Answer:
Step-by-step explanation:
Given
Required
7 units left and 5 units down
First, we have: [7 units left]
The rule is:
So, we have:
Next, we have: [5 units down]
The rule is:
So, we have:
Rewrite as:
Expand
Collect like terms
To write in vertex form, we have
Subtract 15 from both sides
Divide (-8) by 2; Add the square to both sides
Expand
Factorize
Factor out x - 4
Rewrite as:
Make y the subject
The vertex is:
x,y - the numbers
one positive number is 5 less than twice a second number
(1) x - 5 = 2y
their product is 117
(2) xy = 117
(1) x - 5 = 2y <em>add 5 to both sides</em>
x = 2y + 5 <em>substitute it to (2)</em>
(2y + 5)y = 117 <em>use distributive property</em>
(2y)(y) + (5)(y) = 117
2y² + 5y = 117 <em>subtract 117 from both sides</em>
2y² + 5y - 117 = 0
2y² + 18y - 13y - 117 = 0
2y(y + 9) - 13(y + 9) = 0
(y + 9)(2y - 13) = 0 ↔ y + 9 = 0 ∨ 2y - 13 = 0
y + 9 = 0 <em>subtract 9 from both sides</em>
y = -9
2y - 13 = 0 <em>add 13 to both sides</em>
2y = 13 <em>divide both sides by 2</em>
y = 6.5
<em>substitute the values of y to (1)</em>
x = 2(-9) + 5 = -18 + 5 = -13 < 0
x = 2(6.5) + 5 = 13 + 5 = 18
<h3>Answer: x = 18 and y = 6.5</h3>
Answer:
ab/(a+b)
Step-by-step explanation:
Without loss of generality, we can put point C at the origin and define line BD by the equation ...
x/a +y/b = 1
Points (x, y) fall on the line BD, and we have point L where x=y. That value of x, the square's side length, will satisfy ...
x/a +x/b = 1 . . . . . fill in x=y in the equation
x(a+b)/ab = 1 . . . .factor out x, add 1/a+1/b
x = ab/(a+b) . . . . solve for x
The length of the side of the square is ab/(a+b).
Answer:
24
Step-by-step explanation:
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