A 56-inch Woman cast a shadow that is 16 inches long. How tall is her child if his shadow is 14 inches long?
1 answer:
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Answer:
The slope of the parallel line to the given line is
The equation of the parallel line to the given line and passes through the given point is y + 4 = (x + 2)
The y-intercept of the parallel line to the given line and passes through the given point is
Step-by-step explanation:
- The rule of the slope of the line that passes through points (x1, y1) and (x2, y2) is m =
- The point-slope form of the linear equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line
- The slope-intercept form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept
- Parallel lines have the same slopes and different y-intercepts
In the given figure
∵ The given line passes through points (2, 6) and (-6, 8)
∴ x1 = 2 and y1 = 6
∴ x2 = -6 and y2 = 8
→ Substitute them in the rule of the slope above to find it
∵ m = =
=
∴ The slope of the given line is
∵ Parallel lines have the same slopes
∴ The slope of the parallel line to the given line is
∵ The parallel line passes through the point (-2, -4)
∴ x1 = -2 and y1 = -4
∵ m =
→ Substitute them in the point-slope form above
∵ y - (-4) = (x - (-2))
∴ y + 4 = (x + 2)
∴ The equation of the parallel line to the given line and passes through
the given point is y + 4 = (x + 2)
∵ m =
→ Substitute it in the slope-intercept form above
∴ y = x + b
→ To find b substitute x by -2 and y by -4 (coordinates the given point)
∵ -4 = (-2) + b
∴ -4 = + b
→ Subtract from both sides
∴ = b
∵ b is the y-intercept
∴ The y-intercept of the parallel line to the given line and passes
through the given point is
Answer:
Step-by-step explanation:
x-intercepts are when the curve intercepts the x-axis, so when y =0.
Therefore, to find the x-intercepts, substitute y = 0 and solve for x.
The vertex is the turning point: the minimum point of a parabola that opens upward, and the maximum point of the parabola that opens downward. As a parabola is symmetrical, the x-coordinate of the vertex is the midpoint of the x-intercepts.
Equation:
Therefore, the x-intercepts are x = 0 and x = 2
The midpoint of the x-intercepts is x = 1, so the x-coordinate of the vertex is x = 1
Equation:
Therefore, the x-intercepts are x = -5 and x = 4
The midpoint of the x-intercepts is x = -0.5, so the x-coordinate of the vertex is x = -0.5
Equation:
Therefore, the x-intercepts are x = 0 and x = 3
The midpoint of the x-intercepts is x = 1.5, so the x-coordinate of the vertex is x = 1.5