The ratio of the number of red cards to the number of black cards in a deck is 3:10 2 more cards are added to the deck.
The ratio of red to black cards in the deck is now 1:3
How many black cards are in the deck?

Then the black cards=12

Step-by-step explanation:

N of red=3

N of black=10

and we have ratio 3:10

think when we ⇒ add 2 to red, will be 5:10= 1:2 not equal to 1:3

                   ⇒add 1 to red and 1 to black, the ratio will be 4:11 not equal to 1:3

                   ⇒add 2 to black, the ratio will be 3:12 = 1:3

Then the black cards=12

hope this helps!

Either

(1) there were originally 60 black cards, and 2 red cards were added, or

(2) there were originally 20 black cards, and 1 red card and 1 black card were added.

Step-by-step explanation:

The ratio of red cards to black cards is 3:10.

Since we don't know the actual numbers of red and black cards, we can write the ratio of red to black cards as

3k/10k

After adding 2 cards, the ratio of red cards to black cards becomes 1:3.

There are 3 ways of adding 2 cards: (A) both red, (B) 1 red and one black, (C) both black.

Possibility A: add two red cards

(3k + 2)/(10k) = 1/3

10k = 9k + 6

k = 6

3k/10k = 3(6) / 10(6) = 18/60

There were originally 60 black cards.

Possibility B: add 1 red card and 1 black card

(3k + 1)/(10k + 1) = 1/3

10k + 1 = 9k + 3

k = 2

3k/10k = 3(2) / 10(2) = 6/20

There were originally 20 black cards.

Possibility C: add two black cards.

(3k)/(10k + 2) = 1/3

10k + 2 = 9k

k = -2

3k/10k = 3(-2) / 10(-2) = -6 / -20

We cannot have a negative number of cards.

No solution.

Either there were originally 60 black cards, and 2 red cards were added, or there were originally 20 black cards, and 1 red card and 1 black card were added.

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w

step-by-step explanation:

assume that you have 3 different side lengths.   apply the pythagorean theorem here:   square each of the two shortest sides; call them a and b, so that their squares are a² and b².   also square the longest side, calling the result c².

now, if a² + b² = c² is true, the triangle is a right triangle; otherwise it is not a right triangle.