Answer:
x = -1 and y = 1/2
Step-by-step explanation:
Let u = 1/x, and v = 1/y
Then the pair of equations
-3/x + 4/y = 11
1/x - 2/y = -5
Can be written as
-3u + 4v = 11 .................................(1)
u - 2v = -5......................................(2)
From (2)
u = 2v - 5 .......................................(3)
Substituting (3) into (1)
-3(2v - 5) + 4v = 11
-6v + 15 + 4v = 11
-6v + 4v = 11 - 15
-2v = -4
v = 4/2 = 2
Substituting this value of v in (3)
u = 2v - 5
u = 2(2) - 5
= 4 - 5
= -1
That is
u = -1, v = 2
Since u = 1/x, and v = 1/y, we have
1/x = -1
=> x = -1
And
1/y = 2
=> y = 1/2
Therefore
x = -1 and y = 1/2
Question 2 the answer is 4
Answer:
The length of each side is 31.5m, 26.5m, 7m
Step-by-step explanation:
Let the length of the first side of the triangle be x meters.
Then, the second side is x-5 meters.
The third side is given as 7 meters.
The perimeter is 65 meters
This gives us the equation:
The length of each side is 31.5m, 26.5m, 7m
Answer:
M(6,5) and G(2,9)
Step-by-step explanation:
B(3,6)
C(9,4)
m = [(3+9)/2 , (6+4)/2]
= (6,5)
M(5,9)
H(8,9)
G(x,y)
[(x+8)/2 , (y+9)/2]=(5,9)
(x+8)/2 = 5
x+8 = 10
x = 2
(y+9)/2 = 9
y+9 = 18
y = 9
G(2,9)
(Correct me if i am wrong)
Answer:
a. LK = 4√3, JL= 4√6
b. PQ = 10√3, RP = 5√3
Step-by-step explanation:
a. LK =4√3,
LK=KJ= 4√3
sin(45°) = opposite/hypotenuse
hypotenuse (JL)= opposite/sin 45° = 4√3/√2/2 = 8√3/√2 = 8√3√2/2 = 4√6
b.
cos 30° = adjacent/hypotenuse = QR/PQ = 15/PQ
cos 30° = 15/PQ
PQ = 15/cos 30° = 15/√3/2)= 30/√3 = 30√3/3 = 10√3
tan 30° = opposite/adjacent = RP/QR
√3/3 = RP/QR
√3/3 = RP/15
RP = √3*15/3 = 5√3
