Answer:
A
Step-by-step explanation:
Recall that for a quadratic equation of the form:
The number of solutions it has can be determined using its discriminant:

Where:
- If the discriminant is positive, we have two real solutions.
- If the discriminant is negative, we have no real solutions.
- And if the discriminant is zero, we have exactly one solution.
We have the equation:

Thus, <em>a</em> = 2, <em>b</em> = 5, and <em>c</em> = -<em>k</em>.
In order for the equation to have exactly one distinct solution, the discriminant must equal zero. Hence:

Substitute:

Solve for <em>k</em>. Simplify:

Solve:

Thus, our answer is indeed A.
(1 2/5)(x)=7
Simplify both sides of the equation.
7/5x=7
Multiply both sides by 5/7.
(5/7)*(7/5x)=(5/7)*(7)
x=5
Simplifying
5y + -2 = 4y + 7
Reorder the terms:
-2 + 5y = 4y + 7
Reorder the terms:
-2 + 5y = 7 + 4y
Solving
-2 + 5y = 7 + 4y
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-4y' to each side of the equation.
-2 + 5y + -4y = 7 + 4y + -4y
Combine like terms: 5y + -4y = 1y
-2 + 1y = 7 + 4y + -4y
Combine like terms: 4y + -4y = 0
-2 + 1y = 7 + 0
-2 + 1y = 7
Add '2' to each side of the equation.
-2 + 2 + 1y = 7 + 2
Combine like terms: -2 + 2 = 0
0 + 1y = 7 + 2
1y = 7 + 2
Combine like terms: 7 + 2 = 9
1y = 9
Divide each side by '1'.
y = 9
Simplifying
y = 9