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Ainat [17]
2 years ago
11

n Chatty Cathy’s cell phone plan she pays for minutes used plus a fixed monthly charge. For 500 minutes she pays $35 total, and

for 1500 minutes used she pays $55 total. What is her monthly fixed charge?
Mathematics
1 answer:
Vladimir [108]2 years ago
3 0

Answer

Find out  the what is her monthly fixed charge .

To prove

Let us assume that the cost per mintues = x

Let us assume that the monthly charge be = y

As given

n Chatty Cathy’s cell phone plan she pays for minutes used plus a fixed monthly charge.

For 500 minutes she pays $35 total

Than the equation becomes

500x + y = 35

As given

for 1500 minutes used she pays $55 total.

Than the equation becomes

1500x + y = 55

Subtracted 500x + y = 35 from 1500x + y = 55

1500x - 500x + y - y = 55 - 35

1000x = 20

x = \frac{20}{1000}

x = $0.02

Put in the  500x + y = 35

500 × 0.02 + y = 35

10 + y = 35

y = 35 - 10

y = $25

Therefore the monthly fixed charge be $25.




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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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sp2606 [1]

Answer:

The answer is below

Step-by-step explanation:

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Answer:

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