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Estimate the solution of the equation a(x) = b(x)
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The solution of the equation a(x) = b(x) is (9, 5.5)

Step-by-step explanation:

The solution of the system of the linear equations is the common ordered pair in their solutions, this solution is the point of intersection of the lines which represent the two equations graphically

In the given figure

∵ There are two lines, the blue line, and the red line

→ Let the blue line represents a(x) and the red line represents b(x)

∵ The solution of the equation a(x) = b(x) is the point of intersection of

    the two lines

∵ The x-coordinate of this point is 9

∵ The y-coordinate of this point is between 5 and 6 (5.5)

∴ The coordinates of the point of intersection are (9, 5.5)

∴ The solution of the equation a(x) = b(x) is (9, 5.5)

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step-by-step explanation:

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).