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3 years ago

Please help!

Mathematics

2 answers:

Musya8 [376]3 years ago

5 0

Answer:

C. $-6x-2y=12$

Step-by-step explanation:

We are given that a graph.

We have to find the equation of given graph.

The line passes through the point (-2,0) and (0,-6).

Slope:m $=\frac{y_2-y_1}{x_2-x_1}$

By using the formula

$m=\frac{-6-0}{0+2}=-3$

Slope-intercept form: $y=mx+C$

Where m=Slope of line

C=y-intercept

y-intercept: It is that value of y for which x=0

We have y- intercept=-6

Using the formula

Equation of line

$y=-3x-6$

$3x+y=-6$

Multiply by -2 on both sides then we get

$-6x-2y=12$

dezoksy [38]3 years ago

3 0

Answer:

Answer 3 (-6x-2y=12)

Step-by-step explanation: Turn to slope form to check

First- Add the 6x from both sides

-2y=6x+12

Second- Divide by two on both sides

y= -3x-6

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Answer:

Step-by-step explanation:

15 × $\frac{1}{3}$ = 5

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3 years ago

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The yearly cost in dollars, y, at a video game arcade based on total game tokens purchased, x, is y = x + 60 for a member and y

morpeh [17]

We have the yearly cost in dollars y at a video game arcade based on total game tokens purchased $x$ . So we know that:

 $y=x+60:\ equation \ for \ a \ member$ 

 $y=x:\ equation \ for \ a \ nonmember$ 

Then we can study this problem by using the graph in the figure below. We know that if there's no any purchase, the yearly cost for a member will be $60 and for a nonmember there will not be any cost. From this, we can affirm that the cost of membership is equal to $60.

On the other hand, both members and nonmembers will pay the same price on the total game tokens purchased, this is true because of the same slope that members and nonmembers have in the equations.

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3 years ago

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Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1

algol [13]

Find the critical points of $f(x,y)$ :

$\dfrac{\partial f}{\partial x}=-2x=0\implies x=0$

$\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12$

All three points lie within $D$ , and $f$ takes on values of

$\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}$

Now check for extrema on the boundary of $D$ . Convert to polar coordinates:

$f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t$

Find the critical points of $g(t)$ :

$\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0$

$\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2$

$\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi$

where $n$ is any integer. There are some redundant critical points, so we'll just consider $0\le t< 2\pi$ , which gives

$t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3$

which gives values of

$\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}$

So altogether, $f(x,y)$ has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

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3 years ago

The sum of two numbers is 46. The larger number is two less than three times the smaller number. Find the numbers.

melamori03 [73]

Answer: The numbers are: x = 34, y = 12

Step-by-step explanation:

Lets say the numbers are x and y. The two equations are:

x+y=46

x= 3y-2

Next you use substitution for x in the first equation which brings you to

3y-2 + y = 46 which simplyfies to:

4y - 2 = 46

4y = 48

48 / 4 = 12

y = 12

Then you plug back y=12 in either of the equation to solve for x:

x = 3y - 2

x = 3(12) - 2 = 36 - 2 = 34

x = 34, y = 12

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