Given:
y = x - 6 (1)
for the line
x² + y² = r² (2)
for the circle
When the line intercepts the circle, the x and y values will be equal.
Equate the values of y by substituting (1) into (2).
x² + (x - 6)² = r²
x² + x² - 12x + 36 = r²
2x² - 12x + 36 = r²
Answer: r² = 2x² - 12x + 36
Answer:
105cm
Step-by-step explanation:
Call the rat's height r, the cat's height c and the table height t.
The left part says that
(t + c) - (0 + r) = 120 = t + c - r
c - r = 120 - t
Right part says that (t + r) - (0 + c) = 90 = t + r - c
c - r = t - 90
120 - t = t - 90
2t = 210
t = 105
Step-by-step explanation:
45 6
13 6
_____ +
02 6
1
________
6 /..8
..... -6
_______
..... 2
0
_______
6/5
...5
_____
0
Answer: answer is a
Step-by-step explanation:
Answer:
Quadrilateral ABCD is not a square. The product of slopes of its diagonals is not -1.
Step-by-step explanation:
Point A is (-4,6)
Point B is (-12,-12)
Point C is (6,-18)
Point D is (13,-1)
Given that the diagonals of a square are perpendicular to each other;
We know that the product of slopes of two perpendicular lines is -1.
So, slope(m) of AC × slope(m) of BD should be equal to -1.
Slope of AC = (Change in y-axis) ÷ (Change in x-axis) = (-18 - 6) ÷ (6 - -4) = -24/10 = -2.4
Slope of BD = (Change in y-axis) ÷ (Change in x-axis) = (-1 - -12) ÷ (13 - -12) = 11/25 = 0.44
The product of slope of AC and slope of BD = -2.4 × 0.44 = -1.056
Since the product of slope of AC and slope of BD is not -1 hence AC is not perpendicular to BD thus quadrilateral ABCD is not a square.
