve for c:
[tex]\implies c=3f[/tex]
[tex]\implies c=3(21)[/tex]
[tex]\implies c=63[/tex]
Substitute the found value of f into the third equation and solve for e:
[tex]\implies e=f-5[/tex]
[tex]\implies e=21-5[/tex]
[tex]\implies e=16[/tex]
Therefore:
Chau served 63 orders.Elsa served 16 orders.Felipe served 21 orders.Let us assume that,
→ Elsa = x
→ Felipe = x + 5
→ Chau = 3x + 15
Now the required value of x,
→ x + x + 5 + 3x + 15 = 100
→ 5x + 20 = 100
→ 5x = 100 - 20
→ x = 80/5
→ [ x = 16 ]
Then the orders each serve is,
→ Elsa = x = 16
→ Felipe = x + 5 = 16 + 5 = 21
→ Chau = 3x + 15 = 48 + 15 = 63
Hence, the above one is correct.
