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fenix001 [56]
3 years ago
14

A cell phone plan charges $39.95 a month plus 15 cents per text message sent and 15 cents per text message received. Using s to

represent the number of text messages sent in one month and r to represent the number of text messages received in one month, the following equation can be used to calculate the total monthly cost, c:
c = 39.95 + 0.15(s + r)

If it is known that the total monthly cost is $53.45 and 63 text messages were received, solve for s, the total number of text messages sent.
Mathematics
2 answers:
Allisa [31]3 years ago
3 0

Answer:

c= 39.95 +0.15 (s + r) (take the 63 received and plug it in for r and 53.45 in for c then solve)

53.45= 39.95 +0.15 (s +63) (use the distributive property)

53.45 = 39.95 + 0.15s + 9.45 (combine like terms on the right side)

53.45 = 49.40 +0.15s (subtract 49.40 from both sides)

4.05 = 0.15s (divide both sides by 0.15 so isolate s)

s= 27 (how many text messages were sent)

Step-by-step explanation:

I hope this helps :)

Taya2010 [7]3 years ago
3 0

Answer:

s=27

Step-by-step explanation:

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Assoli18 [71]

Answer:  6\sqrt{3}

======================================================

Explanation:

Method 1

We can use the pythagorean theorem to find x.

a^2+b^2 = c^2\\\\6^2+x^2 = 12^2\\\\36+x^2 = 144\\\\x^2 = 144-36\\\\x^2 = 108\\\\x = \sqrt{108}\\\\x = \sqrt{36*3}\\\\x = \sqrt{36}*\sqrt{3}\\\\x = 6\sqrt{3}\\\\

-----------------------------------

Method 2

Use the sine ratio to find x. You'll need a reference sheet or the unit circle, or simply memorize that sin(60) = sqrt(3)/2

\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(60^{\circ}) = \frac{x}{12}\\\\\frac{\sqrt{3}}{2} = \frac{x}{12}\\\\x = 12*\frac{\sqrt{3}}{2}\\\\x = 6\sqrt{3}\\\\

-----------------------------------

Method 3

Similar to the previous method, but we'll use tangent this time.

Use a reference sheet, unit circle, or memorize that tan(60) = sqrt(3)

\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(60^{\circ}) = \frac{x}{6}\\\\\sqrt{3} = \frac{x}{6}\\\\x = 6\sqrt{3}\\\\

-----------------------------------

Method 4

This is a 30-60-90 triangle. In other words, the angles are 30 degrees, 60 degrees, and 90 degrees.

Because of this special type of triangle, we know that the long leg is exactly sqrt(3) times that of the short leg.

\text{long leg} = (\text{short leg})*\sqrt{3}\\\\x = 6\sqrt{3}\\\\

The short leg is always opposite the smallest angle (30 degrees).

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