A radio tower is located on a coordinate system measured in miles. The range of a signal in a particular direction is modeled by

Question

1 year ago

5

A radio tower is located on a coordinate system measured in miles. The range of a signal in a particular direction is modeled by

a quadratic function where the boundary of the signal starts at the vertex at (4, 2). It passes through the point (5, 4). A linear road connects points (–3, 7) and (8, 2). Which system of equations can be used to determine whether the road intersects the boundary of the tower’s signal?
StartLayout Enlarged Left-Brace 1st Row y minus 2 (x minus 4) squared = 2 2nd Row 5 x + 11 y = 62 EndLayout
StartLayout Enlarged Left-Brace 1st Row y minus (x minus 4) squared = 2 2nd Row 5 x + 11 y = 62 EndLayout
StartLayout Enlarged Left-Brace 1st Row y minus (x minus 4) squared = 2 2nd Row 11 x + 5 y = 2 EndLayout
StartLayout Enlarged Left-Brace 1st Row y minus 2 (x minus 4) squared = 2 2nd Row 11 x + 5 y = 2 EndLayout

Mathematics

2 answers:

swat32 · Answer 1 · 2024-07-28T17:43:00+03:00

swat321 year ago

8 0

Answer:

a edge

Step-by-step explanation:

Anuta_ua [19.1K] · Answer 2 · 2024-07-28T16:32:45+03:00

Modeling this scenario with a system of equations using a linear function and a quadratic function yields the following:

y = 2(x - 4)² + 2.

5x + 11y = 62.

<h3>What is the quadratic equation?</h3>

A quadratic function with vertex (h,k), may be represented by the equation:

y = a(x - h)² + k

Because the vertex of this issue is located at (4,2), we may deduce that h = 4 and k = 2, and the equation for this problem is as follows:

y = a(x - 4)² + 2.

Because it goes through the location characterized by its coordinates (5, 4), we may determine a by establishing that when x = 5, y = 4.

4 = a + 2.

a = 2.

Thus the equation is:

y = 2(x - 4)² + 2.

The slope, denoted by m, is the rate of change, or the degree to which y deviates from its initial value for each unit of x that is added.

The y-intercept, denoted by the letter b, is the value of the variable y when the variable x is equal to zero. It may also be construed as the beginning value of the function.

Because the road links the locations (–3, 7) and (8, 2), the slope may be calculated as follows:

m = (2 - 7)/(8 - (-3)) = -5/11.

Then:

y = -5/11x + b.

When x = 8, y = 2, hence we use it to find b as follows:

2 = -40/11 + b

b = 62/11.

Then the equation is:

y = -5/11x + 62/11.

5x + 11y = 62.

The system of equations is:

y = 2(x - 4)² + 2.