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Mariana [72]
3 years ago
6

A lighthouse is located at (1, 2) in a coordinate system measured in miles. A sailboat starts at (–7, 8) and sails in a positive

x-direction along a path that can be modeled by a quadratic function with a vertex at (2, –6). Which system of equations can be used to determine whether the boat comes within 5 miles of the lighthouse?
Mathematics
2 answers:
Dennis_Churaev [7]3 years ago
8 0
For the answer to the question above, <span>The first equation in each set of equations is an equation of a circle. Since you want to know if the sailboat comes within 5 miles of the point (1,2), the radius of the circle will be 5. The equation of a circle shows that the radius is squared. So 5 squared is 25. So answers two and four look good so far. Next, you are given the vertex, (h,k) as (2,-6). So looking at the equation of a parabola, we are looking for an answer with a k value of -6. Answer four has a k value of 8, however, answer two has a k value of -6. </span>
Shkiper50 [21]3 years ago
8 0

Answer:

second answer

Step-by-step explanation:

I took a test

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3 years ago
The function f(x) is shown in this graph
gtnhenbr [62]

Answer:

The correct statement is:

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Step-by-step explanation:

  • We see that the graph of the function f(x) is a line that passes through (0,2) and (1,-1)

Hence, the equation of the function f(x) is calculated by a two-point formula as:

y-2=\dfrac{-1-2}{1-0}\times (x-0)\\\\y-2=\dfrac{-3}{1}\times x\\\\y-2=-3x\\\\y=-3x+2

( On comparing the equation of f(x) with slope intercept form.

i.e. y=mx+c

where m is the slope and c is the y-intercept)

We get slope of f(x)= -3

and y-intercept= 2

  • The function g(x) is given by:

g(x)=-3x-6

Hence, slope of g(x) = -3

and y-intercept= -6

Hence, we get that the slope of f(x) and g(x) is same.

( i.e. -3)

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3 years ago
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Solve using algebreic methods y=x^2+5x, y=7-x
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Answer:

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Step-by-step explanation:

Given that,

y=x^2+5x  ...(1)

and

y = 7 -x ....(2)

Put the value of y from equation (2) in (1)

7-x=x^2+5x\\\\x^2+5x-7+x=0\\\\x^2+6x-7=0\\\\x^2+7x-x-7=0\\\\x(x+7)-1(x+7)=0\\\\(x-1)(x+7)=0

So,

x = 1 and x = -7

Hence, the solution of the given equations is x = 1 and x = -7

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