Answer: The length of the rectangle is 37.5 inches and the width is 12.5 inches
Step-by-step explanation: The dimensions of the rectangle is not given but we have clues given. The length is given as three times it’s width which means if the width is W, then the length would be given as 3W (three times the width). Also the perimeter is given as 100 inches and the formula for the perimeter is;
Perimeter = 2(L + W)
We can now insert the known values as follows;
100 = 2(3W + W)
100 = 2(4W)
100 = 8W
Divide both sides of the equation by 8
12.5 = W
Having calculated the width as 12.5 inches, the length now becomes
L = 3W
L = 3 x 12.5
L = 37.5
Hence the length is 37.5 inches and the width is 12.5 inches
Answer:
- 5
Step-by-step explanation:
Note that - (- 12) = + 12
Thus
- 17 - (- 12) = - 17 + 12 = - 5
It looks like Tom subtracted 12 from - 17, that is - 17 - 12 = - 29
Answer:
1. Consistent equations
x + y = 3
x + 2·y = 5
2. Dependent equations
3·x + 2·y = 6
6·x + 4·y = 12
3. Equivalent equations
9·x - 12·y = 6
3·x - 4·y = 2
4. Inconsistent equations
x + 2 = 4 and x + 2 = 6
5. Independent equations
y = -8·x + 4
8·x + 4·y = 0
6. No solution
4 = 2
7. One solution
3·x + 5 = 11
x = 2
Step-by-step explanation:
1. Consistent equations
A consistent equation is one that has a solution, that is there exist a complete set of solution of the unknown values that resolves all the equations in the system.
x + y = 3
x + 2·y = 5
2. Dependent equations
A dependent system of equations consist of the equation of a line presented in two alternate forms, leading to the existence of an infinite number of solutions.
3·x + 2·y = 6
6·x + 4·y = 12
3. Equivalent equations
These are equations with the same roots or solution
e.g. 9·x - 12·y = 6
3·x - 4·y = 2
4. Inconsistent equations
Inconsistent equations are equations that are not solvable based on the provided set of values in the equations
e.g. x + 2 = 4 and x + 2 = 6
5. Independent equations
An independent equation is an equation within a system of equation, that is not derivable based on the other equations
y = -8·x + 4
8·x + 4·y = 0
6. No solution
No solution indicates that the solution is not in existence
Example, 4 = 2
7. One solution
This is an equation that has exactly one solution
Example 3·x + 5 = 11
x = 2
Answer: the statements and resons, from the given bench, that fill in the blank are shown in italic and bold in this table:
Statement Reason
1. K is the midpoint of segment JL Given
2. segment JK ≅ segment KL <em>Definition of midpoint</em>
3. <em>L is the midpoint of segment KM</em> Given
4. <em>segment KL ≅ segment LM</em> Definition of midpoint
5. segment JK ≅ segment LM Transitive Property of
Congruence
Explanation:
1. First blank: you must indicate the reason of the statement "segment JK ≅ segment KL". Since you it is given that K is the midpoint of segment JL, the statement follows from the very <em>Definition of midpoint</em>.
2. Second blank: you must add a given statement. The other given statement is <em>segment KL ≅ segment LM</em> .
3. Third blank: you must indicate the statement that corresponds to the definition of midpoint. That is <em>segment KL ≅ segment LM</em> .
4. Fourth and fith blanks: you must indicate the statement and reason necessary to conclude with the proof. Since, you have already proved that segment JK ≅ segment KL and segment KL ≅ segment LM it is by the transitive property of congruence that segment JK ≅ segment LM.
