A map scale is give as 1:10000
1 answer:
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The correct option D; models the depth of the submarine.
<h3>Define the term parabola?</h3>- Parabola, also known as an open curve or conic section, is formed when a right circular cone and a plane perpendicular to one of the cone's elements cross.
When a submarine is x miles out of its launch place, we need to figure out which table best represents the depth of the submarine using the function d, wherein d(x) is the depth, in meters.
Both x = 5 as well as x = 40 have zeros.
Since it's a parabola,
D(x) = a(x-5)(x-40)
vertex = (22.5, -146)
Thus,
-146 = a(22.5-5)(22.5-40)
a = -146/(22.5-5)(22.5-40)
a = 0.4767
Put value of a in equation.
D(x) = a(x-5)(x-40)
D(x) = 0.4767(x-5)(x-40)
The equation above is quadratic function model.
We can see from the graph that:
(5) and (0), respectively, are points on the graph (40,0).
Consequently, if x = 5 when y = 0, then.
y(min) > -160.
Additionally, the table in option (D) represents the submarine's depth.
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The graph of the question with the options are attached.
The dimensions of the rectangle are: b=9.65 cm and h=4.35 cm or b=4.35 cm and h= 9.65 cm.
<h3>Quadrilaterals</h3>There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
The area of a rectangle is equal to base x height (A=bh). The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2b+2h.
<h3>System of Linear Equations</h3>System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.
The question gives:
Perimeter=28cm
Area= 42 cm²
If the perimeter is the sum of all sides of the rectangle, you have:
Perimeter= 2b+2h=28
If the area of the rectangle is 42cm², you have:
Area=bh=42 cm²
You can write a system of linear equations.
2b+2h=28 (1)
bh=42 (2)
From equation 2, you have . Then, you can replace it in equation 1.
Now, you should solve the quadratic equation.
If h1=9.65 cm, then , and if h2=4.35 cm, then
.
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