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seraphim [82]
3 years ago
12

A rectangle has a perimeter of 23 cm. Its area is 33 cm2. Determine the

Mathematics
1 answer:
SCORPION-xisa [38]3 years ago
5 0

Answer:

length = 6 cm; width = 5.5 cm

Step-by-step explanation:

Let the length = x. Let the width = y.

We use the formulas for area and perimeter using x and y, and the given values.

area = length * width

perimeter = 2(length + width)

xy = 33

2(x + y) = 23

Solve the first equation for x:

x = 33/y

Substitute 33/y for x in the second equation.

2(33/y + y) = 23

66/y + 2y = 23

Mulrtiply both sides by y.

66 + 2y^2 = 23y

2y^2 - 23y + 66 = 0

(2y - 11)(y - 6) = 0

2y - 11 = 0   or   y - 6 = 0

y = 11/2 = 5.5   or   y = 6

xy = 33

x * 11/2 = 33

x = 33 * 2/11

x = 6

Answer: length = 6 cm; width = 5.5 cm

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5 0
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Read 2 more answers
Numbers that add to -0.5 and multiply to 1
Oliga [24]
Short Answer
There are two numbers
x1 = -0.25 + 0.9682i   <<<< answer 1
x2 = - 0.25 - 0.9582i   <<<< answer 2 
 
I take it there are two such numbers.
Let one number = x
Let one number = y

x + y = -0.5    
y = - 0.5 - x       (1)
xy = 1               (2)

Put equation 1 into equation 2
xy = 1
x(-0.5 - x) = 1
-0.5x - x^2 = 1               Subtract 1 from both sides.
-0.5x - x^2 - 1 = 0          Order these by powers
-x^2 - 0.5x -1 = 0           Multiply though by - 1
x^2 + 0.5x + 1 = 0         Use the quadratic formula to solve this.

\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a}

a = 1
b = 0.5
c = 1


\text{x = }\dfrac{ -0.5 \pm \sqrt{0.5^{2} - 4*1*1 } }{2*1}

x = [-0.5 +/- sqrt(0.25 - 4)] / 2
x = [-0.5 +/- sqrt(-3.75)] / 2
x = [-0.25 +/- 0.9682i

x1 = -0.25 + 0.9682 i
x2 = -0.25 - 0.9682 i

These two are conjugates. They will add  as x1 + x2 = -0.25 - 0.25 = - 0.50.

The complex parts cancel out.  Getting them to multiply to 1 will be a little more difficult. I'll do that under the check.

Check
(-0.25 - 0.9682i)(-0.25 + 0.9682i)
Use FOIL
F:-0.25 * -0.25 = 0.0625
O: -0.25*0.9682i
I: +0.25*0.9682i
L: -0.9682i*0.9682i = - 0.9375 i^2 = 0.9375

Notice
The two middle terms (labled "O" and "I" ) cancel out. They are of opposite signs.

The final result is 0.9375 and 0.0625 add up to 1
 
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Answer:

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