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marshall27 [118]
3 years ago
11

Customers of a phone company can choose between two service plans for long distance calls. The first plan has no monthly fee but

charges $0.20 for each
minute of calls. The second plan has a $19 monthly fee and charges an additional $0.15 for each minute of calls. For how many minutes of calls will the costs of
the two plans be equal?
minutes
Mathematics
1 answer:
alex41 [277]3 years ago
5 0

Answer:

380

Step-by-step explanation:

.20x = 19 + .15x

.05x = 19

x = 380

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Given that A, O & B lie on a straight line segment, evaluate obtuse ∠AOC.
Evgesh-ka [11]

Answer:

AOC = 124°

Step-by-step explanation:

Angle on a straight line is 180°, therefore, the sum of the three angles shown is 180;

This can be written like so:

(3x + 94) + (x + 30) + (2x - 4) = 180

This equation can be solved to find x:

6x + 120 = 180

6x = 180 - 120

6x = 60

x = 10

AOC = 3(10) + 94

= 30 + 94

= 124

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3 years ago
A source of laser light sends rays AB and AC toward two opposite walls of a hall. The light rays strike the walls at points B an
Nataly [62]

Answer:

The distance between the walls is 70 m.

Step-by-step explanation:

Given: A source of laser light is at point A on the ground between two parallel walls BE and CD . The walls are perpendicular to the ground that is

BE ⊥ ED and CD ⊥ ED

AB is a ray of light which strikes the wall on the left at point B which is 30 meters above the ground. that is BE = 30 m

AC is a ray of light which strikes the wall on the right at point C. The length of AC = 80 meters.

The ray AB makes an angle of 45 degrees with the ground that is m∠BAE = 45°

The ray AC makes an angle of 60 degrees with the ground that is m∠CAD = 60°

As shown is figure attached below.

WE have to find the distance between the walls that is Length of ED

Length of ED = EA + AD

Consider the Δ AEB,

Using trigonometric ratio,

\tan\theta=\frac{perpendicular}{base}

Here \theta=45^{\circ} , perpendicular = 30 m  and base we can find.

thus,

\tan 45^{\circ}=\frac{30}{EA}

We know \tan 45^{\circ}=1

thus, EA =  30 m

Consider the Δ AEB,

Using trigonometric ratio,

\cos\theta=\frac{base}{hypotenuse}

Here \theta=60^{\circ} , hypotenuse = 80 m  and base we can find.

thus, \cos 60^{\circ}=\frac{base}{80}

We know, \cos 60^{\circ}=\frac{1}{2}

thus, Base = 40 m

AD = 40 m

Thus, the distance between the walls that is the length of ED = 30 + 40 = 70 m

4 0
3 years ago
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