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Paladinen [302]
2 years ago
14

Graph the linear equation by find 2 = 4x + y

Mathematics
2 answers:
Vinil7 [7]2 years ago
7 0

2=4x+y

y=2-4x

Александр Мазепов

Leya [2.2K]2 years ago
5 0

Step-by-step explanation:

<u>Step 1:  Solve for y</u>

2 = 4x + y

2 - 4x = 4x + y - 4x

y = 2 - 4x

<u>Step 2:  Solve for x</u>

2 - 2 - 4x = 0 - 2

-4x / -4 = -2 / -4

x = 1/2

<u>Step 3:  Solve for y</u>

y = 2 - 4(0)

y = 2

<u>Step 4:  Graph the equation</u>

Graph the x-intercept, (1/2, 0), the y-intercept, (0, 2) and draw a line between them.  Look at the attached picture for the graph:

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A rectangular piece of plywood has a diagonal which measures two feet more than the width. The length of the plywood is twice th
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Answer:

The length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4

Step-by-step explanation:

let l be the length and w be the width of the rectangle respectively;

Diagonal(D) of a rectangle is given by:

D = \sqrt{l^2+w^2}                              ......[1]

As per the given statement we have;

Diagonal(D) = width + 2

and

l = 2 \times w = 2w

Now, substitute these in  [1] we have;

\sqrt{(2w)^2+w^2} = w+5

Squaring both the sides we get;

4w^2+w^2 = (w+2)^2

5w^2 = w^2 + 4 + 4w

or

5w^2 -w^2 = 4w + 4 or

4w^2= 4w + 4

Simplify:

w^2-w-1 =0                         ......[2]

The quadratic equation is in the form  of ax^2+bx+c = 0

the solution is given by:  x = \frac{-b \pm\sqrt{b^2-4ac}}{2a}

On comparing with [1] we get

a= 1 , b = -1 and c = -1

Then the solution is:

w= \frac{-(-1) \pm\sqrt{(-1)^2-4(1)(-1)}}{2(1)}

w =\frac{1 \pm\sqrt{1+4}}{2} = \frac{1 \pm\sqrt{5}}{2}

Simplify:

w \approx 1.62 and w \approx -0.62

Then, the diagonal D = w+2

For w \approx 1.62

D = 1.62 +2 \approx 3.62

For w \approx -0.62

D =-0.62 +2 \approx 1.38

therefore, the length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4





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