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3 years ago

Solve the equation below:

Mathematics

1 answer:

oee [108]3 years ago

3 0

Remember the chain rule.
L(x)=f(g(x))

L'(x)=f'(g(x))g'(x)

take the derivative of f(g(x)). just treat them like they are variables. so you get:

h'=f'(g(x))g'(x)

now plug in your x value and evaluate:

h'(1)=f'(g(1))(g'(1))

substitute in values that you know and evaluate again
h'(1)=f'(3)(-3)

h'(1)=(-5)(-3)=15

You might be interested in

A) x= all real #s<br>B) x>0<br>C) x=5<br>D) x=12

sashaice [31]

Answer:

Set of all real numbers

Step-by-step explanation:

When we talk of domain, we mean the possible values of x that the equation can take without being undefined

So x-values that makes the equation defined are the domain of the graph

From the diagram, we can see that the graph extends from negative infinity to positive infinity

What this mean is that the possible values here come from the top right and extends to the left

So this means that the range of possible values are the set of all real numbers

5 0

3 years ago

The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y + 7 = (x – 10). What is the stan

torisob [31]

The point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ is $\fbox{\begin\\\ \math 2x+5y=-15\\\end{minispace}}$ i.e., $\fbox{\begin\\\ \bf option C\\\end{minispace}}$ .

Further explanation:

It is given that line passes through the points $(-5,-1)$ and $(10,-7)$ .

The objective is to determine the point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ .

The options given are as follows:

Option A: 2x-5y=-15

Option B: 2x-5y=-17

Option C: 2x+5y=-15

Option D: 2x+5y=-17

Consider the point $(-5,-1)$ as $(x_{1},y_{1})$ and $(10,-7)$ as $(x_{2},y_{2})$ .

Slope of a curve is defined as the change in the value of $y$ with respect to change in value of $x$ .

The slope of the line is calculated as follows:

$\fbox{\begin\\\ \math m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\end{minispace}}$

To obtain the value of slope substitute the value of $x_{1},y_{1},x_{2},y_{2}$ in the above equation.

$\begin{aligned}m&=\dfrac{-7-(-1)}{10-(-5)}\\&=\dfrac{-6}{15}\\&=\dfrac{-2}{5}\end{aligned}$

Therefore, the slope of the line is $\fbox{\begin\\\ \math m=\dfrac{-2}{5}\\\end{minispace}}$

The general way to express the equation of a line in its point slope form is as follows:

$\fbox{\begin\\\ \math (y-y_{1})=m(x-x_{1})\\\end{minispace}}$

To obtain the point slope form of the equation of the line substitute the value of $m$ , $x_{1}$ and $y_{1}$ in the above equation.

$\begin{aligned}(y-(-1))&=\dfrac{-2}{5}(x-(-5))\\(y+1)&=\dfrac{-2}{5}(x+5)\\5y+5&=-2x-10\\5y+2x&=-15\end{aligned}$

From the above calculation it is concluded that the point slope form the equation of a line is $\fbox{\begin\\\ \math 5y+2x=-15\\\end{minispace}}$

Figure 1 (attached in the end) represents the graph of the function $5y+2x=-15$ .

This implies that the correct option for the point slope form of the line is option C.

Therefore, the point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ is $2x+5y=-15$ i.e., option C.

Learn more:

1. A problem to complete the square of quadratic function brainly.com/question/12992613

2. A problem to determine the slope intercept form of a line brainly.com/question/1473992

3. Inverse function brainly.com/question/1632445.

Answer details

Grade: High school

Subject: Mathematics

Chapter: Linear equation

Keywords: Equation, linear equation, slope, intercept, x-intercept, y-intercept, intersect, graph, curve, slope intercept form, line, y=3x/2-3, standard form, point slope form.