If we were to put this in terms of a venn diagram, we would have 360 owning only brand X, 500 owning only brand Y, and 80 in between, owning both. Therefore, 80 out of the 580 owners of brand Y may have X as well, which we put into fraction form 80/580, and reduce to 4/29.
All you have to do is substitute the y value from the 1st equation into the second equation and solve...
a) y= 2-x
5x + 4y = 5
Substitute (2-x) into the second equation anywhere there is a y...
5x + 4y = 5
5x + 4(2-x) = 5
Now solve
5x + 8 - 4x = 5
5x - 4x + 8 = 5
x + 8 = 5
x = -3
Now that you have a solution for x, substitute -3 into either of the original equations anywhere there is an x then solve for y...
y = 2 - x
y = 2 - (-3)
y = 2+3 = 5
You solved for x and got -3 and solved for y and got 5, so your solution set is
(-3, 5).
Now check it by substituting both numbers into one of the original equations and you should have a true statement if it is correct...
y = 2 - x
5 = 2 - (-3)
5 = 2+3
5 = 5
True statement... it checks!
note* during the check, if the equation would have worked out to something like 2 = 5, then that is a false statement therefore the solution set would be wrong and you'd have to go back and find the mistake.
Answer:
24^10/24^4
Step-by-step explanation:
Answer:
309 students
Step-by-step explanation:
Out of 600 students who complete the proficiency test, 423 were found to be proficient in reading, 398 were found to be proficient in math, and 512 were found to be proficient in either reading or math. How many were proficient in both reading and math?
We solve the above question using the formula below:
Where R = Proficiency in reading
M = Proficiency in maths
n ( R ∪ M) = n(R) + n ( M) - n ( R ∩ M)
n ( R ∪ M) = 512 students
n(R) = 423
n ( M) = 398
n ( R ∩ M) = ??
Hence:
512 = 423 + 398 - n ( R ∩ M)
n ( R ∩ M) = 423 + 398 - 512
= 821 - 512
= 309
The number of people proficient in both reading and math [n ( R ∩ M)] = 309 students
<span>Start by looking at the leading terms. The divisor's 2x goes into the dividend 6x^3 a 3x^2 number of times. Multiply this by the divisor and you get 6x^3+3x^2. Subtract from the dividend and get -4x^2. 2x goes into this -2x times. Multiply by the divisor and get -4x^2 - 2x. Subtract and get 2x. Bring down the 1 term yielding 2x+1. 2x+1 goes into 2x+1 only 1 time. Thus the quotient is 3x^2-2x+1 which is option b.</span>
