Answer:
There are 45 library books in the classroom.
Step-by-step explanation:
The problem says that Marvin, Latoya and Abdulla each read 3/7 of the library books in the classroom. If Latoya read 3/7 of the books, we can form a proportion to determine the number of total library books in the classroom.
To solve for 'x', we can either cross-multiply and divide, or we can multiply the denominator by the same factor as the numerator to get a product of 15. In this case, the same factor would be 5, so 7 x 5 = 35. If we cross-multiply:
3x = (15)(7) or x = 35.
Answer:
C. (f - g)(x) = 3ˣ - 2x + 14
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra I</u>
- Function Notation
- Combining Like Terms
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = 3ˣ + 10
g(x) = 2x - 4
(f - g)(x) is f(x) - g(x)
<u>Step 2: Find (f - g)(x)</u>
- Substitute: (f - g)(x) = 3ˣ + 10 - (2x - 4)
- Distribute -1: (f - g)(x) = 3ˣ + 10 - 2x + 4
- Combine like terms: (f - g)(x) = 3ˣ - 2x + 14
Answer:
Step-by-step explanation:
(-2, 1) ⇒ x₁ = -2, y₁ = 1
(6, 5) ⇒ x₂ = 6, y₂ = 5
So the slope:
Answer:
C) (x + 5)² = 40
Step-by-step explanation:
Given the quadratic equation, x² + 10x = 15:
To complete the square, take the coefficient of the middle term (b), and divide it by 2<em>a</em>:
x² + 10x + ![[\frac{b}{2a}]^{2}](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bb%7D%7B2a%7D%5D%5E%7B2%7D)
= 15 +
x² + 10x + ![[\frac{10}{2}]^{2}](https://tex.z-dn.net/?f=%5B%5Cfrac%7B10%7D%7B2%7D%5D%5E%7B2%7D)
= 15 +
x² + 10x + 5² = 15 + 5²
x² + 10x + 25 = 40
The trinomial on the left-hand side of the equation provides a perfect square binomial factors: <em>u</em>² + 2<em>uv</em> + v² = (<em>u</em> + <em>v</em>)²
x² + 10x + 25 = 40
(x + 5)² = 40
Therefore, the correct answer is Option C) (x + 5)² = 40
