TaliaArticula

Hey there, Guest!

Step 1: Multiply both sides by x+2.

\(14x+22=−3x^2−7x−2\)

\(14x+22−(−3x^2−7x−2)=−3x^2−7x−2−(−3x^2−7x−2)\)

\(3x^2+21x+24=0\)

Quadratic Formula:

\(x=\frac{−b±√b2−4ac}{2a}\)

\(x=\frac{-7}{2}+\frac{1}{2}\sqrt{17}\)

And that's the answer.

Hope this helped! :)

Hey there, Guest!

So, \(3x² + 12x - K\).

( constant )/( coefficient of \(x²\))
 

\(P × \frac{1}{P} = \frac{-k}{3}\)

1 = \(\frac{-k}{3}\)

K = -3

Hope this helped! :)
( ﾟдﾟ)つ Bye

Hey there, Guest!

120 divided by 15 = 8

8 times 5 = 48

\(\frac{48}{120}\) equals 40%

40% of the cars were previously damaged in an accident.

(120 ÷ 15) ÷ 6 = 40%.

Hope this helped! :)
( ﾟдﾟ)つ Bye

Hallo, Gast!

So...

Schritt 1: Vereinfachen Sie beide Seiten der Gleichung.

\(1+(4)(3)−7−(4−2)=x\)

\(1+(4)(3)−7+−1(4−2)=x\) (Verteilen Sie das negative Vorzeichen)

\(1+(4)(3)+−7+(−1)(4)+(−1)(−2)=x\)

\(1+(4)(3)+−7+−4+2=x\)

\(1+12+−7+−4+2=x\)

\((1+12+−7+−4+2)=x\) (Ähnliche Begriffe kombinieren)

4 = x

Schritt 2: Kehren Sie die Gleichung um.

x = 4

Hoffe das hat geholfen! :)

( ﾟдﾟ)つ Tschüss

(Es tut mir leid, wenn mein Deutsch schlecht ist.)

Hey there, Guest!

There are five choices for each ball: \(5^4\) = 625

Among these 625 distributions, there are 5 cases where the four balls reside in the same box because there are five boxes. So from 625, subtract 5 to count the required.

625 – 5 = 620.

Hope this helped! :)

( ﾟдﾟ)つ Bye

Hey there, Guest!

So, let's say that the second piece is length x.

The first piece is 3 times that, so it is 3x.

The 3rd piece is 20 feet shorter than it, so it is x-20.

Adding them, we get 5x-20, and that equals 100. 

Solving for x, we get 24.

So the lengths are 72, 24 and 4.

Hope this helped! :)

( ﾟдﾟ)つ Bye

Hey there, Guest!

So...

Travelling at 8 Km at 80 km/hr takes 1/10 hours while travelling at \(X\) km at 100 km/hr takes \(\frac{x}{100}\) hours, and travelling at \(Y\) km at 60 km/hr takes \(\frac{y}{60}\) hours; in one direction, the sum of these is 2 hours, so \(\frac{1}{10}\) + \(\frac{x}{100}\) + \(\frac{y}{60}\) = 2. In the other direction, however, whatever was uphill becomes downhill, etc.; so the roles of x and y change, and we get the equation:

1/10 + x/60 +y/100 =3.

That equation can be simplified to get:

6x + 10y = 1140

&

6y + 10x = 1740

Therefore the answer is x=165 km, and y = 15 km.

So the total distance is 165 + 15 + 8 = 188 km.

Hope this helped! :)

( ﾟдﾟ)つ Bye

Hey there, Guest!

Alright, so let's write the individual worths of these variables:

a = a

b = a + 2

c = a + 4

So...

b^2 - a^2 = 348

(b+a)(b-a) = 348

(a+2+a)(a+2-a) = 348

Therefore a = 2.

Let's insert that into both of the equations for b and c.

b =a + 2

b = 2 + 2

b = 3

c = a +4

c = 2 + 4

c = 6

And here we are, back at the original equation, except now we know that:

a = 2

b = 3

c = 6

Let's insert that information into the question:

c^2 - b^2

6^2 - 3^2

36 - 9

= 27

Therefore the answer is 27.

Hope this helped! :)

( ﾟдﾟ)つ Bye

Hey there, Guest!

The number of ways to pick a man is 20. The number of men that shake hands with him is 19. Since every handshake is counted twice, the men shake hands 190 times.

The number of handshakes men had with women is 20×19, thus 380.

Combining the results gives the answer 570+45= 615.

Hope this helped! :)

( ﾟдﾟ)つ Bye

Hey there, Guest!

Okay, so first, let's list all the possibilities out:

1. (8, 8, 12)

2. (9, 9, 10)

3. (10, 10, 8)

4. (11, 11, 6)

5. (12, 12, 4)

6. (13, 13, 2)

So there you have it, there are 6 isosceles triangles.

Hope this helped! :)

( ﾟдﾟ)つ Bye