The length of the long leg of a right triangle is 16 inches more than four times of the shorter leg. the length of the hypotenuse is 17 inches more than four times the length of the shorter leg. find the side lengths of the triangle.

The side lengths of the triangle, in order, are 11 inches, 60 inches, 61 inches.

Step-by-step explanation:

Let the shorter leg be x, the longer leg, y and the hypotenus, z.

y = 16 + 4x

z = 17 + 4x

By Pythagoras rule,

z^2 = x^2 + y^2

(17+4x)^2 = x^2 + (16+4x)^2

that is,

x^2 - 8x - 33 = 0  (A quadratic equation)

By factorising,

(x+3)(x-11)=0

either x = -3 or x = 11.

But length cannot be negative. Hence, -3 is dicarded.

x = 11 inches

y = 16 + 4x = 60 inches

z = 17 + 4x = 61 inches

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation:

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.