Answer:
y = 5x^2-5x-30
Step-by-step explanation:
A parabola with x-intercepts at (-2,0) and (3,0) has the equation
y = a(x+2)(x-3)
where a is to be determined.
We know that it passes through the point (0,-30), so
-30 = a(0+2)(0-3) = -6a
Therefore solve for a to get
a = 5
y = 5(x+2)(x-3)
y = 5(x^2-x+6)
y = 5x^2-5x-30
Answer:
The student answers 15 answers correctly.
Answer:
x>3
Step-by-step explanation:
Answer:
no solution exists:
Step-by-step explanation:
x²−1x+10=0
Step 1: Simplify both sides of the equation.
x²−x+10=0
Step 2: Subtract 10 from both sides.
x²−x+10−10=0−10
x²−x=−10
Step 3: The coefficient of -x is -1. Let b=-1.
Then we need to add (b/2)^2=1/4 to both sides to complete the square.
Add 1/4 to both sides.
x²−x+
1/4=−10+
1/4
x²−x+
1/4=−39
/4
Step 4: Factor left side.
(x -1/2)² = −39
/4
Step 5: Take square root.
x −1
/2 =±√
−39
/4
Step 6: Add 1/2 to both sides.
x =−1/2 + 1/2 = 1/2 ±√
-39/4
x = 1/2 ±√
-39/4
No real solutions.
<h2>HOW TO: SOLVE AN APPLICATION</h2>
Step 1. Identify what you are asked to find and choose a variable to represent it.
Step 2. Write a sentence that gives the information to find it.
Step 3. Translate the sentence into an equation.
Step 4. Solve the equation using good algebra techniques.
Step 5. Check the answer in the problem and make sure it makes sense.
Step 6. Write a complete sentence that answers the question.
Remember that whatever the application, once we write the sentence with the given information (Step 2), we can translate it to a percent equation and then solve it.
Do you pay a tax when you shop in your city or state? In many parts of the United States, sales tax is added to the purchase price of an item. See Figure 6.7. The sales tax is determined by computing a percent of the purchase price.
To find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price. The result is the total cost—this is what the customer pays.
