Evaluate the following expression for the given values of the variables.
1. (2s - t^2) / (st^2) for s = 5 and t = 3
A: 1/45 or 45
Simplify each expression.
2. -x - 3y + 4x - 9y + 2
A: 3x - 12y + 2
3. -4(-a + 2b) - 3(a - 5b)
A: a + 3b
4. 5 - (3m + 2n)
A: 5 - 3m - 2n
5. Enrique is baking muffins and bread. He wants to bake a total of 10 batches. Each batch of muffins bakes for 30 minutes, and each batch of bread bakes for 50 minutes. Let m represent the number of batches of muffins.
a. Write an expression for the total time required to bake a combination of muffins and bread if each batch is backed separately.
b. If Enrique makes 2 batches of muffins, how long will it take to bake all 10 batches?
A:
a. 500 - 20m
b. 460 minutes or 7 hours and 40 minutes.
1. (2s-t^2)/(st^2) = (2*5-3^2)/(5*3^2)=
1/45.
2. -x-3y+4x-9y+2 = 3x - 12y + 2.
3. -4(-a+2b) - 3(a-5b) = 4a-8b-3a+15b =
a + 7b.
4. 5-(3m+2n) = 5-3m-2n.
Tell your mother I said hi, and tell yourself to do the work sweetie. Or else I won't bring cupcakes next month when I come to visit.
1. Substitute the given values into the expression:
(2s - t^2) / (st^2)
= (2*5 - 3^2) / (5 * 3^2)
= (10 - 9) / (5 * 9)
= 1 / (45)
= 1/45
So, the expression evaluates to 1/45.
2. Simplify the given expression:
-x - 3y + 4x - 9y + 2
= (-x + 4x) + (-3y - 9y) + 2
= 3x - 12y + 2
So, the simplified expression is 3x - 12y + 2.
3. Simplify the given expression:
-4(-a + 2b) - 3(a - 5b)
= 4a - 8b - 3a + 15b
= (4a - 3a) + (-8b + 15b)
= a + 7b
So, the simplified expression is a + 7b.
4. Simplify the given expression:
5 - (3m + 2n)
= 5 - 3m - 2n
So, the simplified expression is 5 - 3m - 2n.
5.
a. The total time required to bake a combination of muffins and bread if each batch is baked separately can be calculated as:
Total time = (Time per muffin batch * Number of muffin batches) + (Time per bread batch * Number of bread batches)
Since each muffin batch takes 30 minutes and each bread batch takes 50 minutes, the expression for the total time is:
Total time = (30 * m) + (50 * (10 - m))
= 30m + 500 - 50m
= 500 - 20m
b. If Enrique makes 2 batches of muffins, then we can substitute m = 2 into the expression obtained in part a to find the time required to bake all 10 batches:
Total time = 500 - 20m
= 500 - 20(2)
= 500 - 40
= 460 minutes
So, it will take 460 minutes or 7 hours and 40 minutes to bake all 10 batches.
To evaluate an expression for given values of the variables, we substitute the given values into the expression and then simplify.
1. Expression: (2s - t^2) / (st^2)
Given values: s = 5, t = 3
Substituting the values into the expression:
(2(5) - (3)^2) / (5(3)^2)
(10 - 9) / (5 * 9)
1 / 45
So, the expression evaluates to 1/45 or 0.022.
2. Expression: -x - 3y + 4x - 9y + 2
To simplify this expression, we combine like terms:
Combine x terms: -x + 4x = 3x
Combine y terms: -3y - 9y = -12y
The simplified expression is: 3x - 12y + 2
3. Expression: -4(-a + 2b) - 3(a - 5b)
To simplify this expression, we distribute the negative sign:
Distribute the negative sign: 4a - 8b - 3a + 15b
Combine like terms: (4a - 3a) + (-8b + 15b) = a + 3b
So, the simplified expression is a + 3b.
4. Expression: 5 - (3m + 2n)
To simplify this expression, we distribute the negative sign:
Distribute the negative sign: 5 - 3m - 2n
So, the simplified expression is 5 - 3m - 2n.
5. a. Expression for the total time required to bake a combination of muffins and bread if each batch is backed separately:
For each muffin batch, it takes 30 minutes and for each bread batch, it takes 50 minutes. So, the expression would be:
30m + 50(10 - m)
30m + 500 - 50m
-20m + 500
b. If Enrique makes 2 batches of muffins:
Substituting m = 2 into the expression:
-20(2) + 500
-40 + 500
460 minutes or 7 hours and 40 minutes.
Therefore, it will take 460 minutes or 7 hours and 40 minutes to bake all 10 batches.