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3 years ago

If A=B prove AUB=AnB

1 answer:

6 0

If two sets are same let a and bthen we can say a= b
according to definition of intersection it is function that contains common enements from both setsas a=b so all elemnts are commonso a= a n bor b = a n b
in union the function has all elements of both sets and in set no element repeats so
a u b = aor a u b = b
as a u b = a or b and a n b = a or b so we can conclude here that
a u b = a n b as a = b // defined above

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Triangle EFG is graphed below. If the triangle is translated 4 units to the right and 3 units down, what will be the coordinates

noname [10]

Answer:

A) (3,-2)

Step-by-step explanation:

A) (3,-2)

5 0

3 years ago

Jake wants to enlarge his 12-foot by 14-foot garden. If he multiplies the dimensions by 2, how will the area of the garden be af

erastova [34]

Area = L*W
Original Area = 12*14 = 168
Multiply the dimensions by 2 = 12*2 = 24 and 14*2 = 28
New Area = 24 *28 = 672

New Area divided by original area = 672/168 = 4

The garden will be 4 times bigger in area

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3 years ago

Will mark brainliest

andrew-mc [135]

Answer:

a. The exponential model is $T(t)=69+(111)e^{-0.1368357021t}$

b. It takes the cake 9.32 minutes to cool to the desired temperature

Step-by-step explanation:

Let us solve it by using the Newton's Law of cooling

$T(t)=C+(T_{0}-C)e^{kt}$ , where

T(t) is the temperature at any given time
C is the surrounding temperature

$T_{0}$ is the initial temperature of the heated object
k is a negative constant
t is the time

∵ A cake recipe says to bake the cake until the center is 180 °F

∴ $T_{0}$ = 180 ⇒ initial temperature

∵ The room temperature is 69 °F

∴ C = 69 ⇒ surrounding temperature

- Use the table to substitute t and T to find the constant k

∵ At t = 5 minutes, T = 125 °F

∴ $125=69+(180-69)e^{5k}$

- Subtract 69 from both sides

∴ $56=(111)e^{5t}$

- Divide both sides by 111

∴ $\frac{56}{111}=e^{5k}$

- Insert ㏑ for both sides

∴ $ln(\frac{56}{111})=5k$

- Divide both sides by 5

∴ - 0.1368357021 = k

∴ $T(t)=69+(111)e^{-0.1368357021t}$

a. The exponential model is $T(t)=69+(111)e^{-0.1368357021t}$

∵ The cake cool to 100 °F

∴ The desired temperature is 100°

∴ T(t) = 100 ⇒ cake's temperature at t minute

- Use the model above to find t

∵ $T(t)=69+(111)e^{-0.1368357021t}$

∴ $100=69+(111)e^{-0.1368357021t}$

- Subtract 69 from both sides

∴ $31=(111)e^{-0.1368357021t}$

- Divide both sides by 111

∴ $\frac{31}{111} =e^{-0.1368357021t}$

- Insert ㏑ for both sides

∴ $ln(\frac{31}{111})=-0.1368357021t$

- Divide both sides by - 0.136835702

∴ 9.321711938 = t

∴ t ≅ 9.32 minutes

b. It takes the cake 9.32 minutes to cool to the desired temperature

7 0

3 years ago

Georgia makes trail mix by mixing fruit

atroni [7]

Answer: 12 ounces

Step-by-step explanation:

Let the ounces of fruits that should be added be represented by x.

Based on the information given in the question, this can be represented by:

3/2 = 18/x

Cross multiply

3 × x = 18 × 2

3x = 36

x = 36/3

x = 12

Therefore, 12 ounces of nuts should be added.

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3 years ago

Read 2 more answers

What is the domain of cosine?

Semenov [28]

The domain of a function is the set of values of the independent variable for which the function is valid. In practice, this is the allowable values of X or, in this case, theta. The sine and cosine functions have a domain of all numbers from negative infinity to positive infinity. The tangent function, however, is sine(theta) / cosine(theta).

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3 years ago