We have the following vectors:
u = (a, b)
v = (c, d)
We observe that the vectors form an angle of 90 degrees.
Therefore, the product u.v is equal to zero.
We have then:
u.v = (a, b). (c, d) = 0
u.v = ac + bd = 0
ac = -bd
Answer:
B) ac = -bd
Answer:
Transitive property of equality is not a justification for the proof.
Step-by-step explanation:
We draw a right angle ΔACB. CD is perpendicular to AB.
Let AC = a , BC = b , AB = c and CD = h
Now in ΔABC and ΔACD
∠C = ∠D and ∠A = ∠A
from AA similarity postulate
ΔABC similar to ΔACD.
Hence,
= 
= c × x ·····················(1)
Now in ΔABC and ΔCBD
∠C = ∠D and ∠B = ∠B
from AA similarity postulates
ΔABC similar to ΔCBD
Hence,
= c × y······················(2)
Add equation (1) and (2)
+ = cx + cy
+ = c(x+y)
+ = 
[because x+y=c]
Transitive property is not useful for this proof.
Answer:
1) x- y = 8
x + y = 12
eliminate one variable by adding the equations
2x = 20
divided by 2 on both sides
x = 10
substitute the value of x in the equation 1
10 - y = 8
-y = 8- 10
y =2
[x , y]
[10 , 2]
2) 2x - y = 4
3x + y = 6
eliminate one variable by adding the equations
5x = 10
x = 2
substitute the value of x in the equation
2(2) - y = 4
4 - y = 4
y = 0
[x ; y]
[2; 0]
3) x + 2y = 10
x + 4y = 14
multiply equation 1 by - 1
-x -2y = -10
x + 4y = 14
eliminate one variable by adding the equations
2 y = 4
y = 2
substitute the value of y in the equation 1
x + 2(2) = 10
x + 4 = 10
x = 6
[x ; y]
[6 ; 2]
4 ) 3x + y = 9
y = 3x + 6
simplify the expression
3x + y = 9
- 3x + y = 6
eliminate one variable by adding the equations
2y = 15
y = 15/2
substitute the value of y in equation 1
3x + 15/ 2 = 9
3x = 3/2
x = 1/2
[x ; y]
[1/2 ; 15/ 2]
5) 4x + 5y = 15
6x - 5y = 18
eliminate one variable by adding the equations
10 x = 33
× = 33/10
substitute the value of x in equation I
4 (33/10) + 5y = 15
66/5 + 5y =15
5y = 9/5
y = 9/25
[x ; y]
[33/10 ; 9/25]
6) 5x = 7y
x + 7y = 21
in equation I move the variable to the left
5x - 7y = 0
x + 7 y = 21
eliminate one variable by adding the equations
6x = 21
x = 7/2
substitute the value of x in the equation
5(7/2) = 7y
35/2 = 7y
5/2 = y
[x ; y ]
[7/2 ; 5/2 ]
Answer:
11/13
Step-by-step explanation:
Answer:
If you put it in your calculator you should get the right answer
Step-by-step explanation:
