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Let T be the three dimensional solid bounded from above by the half cylinder described by the equation z = √(9 - y) and from below the cy plane for 0 ≤ x ≤ 2 and -3 ≤ y ≤ 3. Let S be the closed surface that completely surrounds T. Let F➜ = (x,y,y+z). Use the Divergence Theorem to calculate ∫∫S F • n dS
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Using the Divergence Theorem, we get the flux of F across the closed surface S is π/2 (27√2 - 27).
To apply the Divergence Theorem, we will first compute the divergence of F as follows -
div(F) = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z
= 1 + 1 + 1
= 3
Now we will calculate the flux of F across the closed surface S that completely surrounds T. By the Divergence Theorem, this is equal to the triple integral of the divergence of F over the region T and is given by -
∫∫S F•n dS = ∭T div(F) dV
We can describe the region T using cylindrical coordinates:
0 ≤ r ≤ 2
-π/2 ≤ θ ≤ π/2
0 ≤ z ≤ √(9 - r sin θ)
The bounds on r and θ come from the fact that the half cylinder is contained within the plane x = 2, and the plane y = ±3. The bounds on z come from the equation of the half cylinder.
Now we can write the triple integral as follows -
∭T div(F) dV = ∫0^2 ∫-π/2^π/2 ∫0^√(9 - r sin θ) 3 r dz dθ dr
Evaluating this integral, we get,
∭T div(F) dV = π/2 (27√2 - 27)
Therefore, the flux of F across the closed surface S is π/2 (27√2 - 27).
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Cavalleria Pizza sells only pizza. They offer five types of crust, two types of cheese, four meat toppings and
four vegetable toppings. If you must order exactly one type of cheese, one meat topping and one vegetable
topping on your pizza, how many different pizzas can you order at Cavalleria Pizza?
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Answer:
3?
Step-by-step explanation:
im not sure sorry
Beginning with the equation x = tan y, use implicit differentiation to find the derivative of thefunction y = tan^-1 x, expressed in terms of x.
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The derivative of the function y = tan⁻¹ x which is expressed in terms of x will be 1 / (1 + x²).
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
The function is given below.
x = tan y
Get the equation for y, then we have
x = tan y
y = tan⁻¹ x
Differentiate the function with reprect to 'x', then we have
y' = (d/dx) tan⁻¹ x
y' = 1 / (1 + x²)
The derivative of the function y = tan⁻¹ x which is expressed in terms of x will be 1 / (1 + x²).
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A store in Hampton bought a leather chair for $494.47 and marked it up 100% from the original cost. Later on, Sally purchased the leather chair and paid Hampton sales tax of 5.5%. How much, including tax, did she pay for the leather chair?
$
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Sally paid $1,043.33 for the leather chair, including tax.
Leather chair priceThe marked up price of the leather chair is 100% more than the original cost, which means it is twice the original cost.
So, the marked up price is:$494.47 x 2 = $988.94
The sales tax in Hampton is 5.5%, which means Sally paid an additional:$988.94 x 0.055 = $54.39
So, the total amount Sally paid, including tax, is:$988.94 + $54.39 = $1,043.33.
Therefore, Sally paid $1,043.33 for the leather chair, including tax.
The calculation provided is applicable for any problem that involves finding the total cost of an item after a percentage markup and the addition of a sales tax. The general formula for calculating the final cost of an item after a markup and sales tax is:
Final cost = (1 + markup percentage) x original cost x (1 + sales tax percentage)
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a robot building club organizes competitions by weight categories called classes each clas permit a percent error of 0.3% in the 5 kg class one robot weighs 4.925 kg
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The weight of the robot is within the error limit of 0.3%.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a robot building club organizes competitions by weight categories called classes each class permit a percent error of 0.3%. In the 5 kg class one robot weighs 4.925 kg.
Let -
{x} = 0.3% of 5
{x} = 0.3/100 x 5
{x} = 3/1000 x 5
{x} = 15/1000
{x} = 3/200
{x} = 0.015 .... Eq { 1 }
Now -
For the weight of the robot to be under the weight limit -
4.925 ≤ (5 - x)
4.925 ≤ (5 - 0.015)
4.925 ≤ 4.985 ..... Eq { 2 }
which is true.
Therefore, the weight of the robot is within the error limit of 0.3%.
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Imagine that your instructor chose to use the Keep the Highest scoring method in Grade it Now mode. Here are your scores:First attempt: 2/10Second attempt: 10/10Third attempt: 3/10What would be your final score?
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The instructor chose to use the highest score now mode, hence the score of the second attempt would be used that is 10/10.
What is mode?In statistics, the value that consistently appears in a particular set is referred to as the mode. The mode or modal value in a data set is sometimes referred to as the value or number that occurs most frequently in the data set. In addition to mean and median, it is one of the three measures of central tendency.
The scores at different attempts are:
First attempt: 2/10 = 0.2
Second attempt: 10/10 = 1
Third attempt: 3/10 = 0.3
The instructor chose to use the highest score now mode, hence the score of the second attempt would be used that is 10/10.
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Gage drove 96 miles on country roads before driving 66 miles on mountain roads. Gage’s rate of travel on the country roads was 2.4 times the rate of the travel on the mountain roads. His whole travel time was 5.3 hours. What is the equation that can be used to solve the problem? What was gage rate of travel on the punta in roads? What was gage’s rate of travel on country roads ?
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The equation that can be used to solve the problem is 66/x + 40/x = 5.3
gage rate of travel on the mountain roads is 20 mph and on the country roads is 48 mph.
What is an equation?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Finding the values of the variables that result in the equality is the first step in solving an equation with variables.
Given that:
In mountain Road
distance = 66 miles ; rate = x mph
⇒ time = d/r = 66/x hrs
In country Road
distance = 96 miles ; rate = 2.4x mph
⇒ time = d/r = 96/(2.4x)
⇒ time = d/r = 40/x hrs.
Equation:
time + time = 5.3 hrs
⇒ 66/x + 40/x = 5.3
⇒ 106/x = 5.3
⇒ 5.3x = 106
⇒ x = 20 mph on mountain Roads
⇒ 2.4x = 2.4*20 mph on country Roads
⇒ 48 mph on country Roads
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PLS HELP me I am in need of help will mark brainiest
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Answer:
Fourth option: √65/4
Step-by-step explanation:
Since the angles are similar, each of the angles of ΔEFG must be equal to each of the corresponding angles of ΔHIJ
Specifically, m ∠J in ΔHIJ = m∠G in Δ EFG
Let's first find ∠G
Since EFG is a right triangle,
tan(G) = EF/FG = √65/4
tan J must be the same as tan G = √65/4
This is the fourth option
The value of tanJ is in the right angled triangle HIJ√65 / 4
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Two triangles are similar if their corresponding angles are equal to each other.
Given that triangle EFG and triangle HIJ are similar, hence:
Angle G = Angle J
tanJ = tanG = √65 / 4
The value of tanJ is √65 / 4
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a 1.20 kg block is attached to a spring with spring constant 14.0 n/m . while the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 32.0 cm/s .
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The amplitude of subsequent oscillations is 0.093 m.
What is Spring constant?The spring stiffness is quantified by the spring constant, or k. For various springs and materials, it varies. The stiffer the spring is and the harder it is to stretch, the bigger the spring constant.
Given that,
Mass of a block, m = 1.2 kg
Spring constant of the spring, k = 14.0 N/m
While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 32.0 cm/s or 0.32 m/s
We need to find the amplitude of the subsequent oscillations.
We can use the conservation of energy here. Initially, the kinetic energy of the block is maximum and then it gets converted to the potential energy of the spring.
Mathematically,
[tex]\frac{1}{2} mv^2=\frac{1}{2}kv^2[/tex]
A is the amplitude of subsequent oscillations.
[tex]A=\sqrt{(\frac{mv^2}{k} )} \\\\A=\sqrt{\frac{(1.2)(0.32)^2}{14} } \\\\A=0.093m[/tex]
So, the amplitude of subsequent oscillations is 0.093 m.
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hey thank for helping me
Answers
Answer: -1
Step-by-step explanation:
When the graph g hits g=2, the y is -1
Math 5th grade
Roshaun walks around the city park. The square park measures 61 1/4 yards on each side. How far does Roshaun walk?
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Answer: 245 yds
Step-by-step explanation:
61 1/4 times 4 = 245
I need help! Please show your work, thanks!!
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The amount that should be deposited today is given as follows:
$70,663.15.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for this problem are given as follows:
t = 15, A(t) = 115000, r = 0.033, n = 1.
Hence the deposit is obtained as follows:
115000 = P(1.033)^15
P = 115000 x (1.033)^(-15)
P = $70,663.15.
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In a class of 27 students, 17 are dual-enrolled and 10 are not dual-enrolled. Suppose two students are randomly selected from the class (without replacement). Calculate the following probabilities. Round solutions to three decimal places, if necessary.
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Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases.
if 2 non-overlapping events should occur, the probability of both events happening is the product of both individual probabilities.
e.g. the probability to roll two 6 with 2 dice (or in 2 consecutive rolls with 1 die) is 1/6 × 1/6 = 1/36
if 1 of 2 possible non-overlapping events should occur, the probability of one of the events happening is the sum of the individual probabilities.
e.g. the probability to roll a 1 or a 2 with a die is
1/6 + 1/6 = 2/6 = 1/3
both students are dual-enrolled.
in our case, for the first selection we have the totally possible cases of 27.
the desired cases (dual-enrolled) are 17.
so, the probabilty to select a dual-enrolled student is
17/27
for the second selection (without replacement of the first pull) the totally possible cases are now 26 (because we pulled one student from the general pool of candidates in the first selection).
the desired cases are now 16 (because for our case we pulled a dual-enrolled student from the general pool).
the probabilty to select a dual-enrolled student in the second selection is
16/26 = 8/13
the overall probability to select two dual-enrolled students in 2 selections is
17/27 × 8/13 = 136/351 = 0.387464387... ≈ 0.387
the first student is dual-enrolled, the second is not.
for the first selection the totally possible cases are 27.
the desired cases are again 17.
the probability of the first dejection is again
17/27
for the second selection the totally possible cases are 26 (see above).
the desired cases are still 10.
the probably for this second selection is
10/26 = 5/13
the overall probability to select first a dual-enrolled student and then a not-dual-enrolled student is
17/27 × 5/13 = 85/351 = 0.242165242... ≈ 0.242
You purchased 100 shares of stock valued at $55 per share . The stock value increases to $85 per share . What was the rate of increase
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Based on the information given the rate of increase is 55%.
Rate of increase:
Using this formula
Rate of increase=Stock value per share/Number of shares of stock×100
Where:
Stock value per share=$55 per share
Number of shares of stock=100 shares
Let plug in the formula
Rate of increase=$55/100×100
Rate of increase=55%
Inconclusion the rate of increase is 55%
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what is the smallest number that you can add to 17,438 that will make the sum divisible by 25?
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Check the picture below.
Solve with the box method
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The polynomial n² + 6n - 1 can be factored as,
(n + 3 + √10)(n - 3 + √10)(3n - 2).
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, A product of two polynomials (n² + 6n - 1)(3n - 2).
Now, The quadratic expression n² + 6n - 1 can be factored as,
n² + 6n - 1.
[- 6 ± √(36 + 4)]/2.
= [- 6 ± √40]/2.
= [- 6 ± 2√10]/2.
= - 3 ± √10.
Therefore, (n² + 6n - 1)(3n - 2)
= (n + 3 + √10)(n - 3 + √10)(3n - 2).
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rewrite the expression $6j^2 - 4j 12$ in the form $c(j p)^2 q$, where $c$, $p$, and $q$ are constants. what is $\frac{q}{p}$?
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The expression 6j^2 - 4j 12 can be rewritten as [tex]$-24(j\frac{1}{2})^2 -12$[/tex]where , and [tex]$q=-12$[/tex]. Thus,[tex]$\frac{q}{p}=-24$[/tex].
The expression[tex]$6j^2 - 4j 12$[/tex] can be rewritten in the form [tex]$c(j p)^2 q$[/tex], where c, p, and q are constants. To do this, we can factor out a common factor from the expression. In this case, the common factor is j. Then, we can rewrite the expression as [tex]$j(6j - 12)$[/tex] which simplifies to [tex]$-24j^2 -12$[/tex]. Dividing both sides by j, we can rewrite the expression as [tex]$-24(j\frac{1}{2})^2 -12$[/tex] where [tex]$c=-24$[/tex], [tex]$p=\frac{1}{2}$[/tex] and [tex]$q=-12$[/tex]. Thus, [tex]$\frac{q}{p}=-24$[/tex]. To summarize, the expression [tex]$6j^2 - 4j 12$[/tex] can be rewritten in the form [tex]$c(j p)^2 q$[/tex] where c, p, and q are constants, and [tex]$\frac{q}{p}=-24$[/tex].
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An emergency plumber charges $65 as a call out few plus an additional $75 per hour. He arrives at the house at 9:30 and works to repair a water tank. The total repair bill is $196.25. Use the variable t for the number of hours.
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Answer:
Step-by-step explanation:
Answer:
Around 11:15 am
Step-by-step explanation:
Let h represents the number of hours the plumber works
Since the plumber charges $65 fee plus $75 per hour, the bill can be calculated by:
→ bill = 65 + 75h
Since the bill is $195.25
→ 195.25 = 65 + 75h
→ 75h = 130.25
→ h = 1.74
1.74 implies that the plumber worked almost 1 hour and 45 minutes. Since the plumber started at 9:30, the repair was completed around 11:15 am.
23. Nurse Nancy says that dilations will result in the congruence of corresponding angles.
Do you agree?
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Answer:
Yes, dilation does not change the angle measurements.
Step-by-step explanation:
A parking lot is arranged with 9 parking spots in the first row, 15 parking spots in the second row, and 21 parking spots in the third row. If a person is aiming to park in first row, what is his probability in decimal form of getting a parking spot?
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Answer:
21+15+9=45/4=that the answer
There are 80 people at the movie theater today 2/5 of the people are eating popcorn one for eating chocolate candy and the rest are eating record twist how many people are eating record toys
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The people that are eating record toys are 48
How many people are eating record toysFrom the question, we have the following parameters that can be used in our computation:
People at the movies = 80
People are eating popcorn = 2/5
Using the above as a guide, we have the following:
Record toys = (1 - People are eating popcorn) * People at the movies
Substitute the known values in the above equation, so, we have the following representation
Record toys = (1 - 2/5) * 80
Evaluate
Record toys = 48
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Simplify expression[5-6+1]
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Answer: 0
Step-by-step explanation:
Using GEMDAS
- Grouping
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
[5-6+1]
= [-1+1] because you add/subtract from left to right
= [0] because -1+1=0.
Answer is 0
Fill in the Blank: Solve the following system of linear equations graphically. Then, fill in the blanks below with the solution.
Equation #1: y=14x−2
Equation #2: y=x+1
The solution to the system of equations is the ordered pair (
,
)
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The solution to the system of equations is (13/3, 16/3).
The graph is given below.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation.
We have,
y = 14x - 2 _____(1)
y = x + 1 ______(2)
Now,
The graph of the equation is given below.
Now,
From (1) and (2).
14x - 2 = x + 1
14x - x = 1 + 2
13x = 3
x = 13/3
And,
y = x + 1
y = 13/3 + 1
y = 16/3
So,
The solution is (13/3, 16/3)
Thus,
The solution is (13/3, 16/3).
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What number should go in the space?
Multiplying by 1.15 is the same as increasing by _____%.
Answers
Answer: 115%
Step-by-step explanation:
100% = 1
10%=0.1
5%=0.05
100%+10%+5%=115%
1+0.1+0.05=1.15
Answer: 15
Step-by-step explanation:
x+x*15/100
x(1+.15)
1.15x
Angel read for 1/2 hour. Margo read 1/6 hour. Who read for the greater amount of time.
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In a group of 21 students, 8 students take Art courses, 7 students take Music courses. Two students take both courses. A student is chosen randomly from this group.
What is the probability that the student takes either Art or Music courses?
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5x+12y is less than or equal to 30
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Answer:
Step-by-step explanation:
The inequality 5x+12y ≤ 30 represents a shaded region in the xy-plane that includes all the points that satisfy the inequality. To graph this inequality, we can first graph the equation 5x+12y = 30, which is the boundary line of the shaded region.
To graph the boundary line, we can find its x- and y-intercepts:
x-intercept: Set y = 0 and solve for x: 5x + 12(0) = 30, which gives x = 6.
y-intercept: Set x = 0 and solve for y: 5(0) + 12y = 30, which gives y = 2.5.
So the boundary line passes through the points (6, 0) and (0, 2.5).
Next, we can determine which side of the boundary line to shade. One way to do this is to pick a test point that is not on the line and plug it into the inequality. For example, the point (0,0) is a convenient test point. Plugging in x=0 and y=0 into the inequality, we get:
5(0) + 12(0) ≤ 30
which simplifies to 0 ≤ 30. Since this is true, we know that the region containing the point (0,0) is part of the shaded region, and therefore the shaded region is the one that contains the origin.
Putting it all together, we can graph the inequality by drawing the line 5x+12y = 30 and shading the region below the line, as shown in the figure below:
|
3 | x
| /
2 | /
| /
1 | /
| /
0 | /
------------
0 6
The shaded region includes all the points below the line 5x+12y=30, including the points on the line.
Given a simplified rate of (2), determine the percent change.
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The percent change of an object is the ratio of its final value to its initial value.
What is meant by percent change?The percentage of an item's final value versus its starting value is its percent change. By dividing the difference in data by the starting value, you can get the percent change.
"Rate" simply refers to the quantity divided by another number, typically 100, 1,000, or another multiple of 10. A rate per 100 is known as a percentage.
Percentage Change is the difference that results from deducting the old value from the new value, dividing by the old value, and multiplying the result by 100 to represent it as a percentage. In most cases, multiplying a fraction by 100 results in a percent conversion.
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there are 41 students in group 2. Twice has many students playing the Trump elect as playing the trombone but eight students play the saxophone how many students in group to play each instrument use reasoning to write an expression then solve
Answers
The following numbers are the result:
22 play trumpet, 11 play trombone, and 8 play saxophone.
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Given:
There are 41 students in group 2.
Twice as many students play the trumpet as play the trombone,
but 8 students play the saxophone.
Let x be the number of students playing the trombone.
So, according to the question,
x + 2x + 8 = 41
3x = 33
x = 11
Hence, 22 play trumpet, 11 play trombone, and 8 play saxophone.
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Donna, Alonzo, and Kevin served a total of 85 orders Monday at the school cafeteria. Donna served 10 fewer orders than Alonzo. Kevin served 3 times as
many orders as Alonzo. How many orders did they each serve?
Answers
Answer:
So, Donna served 9, Alonzo served 19 and kevin served 57 orders.
Step-by-step explanation:
Let orders be :
Donna - x, Alonzo - y, Kevin - z
x = y - 10 - eqn i
z = 3y - eqn ii
Now, By the question,
x + y + z = 85
we know from eqn i and eqn ii,
y - 10 + y + 3y = 85
or, 5y = 95
so, y = 19
Now,
z = 3(19) = 57
x = 19 - 10 = 9