x2 - 4y2 = 16
∴ (x - 2y)(x + 2y) = 16
2y - x = 2
∴ x = 2y - 2
∴ ([2y - 2] - 2y)([2y - 2] + 2y) = 16
∴ (y - 1 - y)(y - 1 + y) = 16
∴ -1(2y - 1) = 16
∴ 1 - 2y = 16
∴ -2y = 15
∴ y = -7.5
2y - x = -2
∴ -15 - x = -2
∴ x = -13
So the point of intersection is (-13, -7.5)
4yx
2y + 2xy' + 4y + 4xy' = 0 6y + 6xy' = 0 y' = -y/x
Assume we want to graph -2yx = 8. Divide both sides by -2x, so we have: y = -4/x This equation gives two hyperbolas, one in Quad. II and another in Quad. IV. You can graph the function by substituting each x value for the expression to determine the full coordinates of the points. Finally, plot them on the graph and connect them with a line.
If you mean: 2y = x-4 then y = 0.5x-2 whereas the slope is 0.5 or a 1/2 and the y intercept is -2
Imagine that it is a square of a binomial.It would have to be of the form (X+Y)^2, where Y is some real number.Using the FOIL method, expanding the square should get you...X^2+XY+YX+Y^2, which you can simplify to X^2+2YX+Y^2.So, X^2+50X+100 = X^2+2YX+Y^2Y^2 must equal 100, and 2Y must equal 50.But, there's no value for Y like that, is there?
4yx
2y + 2xy' + 4y + 4xy' = 0 6y + 6xy' = 0 y' = -y/x
Assume we want to graph -2yx = 8. Divide both sides by -2x, so we have: y = -4/x This equation gives two hyperbolas, one in Quad. II and another in Quad. IV. You can graph the function by substituting each x value for the expression to determine the full coordinates of the points. Finally, plot them on the graph and connect them with a line.
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "equals" etc. Also use ^ to indicate powers (eg x-squared = x^2).
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "divided by", "equals", "squared", "cubed" etc. Please use "brackets" (or parentheses) because it is impossible to work out whether x plus y squared is x + y^2 or (x + y)^2.
If you mean: 2y = x-4 then y = 0.5x-2 whereas the slope is 0.5 or a 1/2 and the y intercept is -2
18
Imagine that it is a square of a binomial.It would have to be of the form (X+Y)^2, where Y is some real number.Using the FOIL method, expanding the square should get you...X^2+XY+YX+Y^2, which you can simplify to X^2+2YX+Y^2.So, X^2+50X+100 = X^2+2YX+Y^2Y^2 must equal 100, and 2Y must equal 50.But, there's no value for Y like that, is there?
f ( x ) = (x-2)/(x-1)if y = (x-2)/(x-1)yx-y= x - 2yx-x= -2+yx(y-1)=y-2x = (y-2)/(y-1)so g ( x ) the inverse function is also (x-2)/(x-1)
The two equations are:x = 2 - 2yx² + 4y² = 4The points where the first meets the second are the values of x and y that simultaneously satisfy both equations:Substitute using (1) for x in (2) and solve the formed quadratic:x² + 4y² = 4→ (2 - 2y)² + 4y² = 4→ 4 - 8y + 4y² + 4y² -4 = 0→ 8y² - 8y = 0→ 8y(y - 1) = 0→ y = 0 or y = 1Substituting these values back into (1) gives:y = 0 → x = 2 - 2× 0 = 2 - 0 = 2y = 1 → x = 2 - 2× 1 = 2 - 2 = 0→ The line meets the curve at the points (2, 0) and (0, 1)
DefinitionA relationship between two numbers in which an increase in the value of one number results in a decrease in the value of the other number.The inverse of the relation(2,3), (4,5), (2,6), (4,6)is(3,2), (5,4), (6,2), (6,4)Generally we switch the roles of x and y to find the inverse.For functions, we follow the steps below to find the inverse:Step 1: Switch the x and y.Step 2: Solve for y.Step 3: Write in inverse notation.ExampleFind the inverse ofy = 2x + 1SolutionWe writex = 2y + 1We solve:x - 1 = 2yx - 1y =2We writex - 1f -1(x) =2Notice that the original function took x, multiplied by 2 and added 1, while the inverse function took x, subtracted 1 and divided by2. The inverse function does the reverse of the original function in reverse order.
X = 1st numberY = 2nd numberFacts given:X = 2Y (One number is equal to 2 times the second number)2X + 2Y = 20 (2 times the 1st number, plus 2 times the 2nd number is 20)Now we can easily find X and Y.We'll use a method called substitution to help us.Our first equation: X = 2Y is already solved for X. (it equals 2Y's!)So let's substitute x = 2y into the 2nd equation and find out what y is. Remember to use parenthesis!2x + 2y = 202(2y) + 2y = 204y + 2y = 206y = 20y = 20/6y = 10/3We found a number for Y, even though it is a fraction.Let's substitute it back into our 1st equation to figure out what x is.x = 2yx = 2(10/3)x = 20/3In order to check and see if x = 20/3 and y = 10/3, substitute both x and y into either equation. You pick!2x + 2y = 202(20/3) + 2(10/3) = 2040/3 + 20/3 = 2060/3 = 2020 = 20 (check)