The perimeter of a rectangle is the sum of twice the length and twice the width. When a diagonal is drawn across the rectangle, two congruent triangles are formed. The legs of the triangle are the sides of the rectangle. Right triangles indicates that we can use the Pythagorean theorem. Let length = xLet width = y Set the equation based on what we know. 2x + 2y = 22 x + y = 11 eq1 x2 + y2 = [√65]2 eq2 We have two equations to work with. x + y = 11 eq1 x2 + y2 = 65 eq2 Substitute eq1 into eq2. From eq1, x = 11 - y x2 = (11 - y)2 x2 = (11 - y)(11 - y) x2 = 121 - 22y + y2 (121 - 22y + y2) + y2 = 65 121 - 22y + 2y2 = 65 2y2 - 22y + 56 = 0 2(y2 - 11y + 28) = 0 2(y - 7)(y - 4) = 0 y = 7 and y = 4 Substitute these y values into eq1 to solve for x. x = 11 - 7 and x = 11 - 4 x = 4 and x = 7 Each pair of solutions has the same dimensions. Shorter side = 4Longer side = 7
An expression is a set of terms combined using the operations +, -, x or ÷, for example 4 x − 3 or 5 x 2 − 3 x y + 17 . An equation is a statement with an equals sign, which states that two expressions are equal in value, for example 4 b − 2 = 6
An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
50
6m-n
Let m = 9 and n = 4
when m = 5 and n = 38
N-6m6*9-4
Multiply first
54-4
Then subtract
50
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Answer:
x-intercept(s):
4,0
y-intercept(s):
0,8
Step-by-step explanation:
Answer:
x^2 + (y – 3)^2 = 36
Step-by-step explanation:
The standard equation of a circle with center at (h, k) and radius r is
(x - h)^2 + (y - k)^2 = r^2.
If the center lies on the y-axis, then h = 0: (x - 0)^2 + (y - k)^2 = r^2
If the circle diameter is 12, then the circle radius is 6, and so r^2 = 36
So, among the given equations, your
x^2 + (y – 3)^2 = 36 is correct (but only if you use " ^ " for exponentiation).