Cade and Tyce both tried to find the missing side of the right triangle. A right triangle is shown. The legs are labeled 6 and 9. A right angle is labeled in between them.

Cade's Work Tyce's Work
a2 + b2 = c2 a2 + b2 = c2
62 + b2 = 92 62 + 92 = c2
36 + b2 = 81 36 + 81 = c2
b2 = 45 117 = c2
√b2 = √45 √117 = √c2
b ≈ 6.71 10.82 ≈ c

Is either of them correct? Explain reasoning

Cade is not right because in his second step he did 6^2 + b^2 = 9^2. In this problem, you are trying to find the hypotenuse, which is c^2. B^2 is the other leg, but this problem has given the lengths of both the legs. If he did it correct the second step would look like 6^2 + 9^2 = c^2.

Tyce is right since he followed all the steps and did the math correctly :)

Step-by-step explanation:

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.