Find the slope of the line that passes through Point A (-3, 5) and Point B (-6, 7), using m

Mathematics

1 answer:

Alexandra [31]2 years ago

7 0

Answer: -2/3 , you use the y2-y1 / x2-x1 formula

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Identify whether the expressions are equivalent or not equivalent: 11(p + q) and 11p + (7q + 4q)

Stella [2.4K]

Answer:

Yes they are

Step-by-step explanation:

11(p+q) = 11p + 11q

---------------------------

11p + (7q+ 4q)

= 11p + ( q * (7+4))

= 11p + (q * 11)

= 11p+ 11q

See they are the same

3 0

2 years ago

Write a rule for solving equations like 2x=24 without using model. Use a related division sentence to explain your answer.

erica [24]

2×2×2×2×2×2×2×2×2÷2×2×2=24 or 2×12r

5 0

3 years ago

Find f'(x) and state the domain of f': f(x) = In (2x^2+1)

-Dominant- [34]

Answer:

$f'(x) = \frac{4x}{2x^2+1}$

Domain: All Real Numbers

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Calculus

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Derivative: $\frac{d}{dx} [ln(u)] = \frac{u'}{u}$

Step-by-step explanation:

Step 1: Define

f(x) = ln(2x² + 1)

Step 2: Differentiate

Derivative ln(u) [Chain Rule/Basic Power]: $f'(x) = \frac{1}{2x^2+1} \cdot 2 \cdot 2x^{2-1}$
Simplify: $f'(x) = \frac{1}{2x^2+1} \cdot 4x$
Multiply: $f'(x) = \frac{4x}{2x^2+1}$

Step 3: Domain

We know that we would have issues in the denominator when we have a rational expression. However, we can see that the denominator would never equal 0.

Therefore, our domain would be all real numbers.

We can also graph the differential function to analyze the domain.