The relationship between two numbers is described below, where x represents the first number and y represents the second number.
the square of the first number is equal to the sum of the second number and 16. the difference of 4 times the second number and 1 is equal to the first number multiplied by 7.
select the equations that form the system that models this situation. then, select the solution(s) of the system.

See below.

Step-by-step explanation:

x^2 = y + 16

4y - 1 = 7x  

are the 2 equations. (answer)

From the second equation

4y = 7x + 1

y = 7/4 x + 1/4

Substituting in the first equation:

7/4x + 1/4 + 16 = x^2

x^2 - 7/4 x - 16 - 1/4 = 0

x^2 - 7/4 x - 16 1/4 = 0

Multiplying though by 4

4x^2 - 7x - 65 = 0

Using the ac method to solve this  4 * -65 = -260 and we need  factors of this to add up to -7. -20 and 13 look good so we write:

4x^2 - 20x + 13x - 65 = 0

Fatcor by grouping:

4x(x - 5) + 13(x - 5) = 0

(4x + 13)(x - 5) = 0

So the the roots are 5, -3.25

To find the values of y we substitute these values of x into the second equation:

x = 5:  4y - 1 = 7*542y = 36

y = 9.

x = -3.25:

4y - 1 = 7*-3.25

4y =  (7 * -3.25) + 1

y = -5.44.

So the solutions are    (5, 9) and (-3.25, -5.44)  (Answer)

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .