Write an equation to represent each situation. Then solve the equation.
2 answers:
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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.
Answer:
The price of each hamburger is $3
The price of each hot dogs is $2 .
Step-by-step explanation:
Given as :
The total price of 3 hamburger and 2 hot dogs = $13
The total price of 2 hamburger and 5 hot dogs = $16
Let The price of each hamburger = $x
Let The price of each hot dogs = $y
<u>Now, According to question</u>
3 x + 2 y = 13 .........A
2 x + 5 y = 16 .......B
Now, Solving to eq A and B
3 × (2 x + 5 y ) - 2 × (3 x + 2 y ) = 3 × 16 - 2 × 13
Or, (6 x + 15 y) - (6 x + 4 y) = 48 - 26
Or, (6 x - 6 x) + (15 y - 4 y) = 22
Or, 0 + 11 y = 22
∴ y =
i.e y = $2
so, The price of each hot dogs = y = $2
<u>Now, Put the value of y into eq B</u>
i.e 2 x + 5 y = 16
or, 2 x + 5 × 2 = 16
or, 2 x = 16 - 10
or, 2 x = 6
∴ x =
i.e x = $3
So, The price of each hamburger = x = $3
Hence, The price of each hamburger is $3 and The price of each hot dogs is $2 . Answer