All categories

2 years ago

Solve the system of equations below.

Mathematics

1 answer:

Vladimir79 [104]2 years ago

7 0

Answer: y=6, x=2

Step-by-step explanation:

Substitute x=12-y/3

Isolate y, then you get 6 is y

x=12-3/3

x=2

You might be interested in

2. What is the equation in slope-intercept form of the line that passes through thepoints (-4, 47) and (2, -16)?O21 979y=-2*+ 21

trapecia [35]

hello

the points given are (-4, 47) and (2, -16)

let's find the intercept of this equation

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ x_2=2 \\ y_2=-16 \\ y_1=47 \\ x_1=-4 \end{gathered}$ $\begin{gathered} m=\frac{-16-47}{2-(-4)} \\ m=-\frac{21}{2} \\ slope=-\frac{21}{2} \end{gathered}$

now, since we know the value of the slope, we can use that in the standard equation on a straight line

the standard equation of a straight line is given as

$\begin{gathered} y=mx+c \\ m=\text{slope} \\ c=\text{intercept} \end{gathered}$

we can pick any of the points and solve for intercept

let's use (2, -16)

$\begin{gathered} x=2 \\ y=-16 \\ y=mx+c \\ m=-\frac{21}{2} \\ -16=-\frac{21}{2}(2)+c \\ -16=-21+c \\ \text{collect like terms} \\ c=-16+21 \\ c=5 \end{gathered}$

now we know the value of intercept (c) = 5 and the slope (m) = 21/2

let's use this to write equation of the straight line

$\begin{gathered} y=mx+c \\ y=-\frac{21}{2}x+5 \end{gathered}$

from the calculations above, the equation of the straight line is given as y = -21/2x + 5

8 0

11 months ago

When a number is a multiple of another, the GCF of the numbers is the greater of the numbers. Is this always, sometimes, or neve

Mice21 [21]

It depend actually on the number u r given
so technically it is sometimes ☺

3 0

2 years ago

Plz i need help i don't understand it

andreev551 [17]

Answer:

y=5,2 and -3

we have to put the values of X and then solve the equation.

5 0

2 years ago

Read 2 more answers

Find dy/dx for y= x^3 ln (cot x)

ICE Princess25 [194]

<h3>Answer</h3>

$\dfrac{dy}{dx} = 3x^2 \ln(\cot x)-x^3 \csc(x)\sec(x)$

<h3>Explanation</h3>

By the product rule $(d/dx)(f(x)g(x)) = f(x)g'(x) + g(x)f'(x)$ , we have

$\begin{aligned}\frac{dy}{dx} &= \left(x^3 \ln (\cot x) \right)' \\&= x^3\big(\ln (\cot x)\big)' + \ln (\cot x) \cdot \left(x^3\right)' \end{aligned}$

By the chain rule:

$\begin{aligned}\big(\ln (\cot x)\big)' &= \dfrac{1}{\cot x} \cdot (\cot x)' \\ &= \dfrac{1}{\cot x} \cdot -\csc^2 x\\&= -\tan (x) \csc^2(x) \\&= - \frac{\sin x}{\cos x} \cdot \frac{1}{\sin^2 x} = - \frac{1}{\cos x} \cdot \frac{1}{\sin x} \\&= -\csc(x)\sec(x)\end{aligned}$

By the power rule:

$(x^3)' = 3x^2$

thus

$\begin{aligned}\frac{dy}{dx} &= x^3\big(\ln (\cot x)\big)' + \ln (\cot x) \cdot \left(x^3\right)' \\&= x^3\big( -\csc(x)\sec(x) \big) + \ln(\cot x) \cdot (3x^2) \\&= -x^3 \csc(x)\sec(x) + 3x^2 \ln(\cot x) \\&= 3x^2 \ln(\cot x)-x^3 \csc(x)\sec(x)\end{aligned}$

Nothing to do to simplify any further, other than factoring out $x^2$ .

4 0

3 years ago

What is the rate of change between the point (0,0)and (2,100)

Ivenika [448]

The answer would just be 50/1 or just 50

8 0

2 years ago