Answer:
a. 36 blueberries and 12 strawberries
b. 16 blueberries and 4 strawberries
Step-by-step explanation:
The computation of each berry in the bowl is shown below;
a. Total 48 berries
The Ratio of blueberries to strawberries is 9:3
So, the blueberries is = 48 × 9 ÷ (9 + 3) = 36
And, the strawberries is = 48 × 3 ÷ (9 + 3) = 12
b. Total 20 berries
The Ratio of blueberries to strawberries is 4:1
So, the blueberries is = 20 × 4 ÷ (4 + 1) = 16
And, the strawberries is = 20 × 1 ÷ (4 + 1) = 4
Answer: A
<u>Step-by-step explanation:</u>
f(x) = x³ + 4x² + 7x + 6
possible rational roots are ±{1, 2, 3, 6}
Try x = -2
-2 | 1 4 7 6
<u>| ↓ -2 -4 -6</u>
1 2 3 0 ← remainder is 0 so x = -2 is a root ⇒ (x + 2) = 0
The factored polynomial x² + 2x + 3 = 0 is not factorable so use the quadratic formula to find the roots.
a=1, b=2, c=3
The factors are:
![(x - 2)[x - (-1 + i\sqrt{2})][x - (-1 - i\sqrt{2})]](https://tex.z-dn.net/?f=%28x%20-%202%29%5Bx%20-%20%28-1%20%2B%20i%5Csqrt%7B2%7D%29%5D%5Bx%20-%20%28-1%20-%20i%5Csqrt%7B2%7D%29%5D)
Answer:
The system is consistent; it has one solution ⇒ D
Step-by-step explanation:
A consistent system of equations has at least one solution
- The consistent independent system has exactly 1 solution
- The consistent dependent system has infinitely many solutions
An inconsistent system has no solution
In the system of equations ax + by = c and dx + ey = f, if
- a = d, b = e, and c = f, then the system is consistent dependent and has infinitely many solutions
- a = d, b = e, and c ≠ f, then the system is inconsistent and has no solution
- a ≠ d, and/or b ≠ e, and/or c ≠ f, then the system is consistent independent and has exactly one solution
In the given system of equations
∵ -2y + 2x = 3 ⇒ (1)
∵ -5y + 5x = 12 ⇒ (2)
→ By comparing equations (1) and (2)
∵ -2 ≠ -5
∵ 2 ≠ 5
∵ 3 ≠ 12
→ By using the 3rd rule above
∴ The system is consistent independent and has exactly one solution
∴ The system is consistent; it has one solution
