Answer:
System of equations:
L = 5W + 7
2W + 2L = P
L = 62 cm
W = 11 cm
Step-by-step explanation:
Given the measurements and key words/phrases in the problem, we can set up two different equations that can be used to find both variables, length and width, of the rectangle.
The formula for perimeter of a rectangle is: 2W + 2L = P, where W = width and L = length. We also know that the L is '7 more than five times its width'. This can be written as: L = 5W + 7. Using this expression for the value of 'L', we can use the formula for perimeter and solve for width:
2W + 2(5W + 7) = 146
Distribute: 2W + 10W + 14 = 146
Combine like terms: 12W + 14 = 146
Subtract 14 from both sides: 12W + 14 - 14 = 146 - 14 or 12W = 132
Divide 12 by both sides: 12W/12 = 132/12 or W = 11
Put '11' in for W in the equation for 'L': L = 5(11) + 7 or L = 55 + 7 = 62.
If you substitute a variable for each blank, for example x*2+x*3 you get 5x=12, which can then be solved to get that x=12/5, so 12/5 is the answer.
Answer:
m < 2 = 137°
m < 4 = 137°
Step-by-step explanation:
Given that m < 7 = 43°, we can say that it has the same measure as < 3 because they are corresponding angles. Thus, we can establish that m < 3 = 43°.
We can use m < 3 = 43° to find m < 4, as they are supplementary angles that have a sum of 180°.
Therefore:
m < 3 + m < 4 = 180°
Rearrange the formula to isolate m < 4:
m < 4 = 180° - m < 3
Substitute the value of m < 3 into the rearranged formula:
m < 4 = 180° - m < 3
m < 4 = 180° - 43°
m < 4 = 137°
Therefore, m < 4 = 137°.
< 2 and < 4 also have the same measure because they are vertical angles. Two angles are vertical angles if they are opposite angles formed by the intersection of two lines.
Hence, m < 2 = 137°
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