8x^2+6x^2+4x=138 combine like terms on left side
14x^2+4x=138 since the number of seats in the from row is just 4x, subtract 14x^2 from both sides
4x=138-14x^2 that would be the general solution, if you wanted the actual number you would have to solve for x and then multiply that value by 4 to know what "4x" is...
14x^2+4x-138=0
14x^2-42x+46x-138=0
14x(x-3)+46(x-3)=0
(14x+46)(x-3)=0
2(7x+23)(x-3)=0, since x>0
x=3 and thus
4x=12 seats
So there are 12 seats in the front row addition.
9514 1404 393
Answer:
97.42 square units
Step-by-step explanation:
The area of a sector is given by ...
A = (1/2)r²θ
where r is the radius (12.2) and θ is the central angle in radians. Here, you're given the central angle as 75°, so you need to convert that to radians.
75° = (75°)×(π/180°) radians = (5/12)π radians
Then the area is ...
A = (1/2)(12.2²)(5π/12) = 744.2π/24 ≈ 97.42 . . . square units
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Equivalently, you can find the area of the circle in the usual way:
A = πr² = π(12.2²) ≈ 467.59465
Then, multiply by the fraction of the circle that is shaded (75°/360°)
sector area = (467.59465)(75/360) = 94.42 . . . square units
To do these problems, you plug in the ‘n’ value given into the equation.
a. 6j - 3 : j = 4
6(4) - 3
24 - 3
21
b. 1/2b + 5 : b = 14
1/2(14) + 5
7 + 5
12
c. 8 + 4k : k = 3.5
8 + 4(3.5)
8 + 14
22
Answer:
Acute
Step-by-step explanation:
This would not form a triangle because the lengths are too long. If it did, the triangle would be acute.
We can tell if this is a factor of the polynomial shown by using the remainder theorem.
First, we need to set x + 1 equal to 0.
x + 1 = 0
Now, we solve for x.
x = -1
Now, we can plug this value into the polynomial, and if the solution is 0, it means there is a remainder of 0, which means they divide perfectly.
(-1)^3 - 10(-1)^2 + 27(-1) - 12 = -50
x + 1 is not a factor of the provided polynomial.
