Jessica gets more rocks to skip across the surface of the pond than Henry.
To determine who gets more rocks to skip across the surface of the pond, we will take the ratio of rocks that skip to rocks that are thrown for each person.
For Henry, the ratio is 5 rocks that skip to 9 rocks thrown i.e 5/9.
For Jessica, the ratio is 7 rocks that skip to 12 rocks thrown i.e 7/12.
Now to compare the ratios, we need to convert them into like fractions. We will do this by making the denominations of both the fractions same.
We will multiply the numerator and denominator of Henry's ratio by 12 to get -
5/9 x 12/12 = 60/108
Also, we will multiply the numerator and denominator of Jessica's ratio by 9 to get -
7/12 x 9/9 = 63/108
Comparing the numerators we get 60<63.
This implies that 60/108 < 63/108.
Therefore, Jessica gets more rocks to skip across the surface of the pond.
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The complete question is -
Henry and Jessica skipping rocks across the surface of a pond. For every nine rocks Henry throws he got five of them to skip across the pond. For every twelve rocks
Jessica throws she got seven of them to skip across the pond. Who gets more rocks to skip across the surface of the pond?
An employee receives a 2% raise once per year. If the employee initial salary is $78,500.00, what will the employee’s salary be after 10 years
Answer:
Step-by-step explanation:
78,500 x 0.02 = 1,570--year 1 raise
(78,500 + 1,570) x 0.02 = 1,601.4--year 2 raise
(78,500 + 1,570+ 1,601.4) x 0.02 = 1,633.428--year 3 raise
(78,500 + 1,570+ 1,601.4+1,633.428) x 0.02 = 1666.1--year 4 raise
(78,500 + 1,570+ 1,601.4+1,633.428+1666.1) x 0.02 = 1699.42--year 5 raise
just keep doing this till you get to year 10 and then add up the total of money gained to the initial salary
3.
3a
Which is cheaper: 115 plums for $276.00 at Shop ZYX or 198 plums for $633.60 at Shop PWR?
What is the cost of a single plum at Shop ZYX?
= Enter your next step here
dollars
Shop ZYX represents the cheaper plan, with a cost of $2.4 per plum.
How to obtain the cheaper plan?To obtain the cheaper plan, we must obtain the cost of a single plum for each shop.
The cost of a single plum for each shop is obtained using a proportion, with the division of the total cost by the number of plums.
Hence the cost per plum in each shop is given as follows:
Shop ZYX: 276/115 = $2.4.Shop PWR: 633.6/198 = $3.2.(division of the total cost by the number of plums).
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Suppose that when your friend was born, your friend's parents deposited $5000 in an account paying 5.7% interest compounded quarterly. What will the account balance be after 19 years?
Answer:
$337,807.321.
Step-by-step explanation:
every year has 4 quarters, so 19 years = 76 quarters, so it compounds 76 times = (1+5.7%)^76. so punch into the calculator 1.057 then the "xy"button, then 76, it'll spit out 67.56146111 number. then hit times 5000. which is $337,807.321. power of compounding. More than a quarter million $$$.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 5.7\%\to \frac{5.7}{100}\dotfill &0.057\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &19 \end{cases} \\\\\\ A = 5000\left(1+\frac{0.057}{4}\right)^{4\cdot 19} \implies A=5000(1.01425)^{76}\implies A \approx 14655.18[/tex]
Given f (x)=-4x-5 find f(5)
Answer: -25
Step-by-step explanation:
For f(x) functions, all you do is plug in whatever value that is given in the parenthesis into x.
f(5) = -4(5) - 5
= -20 -5
= -25
How do you proof Triangle BSR is congruent to Triangle DUT
From the SSS Property of the triangle, Both triangles BSR and DUT are congruent.
What is the congruent triangle?Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.
Given, In the diagram, ABCD is a square, and R, S, T, and U are the midpoints of the sides of ABCD. Also, RT is perpendicular to SU and SV are equals to VU.
Since, R, S, T, and U are midpoints, and since RT is perpendicular to SU
in triangle DUT.
UD = TD
UD is also equal to VT since RT is perpendicular to SU
UD = TD = VT...(1)
And, From the Pythagorean theorem
UT = √(TD² + UD²)
In TRiangle BSR
BR = BS
BS is also equal to RV since RT is perpendicular to SU
BR = BS = RV...(2)
And, From the Pythagorean theorem
SR = √(BR² + BS²)
Since SV is equal to VU.
Thus, RV = VT
From equation 1 and 2
BR = BS = RV = UD = TD = VT
Therefore, From the SSS Property of the triangle, Both triangles BSR and DUT are congruent.
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m Solve for measurement(s) of angle c
The measure of angle C of the given triangle is 42.8°.
Solve for measurement(s) of angle c?To find the angle C, the law of sines formula is used, it is the ratio of the length of the side of the triangle to the sine of the angle thus formed between the other two remaining sides, given by,
sin A / a = sin B / b = sin C / c
where, a, b, and c are the lengths of the triangle and A, B, and C are the angles of the triangle.
Given ∠A = 61°, c = 35, a = 45
∴( sin A)/a = (sin C)/c
(sin 61° )/ 45 = (sin C) / 35
sin c = ((sin 61°) / 45) × 35
sin c = 0.68
c ≈ 42.8°
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Complete question:
You have given a triangle ΔABC, where ∠A = 61°, c = 35, a = 45. Solve for measurement(s) of angle c.
Help plsssssssssssssssssssss
Answer:
1) False
2)True
3)True
4)False
In the figure below m<2=27, and m
The measure of angle 8 in the figure is given as follows:
m < 8 = 27º.
What are alternate interior angles?Alternate interior angles happen when there are two parallel lines cut by a transversal lines.
The two alternate exterior angles are positioned on the inside of the two parallel lines, and on opposite sides of the transversal line.
The alternate interior angles for this problem are given as follows:
2 and 8.
They are congruent, hence the measure of angle 8 is given as follows:
m < 8 = 27º.
Missing InformationThe diagram is given by the image presented at the end of the answer.
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The teachers have $25 to buy supplies. Write and evaluate a numerical expression to show how much more money they will need to buy the cups and napkins.
Cups : $3.50 - 12 per package
Napkins : $4.25 - 10 per package
Please explain ty!!
The amount of money that will be needed more to buy the amount of cups and napkins by the teacher would be = $57.5
How to calculate the extra amount of money needed?The amount of cups needed = 12 packages
The price per package of cup = $3.50
The total money needed for cup = 12× $3.50 = $42
The amount of napkins needed = 10 package
The price per package of napkins = $4.25
The total money needed for napkins = 10×4.25 = $42.5
The total amount needed = 42+42.5 = $82.5
The difference between the amount available and the total amount = the extra money needed ;
= 82.5-25 = $57.5
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I need help asap with this question
The angles of the triangle are ∠Q=59°, ∠R=90°,∠S=31°.
What is a triangle?
In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.
Based on the sides of a triangle, a triangle is classified into 3 types, namely:
Scalene Triangle – All the sides are of different measures.
Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.
Equilateral Triangle – All the 3 sides of a triangle are of the same measure.
Based on the angles of a triangle, a triangle is classified into 3 types, namely:
Acute Angle Triangle – All the angles of a triangle are less than 90°.
Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.
Right Angle Triangle – One of the angles of a triangle is equal to 90°.
Now,
As sum of all angles of triangles=180°
90+2x+33+5x-34=180
7x=90+1
x=13
Therefore,
∠Q=59°, ∠R=90°,∠S=31°
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Does someone mind helping me with this problem? Thank you!
Answer: Amber has 50 pennies and 10 dime
Step-by-step explanation:
The number of pennies is represented by x, while the number of dimes is represented by y. This means that the statement, "there are five times as many pennies as dimes" can be written as x = 5.
The sum of the coins is $1.50, which can now be written as
0.01x + 0.1y = 1.50
0.01(5y) + 0.1y = 1.50
0.05y + 0.1y = 1.50
0.15y = 1.50
y = 10
Next up:
x = 5y
x = 5(10)
x = 50
Finally, we can conclude that Amber has 50 pennies and 10 dimes
I hope this helps!
-4y+x=4
-6y+x=6
how would I solve this
please help me understand the problem
[tex] - 4 = 4 \\ - 6 = 6[/tex]
I don't understand how to solve with the system if equations
Answer: (0, -1)
Step-by-step explanation:
Hello! One method you can use to solve a system of equations is the elimination method. Here are the steps to use the elimination method in this equation:
-4y + x = 4 -4y - (-6y) = -4y + 6y = 2y, x -x = 0, 4 - 6 = -2
- (-6y + x = 6)
_________
2y = -2
__ __
2 2
y = -1
You now know that y = -1 for both lines to intersect. Let's now find x using the substitution method.
Use the equation -4y + x = 4. Substitute -1 for y in the equation.
-4(-1) + x = 4
4 + x = 4
-4 = -4
x = 0.
You now know that x = 0 and y = -1. Coordinate pairs are represented as (x, y). Substitute 0 in for x and -1 in for y. Your answer is (0, -1).
Can someone check my answer for the first one and help me with the rest? Thank you!
Step-by-step explanation:
First one is good, all you have to do is combine like terms
-28x and +4x are like terms because they both have X
Combining those is -28x+4x=+24x
Making #1 7+24x
Answer:
(Their all down there)
Step-by-step explanation:
Okie dokie so! Your answer for 17 is technically correct but you need to imply it further so it would be [tex]7-24x[/tex]
18. [tex]-2(-6+5k)-1[/tex]
do distributive property
[tex]12-10k-1[/tex] combine like terms (12 and -1)
[tex]-10k+11[/tex]
19. [tex]6(v-5)+1\\[/tex]
do distributive property
[tex]6v-30+1[/tex] combine like terms (-30 and 1)
[tex]6v-29\\[/tex]
20. [tex]10(n+5)-5n[/tex]
do distributive property
[tex]10n+50-5n[/tex] combine like terms (10n and -5n)
[tex]5n+50[/tex]
21. [tex]-7(8+8x)-6x[/tex]
do distributive property
-[tex]56-56x-6x[/tex] combine like terms (-56x and -6x)
[tex]-56-62x[/tex]
22. [tex]6(x-9)+5[/tex]
do distributive property
[tex]6x-54+5[/tex] combine like terms (-54 and 5)
[tex]6x-49[/tex]
PLEASE HELP
On a recent bird-watching expedition, Eriq and Salle saw several different kinds of waterfowl. They saw grebes (G), ducks (D), cormorants (C), geese (E), and spoonbills (S). They saw some of the birds at the beach (B), some at the lake (L), and some in a field (F). Write an expression to represent each of the following pieces of information.
a. The total number of birds that they saw
b. The percentage of birds that they saw at the lake
c. The fraction of birds that were geese or duck
Answer:
A. Total number of Birds: G + D + C + E + S or B + L + F
B. [tex]\frac{L}{B+L+F}[/tex]
C. [tex]\frac{G+D}{B+L+F}[/tex]
Step-by-step explanation:
first divide you duck by one two three and then subtracted by 578
One angle measures 18°, and another angle measures (6d − 6)°. If the angles are complementary, what is the value of d?
Answer:
By definition, if two angles are complementary, they both will add up to 90 degrees. Knowing this add 18 and (6d-6) together to equal 90.
18+(6d-6)=90
Subtract 18 from both sides, then add 6. This leaves you with 6d equal to 78. Divide by 6 to get 13.
(6d-6)=72
6d=78
d=13 degrees
Make sure of your answer. You know that d is 13, so plug it back into the equation to see if it equals 90 degrees.
18+6(13)-6=90
18+78-6=90
90=90
Jill has launched a model rocket from the Earth with an upward speed of 80 feet per second. The path of the rocket can be modeled by the equation h(t) = -16t2 + 80t. What is the range?
The range is 5 feet
The path of the rocket can be modeled by the equation
h(t) = -16t² + 80t
We know that the range of a projectile is nothing but the horizontal distance the projectile travels from the time it is launched to the time it comes back down to the same height at which it is launched.
To find the horizontal distance we find the distance between the points on the horizontal axis.
i.e., to find the value of t for which h(t) = 0
Let us assume that the value of equation h(t) = 0
h(t) = 0
-16t² + 80t = 0
t(-16t + 80) = 0
t = 0 OR -16t + 80 = 0
t = 0 OR -16t = -80
t = 0 OR t = 5
So, the range would be,
R = 5 - 0
R = 5 feet
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what is the total number n of distinct solutions after we impose that x, y and z are all nonnegative integers?
The total number (n) of distinct solutions of the equation (x + y + z = 15) with the assumption that x, y and z are all nonnegative integers is 153.
The generating function for the number of solutions of the equation (x + y + z = n) is given by the binomial coefficient (n+2)C2, where C2 is the number of ways to choose 2 objects from a set of n+2 objects.
The number of solutions for the given equation (x + y + z = 15) is then given by:
(15+2)C2 = (17C2)
We can also use the formula for binomial coefficient: nCr = n! / (r! (n-r)!)
17C2 = (17!) / (2! * 15!) = 153
So the total number of distinct solutions of the equation (x + y + z = 15) with x, y, z non-negative integers is 153.
"
Complete question
what is the total number n of distinct solutions the equation (x + y + z = 15) after we impose that x, y and z are all nonnegative integers?
"
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What is the domain of this function?
f(x) = 3/4|x - 3| + 1
A. [1, ∞)
B. (-∞,∞)
C. (-∞, 3/4]
D. (-∞, 3)
Answer:
B. (-∞,∞)
Step-by-step explanation:
Function is
[tex]f(x) = \frac{3}{4}\cdot \left|x-3\right|\:+\:1[/tex]
There are no bounds on this function.
x values can range from -∞ to +∞ (but will never reach infinity)
Therefore domain is:
- ∞ < x < ∞
which in interval notation is Option B
How many different pizzas can be ordered with on cheese and one topping
Answer: depending on how much it cost
Step-by-step explanation:
Answer:
Depends on the pizza prices
if there is a 50% probability that bond a will default next year and 30% probability that bond b will default what is the range of probability that at least one will default
So the range of probability that at least one bond will default next year is between 0% and 80%.
The probability that at least one of two events will occur is the sum of the probability of each event minus the probability that both events will occur. In this case, the probability that at least one bond will default is:
P(A or B) = P(A) + P(B) - P(A and B)
Where P(A) is the probability of bond A defaulting (50%), P(B) is the probability of bond B defaulting (30%), and P(A and B) is the probability that both bonds will default (which we don't know).
So the range of probability that at least one bond will default is:
P(A or B) = 50% + 30% - P(A and B)
The maximum possible probability of both bonds defaulting is (0.5 * 0.3) = 15% and the minimum possible probability of both bonds defaulting is 0%. Therefore, the range of probability that at least one bond will default is:
P(A or B) = 80% - 0% = 80%
So the range of probability that at least one bond will default next year is between 0% and 80%.
It's important to note that the above formula and the range of probability is based on the assumption of independence, i.e the events of Bond A defaulting and Bond B defaulting are independent and don't affect each other.
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three computer viruses arrived as an e-mail attachment. virus a damages the system with probability 0.4. independently of it, virus b damages the system with probability 0.5. independently of a and b, virus c damages the system with probability 0.2. what is the probability that the system gets damaged?
The probability that the system gets damaged is 0.685.
Virus A damages the system with probability 0.4.
Independently of it, virus B damages the system with probability 0.5.
Independently of A and B virus C damages the system with probability 0.2.
We have to find the probability that the system gets damaged.
P(system will not be damaged by virus 1) = 1 - 0.1 = 0.9
P(system will not be damaged by virus 2) = 1 - 0.5 = 0.5
P(system will not be damaged by virus 3) = 1 - 0.3 = 0.7
P(the system will be damaged) = 1 - P(system will not be damaged)
P(the system will be damaged) = 1 - P(system will not be damaged by virus 1) x P(system will not be damaged by virus 2) x P(system will not be damaged by virus 3)
P(the system will be damaged) = 1 - 0.9x0.5x0.7
P(the system will be damaged) = 0.685
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1. If mA = 3x° and
m
what is the value
of x?
Answer: here
Step-by-step explanation:
Divide each term in ma=3xma=3x by aa and simplify.m=3xa
Ryan needs 3 and 1/4 cups of flour for the cookie recipe she is baking. She has already added 2 and 1/2 cups of flour. How much more flour does she need to add? Please help-
The quantity of more flour that she needs to add would be = 3/4
What is a fraction?A fraction is defined as the representation of the part of a whole data in a form of numerator and denominator.
The quantity of flour Ryan needs for baking = 3¼
The quantity of flour she has already added = 2½
The remaining amount that she needs to add;
= 3¼-2½
= 3/4
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he ratio of yes votes to no votes was to . if there were no votes, what was the total number of votes?
The given ratio of yes votes to no votes is 3:4
Then,
The ratio of yes votes: to no votes = 3:4
Yes votes = 2721,
Now,
2721/3 = 907
907 × 4 = 3628.
Hence, there were 3628 no votes.
To calculate the ratio, use this formula:
Ratios equate two numbers, usually by dividing them. If you are comparing one data point (x) to any other data point (y), your formula would be x/y. This means you are dividing information x by information y.
For example, if A is 50 and B is 100, your ratio will be 50/100 the ratio will be 1:2.
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Solve for P please
17.5 - 6.3p =
The value of p from the equation 17.5 - 6.3p = 25 is 1.19
What are algebraic expression?Algebraic expression can be defined as a mathematical expression that are variables, terms, factors, constants and coefficients.
These expressions are also composed of mathematical or arithmetic operations, which includes;
DivisionAdditionSubtractionFloor divisionMultiplicationBracketParenthesesFrom the information given, we have that;
17.5 - 6.3p = 25
Now, let's take the following steps
collect like terms
-6.3p = 25 - 17.5
subtract the like terms
-6.3p = 7.5
Divide both by the coefficient of p, we get;
p = 7.5/-6.3
p = 1.19
Hence, the value is 1.19
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Complete question:
Solve for P please
17.5 - 6.3p = 25
3. Sketch the distance-time graphs for the following scenarios.
a. Stand one meter from the sensor, walk
at a constant (steady) slow pace away
from the sensor.
b. Stand one meter from the sensor, walk
away from the sensor changing your
pace from slow to fast.
The distance-time graphs for the given scenarios have been attached below. The solution has been obtained using distance-time function.
What is distance-time function?
The distance between a person and an object through time is described by distance-time functions. Depending on the kind of movement, a distance-time function may be linear or non-linear, increasing, decreasing, or constant. We need to tell where the object starts, what direction it moves in, how quickly it moves, and whether it is speeding up, slowing down, or travelling at a constant speed in order to explain a distance-time function.
a. The distance-time graph for this scenario is the first graph wherein the line is less steeper than the other graph because the speed is constant.
b. The distance-time graph for this scenario is the second graph wherein the line is steeper than the first one because the speed is changing from slow to fast.
Hence, the distance-time graphs for the given scenarios have been obtained.
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The owner of a bike shop sells tricycles (3 wheels) and bicycles (2 wheels), keeping inventory by counting seats and wheels. One day she counts 35 seats and 80 wheels. How many of each type cycle are there?
The required number of each type of cycles are 25 bicycle and 10 tricycle.
Explain tricycles (3 wheels) and bicycles (2 wheels).Tricycles will offer better stability and assistance. They can also be applied in a wider variety of circumstances, such as therapy sessions for people with disabilities. The most common vehicle will be a bicycle because they are smaller, lighter, faster, more suited for off-roading, and more widely available.
According to question:The seats are counted by 1 for both tricycles and bicycles, so t + b has to equal 35. The only answer choice that has t + b = 35
t = 35 - b
And
3t + 2b = 80
3(35 - b) + 2b = 80
105 - 3b + 2b = 80
105 - b = 80
b = 25
Put value of b in t = 35 - b,we get
t = 35 - 25
= 10
Thus, There are 25 bicycle and 10 tricycle.
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Pedro buys lunch at school every day. He always gets pizza when it is
available. The cafeteria has pizza about 80% of the time.
Pedro runs a simulation to model this using a random number generator. He
assigns these digits to the possible outcomes for each day of the week:
• Let 0 and 1 = no pizza available
• Let 2, 3, 4, 5, 6, 7, 8, and 9 = pizza available
The table shows the results of the simulation.
95032 47150 71709 38889 94007
35013 57890 72924 19365 47879
What is the estimated probability that Pedro will eat pizza for lunch every way
next week?

The estimated probability that Pedro will eat pizza for lunch every way next week is 1/2
The term called probability in math is known as branch of mathematics that measures the uncertainty of the occurrence of an event using numbers
Here we know that the cafeteria has pizza about 80% of the time.
And here we have also know that Pedro runs a simulation to model this using a random number generator.
The result of the table shows the results of the simulation.
Here we need to estimate the probability that Pedro will eat pizza for lunch every way next week and it can be calculated as,
Here we have know that in each box, here there are 5 digits to represent the 5 days in a week.
And here there’s 10 boxes to represents 10 weeks.
Then in each box there’s a chance out of 5 for Pedro to get pizza.
Then the probability is calculated as,
=> 5/10
=> 1/2
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∆ is an equilateral triangle with a side length of 12 inches. What is the height of ∆? Provide your answer in simplest radical form.
Answer:
Step-by-step explanation:
f f
What number goes in the blank to make the number sentence true? 3 x (1 + 6) = (3 x 1) + ( x6)
The required value of x to satisfied the given condition is 1/5.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
According to question:We have,
3x (1 + 6) = (3 x 1) + ( 6x)
3x(7) = 3 + 6x
21x = 3 + 6x
15x = 3
x = 1/5
Thus, required value of x is 1/5.
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In order to satisfy the requirement, x must be 1/5 of the desired value.
What is an equation?An equation is a mathematical statement that proves the equality of two mathematical expressions, according to the definition of an equation in algebra. For instance, the two equations 3x + 5 and 14 are combined to form the equation 3x + 5 = 14, which is denoted by the equal sign.According to what we have3x (1 + 6) = (3 x 1) + ( 6x) ( 6x)3x(7) = 3 + 6x21x = 3 + 6x15x = 3x = 1/5A value of 1/5 for x is therefore necessary.To lean more about Equation refer:
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