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3 years ago

Find the equation of a line that passes through the points (-1,5) and (3,-3). Write the equation in slope-intercept, point-slope

, and standard form.

Mathematics

1 answer:

Vesnalui [34]3 years ago

6 0

$\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\qquad 
(\stackrel{x_2}{3}~,~\stackrel{y_2}{-3})
\\\\\\
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-3-5}{3-(-1)}\implies \cfrac{-3-5}{3+1}\implies -2
\\\\\\
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-5=-2[x-(-1)]
\\\\\\
\boxed{y-5=-2(x+1)}\implies y-5=-2x-2\implies \boxed{\stackrel{slope-intercept~form}{y=-2x+3}}
\\\\\\
\boxed{\stackrel{standard~form}{2x+y=3}}$

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3 years ago

Elizabeth is draining the water from a public pool. The pool is being drained at a rate of 714 gallons per hour. Which graph app

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B
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2 years ago

Find the first partial derivatives of the function f(x,y,z)=4xsin(y−z)

Amanda [17]

Answer:

$f_x(x,y,z)=4\sin (y-z)$

$f_x(x,y,z)=4x\cos (y-z)$

$f_z(x,y,z)=-4x\cos (y-z)$

Step-by-step explanation:

The given function is

$f(x,y,z)=4x\sin (y-z)$

We need to find first partial derivatives of the function.

Differentiate partially w.r.t. x and y, z are constants.

$f_x(x,y,z)=4(1)\sin (y-z)$

$f_x(x,y,z)=4\sin (y-z)$

Differentiate partially w.r.t. y and x, z are constants.

$f_y(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial y}(y-z)$

$f_y(x,y,z)=4x\cos (y-z)$

Differentiate partially w.r.t. z and x, y are constants.

$f_z(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial z}(y-z)$

$f_z(x,y,z)=4x\cos (y-z)(-1)$

$f_z(x,y,z)=-4x\cos (y-z)$

Therefore, the first partial derivatives of the function are $f_x(x,y,z)=4\sin (y-z), f_x(x,y,z)=4x\cos (y-z)\text{ and }f_z(x,y,z)=-4x\cos (y-z)$ .

4 0

3 years ago

−6x + 14 < −28 OR 9x + 15 ≤ −12. solve for x.

sasho [114]

Answer:

x>7 or x ≤ -3

Step-by-step explanation:

Solving the 1st inequality

-6x +14 < -28 --------------- (Collect like terms)

-6x < -28 - 14

-6x < - 42 -------------------- (Divide both sides by -6)

Note: If you decide an inequality expression by a negative value, the inequality sign changes)

-6x/-6 > -42/-6

x > 7

Solving the 2nd inequality

9x + 15 ≤ −12 ----------- (Collect like terms)

9x ≤ −12 - 15

9x ≤ −27 ------------------(Divide both sides by 9)

9x/9 ≤ −27/9

x ≤ -3

Bring both results together, we get

x>7 or x ≤ -3

The final result is complex (i.e. can't be combined together).

4 0

3 years ago

Fill in the blank.<br>-9+____=-14

faust18 [17]

Answer:

-5

Step-by-step explanation:

-9+x = -14

Add 9 to each side

-9+x+9 = -14+9

x = -5

4 0

2 years ago

Read 2 more answers