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-BARSIC- [3]
3 years ago
6

Determine the x- and y-intercepts of the linear equation. Type a numerical answer in the space provided. Type the x-intercept fi

rst, then the y-intercept second. Separate the intercepts with a comma. For example, if the x-intercept is (-10,0) and the y-intercept is (0,5), type -10,5.
x - y = 3
Mathematics
1 answer:
Gnom [1K]3 years ago
7 0

3, - 3

To find the intercepts

let x = 0, in the equation for y- intercept and y = 0 for the x- intercept

x = 0 → - y = 3 ⇒ y = - 3 ⇒ (0, -3) is y- intercept

y = 0 → x = 3 ⇒ (3 , 0) is the x- intercept

that is 3, - 3


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At 7:00 A.M., Alicia pours a cup of tea whose temperature is 200°F. The tea starts to cool to room temperature (72°F). At 7:02 A
alexgriva [62]

Answer: A) Option B

B) 22.3 minutes.

Step-by-step explanation:

The temperature decreases in an exponential decrease, this means that we can write the equation as:

T(x) = A*r^x + B

Where A is the difference between the initial temperature and the room temperature, B is the room temperature, and r is a positive number smaller than 1, that says "how fast" the temperature decreases (and x is the variable, in units of time)

We know that the initial temperature

A = 200° - 72° = 128°

B = 72°

T(x) = 128°r^x + 72°

The only option with those two values is option B.

T(x) =  128(0.989)^x + 72

We should check that when x = 2m, the temperature must be 197°

T(2m) = 128*(0.989)^2 + 72 = 197.2° (that we can round down to 197°)

So this equation is correct

Now we want to find the time such the temperature is 172°F

then:

172° = 128°(0.989)^x + 72°

100° = 128°(0.989)^x

100/128 = (0.989)^x

x = ln(100/128)/ln(0.989) = 22.3 minutes.

Let's check in our equation:

T(22.3) =  128°(0.989)^22.3 + 72 = 172°

8 0
3 years ago
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