Answer:
(32/5, -48/5)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Algebra I</u>
- Terms/Coefficients
- Coordinates (x, y)
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
-4x + 16 = y
2x - 32 = 2y
<u>Step 2: Solve for </u><em><u>x</u></em>
<em>Substitution</em>
- Substitute in <em>y</em>: 2x - 32 = 2(-4x + 16)
- Distribute 2: 2x - 32 = -8x + 32
- [Addition Property of Equality] Add 8x on both sides: 10x - 32 = 32
- [Addition Property of Equality] Add 32 on both sides: 10x = 64
- [Division Property of Equality] Divide 10 on both sides: x = 32/5
<u>Step 3: Solve for </u><em><u>y</u></em>
- Define original equation: -4x + 16 = y
- Substitute in <em>x</em>: -4(32/5) + 16 = y
- Multiply: -128/5 + 16 = y
- Add: -48/5 = y
- Rewrite/Rearrange: y = -48/5
We will use the segment addition postulate.
PQ + QR = PR
4x - 1 + 3x - 1 = 54
7x - 2 = 54
7x = 56
x = 8
So QR is 3(8) - 1 or 24 - 1 which is 23.
Answer:
Constant of proportionality = 24
Equation: 
Step-by-step explanation:
Given:
'x' and 'y' are proportional to each other.
At 
Now, for a proportional relationship, the constant of proportionality is given as the ratio of the two values of the two variables that are in proportion.
Here, 'x' and 'y' are in proportion. So, the constant of proportionality is given as:
Therefore, the constant of proportionality is 24.
Now, a proportional relationship in 'x' and 'y' is given as:
Now, plug in the given value of 'k' and complete the equation. This gives,
Therefore, the equation that relates 'x' and 'y' is
