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dimulka [17.4K]
3 years ago
8

for his long distance phone service, lamar pays a $3 monthly fee plus 11 cents per minute. last month, lamar's long distance bil

l was $20.82 . for how many minutes was lamar billed
Mathematics
1 answer:
e-lub [12.9K]3 years ago
4 0
Let the number of minutes be = x.

Cost per minute = 11 cents = 0.11

Phone Bill = Monthly fee  +    0.11* x 

Substituting from the question

20.82 = 3 + 0.11x

3 + 0.11x = 20.82

0.11x = 20.82 - 3

0.11x = 17.82

x = 17.82/0.11

x = 162  

<span>Lamar was billed for 162 minutes.</span>
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A rocket is launched straight up from the ground with an initial velocity of 192 feet per second. The equation for the height of
Ivenika [448]

The equation for the height of the rocket at time t given

h= -16t^2+192t

We have to find the time t, when the rocket reaches 560 feet.

That means we have to find t when h = 560 ft. we will place 560 in the place of h to find t now.

h= -16t^2+192t

560 = -16t^2+192t

In the right side, we can check -16 is the common factor. So we will take out -16 from the rigbht side.

560 = -16(t^2 - 12t)

To get rid of -16 from the right side and move it to left side, we will divide both sides by -16.

560/-16 = -16(t^2-12t)/-16

-35 = t^2 -12t

Now we will move -35 to the righ side by adding 35 to both sides.

-35+35 = t^2-12t+35

0 = t^2 -12t+35

t^2-12t+35 = 0

We will factorize thee left side to find the values of t now. We need to find a pair of factors of 35 that by adding them we will get -12.

The pair of factors of 35 are -5 and -7 and by adding -5-7 we will get -12.

t^2-12t+35 =0

(t-5)(t-7) =0

So by using zero product property we will get

t-5 =0

t-5+5 = 0+5

t=5

Also t-7 =0

t-7+7 = 0+7

t=7

So we have got the rocket reaches at 560ft when t = 5 seconds and also when t = 7 seconds.

Now part b.

When the rocket completes its trajectory and hits the ground then the height or h = 0. So we will place h = 0 there in the equation.

h= -16t^2+192t

0= -16t^2 + 192 t

0 = -16(t^2-12t)

-16(t^2-12t) = 0

We will move -16 to the other side by dividing it to both sides.

-16(t^2-12t)/-16 = 0/-16

t^2-12t = 0

We will take out the common factor t from the left side. By taking out t we will get,

t(t-12) = 0

We will use zero product property now. By using that we will get,

t = 0

ans also t-12 = 0

t-12+12 = 0+12

t = 12

When the rocket completes its trajectory and hits the ground the time t can not be 0. When t =0, the rocket starts the trajectory.

So when the rocket completes its trajectory and hits the ground ,

then t = 12seconds.

So we have got the required answers.

6 0
3 years ago
PLEASE help me and PLEASE show the work PLEASE.
Dafna1 [17]

20(4×-2)

________

(4 - (-2))²

simplified;

20(-8)

_____

(6)²

simplified;

-160

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36

simplified;

-4 16/36

simplified;

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3 0
3 years ago
Can anyone help me I was self isolating when my class was taught this and I can't get in contact with my teacher
Aleonysh [2.5K]

Answer:

Step-by-step explanation:

3x +2y = 13   -----------------(i)

x + 2y = 7    ----------------(ii)

Multiply the equation (ii) by (-1) and then add.

(i)              3x + 2y = 13

(ii)*(-1)      <u>-x    - 2y = -7 </u>        {Now, add and y will be eliminated}

                 2x       = 6

                        x = 6/2

x = 3

Plug in x = 3 in equation (i)

3*3 + 2y = 13

  9 + 2y = 13

         2y= 13 - 9

         2y = 4

           y = 4/2

y = 2

5 0
3 years ago
Read 2 more answers
Three rats in a lab are injected a type of medicine. The independent probabilities for each rat exhibiting side effects are 0.5,
EleoNora [17]

Step-by-step explanation:

There are four possible values of X: 0 rats show side effects, 1 rat shows side effects, 2 rats show side effects, or all 3 rats show side effects.

Probability X = 0:

P = (1 − 0.5) (1 − 0.4) (1 − 0.3)

P = 0.21

Probability X = 1:

P = (0.5) (1 − 0.4) (1 − 0.3) + (1 − 0.5) (0.4) (1 − 0.3) + (1 − 0.5) (1 − 0.4) (0.3)

P = 0.44

Probability X = 2:

P = (0.5) (0.4) (1 − 0.3) + (0.5) (1 − 0.4) (0.3) + (1 − 0.5) (0.4) (0.3)

P = 0.29

Probability X = 3:

P = (0.5) (0.4) (0.3)

P = 0.06

7 0
3 years ago
What is 100 minus 6x equals 160 - 10x answer
In-s [12.5K]
10 - 6x = 160 - 10x
     +6x            +6x

-10 + 6 = -4

10 = 160 - 4x
         -160

10 - 160 = -150

-4x = -150

-4x/4 = -150/-4 

x= 37.5
4 0
3 years ago
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