1/2(x+2y)+5/3(3x-2y)=-3/2; 5/4(x+2y)-3/5(3x-2y)=61/60. Find x and y?
Answers
Answer:
(x, y) = (-1/6, 1/4)
Step-by-step explanation:
This is a system of equations in expressions of two variables. You could solve it by expanding the expressions to the base variables, or you could solve it by first finding the values of the expressions.
Let's see what happens when we expand the equations all the way.
First equation:
[tex]\dfrac{1}{2}(x +2y)+\dfrac{5}{3}(3x-2y)=-\dfrac{3}{2}\\\\3(x+2y)+10(3x-2y)=-9\qquad\text{multiply by 6}\\\\3x+6y+30x-20y=-9\qquad\text{eliminate parentheses}\\\\\boxed{33x-14y+9=0}\qquad\text{collect terms, add $9$ to get general form}[/tex]
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Second equation:
[tex]\dfrac{5}{4}(x+2y)-\dfrac{3}{5}(3x-2y)=\dfrac{61}{60}\\\\75(x+2y)-36(3x-2y)=61\qquad\text{multiply by 60}\\\\75x+150y-108x+72y=61\qquad\text{eliminate parentheses}\\\\-33x +222y = 61\qquad\text{collect terms}\\\\\boxed{33x-222y+61=0}\qquad\text{write in general form}[/tex]
__
The solution process looks like it might be messy for either substitution or elimination, so we choose to solve these equations using the cross-multiplication method.
Δ1 = (33)(-222) -(33)(-14) = -6864
Δ2 = (-14)(61) -(-222)(9) = 1144
Δ3 = (9)(33) -(61)(33) = -1716
x = Δ2/Δ1 = 1144/-6864 = -1/6
y = Δ3/Δ1 = -1716/-6864 = 1/4
The solution is (x, y) = (-1/6, 1/4).
_____
Additional comment
The weird numbers notwithstanding, the solution by elimination might be easily achieved by subtracting the second equation from the first. This would give ...
208y -52 = 0 ⇒ y = 52/208 = 1/4
Direct substitution of this into either equation will require arithmetic with fractions to obtain the solution for x.
This system can be directly solved by a graphing calculator using the equations as given.
__
You can read more about the cross multiplication method of solving a system of linear equations here:
https://brainly.com/question/26397343
Step-by-step explanation:
Given equation are: [1/{2(x+2y)}] + [5/{3(3x-2y)}] = -3/2 →Eqn(1)
[5/{4(x+2y)}] - [3/{5(3x-2y)}] = 61/60 →Eqn(2)
Let {1/(x+2y)} = a ; {1/(3x-2y)} = b then
{1/(2a)} + {5/(3b)} = -3/2 →Eqn(3) * 5/2
{5/(4a)} - {3/(5b)} = 61/60 →Eqn(4) * 1
__________________________________
{5/(4a)} + {25/(6b)} = -15/4
{5/(4a)} - {3/(5b)} = 61/60
(-) (+) (-)
______________________
{23/(6b)} + {3/(5b)} = -(15/4) - (61/60)
⇛{(125b + 18b)/(30b²)} = {(-225 - 61)/60}
⇛{(143b)/(30b²)} = -286/60
⇛{143/(30b)} = -286/60
⇛1/b = -1
Therefore, b = -1
Substitute the value of b in equation (3) then we have
{1/(2a)} + (5/3) = -3/2
⇛{1/(2a)} = -(3/2) - (5/3)
= (-9-10)/6
⇛{1/(2a)} = -19/6
⇛1/a = -19/3
a = -3/19
Now, {1/(x+2y)} = a ⇛-3/19
⇛x+2y = -19/3. ⇛3x + 6y = -19 →Eqn(5)
{1/(3x-2y)} = 1⇛ 3x - 2y = 1 →Eqn(6)
(-) (+) (-)
______________
8y = -20
y = -20/8
Therefore, y = -5/2From equation (6)
3x - 2 * (-5/2) = 1
⇛3x - 5 = 1
⇛3x = 1+5
⇛3x = 6
⇛x = 6/3
Therefore, x = 2/1 = 2Answer: Hence, the required value of x and y with be -5/2 and 2 respectively.
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Related Questions
1. Mike has four cards numbered one to four. He draws one card and records the number. Calculate the probability that the result will be:
A a multiple of three
B a multiple of two
C a factor of three
Answers
Answer:
A) [tex]\frac{1}{4}[/tex]
B)[tex]\frac{2}{4}[/tex]
C)[tex]\frac{2}{4}[/tex]
Step-by-step explanation
sample space (S) = {1,2,3,4}
n(S) = 4
multiples of three (a) = {3}
n(a) = 1
probability of a = [tex]\frac{n(a)}{n(S)}[/tex]
= [tex]\frac{1}{3}[/tex]
multiples of two(b) = {2,4}
n(b) = 2
probability of b = [tex]\frac{n(b)}{n(S)}[/tex]
= [tex]\frac{2}{4}[/tex]
factors of three(c) = {1,3}
n(c) = 2
probability of c = [tex]\frac{n(c)}{n(S)}[/tex]
= [tex]\frac{2}{4}[/tex]
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4y=2x+8
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Step-by-step explanation:
What is the product
(3x-6)(2x^2-7x+1)
Answers
Answer:
6x^3-33x^2+45x-6 (third answer)
Step-by-step explanation:
(3x-6)(2x^2-7x+1)
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A project is graded on a scale of 1 to 5. if the random variable, x, is the project grade, what is the mean of the probability distribution below? a probability distribution is shown. the probability of 1 is 0.1; 2 is 0.2; 3 is 0.4; 4 is 0.2; 5 is 0.1. 0.2 0.4 1 3
Answers
For a particular data generation process, a probability distribution represents the predicted outcomes of various values. The mean of the probability distribution is 3.
What is a probability distribution?For a particular data generation process, a probability distribution represents the predicted outcomes of various values. The mean, standard deviation, skewness, and kurtosis are all features of probability distributions, which are characterized by the mean, standard deviation, skewness, and kurtosis.
The mean of the probability distribution is determined by the given formula,
[tex]\mu = \sum (x\times P(x))[/tex]
Now, substituting the value to know the probability distribution, we will get,
[tex]\mu = (1 \times 0.1)+(2 \times 0.2)+(3 \times 0.4)+(4 \times 0.2)+(5 \times 0.1)\\\\\mu = 0.1+0.4+1.2+0.8+0.5 = 3[/tex]
Hence, the mean of the probability distribution is 3.
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Answer:
its 3
Step-by-step explanation:
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Answers
Answer:
97
Step-by-step explanation:
(a - 48) + a = a + 49
2a - 48 = a + 49
a = 97
We can do this because the angles of a triangle all add up to 180 and 2 angles of a line add up to 180.
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Step-by-step explanation:
Since y represents the amount of time the car goes at 35 miles per hour, and it is given that the car spends no time at 35 miles per hour, y = 0.
We can plug y into the equation given to find x, which would be the time travelled at 55 miles per hour, or the total time in this case.
55x + 35*0 = 200
55x = 200
x = 200/55
x = 40/11 hours
Write the decimals and percents illustrated by the picture below
(can someone help me with this question? the pic is down below! i js need a decimal and percent) thanks
Answers
Answer:
Decimal: 0.16
Percent: 16%
Step-by-step explanation:
There is 16 blocks shaded out of 100 blocks.
16/100=
0.16
16%
lan is going bowling. The shoe rental is $5.00 for
the evening. Each game costs $3.00. He only has
$20 in his pocket. How many games can he play?
Let y represent the number of games in this
inequality:
$5.00 + 3y <$20
Ay 25
BY
C.y = 5
D.y > 5
Answers
Answer:
choose the last answer D I did this quiz and i am foolproof it is correct
Step-by-step explanation:
Answer:
he can play 5 more games.
Step-by-step explanation:
he has $20 and he uses $5 for shoes so he has $15 left. each game costs $3 so 3x5 = 15
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y < 3
Answers
Answer:
< means y is smaller than 3, it's not equal, so it's open dots.
(number line see the attach image.)
A wedding planner is organizing the seating for a wedding. he can represent the number of rows by the function f(x) = 13x and the number of seats in each row by the function g(x) = 5x – 2. which function represents the total number of seats? 65x 26 65x – 26 65x2 26x 65x2 – 26x
Answers
65 x²-26 x function represents the total number of seats. A function is an association between a bunch of information that each has one outcome.
What is a function?A function is a relationship between a group of inputs that each have one output. A function. It is a connection between information in which each information is associated with only one outcome.
The function is found by the multiplication of the number of rows and the number of seats per row.
[tex]\rm f(x) \times g(x)\\\\ 13x \times (5x-2) \\\\ 65 x^2-26x[/tex]
Hence 65 x²-26 x function represents the total number of seats.
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Answer:
d
Step-by-step explanation:
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Answers
Answer:
x = 9
PQ = 19
QR = 19
RP = 10
Step-by-step explanation:
if 3x - 8 = 2x+1
then,
3x -2x = 1+8
x = 9
for pq,
2x+1
2x + 1 = 2*9+1
=>18 +1 = 19
for qr,
3x-8 = 3*9-8
=>27-8 =19
for rp,
x+1=9+1
=> 10
pls help asap. i hate these questions
Answers
Answer:
5. 8
6. 5
7. 7
8. 6
9. 3
10. 4
Step-by-step explanation:
The unknown number is the the larger number divided by 10.
Like in #5 : 80 ÷ 10 = 8
what does b=. pls help
Answers
Answer:
Step-by-step explanation:
b=-13
2x – 20 < -14 please help i have to find the inequality and graph the solution
Answers
Answer:
x < 3
Step-by-step explanation:
Step 1: Add 20 to both sides.
[tex]2x-20+20 < -14+20[/tex] [tex]2x < 6[/tex]Step 2: Divide both sides by 2.
[tex]2x/2 < 6/2[/tex] [tex]x < 3[/tex]can anyone help me please ?
Answers
In descending order of b powers means the term whose b has the greatest power comes first, followed by the nxt and the one with the lowest power be the last in that order
From is the powers of b in the expression are 3,6,4
Arranging this in descending (biggest to smallest)
= 6,4,3
Hence the expression in descending order of the powers of b is
4a2b6 -5b4 + 3ab3
(6 - 7) + (-11 + -2) =
Answers
Answer:
-14
Step-by-step explanation:
(6 - 7) + ( - 11 + -2)
= -1 + -13
= -14
Answer: - 14
Step-by-step explanation: 6 - 7 = -1 -11+ -2 = - 13 -13 + - 1 = -14
Hope that helps! :)
help, please ????? ???????????
Answers
Exponential
Exponential
Linear
Linear
Non
Brainliest pls!!!
Hurry please!
What is the slope of a line perpendicular to the line whose equation is x – 3y = 27.
Fully simplify your answer.
Answers
Answer:
So a line perpendicular to this equation would be any line with a slope of -3/4 (the negative reciprocal of the slope)
Step-by-step explanation:
First convert the original equation into y = form to find the slope.
Subtract 4x on both sides leaving -3y = -27 - 4x
This leaves y = (-27 - 4x)/(-3)
You can divide both -27 and -4x by -3 individually to get 9 and 4/3 respectively
This makes your equation y = 9 + (4/3)x
Whenever an equation is in y = mx + b form, the 'm' represents the slope. In this case the slope is 4/3.
What formula can we use to find the surface area of a rectangular prism? Question 4 options: SA = 2lw 2lh 2wh SA = 2lwh SA = πr2 SA = lw lh wh.
Answers
Check the picture below.
please answer answer math question
Answers
Only option d is the correct answer as x = 3 is a solution to the equation.
To solve this problem, we have to substitute the value of x into the equation and see if it is equal to zero.
Solution of an Equationa)
[tex]3x+7 = x - 8[/tex]
when x = -6
substitute the value of x
[tex]3x+ 7 = x - 8\\x = -6\\3x-x = -8-7\\2x = -15\\2(-6) = -15\\-12 \neq -15[/tex]
equation (a) is wrong.
b)
[tex]-2x-8=-4x-1\\x = 3[/tex]
collect like terms and substitute for x
[tex]-2x-8=-4x-1\\x = 3\\-2x+4x= -1+8\\2x = 7\\2(3) = 7\\6\neq 7[/tex]
equation(b) is wrong
c)
[tex]-5x+7 = 2x - 14\\x = -8\\[/tex]
collect like terms and substitute for x
[tex]-5x+7 = 2x - 14\\x = -8\\7+ 14 = 2x + 5x\\21 = 7x\\21 = 7(-8)\\21 \neq -42[/tex]
d)
[tex]-(x-1)=4x-5-3x\\x = 3\\-(x-1) = 4x -5 -3x\\-x+1 = x- 5\\2x = 6\\2(3) = 6\\6 = 6\\[/tex]
From the above calculation, only option d is the correct answer as x = 3 is a solution to the equation.
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29 divided by a number s as an algebraic expression
Answers
Answer:
29/s
Step-by-step explanation:
Is 2 the same as 2.5 I forgot
Answers
Answer:
2.5 is greater than 2.
They are not equal
2.5 is in between 2 and 3
Since 3 is greater than 2, and 2.5 is in between them, 2.5 is greater than 2.
The height of a golfball hit off a 128-foot hill is modeled by the function h(t) = −16t2 + 32t + 128, where h is height in feet and t is time in seconds. Find the time the golf ball takes to reach the ground.
Answers
The time taken for the golf ball to reach the ground is 1 s.
Motion of the golf ballThe path of motion of the golf ball can be described as parabolic because it is projectile.
When the golf ball reaches the ground, the final velocity will be zero.
Velocity of the golf ball is change in height with time.
v = dh/dt
h(t) = -16t² + 32t + 128
dh/dt = -32t + 32
0 = -32t + 32
32t = 32
t = 1 s
Thus, the time taken for the golf ball to reach the ground is 1 s.
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Answer:
6 seconds, the other dude is a dimwit
Step-by-step explanation:
Give three pros and cons of getting a pug, and the same for a poodle.
Answers
Answer:
Step-by-step explanation:
pugs;
pros= Pugs are small in size and thus, making them suitable for small-sized rooms or apartments. Pugs have a friendly and lapdog temperament, get along well with most people and pets. Pugs are low to medium-shed breeds, which implies you are less likely going to be troubled with shedding.
cons= Pugs are prone to various throats, ears, eyes, folds, facial infections, and breathing troubles; hence they will require regular health check-ups. Pug dogs are not highly trainable – it will be difficult to train a pug to do not-so-easy activities even if you hire a professional.
poodle;
pros=They don't shed. Poodles have long hair, instead of fur so they do not shed. ...
They're easy to train. The poodle's intelligence and eagerness to please make them easy to train. ...
They're good with children or other dogs. ...
They make great service dogs or therapy dogs.
cons= Their hair requires some serious maintenance. Because poodles can grow their hair long, they require a lot more maintenance than breeds with short, flat coats. ...
They require a lot of mental stimulation. ...
They can be emotionally sensitive.
Answer: brainliest please!
Pros of a Pug
! Pugs are small in size and thus, making adaptable small-sized rooms or apartments.
! Pugs have a friendly temperament and get along well with other people/pets.
! Pugs are low to medium-shed breeds which mean you are less likely going to be troubled with shedding.
! Can take simple commands without hiring a professional trainer/ train on your own
Cons of a Pug
! Gains weight easily and lack of daily exercises like a walk or run can easily have them gain weight and affect their health.
! Pug dogs are not highly trainable ~ can do simple tricks like:
sit, stand, run, fetch but not complicated ones
! Health risks ~ Pugs are prone to throat, ears, eyes, facial infections, and breathing troubles :; hence they will require regular health check-ups.
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Pros of Poodle
! They don’t shed. Poodles have long hair, instead of fur so they do not shed.
! super easy to train compared to pugs and easily learn hard tricks and so.
! They're good with children or other dogs
! They make great service dogs or therapy dogs
Cons of Poodle
! Their hair requires some serious maintenance
! They can be emotionally sensitive
! IMPORTANT - They require a lot of mental stimulation
These pups have trained to live a luxurious lifestyle they’re rarely content to live as lap dogs. They will use their intelligence for less desired behaviors like digging, chewing, or excessive barking. If your lifestyle doesn’t allow you to provide ample mental stimulation for your dog, it might be worth considering another breed.
can some1 help? im a little confused:(
Answers
Answer:
16
Step-by-step explanation:
https://brainly.com/question/1701683
url to the help thingy
I NEED THE ANSWER PLEASE I DONT UNDERSTAND I JUST NEED THE ANSWER FOR 23,21,18
Answers
Step-by-step explanation:
follow the picture uploaded. everythinh has been solves systematically
2(n+5)=-2
I need the steps
Answers
Answer:
n = -6
Step-by-step explanation:
2 ( n + 5 ) = -2
First, solve the brackets.
2n + 10 = -2
Now take 10 to the right side.
2n + 10 -10 = -2 - 10
2n = -12
Then divide both sides by 2.
[tex]\frac{2n}{2} =\frac{-12}{2}[/tex]
And now you'll the value of n.
n = ( -6 )