Answer/Step-by-step explanation:
1. <ABC and <BCD are alternate interior angles. Alternate interior angles are equal, therefore, since m<ABC = 38°, then m<BCD = 38°
2. m<ECF = m<BCD (corresponding angles)
m<ECF = 38° (substitution)
3. m<DCF + m<ECF = 180° (linear pair)
m<DCF + 38° = 180° (substitution)
m<DCF = 180° - 38° (Subtraction property of equality)
m<DCF = 142°
Answer:
f(x + h) = 3x³ + x² + 9h²x + 3h³ + h² + 9hx² + 2hx
General Formulas and Concepts:
- Order of Operations: BPEMDAS
- Distributive Property
- Expand by FOIL (First Outside Inside Last)
- Combining like terms
Step-by-step explanation:
<u>Step 1: Define function</u>
f(x) = x² + 3x³
f(x + h) is x = x + h
<u>Step 2: Simplify</u>
- Substitute: f(x + h) = (x + h)² + 3(x + h)³
- Expand by FOILing: f(x + h) = (x² + 2hx + h²) + 3(x + h)³
- Rewrite: f(x + h) = (x² + 2hx + h²) + 3(x + h)²(x + h)
- Expand by FOILing: f(x + h) = (x²+2hx+h²) + 3(x² + 2hx + h²)(x+h)
- Distribute/Expand: f(x + h) = (x²+2hx+h²) + 3(x³+3hx²+3h²x+h³)
- Distribute 3: f(x + h) = (x²+2hx+h²)+(3x³+9hx²+9h²x+3h³)
- Combine like terms: f(x + h) = 3x³+x²+9h²x+3h³+h²+9hx²+2hx
Answer:
Read a bit so you can understand which one you want.
<u>Percentage</u>
15 skittles, 3 of the 15 are orange.
3 over 15, or 0.2 as a percentage.
So there is a 0.8% chance that he will NOT pick an orange skittle.
<u>Fraction</u>
15 skittles, 3 over 15.
3 over 15 can be 1 over 5.
So there is a 4 over 5 chance that he WONT grab an orange skittle, pretty good odds.
The equation of the function is f"(x) = 2x^2 - 3
<h3>How to determine the equation?</h3>
The parent function is given as:
f(x) = x^4
When it is stretched vertically by a factor of 2, the rule is
f'(x) = 2f(x)
So, we have
f'(x) = 2x^2
When shifted down 3 spaces, the rule is
f"(x) = f'(x) - 3
So, we have:
f"(x) = 2x^2 - 3
Hence, the equation of the function is f"(x) = 2x^2 - 3
Read more about function transformation at:
brainly.com/question/13810353
#SPJ1
Answer:
7
Step-by-step explanation: