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Viktor [21]
2 years ago
15

() Susan set up a lemonade stand to raise money for a children's hospital. She's selling

Mathematics
1 answer:
murzikaleks [220]2 years ago
4 0

Solving the system of equations, it is found that 120 cups of lemonade and 160 brownies were sold.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The variables are given as follows:

  • Variable x: Number of cups of lemonade sold.
  • Variable y: Number of brownies sold.

In this problem, the system is:

  • x + y = 280.
  • 2.5x + 1.5y = 540.

From the first equation, y = 280 - x, hence, replacing in the second:

2.5x + 1.5y = 540

2.5x + 1.5(280 - x) = 540

x = 540 - 1.5 x 280

x = 120

y = 280 - x = 280 - 120 = 160.

120 cups of lemonade and 160 brownies were sold.

More can be learned about a system of equations at brainly.com/question/24342899

#SPJ1

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Answer:

When kicked, the height of the ball is 1 feet. The highest point for the ball's trajectory is 12 feet.

Step-by-step explanation:

We are given that the height is given by f(x)=-0.11x^2+2.2x+1. The distance between the ball to the point where it was kicked is 0 right at the moment the ball was kicked. So, the height of the ball, when it was kicked is f(0) = -0.11*0 + 2.2*0 +1  = 1.

To determine the highest point, we will proceed as follows. Given a parabola of the form x^2+bx + c, we can complete the square by adding and substracting the factor b^2/4. So, we get that

x^2+bx+c = x^2+bx+\frac{b^2}{4} - \frac{b^2}{4} +c = (x+\frac{b}{2})^2+c-\frac{b^2}{4}.

In this scenario, the highest/lowest points is c-\frac{b^2}{4}[/tex} (It depends on the coefficient that multiplies x^2. If it is positive, then it is the lowest point, and it is the highest otherwise). Then, we can proceed as follows. [tex] f(x) = -0.11x^2+2.2x+1 = -0.11(x^2-20x)+1

We will complete the square for x^2-20x. In this case b=-20, so

f(x) = -0.11(x^2-20x+\frac{400}{4}-\frac{400}{4})+1 = -0.11(x^2-20x+100-100)+1

We can distribute -0.11 to the number -100, so we can take it out of the parenthesis, then

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So, the highest point in the ball's trajectory is 12 feet.

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