Answer:
System A has 4 real solutions.
System B has 0 real solutions.
System C has 2 real solutions
Step-by-step explanation:
System A:
x^2 + y^2 = 17 eq(1)
y = -1/2x eq(2)
Putting value of y in eq(1)
x^2 +(-1/2x)^2 = 17
x^2 + 1/4x^2 = 17
5x^2/4 -17 =0
Using quadratic formula:

a = 5/4, b =0 and c = -17

Finding value of y:
y = -1/2x


System A has 4 real solutions.
System B
y = x^2 -7x + 10 eq(1)
y = -6x + 5 eq(2)
Putting value of y of eq(2) in eq(1)
-6x + 5 = x^2 -7x + 10
=> x^2 -7x +6x +10 -5 = 0
x^2 -x +5 = 0
Using quadratic formula:

a= 1, b =-1 and c =5

Finding value of y:
y = -6x + 5
y = -6(\frac{1\pm\sqrt{19}i}{2})+5
Since terms containing i are complex numbers, so System B has no real solutions.
System B has 0 real solutions.
System C
y = -2x^2 + 9 eq(1)
8x - y = -17 eq(2)
Putting value of y in eq(2)
8x - (-2x^2+9) = -17
8x +2x^2-9 +17 = 0
2x^2 + 8x + 8 = 0
2x^2 +4x + 4x + 8 = 0
2x (x+2) +4 (x+2) = 0
(x+2)(2x+4) =0
x+2 = 0 and 2x + 4 =0
x = -2 and 2x = -4
x =-2 and x = -2
So, x = -2
Now, finding value of y:
8x - y = -17
8(-2) - y = -17
-16 -y = -17
-y = -17 + 16
-y = -1
y = 1
So, x= -2 and y = 1
System C has 2 real solutions
Answer:
true
Step-by-step explanation:
<u>NO MARK ME BRAINLIEST PLZ</u>
The answer is - 23/6 it should be
Answer:
linear
Step-by-step explanation:
To answer this item, we have 4 as the speed of the kayaker in still water and the speed of current be y.
When the karayaker moves upstream or against the current, his speed would be 4 - y. Further, if he moves downstream or with the current, the total speed would be 4 + y. The time utilized for the travel is equal to the ratio of the distance and the speed.
Total time = 9/(4 - y) + 9/(4 + y) = 6
We multiply the equation by (4-y)(4+y)
9(4-y) + 9(4 + y) = 6(4-y)(4+y)
Simplifying,
72 = 96 - 6y²
Transposing all the constants to only one side of the equation and rearranging,
6y² = 96 - 72
y² = 4
y = 2
Hence, the speed of the river's current is 2 miles/hr. <em>The answer is letter B.) 2 miles/hour.</em>