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?

Answers

Answer 1

Answer: Given that the range of the signal is a quadratic function: (x-h)^2 = 4a (y - k) (5-4)^2 = 4a (4 - 2) 4a =1/2 therefore, (x -4)^2 = (1/2)(y – 2) The road is a line. Slope of the road is (7 -2)/(-3 -8) =-5/11 Therefore the equation of the line: 5x + 11y = 5(8) + 11(2) 5x + 11y = 62

Answer 2

Answer:

The system of equations can be used to determine whether the road intersects the boundary of the tower’s signal; y = 2( x - 4 )² + 2 and 5 x + 11 y = 62.

What is the vertex form of a quadratic equation?

If a quadratic equation is written in the form

y = a(x-h)^2 + k

then it is called to be in vertex form.

It is called so because when you plot this equation's graph, you will see the vertex point is on (h,k).

To determine a quadratic function in vertex form:

y = a ( x - 4 )² + 2

4 = a ( 5 - 4 )² + 2

4 = a + 2

a = 2

y = 2 ( x - 4 )² + 2

Then we will determine a linear function in standard form, that passes through the points ( -3, 7 ) and ( 8, 2 ).

7 = -3 m + b

2 = 8 m + b / ·(-1)

7 = - 3 m + b

- 2 = - 8 m - b

5 = - 11 m

m = -5/11,

2 = -5/11 · 8 + b,

b= 2 + 40/11,

b = 62/11

Substitue,

y = - 5/11 x + 62/11 / ·11

11 y = - 5 x + 62

5 x + 11 y = 62

Finally the system of equations is:

y = 2( x - 4 )² + 2

5 x + 11 y = 62

Learn more about vertex form of a quadratic equation here:

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$0.63 + _______ = $1.00

Answers

$1.00 - $0.63 =$0.37

0.37$ 1.00 - 0.63 ______ 0.37

Can Somebody Help Me please ?

Answers

Answer:

I think its 5 to the third (the second option). but I'm not sure. Im not the best with exponents.

It’s the third one (1/25) and the decimal form for it is 0.008 , Incase you wanted to know :p
Can you brainliest if I’m right ??

I dont understand graphs at all

Answers

Answer:

cool?

Step-by-step explanation:

Same same same same same

For the function y = x + 9, what is the output value if 4 is the input value? y = 5
y = 13
y = 36
y = 49

Answers

y = 13.

Explanation
Replacing the value x with 4 in the function gives that y= 4+9
y= 13

F(x)=2x+3/4x+5
find f(-9)

Answers

$\huge\textsf{Hey there!}$

$\mathsf{f(x) = (2x + 3)/(4x + 5)}$

$\mathsf{y = ( 2x + 3)/(4x + 5)}$

$\mathsf{y = (2(-9) + 3)/(4(-9) + 5)}$

$\mathsf{2(-9)}$

$\mathsf{\bf = -18}$

$\mathsf{y = \frac{-18 + 3} {4(-9) + 5}}$

$\mathsf{-18 + 3}\n\mathsf{= \bf -15}$

$\mathsf{y = \frac{ -15} {4(-9) + 5}}$

$\mathsf{4(-9)}\n\mathsf{\bf = -36}$

$\mathsf{y = (-15)/(-36 + 5)}$

$\mathsf{-36 + 5}\n\mathsf{= \bf-31}$

$\mathsf{y = (-15)/( -31)\rightarrow\boxed{\bf (15)/(31)}}$

$\boxed{\boxed{\huge\text{Answer: } \boxed{\bf f(-9) = (15)/(31)}}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

$\implies {\blue {\boxed {\boxed {\purple {\sf { f(-9)= 0.48}}}}}}$

$\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}$

$f(x) = (2x + 3)/(4x + 5) \n$

For $f(-9)$ , put " $-9$ " for every value of " $x$ ".

$↬f( - 9) = (2( - 9) + 3)/(4( - 9) + 5)\n$

$↬ f(-9) = ( - 18 + 3)/( - 36 + 5) \n$

$↬ f(-9) = ( - 15)/( - 31)\n$

$↬ f(-9)= (15)/(31)\n$

$↬f(-9)= 0.48\n$

$\bold{ \green{ \star{ \red{Mystique35}}}}⋆$

How many intersections are there of the graphs of the equations below? x + 5y = 6 3x + 30y = 36

Answers

The answer is one. First, these are both straight lines, meaning they will have one intersection point. In order to find the intersections of these two lines, we must set them equal to one another. So x + 5y = 6 equals 3x + 30y = 36. When you solve the two equations together, you'll get one intersection point at (0 , 1.2).

Answer:

option B. one

Step-by-step explanation:

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