Since the two angles that you have are vertical angles, we know that vertical angles are congruent, so you have to set them to equal each other.
x+24=5x-36
-4x+24=-36
-4x=-60
x=15
We now have the value of x so now we plug it in for each expression of each angle.
x+24=?
15+24=39
5x-36=?
5(15)-36=?
75-36=39
If I am not mistaken the inequality would be 45x is greater than or equal to y since the minimum would be 45 minutes a day.
Answer: The answer to this is 
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I looked it up on my scientific calculator. I hope this helps!! :)
Answer:
120 pounds
Step-by-step explanation:
We can use systems of equations to solve this problem. Assuming j is Jim's weight and b is Bob's weight, the equations are:
j + b = 180
b - j = 1/2b
Let's get b - j = 1/2b into standard form (b, then j, then the equal sign, then the constant.)
Now we can solve using the process of elimination.
Now we know how much Bob weighs, for fun, let's find Jim's weight by substituting into the equation.
So Bob weighs 120 pounds and Jim weight 60 pounds.
Hope this helped!
To start, the question is asking for surface area of a cylinder, meaning you will have to use this formula to find it: A=2πrh+2πr^2.
Since you already know that the diameter of the plastic cylinder is 4 marbles long, and each marble is 2 cm in diameter, you would multiply 4 and 2 to get that your diameter is 8 cm. However, since the surface area of a cylinder formula uses radius, you would simply divide 8 by 2 to get that the radius of the cylinder is 4 cm.
Now, since you already know that the height of the cylinder is equal to 10 marbles, multiply the amount of marbles by 2 to get that the height of the cylinder is 20 cm.
Now that you know the height and the diameter of the cylinder, plug the values into the formula: A=2π(4)(20)+2π(4)^2.
Assuming that pi is 3.14, simplify the equation as according to PEMDAS and you get that the area of plastic needed to make one cylinder is 602.88 cm squared
