If we draw a rhombus OABC on a coordinate grid with one vertex at the point O (0,0)
and let its height be 1 then (using the Pythagoras theorem) the coordinates of the 4 points will be as follows:-
O = (0,0) , A = (1, 1), B = (sqrt2+ 1 , 1) , C = (sqrt2, 0)
Slope of the diagonal OB = 1 / (sqrt2 + 1)
Slope of the other diagonal AC = - 1 / (sqrt2 - 1)
Product of the slopes = - 1 / ( sqrt2 + 1)(sqrt2 - 1) = -1 / 1 = -1
This proves that the diagonals are perpendicular.
Answer:
69 3/4
Step-by-step explanation:
The stock market goes down to 50 3/4 at the beginning of the day
At the end of the day it goes up to 120 1/2
Therefore total change in the stock market from the beginning to the end of the day can be calculated as follows
= 120 1/2 - 50 3/4
= 241/2 - 203/4
= 279/4
= 69 3/4
Hence the total change in the stock market from the beginning to the end of the day is
69 3/4
Answer:
Step-by-step explanation:
y = ax² + bx + c
Plug the points into the equation to get a system of 3 equations with 3 unknowns a, b, and c.
-27 = 4a - 2b + c
-42 = 9a + 3b + c
-12 = a + b + c
(a,b,c) = (-4,1,-9)
y = -4x² + x - 9
Answer:
21x - 42, see below :)
Step-by-step explanation:
Hello!
We know that f(x) is equal to 3x - 6
We want to know what 7 * f(x) is so we should first substitute f(x) for 3x - 6
7 * f(x)
7(3x-6)
We use distributive property to open the parenthesis:
7 * 3x + 7 * -6
21x - 42
Answer:
1/4 cup for every cup
Step-by-step explanation:
If you divide 2 by 5, you would get this answer. Sorry if it's wrong!
