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Use the functions f(x) = 4x − 5 and g(x) = 3x + 9 to complete the function operations listed below.

vlada-n [284]

A. (f + g)(x) = f(x) + g(x) = 4x - 5 + 3x + 9 = 7x + 4

B. f.g (x) = f(x) * g(x) = (4x - 5)*(3x + 9) = 12x^2 + 36x - 15x - 45
= 12x^2 + 21x - 45

C Replace the x in f(x) by g(x):-
= 4(3x + 9) - 5
= 12x + 36 - 5
= 12x + 31

8 0

3 years ago

Using the discriminant, describe the nature of the roots for the equation <br> 49x^2 − 28x + 4 = 0.

scZoUnD [109]

Answer:

Put the equation in standard form by bringing the 4x + 1 to the left side.

7x2 - 4x - 1 = 0

We use the discriminant to determine the nature of the roots of a quadratic equation. The discriminant is the expression underneath the radical in the quadratic formula: b2 - 4ac.

b2 - 4ac In this case, a = 7, b = -4, and c = -1

(-4)2 - 4(7)(-1)

16 + 28 = 44

Now here are the rules for determining the nature of the roots:

(1) If the discriminant = 0, then there is one real root (this omits the ± from the quadratic formula, leaving only one possible solution)

(2) If the discriminant > 0, then there are two real roots (this keeps the ±, giving you two solutions)

(3) If the discriminant < 0, then there are two imaginary roots (this means there is a negative under the radical, making the solutions imaginary)

44 > 0, so there are two real roots

4 0

3 years ago

12. The Opera is collecting monies in advance for ticket sales. The tickets cost $17.50 each.

Debora [2.8K]

Answer:

The number of tickets they have sold in advance are summed up with the following equation and solution:

Equation: $\frac{6842.50}{17.50}$ [the final answer should be in dollars]

Solution: The Opera sold 391 tickets in advance.

Step-by-step explanation:

First: Review some background information:

Let's see what the problem gives us to answer it. I'll bold out the important parts:

The Opera is collecting monies in advance for ticket sales. The tickets cost $17.50 each. If they have collected $6842.50 already, then how many tickets have they sold in advance?

We know how much the tickets cost and how much money they have earned from selling tickets, we can find out how much tickets they have sold.

Second: Solve the problem:

We can solve this problem using many ways, but I'm just going to pick one. We will use proportions to answer this. Now thoughts might be going through your head like this: What is this guy saying? What in the world is proportions? Well hopefully you learn from this example (Please don't take offense if you <em>do</em> know how to do proportions).

First we set up two fractions. One ticket costs $17.50, so we will use it to set up our first fraction: $\frac{1}{17.50}$ . We don't know how many tickets all together cost $6842.50 so we will use the variable: x. Now, we can set up our second fraction. x tickets costs $6842.50 so our second fraction will be: $\frac{x}{6842.50}$ . Now we must use cross multiplication. We multiply the numerator of the first fraction times the denominator of the second fraction, and then we multiply the denominator o the first fraction times the numerator of the second fraction. That's what we would do usually. But now, since we have a variable, we must use cross multiplication to solve for this variable. So we multiply the the numerator of the first fraction times the denominator of the other fraction and then we divide that answer times the denominator of the first fraction (You don't have to set it up like this).So let's solve this question: