Here is a balanced hanger diagram
1 answer:
Based on the mass of the circle and the triangle, we can find the mass of the square to be<u> 3.33 grams</u>
<h3>Mass of each side of hanger </h3>Assuming the mass of the square is x, the equation for the first side is:
= (3 x mass of circle) + (2 x mass of triangle) + (6 x mass of square)
= ( 3 x 2) + ( 2 x 4) + ( 6 × x)
= 6 + 8 + 6x
Mass of other side:
= (2 x mass of circle) + (5 x mass of triangle) + (3 x mass of square)
= ( 2 x 2) + ( 5 x 4) + ( 3 × x)
= 4 + 20 + 3x
<h3>Mass of square </h3>As both sides are equal, equate both formulas to find x:
6 + 8 + 6x = 4 + 20 + 3x
6x - 3x = 24 - 14
3x = 10
x = 10/3
x = 3.33 grams
In conclusion, each square is 3.33 grams.
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Answer:
Option (B)
Step-by-step explanation:
There are two lines on the graph representing the system of equations.
First line passes through two points (-3, 1) and (-2, 3).
Slope of the line =
=
m = 2
Equation of the line passing through (x', y') and slope = m is,
y - y' = m(x - x')
Equation of the line passing through (-3, 1) and slope = 2 will be,
y - 1 = 2(x + 3)
y = 2x + 7 ----------(1)
Second line passes through (0, 1) and (-1, 4) and y-intercept 'b' of the line is 1.
Let the equation of this line is,
y = mx + b
Slope 'm' =
=
= -3
Here 'b' = 1
Therefore, equation of the line will be,
y = -3x + 1 ---------(2)
From equation (1) and (2),
2x + 7 = -3x + 1
5x = -6
x =
x =
From equation (1),
y = 2x + 7
y =
=
=
=
Therefore, exact solution of the system of equations is .
Option (B) will be the answer.