Find the least common denominator (LCD) for the fractions. 1/12 and 3/4 A. 12 B. 4
2 answers:
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Question is Incomplete; Complete question is given below;
James and Amy played 12 games of checkers last week. This week they played 7 games on Monday and 2 games on Wednesday.James and Amy play 3 more games. They have played the same number of games as last week. Fill in the blanks to make the equation true. Use +,-, or =. 12_7_2_3 Explain how you chose the symbols.
Answer:
12<u> = </u>7<u> + </u>2<u> + </u>3
Step-by-step explanation:
Given:
Number of games played last week = 12
Number of games played on Monday this week = 7
Number of games played on Wednesday this week = 2
Also given:
James and Amy play 3 more games.
So Number of games played more = 3
We need to fill in the blanks 12 __ 7__2__3 with signs '+', '-','='.
Solution:
It is given that they have played the same number of games as last week.
So we can say that;
Number of games played last week is equal to Number of games played on Monday this week plus Number of games played on Wednesday this week plus Number of games played more.
framing in equation form we get;
Hence we have fill the blanks as 12<u> = </u>7<u> + </u>2<u> + </u>3.
Answer:
The area of the parallelogram is;
32 square units
Step-by-step explanation:
The given parameters are;
The coordinates of the parallelogram RSTU = R(-4, 4), S(2, 6), T(6, 2), and U(0, 0)
We note that the area of a parallelogram = Base length × Height
From the drawing of the parallelogram RSTU, we have;
The base length = The length of = The length of
= √((2 - (-4))² + (6 - 4)²) = 2·√10
The height of a parallelogram is perpendicular to its base length = The line
∴ Where, the slope of the base length = m, the slope of the height = -1/m
The slope, 'm' of = (6 - 4)/(2 - (-4)) = 1/3
Therefore, the slope of the height = -1/(1/3) = -3
We note that a point on the height is the point 'T', therefore, the equation of the line in point and slope form is therefore;
y - 0 = -3·(x - 0)
∴ y = -3·x
Therefore, the coordinates of the point 'V' is given by the simultaneous solution of the equations of and
The equation of the line in point and slope form from the point 'R' and the slope 'm = 1/3' is given as follows;
y - 4 = (1/3) × (x - (-4)) = (1/3) × (x + 4)
y = x/3 + 4/3 + 4 = x/3 + 16/3
y = x/3 + 16/3
We then have the coordinate at the point 'V' (x, y) is given as follows;
-3·x = x/3 + 16/3
-9·x = x + 16
-10·x = 16
x = -16/10 = -1.6
x = -1.6
∴ y = -3·x = -3 × -1.6 = -4.8
y = 4.8
The coordinate at the point, V = (-1.6, 4.8)
The length of the line = The height of the parallelogram = √((-1.6 - 0)² + (4.8 - 0)²) = 8/5·√10
The height of the parallelogram = 8/5·√10
The area of the parallelogram, A = Base length × Height
∴ A = 2·√(10) × 8/5·√(10) = (16/5) × 10 = 32
The area of the parallelogram, A = 32 square units.
