Answer:
(4/3, 7/3)
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>Algebra I</u>
- Terms/Coefficients
- Coordinates (x, y)
- Solving systems of equations of using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
7x - y = 7
x + 2y = 6
<u>Step 2: Rewrite Systems</u>
Equation: x + 2y = 6
- [Subtraction Property of Equality] Subtract 2y on both sides: x = 6 - 2y
<u>Step 3: Redefine Systems</u>
7x - y = 7
x = 6 - 2y
<u>Step 4: Solve for </u><em><u>y</u></em>
<em>Substitution</em>
- Substitute in <em>x</em>: 7(6 - 2y) - y = 7
- Distribute 7: 42 - 14y - y = 7
- Combine like terms: 42 - 15y = 7
- [Subtraction Property of Equality] Subtract 42 on both sides: -15y = -35
- [Division Property of Equality] Divide -15 on both sides: y = 7/3
<u>Step 5: Solve for </u><em><u>x</u></em>
- Define original equation: x + 2y = 6
- Substitute in <em>y</em>: x + 2(7/3) = 6
- Multiply: x + 14/3 = 6
- [Subtraction Property of Equality] Subtract 14/3 on both sides: x = 4/3
For the given expressions we will have:
y = exp(x - 4) →we have a shift of 4 units to the right.
y = exp (x +9) → we have a shift of 9 units to the left.
y = exp(x) + 7 → we have a shift of 7 units up.
y = exp(x) - 6 → we have a shift of 6 units down.
<h3>
How to work with vertical and horizontal shifts?</h3>
Remember that the shifts work as follows.
For a function f(x), we define a vertical shift of N units as:
g(x) = f(x) + N
- If N > 0, the shift is upwards.
- If N < 0, the shift is downwards.
For a function f(x), we define a horizontal shift of N units as:
g(x) = f(x + N)
- If N > 0, the shift is to the left.
- If N < 0, the shift is to the right.
Then, if we have:
exp(x - 4) we have a shift of 4 units to the right.
exp (x +9) we have a shift of 9 units to the left.
exp(x) + 7 we have a shift of 7 units up.
exp(x) - 6 we have a shift of 6 units down.
Learn more about translations
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Let's take the non-linear equation:
First Make The Equation To Be In Terms of Y
*Divide Both sides by
*Simplify
You shouldn't keep a radical in the denominator, however we leave it for the purpose of the reciprocal.
*Take The Reciprocal Of Both Sides
A Linear Equation Takes The Format:
So,
Resulting in :
Answer:
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Step-by-step explanation:
<h2>¡Hola! </h2>
<h2>Explicación paso a paso Espero que te ayude</h2>
<h2>Espero que te ayude </h2>