Answer:
<em>The maximum number of kilowatt-hours is 235</em>
Step-by-step explanation:
<u>Inequalities</u>
Robert's monthly utility budget is represented by the inequality:
0.1116x + 23.77 < 50
Where x is the number of kilowatts of electricity used.
We are required to find the maximum number of kilowatts-hours used without going over the monthly budget. Solve the above inequality:
0.1116x + 23.77 < 50
Subtracting 23.77:
0.1116x < 50 - 23.77
0.1116x < 26.23
Dividing by 0.1116:
x < 26.23/0.1116
x < 235
The maximum number of kilowatt-hours is 235
Answer:
The correct answer is the last option, that is, 
Step-by-step explanation:
We have been given that the first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. Therefore, amount of money in the account of first running after m months will be: 
We have been given that the second runner has $50 in savings and will save $60 each month. Therefore, amount of money in the account of second running after m months will be: 
In order for amount of money to be equal in accounts of both the runners, we set up:
Upon rewriting the left hand side using commutative law, we get:
Therefore, we can see that the last option is the correct answer.
Given: AD ≅ BC and AD ∥ BC
Prove: ABCD is a parallelogram.
Statements Reasons
1. AD ≅ BC; AD ∥ BC 1. given
2. ∠CAD and ∠ACB are alternate interior ∠s 2. definition of alternate interior angles
3. ∠CAD ≅ ∠ACB 3. alternate interior angles are congruent
4. AC ≅ AC 4. reflexive property
5. △CAD ≅ △ACB 5. SAS congruency theorem
6. AB ≅ CD 6. Corresponding Parts of Congruent triangles are Congruent (CPCTC)
7. ABCD is a parallelogram 7. parallelogram side theorem
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