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3 years ago

Located at O(1, 2) and N(3, 1). Using slope-intercept form, write the equation of line

Mathematics

2 answers:

Leto [7]3 years ago

3 0

The equation for those points is:

y = -1/2x + 5/2

Shtirlitz [24]3 years ago

3 0

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
O&({{ 1}}\quad ,&{{ 2}})\quad 
% (c,d)
N&({{ 3}}\quad ,&{{ 1}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-2}{3-1}$

$\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad 
\begin{array}{llll}
\textit{plug in the values for }
\begin{cases}
y_1=2\\
x_1=1\\
m=\boxed{?}
\end{cases}\\
\textit{and solve for "y"}
\end{array}\\

\left. \qquad \right. \uparrow\\
\textit{point-slope form}$

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How is -16/20 and 20/-25 represent the same rational number

sammy [17]

Answer:

-.8

Step-by-step explanation:

ok so if you divide -16 by 20 you will get -0.8

and if you divide 20 by -25 your answer also be -0.8

they are equal

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3 years ago

Evaluate the formula V=BH/3 for B=4cm^2 and h=6 cm

Tom [10]

V=BH/3
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3 years ago

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636366 what is the area

mixas84 [53]

Answer:

Thats not a full question

Step-by-step explanation:

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3 years ago

Help pls first correct answer gets brainleist

nevsk [136]

Answer:

Step-by-step explanation:

a^2 + b^2 = c^2

in this case 24 is a and 30 is c

24^2 = 576

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900 - 576 = 324

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2 years ago

A home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 1584 cubic feet

liq [111]

Answer:

The room dimensions that will minimize the cost of the paint are 12 ft x 12 ft x 11 ft.

Step-by-step explanation:

We can find first the volume equation using the formula of the volume of a box.

$V= xyz$

Thus we get the constraint function

$1584 = xyz$

Then since we are asked to minimize the cost, we can write the cost function which is the area of each one of the walls and ceiling multiplied by the painting cost.

$C=0.11 xy+ 2(0.06)xz+2(0.06yz \\ C =0.11 xy+0.12xz+0.12yz$

Lagrange Multipliers to find minimum cost.

We can continue finding the partial derivatives to build the system of equations required for Lagrange Multipliers method.

$C_x=\lambda V_x \\ C_y = \lambda V_y \\ C_z = \lambda V_z$

And the constraint function

$xyz=1584$

So we get

$0.11y+0.12z=\lambda yz \\ 0.11x+0.12z=\lambda xz \\ 0.12x+0.12y=\lambda xy\\ xyz=1584$

We can multiply each side of each equation by the dimension which is missing to get the full volume on the right side.

$0.11xy+0.12xz=\lambda xyz \\ 0.11xy+0.12yz=\lambda xyz \\ 0.12xz+0.12yz=\lambda xyz$

Then we can set each the equations equal to each other, so from the first one and the second equation we get

$0.11xy+0.12xz= 0.11xy+0.12yz$

We can subtract 0.11xy from both sides.

$0.12xz=0.12yz$

And we can divide both sides by 0.12z to get

$x=y$

We can repeat the process by setting the first and third equation equal to each other.

$0.11xy+0.12xz= 0.12xz+0.12yz$

We can subtract 0.12 xz from both sides

$0.11xy=0.12yz$

And we can solve by z

$z= \cfrac{0.11x}{0.12}\\ z = \cfrac{11x}{12}$

So if we replace that as well y = x on the constraint for the volume euqation we get

$1584=x(x)\left(\cfrac{11}{12}x\right) \\ 1584=\cfrac{11}{12}x^3$

We can then solve for x

$x^3 = \cfrac{1584(12)}{11}$

And taking the cube root

$x = \sqrt[3]{\cfrac{1584(12)}{11}}$

$x = \sqrt[3]{1728}$

$x=12 ft$

So then we can use the equations we have found for y and z in terms of x

$y = x \\ y = 12 ft$

And

$z= \cfrac{11x}{12}\\z= \cfrac{11(12)}{12} \\ z=11ft$

Then the dimensions of the room that will minimize the cost are 12ft x 12 ft x 11 ft. Since you have to enter using commas you can write 12, 12, 11, please check as well if you have to insert the units that are feet for each.

5 0

4 years ago