Please help struggling in math & this is for practice
The given functions are
[tex]\begin{gathered} f(t)=\frac{11}{t-2} \\ g(t)=\frac{22t}{t^2-4} \end{gathered}[/tex]The first part consists in adding the functions f(t) + g(t)
[tex]f(t)+g(t)=\frac{11}{t-2}+\frac{22t}{t^2-4}=\frac{11(t^2-4)+22t(t-2)}{(t-2)(t^2-4)}[/tex]Let's factor the square difference
[tex]\frac{11(t+2)(t-2)+22t(t-2)}{(t-2)(t^2-4)}=\frac{11(t+2)+22t}{t^2-4}[/tex]Now, we simplify
[tex]\frac{11t+22+22t}{t^2-4}=\frac{33t+22}{t^2-4}[/tex]Hence, the addition of the given functions is
[tex]f(t)+g(t)=\frac{33t+22}{t^2-4}[/tex]On other hand, let's solve the difference
[tex]\begin{gathered} f(t)-g(t)=\frac{11}{t-2}-\frac{22t}{t^2-4}=\frac{11(t^2-4)-22t(t-2)}{(t-2)(t^2-4)} \\ f(t)-g(t)=\frac{11(t+2)(t-2)-22t(t-2)}{(t-2)(t^2-4)} \\ f(t)-g(t)=\frac{11(t+2)-22t}{t^2-4}=\frac{11t+2-22t}{t^2-4} \end{gathered}[/tex]Hence, the difference is
[tex]f(t)-g(t)=\frac{-11t+2}{t^2-4}[/tex]ProgScore: 2/101/5 answeredQuestion 2<>A population has parameters u = 245.9 and o= 16.7. You intend to draw a random sample of size n = 83.What is the mean of the distribution of sample means?Hy =What is the standard deviation of the distribution of sample means?(Report answer accurate to 2 decimal places.)=Question Help: D VideoSubmit Question
For a population with parameters as shown in the image below
(a) Mean of the distribution
[tex]\begin{gathered} \mu_{\bar{x}}\text{ = }\mu\text{ = 245.9} \\ \operatorname{mean}\text{ of the distribution = 245.9} \end{gathered}[/tex](b)Standard deviation of the distribution
[tex]\begin{gathered} \sigma_{\bar{x}\text{ }}\text{ = }\frac{\sigma}{\sqrt[]{n}} \\ \sigma_{\bar{x}\text{ }}\text{ = }\frac{16.7}{\sqrt[]{83}} \\ \sigma_{\bar{x}\text{ }}\text{ = }\frac{16.7}{9.11} \\ \sigma_{\bar{x}\text{ }}\text{ = 1.833} \\ \sigma_{\bar{x}\text{ }}\text{ = 1.83 (2 d.p)} \end{gathered}[/tex]Hence the value of the mean of the distribution = 245.9 and the standard deviation of the distribution = 1.83
Ethan says that the value of 40.7 is 10 times the value of 4.07
The assumption Ethan made was correct
What is Fraction?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
Ethan said that the result of 10 and 4.07 is 40.7, thus we must verify that his computation is accurate.
In order to do such, we must multiply 10 by 4.07 as illustrated below:
= 10 x 4.07
= 10 x 407/100
= 4070/100
= 40.70
Since the outcome matches Ethan's hypothesis,
The conclusion is valid.
Hence, The result of Ethan is correct
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write the slope intercept form:through: (5, 1), perp. to x= -1
-A fisherman illegally introduces some fish into a lake, and they quickly propagate. The growth of thepopulation of this new species (within a period of a few years) is modeled P(x) = 5b>, where x is thetime in weeks following the introduction and b is a positive unknown base.a. Exactly how many fish did the fisherman release into the lake?
Equation:
P(x)= 5b^x
Where:
x = time in weeks
b= unknown base
When t= 0
P(0)= 5 b^0
P(0)= 5
a. The fisherman released 5 fish into the lake.
Which is true about the domain and range of a function in the form f(x) = m√x, where m is a real number greater
than 0?
O The only value that must be in both the domain and range is 0.
O The only values that must be in both the domain and range are 0 and 1.
O There are no values that are in the domain and the range.
O There is an infinite number of values that are in both the domain and range.
Mark this and return
Save and Cult
There is an infinite number of values that are in both the domain and range.
Define domain and range.The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values. The collection of all potential inputs for a function is its domain.
Given Data
Range of a function in the form f(x) = m√x, where m is a real number greater than 0
There is an infinite number of values that are in both the domain and range.
The range of a function always has an unlimited number of values when the domain of the function does. The claim is untrue because more than one input and output might have been matched.
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Connor went to New York for vacation. He spent threenights at a hotel and rented a car for four days. Jillian stayed at the samehotel but spent four nights and rented a car for five days from the samecompany. If Connor paid $675 and Jillian paid $875, how much did onenight at the hotel cost?
Solution:
Let x the cost for a night and y the cost to rent a car for a day.
Connor = 3 nights and 4 days = 3x + 4y = 675
Jillian = 4 nights and 5 days = 4x + 5y = 875
3x + 4y = 675 Multiply by 5
4x + 5y = 875 Multiply by 4
we get:
15x + 20y = 3375
16x + 20y = 3500
now, subtracting the two previous equations we obtain:
15x + 20y = 3375
-
16x + 20y = 3500
________________
-x + 0 = -125
x = 125
then, we can conclude that the correct answer is:
$125
How much more will his shirt cost in Fresno than Bakersfield (in dollars)? (Round each to the nearest cent and write your answer as a decimal).
The amount of money more that his shirt cost in Fresno than Bakersfield is $0.145.
How to calculate the value?Given that the amount of shirt is $20. The value of the shirt in Fresno will be:
= Cost + Tax
= $20 + (8.225% × $20)
= $20 + $1.645
= $21.645
The value in Bakersfield will be:
= Cost + Tax
= $20 + (7.5% × $20)
= $20 + $1.5
= $21.5
The difference will be:
= $21.645 - $21.5
= $0.145
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I need help with this problem
Answer:
f(1) + g(2) = 7
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=-x^2+2x-3\\g(x)=10-\dfrac{1}{2}x \end{cases}[/tex]
To find f(1), substitute x = 1 into function f(x):
[tex]\begin{aligned}x=1 \implies f(1)& =-(1)^2+2(1)-3\\& = -1+2-3\\&=1-3\\&=-2\end{aligned}[/tex]
To find g(2), substitute x = 2 into function g(x):
[tex]\begin{aligned}x=2 \implies g(2)& =10-\dfrac{1}{2}(2)\\& =10-1\\&=9\end{aligned}[/tex]
Therefore, to evaluate f(1) + g(2), sum the two values found for f(1) and g(2):
[tex]\begin{aligned}\implies f(1)+g(2)&=-2+9\\&=7\end{aligned}[/tex]
As one calculation:
[tex]\begin{aligned}\implies f(1)+g(2)&=-(1)^2+2(1)-3+10-\dfrac{1}{2}(2)\\&=-1+2-3+10-1\\&=1-3+10-1\\&=-2+10-1\\&=8-1\\&=7\end{aligned}[/tex]
Doreen Schmidt is a chemist. She needs to prepare 32 ounces of a 9% hydrochloric acid solution. Find the amount of
16% solution and the amount of 8% solution she should mix to get this solution.
how many ounces of the 16% acid solution should be in the mixture?
how many ounces of the 8% acid solution should be in the mixture?
Answer:
See below
Step-by-step explanation:
She needs 32 ounces finshed product
x = 16 % amount amount of acid = .16x
then (32-x) = 8% amount amount of acid = .08(32-x)
final product 9% acid = .09 (32)
.16x + .08 ( 32-x) = .09(32)
solve for x = 16% amount = 4 ounces 8% then is 28 ounces
Yesterday, Reuben had 143 baseball cards. Today, he gave b away. Using b, write an expression for the number of cards Reuben has left. II +0 O-O ローロ Х 5 ? Continue Save For La 2022 McGraw Hill LLC. All Rights Reserved. Terms of U hp
ANSWER:
143 - b
STEP-BY-STEP EXPLANATION:
Given:
Original quantity: 143
Amount given away: b
The amount of cards Ruben has today will be equal to the difference between the original amount and the given amount, it will be written as the following expression:
[tex]143-b[/tex]Hi - I am trying to get help with a math prob
1) In this case, let's do it by PEMDAS order of operations.
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
2) So let's begin with the parentheses:
[tex]\begin{gathered} 8\div2(2+2)= \\ 8\div2(4) \\ 4(4) \\ 16 \end{gathered}[/tex]Select the correct answer, What is the least common multiple of the numbers 5, 25, and 157 A 25 B, 50 C. 75 D 100 E, 125
Given the function p(c)=c² +c:
a. Evaluate p(-3).
b. Solve p(c) = 2.
Answer: a. p(-3) = 6 b. c = -2 , c = 1
Step-by-step explanation:
a. Evaluate p(-3):
Step 1: Plug in -3 into c
p(-3) = (-3)^2-3
Step 2: Use PEMDAS
p(-3) = 9-3
Step 3: Subtract
p(-3) = 6
b. Solve p(c) = 2:
Step 1: Set the equation equal to 2
2 = c^2+c
Step 2: Bring the 2 to the right
c^2+c-2 = 0
Step 3: Factor
(c+2)(c-1) = 0
Step 4: Use the Zero Product Property
c = -2 , c = 1
Step-by-step explanation:
a.
this is totally easy.
we need to put the given value for c (-3) into all the places of c in the functional expression and then calculate.
p(-3) = (-3)² + -3 = 9 - 3 = 6
b.
this is a bit trickier.
p(c) = 2
so,
c² + c = 2
c² + c - 2 = 0
remember, how 2 sums are multiplied with each other :
(a + b)(c + d) = ac + ad + bc + bd
to make it clearer, the functional expression suggests that a = c.
so,
(c + b)(c + d) = c² + cd + bc + bd = c² + c(d + b) + bd
when we compare this to our equation c² + c - 2 = 0, that means
d + b = 1
-2 = bd
when we think about integer numbers, what comes to mind ?
d = 2
b = -1
or vice versa. but the sequence does not matter, because we bring them together in an addition and in a multiplication, where the commutative principle is active (the sequence does not matter).
so,
c² + c - 2 = (c + 2)(c - 1)
and that must be 0.
so,
(c + 2)(c - 1) = 0
when is a product 0 ? when at least one of the factors is 0.
therefore, either
c + 2 = 0
c = -2
or
c - 1 = 0
c = 1
the solution is
c = -2
or
c = 1
What is 4 x 1/7
Give your answer in simplify fully
Answer: 4/7 or 0.571428
Step-by-step explanation:
convert the expression
4/1 x 1/7
multiply the fractions
4x1 / 1x7
calculate the products
4/7 or 0.571428
Answer:
4 * 1/7 simplified is 4/7
Step-by-step explanation:
let me know if you want a thorough explanation!
stephen needs to place several cubic packages in a shipping box that measures 12 inches by 18 inches by 24 inches.
648cubes
Explanations
The formula for calculating the volume of a box is expressed as
[tex]V=lwh[/tex]where;
l is the length
w is the width
h is the height
Find the volume of the shipping box
[tex]\begin{gathered} V=12in\times18in\times24in \\ V=5184in^3 \end{gathered}[/tex]Determine the dimension of the cubic package
[tex]\begin{gathered} V_c=2in\times2in\times2in \\ V_c=8in^3 \end{gathered}[/tex]Determine the number of cubes that can fit in the shipping box.
[tex]\begin{gathered} number\text{ of cubes}=\frac{5184in^3}{8in^3} \\ number\text{ of cubes}=648cubes \end{gathered}[/tex]Therefore the maximum number of cubes that can fit into the box is 648cubes
Given the equation 6x-y=98, find x if y=-2
x=16
Explanationgiven the function
[tex]6x-y=98[/tex]Step 1
as we need x is terms of y, let's solve for x
[tex]6x-y=98[/tex]a) add y in both sides
[tex]\begin{gathered} 6x-y+y=98+y \\ 6x=98+y \end{gathered}[/tex]b) divide both sides by 6
[tex]\begin{gathered} 6x=98+y \\ \frac{6x}{6}=\frac{98+y}{6} \\ x=\frac{98}{6}+\frac{y}{6}\Rightarrow equation \\ \end{gathered}[/tex]Step 2
now, evaluate for y=-2
[tex]\begin{gathered} x=\frac{98}{6}+\frac{y}{6}\operatorname{\Rightarrow}equat\imaginaryI on \\ replace \\ x=\frac{98}{6}-\frac{2}{6} \\ x=\frac{96}{6}=16 \\ x=16 \end{gathered}[/tex]therefore, the answer is
x=16
I hope this helps you
a ferris wheel has a radius of 16 feet. how far will you travel if you go around 5 times ? pi= 22/7
Answer
Total distance travelled = 502.86 feet
Explanation
To know how far one would go, we need to first find the circumference of the ferris wheel. Since it is circular in shape,
Circumference = 2πr
where
π = pi = (22/7)
r = radius of the ferris wheel = 16 feet
Circumference = 2πr
Circumference = 2 × (22/7) × 16
Circumference = 100.57 feet
So, if one now goes round this exactly 5 times,
Total distance travelled = 5 (Circumfernce of the ferris wheel)
Total distance travelled = 5 (100.57)
Total distance travelled = 502.86 feet
Hope this Helps!!!
what’s the correct answer answer asap for brainlist please.
Answer:
nitrogen is most abundant in atmosphere and soil
Find the values for x given the equation7. (x - 5) (x + 1) = 0
Solution:
Given the equation;
[tex](x-5)(x+1)=0[/tex]Thus, the solution of the quadratic equation is;
[tex]\begin{gathered} x-5=0,x+1=0 \\ \\ x=5,x=-1 \end{gathered}[/tex]The life, in years, of a certain type of electrical switch has an exponential distribution with an average life of β = 5 years. If 200 of these switches are installed in different systems, what is the probability that at most 30 fail during the first year?
The probability that at most [tex]30[/tex] fail during the first year is 0.14550.
A certain type of electrical switch has an exponential distribution with an average life of [tex]\beta =5[/tex] years.
The installed switches in different systems n = 200.
We have to find the probability that at most 30 fail during the first year.
We can find the probability using,
P [tex]=1-e^{-1/\beta }[/tex]
Putting the value
P [tex]=1-e^{-1/5 }[/tex]
P [tex]=1-e^{-0.2}[/tex]
P [tex]=1-0.8187[/tex]
P = 0.1813
Now we find the mean[tex](\mu)[/tex].
[tex]\mu=n\times[/tex] P
[tex]\mu=200\times 0.1813[/tex]
[tex]\mu=36.26[/tex]
Now finding the standard deviation[tex](\sigma)[/tex].
[tex]\sigma=\sqrt{\mu(1-P)}[/tex]
Now putting the value
[tex]\sigma=\sqrt{36.26(1-0.1813)}[/tex]
[tex]\sigma=\sqrt{36.26\times0.8187}[/tex]
[tex]\sigma=\sqrt{29.686}[/tex]
[tex]\sigma=5.448[/tex]
z score,
[tex]z=\frac{(x-\mu)}{\sigma}[/tex]
Now probability that at most 30 fail during the first year.
From the continuity correction,
P(x ≤ 30) [tex]=P(x < 30.5)[/tex]
P(x ≤ 30) [tex]=P(\frac{x-\mu}{\sigma} < \frac{30.5-36.26}{5.448})[/tex]
P(x ≤ 30) [tex]=P(\frac{x-\mu}{\sigma} < \frac{-5.76}{5.448})[/tex]
P(x ≤ 30) [tex]=P(\frac{x-\mu}{\sigma} < -1.058)[/tex]
From the standard table
P(x ≤ 30) = 0.1455
Hence, the probability that at most [tex]30[/tex] fail during the first year is [tex]0.1455[/tex].
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Find the quadratic model in standard form for the set of values (3, -6), (1,-2), (6,3)
We are asked to determine a quadratic equation given a set of points. To do that, let's remember that a quadratic function is of the following form:
[tex]y=ax^{2^{}}+bx+c[/tex]Now we replace the given points:
Replacing (3, -6)
[tex]\begin{gathered} -6=a(3)^2+3b+c \\ -6=9a+3b+c,(1) \end{gathered}[/tex]Replacing (1, -2)
[tex]\begin{gathered} -2=a(1)^2+b(1)+c \\ -2=a+b+c,(2) \end{gathered}[/tex]Replacing (6, 3)
[tex]\begin{gathered} 3=a(6)^2+b(6)+c \\ 3=36a+6b+c,(3) \end{gathered}[/tex]We get a system of three equations and three variables, these are:
[tex]\begin{gathered} 9a+3b+c=-6,(1) \\ a+b+c=-2,(2) \\ 36a+6b+c=3,(3) \end{gathered}[/tex]Solving for "c" in equation (1):
[tex]c=-6-3b-9a,(4)[/tex]Solving for "c" in equation (2):
[tex]c=-2-b-a,(5)[/tex]Solving for "c" in equation (3)
[tex]c=3-6b-36a,(6)[/tex]equating equations (4) and (5):
[tex]-6-3b-9a=-2-b-a[/tex]Rewritting:
[tex]\begin{gathered} -3b+b-9a+a=-2+6 \\ -8a-2b=4,(7) \end{gathered}[/tex]equating equation (5) and (6):
[tex]-2-b-a=3-6b-36a[/tex]Rewritting:
[tex]\begin{gathered} -b-a+6b+36a=3+2 \\ 35a+5b=5,(8) \end{gathered}[/tex]Now we solve for "a" in equation (7):
[tex]\begin{gathered} -8a=4+2b \\ a=-\frac{1}{2}-\frac{1}{4}b \end{gathered}[/tex]Replacing the value of 2a" in equation (8)
[tex]35(-\frac{1}{2}-\frac{1}{4}b)+5b=5[/tex]Solving the operations:
[tex]-\frac{35}{2}-\frac{35}{4}b+5b=5[/tex]Solving for "b":
[tex]\begin{gathered} -\frac{7}{2}-\frac{7}{4}b+b=1 \\ -\frac{7}{2}-\frac{3}{4}b=1 \end{gathered}[/tex]Adding 7/2 to both sides:
[tex]\begin{gathered} -\frac{3}{4}b=1+\frac{7}{2} \\ -\frac{3}{4}b=\frac{9}{2} \\ b=-6 \end{gathered}[/tex]Therefore, b = 9.
Replacing this value in equation (7)
[tex]\begin{gathered} a=-\frac{1}{2}-\frac{1}{4}(-6) \\ a=1 \end{gathered}[/tex]Replacing in equation (2)
[tex]\begin{gathered} 1-6+c=-2 \\ \end{gathered}[/tex]Adding like terms:
[tex]-5+c=-2[/tex]Adding 5 to both sides:
[tex]\begin{gathered} c=-2+5 \\ c=3 \end{gathered}[/tex]Therefore, the quadratic equation is:
[tex]y=x^2-6x+3[/tex]Solve for x.
-
5(x − 2) = -x + 2
3
x = [?]
I
Enter
Answer: x= -13/4 OR -13=4
Step-by-step explanation: There you go just follow the distribution and then the multi step equations to solve the answer
−5(−2)=−+23
−5+10=−+23
−5=−+13
x = -13/4
help meeeeeeeeeeeeeeeeeeeeeee
thank you
Answer:
v-x=&56
Step-by-step explanation:
i catrostiphically BELIVE THT IT IS THE FLYRIDE ANDREW TATE INN ADOPT ME
Owen bought 15 bananas for $9. What was the cost in banana per dollar
Answer: 0.6 I think.
Step-by-step explanation:
9 / 15 is 0.6
if I'm wrong I'm sorry!
I don't want to give people the wrong answers!
Write four properties of cube numbers?
1. Cubes of all even natural numbers are even.
2. Cubes of all odd natural numbers are odd.
3. The sum of the cubes of first \ (n\) natural numbers is equal to the square of their sum.
4. Cubes of the numbers ending with \ (4, 5, 6\) and \ (9\) are the numbers ending in the same digit. ...
Hope this helps!
Which number is the additive inverse of -10 1/4 ?
10 1/4
-4 1/10
0
4/41
The additive inverse is 10(1/4)
What is additive inverse?By merely switching the integer's sign, you can add the original number and the additive inverse to produce a result equal to 0. The attributes of additive inverse are outlined below based on the negation of the original number. For instance, if the beginning integer is x, the additive inverse of x is -x.
The additive inverse of a number is the one that, when added to, yields zero. Other names for this exact number include sign change, negation, and the opposite (number).
Given -10(1/4)
-10(1/4) + 10(1/4) = 0
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pls help a washer and a dryer cost $649 combined.The washer costs $51 less than the dryer.What is the cost of the dryer?
Given in the question:
a.) A washer and a dryer cost $649 combined.
b.) The washer costs $51 less than the dryer.
From the given description, let's transform them into an equation.
Let,
x = Cost of washer
y = Cost of dryer
a.) A washer and a dryer cost $649 combined.
[tex]\text{ x + y = \$649}[/tex]b.) The washer costs $51 less than the dryer.
[tex]\text{ x = y - \$51}[/tex]From the generated equation, substitute x = y - $51 to x + y = $649.
We get,
[tex]\text{ x + y = \$649}[/tex][tex]\text{ (y - \$51) + y = \$649}[/tex][tex]\text{ y - \$51 + y = \$649}[/tex][tex]\text{ 2y = \$649 + \$51}[/tex][tex]\text{ 2y = \$7}00[/tex][tex]\text{ }\frac{\text{2y}}{2}\text{ = }\frac{\text{\$7}00}{2}[/tex][tex]\text{ y = \$350}[/tex]Therefore, the cost of the dryer is $350.
Let's find the cost of the washer.
[tex]\text{ x = y - \$51}[/tex][tex]\text{ x = \$350 - \$51}[/tex][tex]\text{ x = \$}299[/tex]Therefore, the cost of the washer is $299.
The question is in the photo please answer with each one
Answer:
Solution(s) below.
Step-by-step explanation:
This question involves the concept of reading values from graph.
The first 3 questions are basically asking you to find the value of y when x is a certain value.
a) g(7) is asking to find the value of y when x = 7.
So we can see from the graph, when x = 7, y = 4.
b) g(0) is asking to find the value of y when x = 0.
So we can see from the graph, when x = 0, y = 7.
c) g(-5) is asking to find the value of y when x = -5.
So we can see from the graph, when x = -5, y = 6 (Read from the value of 5 on the left side of the graph since x is negative.)
d) This question is asking us to do the opposite compared to the other 3 questions, its asking us to find the value of x when y = 3.
So, we can see from the graph, when y = 3, x = 9.
Joe bought 2 pairs of jeans and 1 shirt for 120 Sam bought 1 pair of jeans and 3 shirts for 135 How much does one shirt cost
Answer:
One shirt costs $80 and a pair of jeans equals $`15.
Step-by-step explanation:
If the shirt would cost $80 and you get 1, the jeans would equal 15. 2 pairs of jeans is 30, leaving $80 for the 1 shirt. You buy 1 pair of jeans, 15, and get 3 shirts for 135, 3 shirts would be 120. 120 + 15= 135. 80 + 15 + 15= 120.
Answer:
One shirt costs 30
Step-by-step explanation:
So, we don't know the prices for 1 shirt & 1 jeans, and we're to find the value of 1 shirt. Let's take it that:
1 shirt costs: x
1 jeans costs: y
Given that two persons in the names of Joe and Sam bought 2 pairs of jeans and 1 shirt for 120 and 1 pair of jeans and 3 shirts for 135 respectively, we can actually see that both persons bought jeans and shirts for different values. With the information, we convert to simultaneous equation.
The first info states that:
[tex]2y + x = 120→equ(i)[/tex]
The second info states that:
[tex]y + 3x = 135→equ(ii)[/tex]
Now, since we are to find the cost of 1 shirt (x), we make y the subject of formula in equation (ii) to solve for x.
[tex]y = 135 - 3x→equ(iii)[/tex]
Replace for the value of y in equation (i)
[tex]2(135 - 3x) + x = 120[/tex]
[tex]270 - 6x + x = 120[/tex]
Take like terms
[tex]-5x = 120 - 270[/tex]
[tex]-5x = -150[/tex]
Divide both sides by -5 to find the value of x
x = -150/ -5
Therefore: x = 30
Replace for the value of x in any of the equations
y = 45
