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puteri [66]
1 year ago
13

Solve x^2 + x - 12 = 0

Mathematics
1 answer:
bogdanovich [222]1 year ago
6 0

Answer:

x₁ = -4

x₂ = 3

Step-by-step explanation:

x²+ x + 12 = 0

x = {-1±√((1²)-(4*1*-12))} / (2*1)

x = {-1±√(1+48)} / 2

x = {-1±√49} / 2

x = {-1±7} / 2

x₁ = {-1-7} / 2 = -8/2 = -4

x₂ = {-1+7} / 2 = 6/2 = 3

Check:

x₁

-4² + (-4) - 12 = 0

16 - 4 - 12 = 0

x₂

3² + 3 - 12 = 0

9 + 3 - 12 = 0

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Please help due today
marusya05 [52]

Answer:

15

Step-by-step explanation:

Let the smallest integer be x. The integers will be x, x+1, x+2, all the way up to x+6.

119 = 7x + (1+2+3+4+5+6)

119 = 7x + 21

7x = 98

x = 14

The second smallest integer will be x+1, so x+1 = 15.

5 0
2 years ago
Consider the game of rock-paper-scissors to be an experiment. In the long run, roommate A chooses rock 21% of the time, and room
coldgirl [10]

Answer:

0.3597 = 35.97% probability that roommate A wins the game and thus does not have to wash the dishes.

Step-by-step explanation:

Independent events:

If two events are independent, the probability of both happening is the multiplication of their probabilities.

Rock-paper-scissors rules:

A player that choose rocks beats one who chooses scissors.

A player that choose paper beats one who chooses rocks.

A player that choose scissors beats one who chooses paper.

Probability that roommate A wins the game and thus does not have to wash the dishes.

3 possible events:

Roommate A - Rocks(21% of the time) and Roommate B - Scissors(18% of the time)

So

p_R = 0.21*0.18 = 0.0378

Roommate A - Paper(39% of the time) and Roommate B - Rocks(61% of the time).

So

p_P = 0.39*0.61 = 0.2379

Roommate A - Scissors(40% of the time) and Roommate B - Paper(21% of the time).

So

p_S = 0.4*0.21 = 0.084

Probability of roommate A winning:

p = p_R + p_P + p_S = 0.0378 + 0.2379 + 0.084 = 0.3597

0.3597 = 35.97% probability that roommate A wins the game and thus does not have to wash the dishes.

8 0
3 years ago
Frodo ran 2 1/5 miles in 7/12 of an hour. How many miles can Frodo run in one hour?
iVinArrow [24]

Answer:

\frac{132}{35}

Step-by-step explanation:

In \frac{7}{12} of an hour, Frodo ran 2\frac{1}{5} miles

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So,

Multiplying both sides by \frac{12}{7} , we get,


In \frac{7}{12}*\frac{12}{7} hour, Frodo ran \frac{11}{5}*\frac{12}{7}

                                         = \frac{132}{35} miles

4 0
3 years ago
The distance Grayson hikes VARIES DIRECTLY with how long it takes him. Write the EQUATION that matches this situation.​
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2 years ago
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Answer:

About 220 minutes.

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