Answer:
a. True. Rational numbers are closed under the sum operation, therefore, the sum of two rational numbers is always a rational number.
b. True. irrational numbers are closed under the sum operation, therefore, the sum of two irrationals numbers is always a irrational number.
c. True. The square of a real number is always a number greater than zero, and the sum of two numbers greater than zero is greater than zero.
d. True. The real numbers are closed under the product operation, then if a and b are reals numbers, the product ab is also a real number.
Step-by-step explanation:
I can’t see the exact numbers because the pic is blurry but here’s how to solve it.
The three angles in a triangle always add up to 180. So subtract the angle that’s given and you’ll have the sum of the two other angles. Since it’s an equilateral triangle, the other two angles are the same.
So write the equation 2(whatever the angle is) = the number you get when you do 180-the given angle
For example (I’m not sure these numbers are right because the pic is blurry)
2(9x+7)=114
Then you would solve for x and once you get x, plug it into the angle expression 9x+ 7 or whatever to get the angle measure.
Answer:
100b
Step-by-step explanation:
Since 100 cm = 1 meter, we need to multiply b*100 to get the number of centimeters.
Pls, mark brainliest!
Answer:
![Fraction = \frac{1}{18}](https://tex.z-dn.net/?f=Fraction%20%3D%20%5Cfrac%7B1%7D%7B18%7D)
Step-by-step explanation:
Given
![Pizza = \frac{1}{3}](https://tex.z-dn.net/?f=Pizza%20%3D%20%5Cfrac%7B1%7D%7B3%7D)
![Girls = 6](https://tex.z-dn.net/?f=Girls%20%3D%206)
Required [Missing Information]
Determine the fraction each girl gets
To do this, we simply divide the pizza by the number of girls i.e.
![Fraction = \frac{Pizza}{Girls}](https://tex.z-dn.net/?f=Fraction%20%3D%20%5Cfrac%7BPizza%7D%7BGirls%7D)
![Fraction = \frac{1}{3} / 6](https://tex.z-dn.net/?f=Fraction%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%2F%206)
Change / to *
![Fraction = \frac{1}{3} *\frac{1}{6}](https://tex.z-dn.net/?f=Fraction%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%2A%5Cfrac%7B1%7D%7B6%7D)
![Fraction = \frac{1}{18}](https://tex.z-dn.net/?f=Fraction%20%3D%20%5Cfrac%7B1%7D%7B18%7D)
<em>Hence, each girl gets 1/18</em>
The temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C
From Newton's law of cooling, we have that
![T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}](https://tex.z-dn.net/?f=T_%7B%28t%29%7D%3D%20T_%7Bs%7D%2B%28T_%7B0%7D%20-%20T_%7Bs%7D%29e%5E%7Bkt%7D)
Where
![(t) = \ time](https://tex.z-dn.net/?f=%28t%29%20%3D%20%5C%20time)
![T_{(t)} = \ the \ temperature \ of \ the \ body \ at \ time \ (t)](https://tex.z-dn.net/?f=T_%7B%28t%29%7D%20%3D%20%5C%20the%20%5C%20temperature%20%5C%20of%20%5C%20the%20%5C%20body%20%5C%20at%20%5C%20time%20%5C%20%28t%29)
![T_{s} = Surrounding \ temperature](https://tex.z-dn.net/?f=T_%7Bs%7D%20%3D%20Surrounding%20%5C%20temperature)
![T_{0} = Initial \ temperature \ of \ the \ body](https://tex.z-dn.net/?f=T_%7B0%7D%20%3D%20Initial%20%5C%20temperature%20%5C%20of%20%5C%20the%20%5C%20body)
![k = constant](https://tex.z-dn.net/?f=k%20%3D%20constant)
From the question,
![T_{0} = 86 ^{o}C](https://tex.z-dn.net/?f=T_%7B0%7D%20%3D%2086%20%5E%7Bo%7DC)
![T_{s} = -20 ^{o}C](https://tex.z-dn.net/?f=T_%7Bs%7D%20%3D%20-20%20%5E%7Bo%7DC)
∴ ![T_{0} - T_{s} = 86^{o}C - -20^{o}C = 86^{o}C +20^{o}C](https://tex.z-dn.net/?f=T_%7B0%7D%20-%20T_%7Bs%7D%20%3D%2086%5E%7Bo%7DC%20-%20-20%5E%7Bo%7DC%20%3D%2086%5E%7Bo%7DC%20%2B20%5E%7Bo%7DC)
![T_{0} - T_{s} = 106^{o} C](https://tex.z-dn.net/?f=T_%7B0%7D%20-%20T_%7Bs%7D%20%3D%20106%5E%7Bo%7D%20C)
Therefore, the equation
becomes
![T_{(t)}=-20+106 e^{kt}](https://tex.z-dn.net/?f=T_%7B%28t%29%7D%3D-20%2B106%20e%5E%7Bkt%7D)
Also, from the question
After 1 hour, the temperature of the ice-cream base has decreased to 58°C.
That is,
At time
, ![T_{(t)} = 58^{o}C](https://tex.z-dn.net/?f=T_%7B%28t%29%7D%20%3D%2058%5E%7Bo%7DC)
Then, we can write that
![T_{(1)}=58 = -20+106 e^{k(1)}](https://tex.z-dn.net/?f=T_%7B%281%29%7D%3D58%20%3D%20-20%2B106%20e%5E%7Bk%281%29%7D)
Then, we get
![58 = -20+106 e^{k(1)}](https://tex.z-dn.net/?f=58%20%3D%20-20%2B106%20e%5E%7Bk%281%29%7D)
Now, solve for ![k](https://tex.z-dn.net/?f=k)
First collect like terms
![58 +20 = 106 e^{k}](https://tex.z-dn.net/?f=58%20%2B20%20%3D%20106%20e%5E%7Bk%7D)
![78 =106 e^{k}](https://tex.z-dn.net/?f=78%20%3D106%20e%5E%7Bk%7D)
Then,
![e^{k} = \frac{78}{106}](https://tex.z-dn.net/?f=e%5E%7Bk%7D%20%3D%20%5Cfrac%7B78%7D%7B106%7D)
![e^{k} = 0.735849](https://tex.z-dn.net/?f=e%5E%7Bk%7D%20%3D%200.735849)
Now, take the natural log of both sides
![ln(e^{k}) =ln( 0.735849)](https://tex.z-dn.net/?f=ln%28e%5E%7Bk%7D%29%20%3Dln%28%200.735849%29)
![k = -0.30673](https://tex.z-dn.net/?f=k%20%3D%20-0.30673)
This is the value of the constant ![k](https://tex.z-dn.net/?f=k)
Now, for the temperature of the ice cream 2 hours after it was placed in the freezer, that is, at ![t = 2 \ hours](https://tex.z-dn.net/?f=t%20%3D%202%20%5C%20hours)
From
![T_{(t)}=-20+106 e^{kt}](https://tex.z-dn.net/?f=T_%7B%28t%29%7D%3D-20%2B106%20e%5E%7Bkt%7D)
Then
![T_{(2)}=-20+106 e^{(-0.30673 \times 2)}](https://tex.z-dn.net/?f=T_%7B%282%29%7D%3D-20%2B106%20e%5E%7B%28-0.30673%20%5Ctimes%202%29%7D)
![T_{(2)}=-20+106 e^{-0.61346}](https://tex.z-dn.net/?f=T_%7B%282%29%7D%3D-20%2B106%20e%5E%7B-0.61346%7D)
![T_{(2)}=-20+106\times 0.5414741237](https://tex.z-dn.net/?f=T_%7B%282%29%7D%3D-20%2B106%5Ctimes%200.5414741237)
![T_{(2)}=-20+57.396257](https://tex.z-dn.net/?f=T_%7B%282%29%7D%3D-20%2B57.396257)
![T_{(2)}=37.396257 \ ^{o}C](https://tex.z-dn.net/?f=T_%7B%282%29%7D%3D37.396257%20%5C%20%5E%7Bo%7DC)
![T_{(2)} \approxeq 37.40 \ ^{o}C](https://tex.z-dn.net/?f=T_%7B%282%29%7D%20%5Capproxeq%20%2037.40%20%5C%20%5E%7Bo%7DC)
Hence, the temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C
Learn more here: brainly.com/question/11689670