Answer:
see explanation
Step-by-step explanation:
To find the roots factor the left side
x³ + 7x² + 12x = 0 ← factor out x from each term
x(x² + 7x + 12) = 0
x(x + 3)(x + 4) = 0
Equate each factor to zero and solve for x
x = 0
x + 3 = 0 ⇒ x = - 3
x + 4 = 0 ⇒ x = - 4
Roots are x = - 4, x = - 3, x = 0
Answer:
1/3
Step-by-step explanation:
4/12÷3/3 = 1/3 ÷ 1 = 1/3
Refer to the diagram shown below.
Because tan θ = 12/5 and cos θ = -5/13, therefore θ is in quadrant 3.
The sine function is negative in quadrant 3, therefore
sin θ = - 12/13
Answer: - 12/13
Answer:
It'll take 25 hours to get to the auto shop
Step-by-step explanation:
Given
Distance = 5 miles
Speed =1056 feet per hour
Required
How long will it take to the auto shop
This can be solved using Speed's formula;

Substitute values for Speed and Distance

1 mile = 5280 feet;
So:


Cross Multiply

Divide both sides by 1056ft



<em>Hence, it'll take 25 hours to get to the auto shop</em>
Answer:
6 liters.
Step-by-step explanation:
So we have a glass, a jar, and a pitcher and together, they hold 54 liters.
We are told that the jar has the same volume as 3 glasses and the pitcher has the same volume as 5 glasses. In other words, let g denote glasses, j denote jars, and p denote pitchers:

Since jar is the same as 3 glasses, this means that j=3g. And since the pitcher is the same as 5 glasses, this means that p=5g. Substitute:

Combine like terms:

Divide both sides by 9. The left cancels:

Therefore, the volume of the glass is 6 liters.