George is an landscape architect and is designing his backyard in a blueprint. In the yard, he wants a garden in the shape of a
2 answers:
Answer:
The length of the shortest side on the blueprint is <u>10 centimeters</u>.
Step-by-step explanation:
Given:
George is an landscape architect and is designing his backyard in a blueprint. In the yard, he wants a garden in the shape of a triangle. The length of the longest side of the garden will be 600 centimeters, and the length of the shortest side of the garden will be 400 centimeters. If the length of the garden's longest side on the blueprint is 15 centimeters.
Now, to find the length of the shortest side on the blueprint by using an equation.
Let the length of the shortest side on the blueprint be
The length of the garden's longest side on the blueprint = 15 centimeters.
The length of the longest side of the garden = 600 centimeters.
The length of the shortest side of the garden = 400 centimeters.
If, 600 centimeters is equivalent to 400 centimeters.
So, 15 centimeters is equivalent to .
Now, to set an equation that can be used to get the length of the shortest side on the blueprint through cross multiplication method:
<em>By cross multiplying we get:</em>
<em>Dividing both sides by 600 we get:</em>
Therefore, the length of the shortest side on the blueprint is 10 centimeters.
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Answer:
The answer is C.
Step-by-step explanation:
You have to use Ditributive Law,
So for this question :
Answer:
1) Please find the attached drawing of the archway created with MS Excel
2) The y-intercept is (0, 24)
The x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base is 11
The height of the archway at its highest point = 30.25
Step-by-step explanation:
The given function representing the archway is y = -x² + 5·x + 24
1) Please find attached the required drawing of the archway created with MS Excel
2) The y-intercept is given by the point where x = 0
Therefore, we have, the y-value at the y-intercept = -0² + 5×0 + 24 = 24
The y-intercept = (0, 24)
The x-intercept is given by the point where y = 0
Therefore, the x-values at the x-intercept are found using the following equation;
0 = -x² + 5·x + 24
x² - 5·x - 24 = 0
By inspection, we have;
x² - 8·x + 3·x - 24 = 0
x·(x - 8) + 3·(x - 8) = 0
∴ (x + 3) × (x - 8) = 0
Either (x + 3) = 0, and x = -3, or (x - 8) = 0, and x = 8
Therefore, the x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base = The distance between the x-values at the two x-intercepts
∴ The width of the archway at its base = 8 - (-3) = 11
The highest point of the arch is given by the vertex of the parabola, y = a·x² + b·x + c, which has the x-value of the vertex = -b/(2·a)
∴ The x-value of the vertex of the given parabola, y = -x² + 5·x + 24, is x = -5/(2×(-1)) = 2.5
Therefore;
The y-value of the vertex, is y = -(2.5)² + 5×2.5 + 24 = 30.25 = The height of the archway at its highest point
∴ The height of the archway at its highest point = 30.25.
