Find the unknown angles

Annette [7]

Answer:

The equation of line in the form of Ax + By = C is: $\mathbf{4x+y=-17}$

Step-by-step explanation:

We need to find the equation of line, having slope m = -4 and passes through point (-2,-9)

First we need to find slope and y-intercept of the line.

The slope is given i.e. m = -4

Now, we need to find the y-intercept

Using the point (-2,-9) and slope m = -4, y-intercept can be found using:

$y=mx+b\\-9=-4(-2)+b\\-9=8+b\\b=-9-8\\b=-17$

Now, the equation of required line having slope m = -4 and y-intercept b = -17 is:

$y=mx+b\\y=-4x-17$

Now writing in form of Ax + By = C

$y=-4x-17\\4x+y=-17$

So, the equation of line in the form of Ax + By = C is: $\mathbf{4x+y=-17}$ .

5 0

2 years ago

KonstantinChe [14]

Answer:

b. $\displaystyle \frac{1}{2}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

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

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle H(x) = \sqrt[3]{F(x)}$

Step 2: Differentiate

Rewrite function [Exponential Rule - Root Rewrite]: $\displaystyle H(x) = [F(x)]^\bigg{\frac{1}{3}}$
Chain Rule: $\displaystyle H'(x) = \frac{d}{dx} \bigg[ [F(x)]^\bigg{\frac{1}{3}} \bigg] \cdot \frac{d}{dx}[F(x)]$
Basic Power Rule: $\displaystyle H'(x) = \frac{1}{3}[F(x)]^\bigg{\frac{1}{3} - 1} \cdot F'(x)$
Simplify: $\displaystyle H'(x) = \frac{F'(x)}{3}[F(x)]^\bigg{\frac{-2}{3}}$
Rewrite [Exponential Rule - Rewrite]: $\displaystyle H'(x) = \frac{F'(x)}{3[F(x)]^\bigg{\frac{2}{3}}}$

Step 3: Evaluate

Substitute in x [Derivative]: $\displaystyle H'(5) = \frac{F'(5)}{3[F(5)]^\bigg{\frac{2}{3}}}$
Substitute in function values: $\displaystyle H'(5) = \frac{6}{3(8)^\bigg{\frac{2}{3}}}$
Exponents: $\displaystyle H'(5) = \frac{6}{3(4)}$
Multiply: $\displaystyle H'(5) = \frac{6}{12}$
Simplify: $\displaystyle H'(5) = \frac{1}{2}$