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Bond [772]
3 years ago
6

The quadratic x^2-6x+66 can be written in the form (x+b)^2+c, where b and c are constants. What is b+c?

Mathematics
1 answer:
jekas [21]3 years ago
7 0
Complete the square!

x^2-6x+66
=((x-3)^2-9) + 66
=(x-3)^2+57
so
b=-3, c=57
b+c=-3+57=54

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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
Find g(a-2)+3g(2a) if g(x)=x²-5x+8
sertanlavr [38]

Answer:

13a² - 39a + 46

Step-by-step explanation:

To find g(a-2)+3g(2a), find each part using the function g(x)=x²-5x+8.

g(a-2) = (a-2)²-5(a-2)+8 = a² - 4a + 4-5a + 10+8 = a² - 9a + 22

3g(2a) = 3{(2a)²-5(2a)+8} = 3{ 4a² - 10a + 8} = 12a² - 30a + 24

Combine the values to find g(a-2)+3g(2a).

g(a-2)+3g(2a) = (a² - 9a + 22) + (12a² - 30a + 24) = 13a² - 39a + 46

4 0
3 years ago
Find an equivalent expression to y + 4 + 3 (y + 2) please answer today
vekshin1
My answer would be 2y + 9
8 0
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Delicious77 [7]
The answer is d. No probs! 
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Warren started making oatmeal cookies at 3:30 pm.It took him 30 minutes to make the dough and 2 hours to bake all of the cookies
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6PM I believe because 3:30 + 30 min = 4:00 + 2 hr (2:00) = 6:00!

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<3
8 0
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