Distance between the places is :
- 30 km
Time taken to cover that distance is :
- 1.5 hour
Average speed of the cyclist will be :
Avg speed = 20 km / h
Factor x^2 +11xy+30y^2
1 answer:
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Option C and Option D
3x + 2(x - 2) + 6 = 2(2x + 3) + x - 4 has infinite number of solutions
4(x + 2) + x + 1 = 2x - 3 + 3(x + 4) has infinite number of solutions
<h3><u>Solution:</u></h3>Given that we have to find the equations that has infinite number of solutions
If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x, then we have infinite solutions.
If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.
<h3><u>Option A</u></h3>-2(x - 2) + 3x = x - 4
Multiply the terms inside the bracket
-2x + 4 + 3x = x - 4
x + 4 = x - 4
Thus this equation does not have infinite number of solutions
<h3><u>Option B</u></h3>2x + 4(x - 1) = 3(2x + 1) - 2(x - 1)
2x + 4x - 4 = 6x + 3 - 2x + 2
6x - 4 = 4x + 5
6x - 4x = 5 + 4
2x = 9
Thus this equation has only one solution.
Thus this equation does not have infinite number of solutions
<h3><u>Option C</u></h3>3x + 2(x - 2) + 6 = 2(2x + 3) + x - 4
3x + 2x - 4 + 6 = 4x + 6 + x - 4
5x + 2 = 5x + 2
Thus this equation has infinite number of solutions
<h3><u>Option D</u></h3>4(x + 2) + x + 1 = 2x - 3 + 3(x + 4)
4x + 8 + x + 1 = 2x - 3 + 3x + 12
5x + 9 = 5x + 9
Thus this equation has infinite number of solutions
Answer:
$1020
Step-by-step explanation:
Let x and y represent the numbers of Platter A and Platter B the organizer needs to purchase, respectively. The given conditions can be summarized as ...
x + 2y ≥ 80 . . . . . . 80 or more hamburgers are required
3x + y ≥ 95 . . . . . . 95 or more hot dogs are required
5x +8y ≥ 380 . . . . 380 or more chicken wings are required
16x +20y = c . . . . . c must be minimized
__
It is useful to graph these inequalities, and look for the vertex of the feasible region that is closest to the origin. That vertex is (x, y) = (20, 35). The other vertex that is close to the origin is (60, 10). The cost of that order would be $1310.
The value of an order of 20 Platter A and 35 Platter B is ...
20×$16 +35×$20 = $320 +700 = $1020
The minimum cost of the picnic food is $1020.
