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katen-ka-za [31]

3 years ago

6

Given the following sets. A=(0,1,2,3)B=(a,b,c,d)C=(0,a,2,b)Find A n C.

1 answer:

MakcuM [25]3 years ago

6 0

Answer:

A ∩ C = {0, 2}

Step-by-step explanation:

The elements that sets A and C have in common are {0, 2}.

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The sum of two numbers is 45 and there difference is 5 what are the two numbers?

Kamila [148]

Let the two numbers be x and y.
The sum is 45, therefore
x + y = 45 (1)

The difference is 5, therefore
x - y = 5 (2)

Add equations (1) and (2).
x + y + (x - y) = 45 + 5
2x = 50
x = 25

From (1), obtain
25 + y = 45
y = 45 - 25 = 20

Answer: 20 and 25

5 0

4 years ago

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fomenos

I got 499 seconds, the difference may be because of the conversion from meters to kilometers in order to calculate the time

6 0

3 years ago

Solve for x if log 9 base x + log 3 base x^2 = 2.5

Y_Kistochka [10]

Not sure if the equation is

$\log_9x+\log_3(x^2)=\dfrac52$

or

$\log_x9+\log_{x^2}3=\dfrac52$

If it's the first one:

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot9^{\log_3(x^2)}$

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot(3^2)^{\log_3(x^2)}$

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot3^{2\log_3(x^2)}$

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot3^{\log_3(x^2)^2}$

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot3^{\log_3(x^4)}$

$9^{\log_9x+\log_3(x^2)}=x\cdot x^4$

$9^{\log_9x+\log_3(x^2)}=x^5$

On the other side of the equation, we'd get

$9^{5/2}=(3^2)^{5/2}=3^{2\cdot(5/2)}=3^5$

Then

$x^5=3^5\implies\boxed{x=3}$

If it's the second one instead, you can use the same strategy as above:

$x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot x^{\log_{x^2}3}$

$x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot\left((x^2)^{1/2}\right)^{\log_{x^2}3}$

(Note that this step assume $x>0$ )

$x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot(x^2)^{(1/2)\log_{x^2}3}$

$x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot(x^2)^{\log_{x^2}\sqrt3}$

$x^{\log_x9+\log_{x^2}3}=9\sqrt3$

Then we get

$9\sqrt3=x^{5/2}\implies x=(9\sqrt3)^{2/5}\implies\boxed{x=3}$

6 0

3 years ago

Which classification best represents a triangle with side lengths 6 cm 10 cm and 12cm ?

crimeas [40]

A scalene triangle..

6 0

4 years ago

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There are blue, red and yellow marbles in a bag. The probability of choosing a blue marble is 1/8, and the probability of choosi

erma4kov [3.2K]

Answer:

3/8

Step-by-step explanation:

1/8 of the bag is blue, 1/2 is red add that and you get 5/8 then subtract 8/8 with 5/8 and that gives you 3/8.

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4 years ago

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