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neonofarm [45]
2 years ago
6

Jessica purchased a 600-minute pre-paid phone card and called her sister at college. After talking to her sister "t" minutes, sh

e had less than 600 minutes on her calling card. (a) Write an equation to determine the number of minutes remaining on the card. (b) Now, suppose she talked to her sister for 65 minutes, determine how many minutes she has left on her card.
Mathematics
1 answer:
Vesna [10]2 years ago
6 0

Answer:

1) 600-t

2) 600-t=65

=>t=535

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Point P'P
Snowcat [4.5K]

<u>Given</u>:

The point P' is the image of the point P under the translation (x,y) \implies (x-6, y-1)

The coordinates of the point P are (6,0)

We need to determine the coordinates of the point P'

<u>Coordinates of the point P':</u>

The coordinates of the point P' can be determined by substituting the coordinates of the point P(6,0) in the translation.

Thus, substituting the coordinates, we have;

(6,0)\implies (6-6,0-1)

Simplifying the coordinates, we get;

(6,0)\implies (0,-1)

Thus, the coordinates of the point P' is (0,-1)

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3 years ago
Each pair of points lies on a line with the given slope. Find x.
Gwar [14]

Answer:

the answer is -2 inorder to get -1 slope

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3 years ago
List at least two advantages each of using a credit card and using cash.
Sonbull [250]
Credit Cards: You don't have to worry about how much cash you have at hand. You can get money when you need it.

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3 years ago
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We take a milk carton from the refrigerator and put it on the table at room temperature. We assume that the temperature of the c
Kisachek [45]
We can solve this problem using separation of variables.

Then apply the initial conditions

EXPLANATION

We were given the first order differential equation

\frac{dT}{dt}=k(T-a)

We now separate the time and the temperature variables as follows,

\frac{dT}{T-a}=kdt

Integrating both sides of the differential equation, we obtain;

ln(T-a)=kt +c

This natural logarithmic equation can be rewritten as;

T-a=e^{kt +c}

Applying the laws of exponents, we obtain,

T-a=e^{kt}\times e^{c}

T-a=e^{c}e^{kt}

We were given the initial conditions,

T(0)=4

Let us apply this condition to obtain;

4-20=e^{c}e^{k(0)}

-16=e^{c}

Now our equation, becomes

T-a=-16e^{kt}

or

T=a-16e^{kt}

When we substitute a=20,
we obtain,

T=20-16e^{kt}

b) We were also given that,

T(5)=8

Let us apply this condition again to find k.

8=20-16e^{5k}

This implied

-12=-16e^{5k}

\frac{-12}{-16}=e^{5k}

\frac{3}{4}=e^{5k}

We take logarithm to base e of both sides,

ln(\frac{3}{4})=5k

This implies that,

\frac{ln(\frac{3}{4})}{5}=k


k=-0.2877

After 15 minutes, the temperature will be,


T=20-16e^{-0.2877\times 15}

T=20-0.21376


T=19.786

After 15 minutes, the temperature is approximately 20°C


6 0
3 years ago
What is the solution of the simultaneous equations 3x 2y 14 and 4x 3y 13?.
lara31 [8.8K]

The solution of simultaneous equations is x=4 and y = -1.

<h3>What are Simultaneous equations?</h3>

Simultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables satisfies all such equations.

We can solve simultaneous equations by various methods. here we will solve it by elimination method.

Here we have two simultaneous equations

      3x -2y = 14 --- (i)

and 4x + 3y = 13---(ii)

Now multiplying (i) by 3 and (ii) by 2 we get

 9x -6y = 42 and 8x + 6y = 26.

Now adding both we get

17x = 68 ⇒ x = 68/17 ⇒ x = 4.

Substituting the value of x in (i), we get

3*4 - 2y = 14 ⇒ -2y = 14-12 = 2 = -2/2 ⇒ y = -1.

Therefore, the values of x and y are 4 and -1 respectively .

To know more about simultaneous equations, visit

brainly.com/question/16863577

#SPJ4

<u>NOTE</u> : The question given here is not complete. The complete question is given below.

Question: What is the solution of the simultaneous equations 3x- 2y= 14 and 4x+ 3y= 13?.

6 0
1 year ago
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