Answer: The total number of logs in the pile is 6.
Step-by-step explanation: Given that a stack of logs has 32 logs on the bottom layer. Each subsequent layer has 6 fewer logs than the previous layer and the top layer has two logs.
We are to find the total number of logs in the pile.
Let n represents the total number of logs in the pile.
Since each subsequent layer has 6 fewer logs then the previous layer, so the number of logs in each layer will become an ARITHMETIC sequence with
first term, a = 32 and common difference, d = -6.
We know that
the n-th term of an arithmetic sequence with first term a and common difference d is

Since there are n logs in the pile, so we get

Thus, the total number of logs in the pile is 6.
Answer:
12 pieces
Step-by-step explanation:
Given the information:
- Number of bars: 3
- Number of equal parts cut in each bar: 4
=> total number of size pieces of granola bar Adrian has is:
= Number of bars * Number of equal parts in each bars
= 3 * 4
= 12 pieces.
Please have a look at the attached photo (lines in the model to find the answer)
Y varies as x
y=kx
y=12 when x=4
12=k4
divide 4
3=k
y=3x is equation
answer is B
Answer:
The function is

The graph is attached.
Step-by-step explanation:
We have a function g(x) and we need to graph a new function that is function of g(x).
The final function is

We start by calculating g(x-2):

Then, we can calculate f(x) as:

Answer:
D. (-1, 3/2)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Distributive Property
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Algebra I</u>
- Coordinates (x, y)
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define System</u>
4x + 2y = -1
3x + 4y = 3
<u>Step 2: Rewrite System</u>
4x + 2y = -1
- [Multiplication Property of Equality] Multiply -2 on both sides: -2(4x + 2y) = 2
- [Distributive Property] Distribute -2 on both sides: -8x - 4y = 2
<u>Step 3: Redefine Systems</u>
-8x - 4y = 2
3x + 4y = 3
<u>Step 4: Solve for </u><em><u>x</u></em>
- Combine equations: -5x = 5
- [Division Property of Equality] Divide -5 on both sides: x = -1
<u>Step 5: Solve for </u><em><u>y</u></em>
- Substitute in <em>x</em> [Original Equation]: 3(-1) + 4y = 3
- Multiply: -3 + 4y = 3
- [Addition Property of Equality] Add 3 on both sides: 4y = 6
- [Division Property of Equality] Divide 4 on both sides: y = 3/2