A rectangular painting has an area of (2x^2 + 8x + 6) cm^2 . Its length is (2x + 2) cm. Find the width of the painting.

Mathematics

1 answer:

Gnesinka [82]4 years ago

8 0

Answer:

Width = x + 3

Step-by-step explanation:

The formula for the area of a rectangle is: A = LW, where A=area, L = length and W = width. In order to get the expression for the value of the width, you first need to factor each equation given for both the area and the length. Starting with the length (2x + 2), you can factor out the 2 to get: 2(x+1). With the area: 2x² + 8x + 6, you can first factor out the 2 to get: 2(x² + 4x + 3). Next, you can factor the polynomial: 2(x + 3)(x + 1). Lastly, in order to find the width, you divide the area by the length:

$\frac{2(x + 3)(x + 1)}{2(x+1)}$

Crossing out the common terms from the numerator and denominator, '2' and '(x + 1)', we get a final answer of W = x + 3.

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vovikov84 [41]

Answer:

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Avery can run at 10 uph. The bank of a river is represented by the line 4x + 3y = 12, and Avery is at (7, 5). How much time does

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4x+3y=12

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y=-4x/3+12/3

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5=3(7)/4+b

5=21/4+b

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-1/4=b so the perpendicular line is:

y=3x/4-1/4

So now we want to know the point where this perpendicular line meets with the river bank. When it does y=y so we can say:

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3(3x-1)=4(-4x+12)

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x=51/25

x=2.04

y=(3x-1)/4

y=(3*2.04-1)/4

y=1.28

So now that we know the point on the river that is closest to Avery we can calculate his distance from that point...

d^2=(x2-x1)^2+(y2-y1)^2

d^2=(7-2.04)^2+(5-1.28)^2

d^2=38.44

d=√38.44

d=6.2 units

Since he can run at 10 uph...

t=d/v

t=6.2/10

t=0.62 hours (37 min 12 sec)

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