Answer:
6y³ + 17y² + 22y + 15
Step-by-step explanation:
(2y + 3)(3y² + 4y + 5)
6y³ + 8y² + 10y + 9y² + 12y + 15
6y³ + 8y² + 9y² + 10y + 12y + 15
6y³ + 17y² + 22y + 15
210 adult tickets
85 children tickets
210 x $5 = $1,050
85 x $2 = $170
1,050 + 170 =1,220
So Angle GEN and FED are vertical angles, which means that their angles are congruent. Therefore, Angle FED is 60°
Angle GEN and DEN are a linear pair, which means that they are supplementary angles (add up to 180). To find Angle DEN, we have to form the equation: 60 + DEN = 180
For this, all you have to do is subtract 60 on both sides, and your answer will be: DEN = 120°
Answer:
We know that the equation of the circle in standard form is equal to <em>(x-h)² + (y-k)² = r²</em> where (h,k) is the center of the circle and r is the radius of the circle.
We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :
1 - We first group terms with the same variable :
(x²+8x) + (y²+22y) + 37 = 0
2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)
(x²+8x) + (y²+22y) = - 37
3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process <u><em>"completing the square"</em></u>.
x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²
y²+22y = (y²+22y+11²)-11² = (y+11)²-11²
4 - We plug the new values inside our equation :
(x+4)² - 4² + (y+22)² - 11² = -37
(x+4)² + (y+22)² = -37+4²+11²
(x+4)²+(y+22)² = 100
5 - We re-write in standard form :
(x-(-4)²)² + (y - (-22))² = 10²
And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)
Answer:
Total number of ways= 144 ways
Step-by-step explanation:
Number of ways 3 can order chicken
= 3!
= 3*2*1
= 6
Number of ways 4 can order steak
= 4!
= 4*3*2*1
= 24
Number of ways 1 can order lobster
= 1!
= 1
Total number of ways= 24*6*1
Total number of ways= 144 ways
