Answer:
the graph is shifted down 3 units
Step-by-step explanation:
5x-3
meaning the original graph of 5x going down three units
Answer:
f(x + 1) = 2x² + 4x + 5
Step-by-step explanation:
Step 1: Plug in (x + 1) in as <em>x</em> in f(x)
f(x + 1) = 2(x + 1)² + 3
Step 2: Expand and distribute
f(x + 1) = 2(x² + 2x + 1) + 3
f(x + 1) = 2x² + 4x + 2 + 3
f(x + 1) = 2x² + 4x + 5
<h2>Greetings!</h2>
Answer:
x + 20 = area
Step-by-step explanation:
You need to recall the equation for a rectangle:
Width x Length = Area
So simply plug the values into this:
(0.5x+10) * 6
(0.5x * 6) + (10 * 6)
= 3x + 60
Simplified down by dividing by three:
= area
<h3>x + 20 = area</h3>
<h2>Hope this helps!</h2>
Answer:
20 people
Step-by-step explanation:
The volume of a cuboid is equal to length * breadth * height.
First, we want to figure out the values relative to each other. Everything is in centimeters except the breadth, which is 0.07m. To convert meters to centimeters, we can multiply by 100: 0.07 * 100 = 7, so the breadth is 7cm.
Next, the volume is length * breadth * height = 5cm * 7cm * 8cm = 280cm³. Each person occupies 14cm³. To find how many people can occupy the cube, we can divide the volume by the space each person takes, so
280cm³/14cm³ = 20 people
Note that we can divide because each person takes x amount of space, and the total space, z, can be represented by x * y = z, with y representing the amount of people, because we add x space for each person. Dividing both sides by x, we get y = z/x
Answer:
76
2 real solutions
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
Standard Form: ax² + bx + c = 0
Discriminant: b² - 4ac
- Positive - 2 solutions
- Equal to 0 - 1 solution
- Negative - No solutions/Imaginary
Step-by-step explanation:
<u>Step 1: Define</u>
x² - 6x - 10 = 0
<u>Step 2: Identify Variables</u>
<em>Compare quadratic.</em>
x² - 6x - 10 = 0 ↔ ax² + bx + c = 0
a = 1, b = -6, c = -10
<u>Step 3: Find Discriminant</u>
- Substitute in variables [Discriminant]: (-6)² - 4(1)(-10)
- [Discriminant] Evaluate exponents: 36 - 4(1)(-10)
- [Discriminant] Multiply: 36 + 40
- [Discriminant] Add: 76
This tells us that our quadratic has 2 real solutions.
