A right triangle is shown. One leg is labeled 5 and the other is labeled 13. A right angles is labeled in between the legs. Mckenzie's Work Cara's Work

a2 + b2 = c2 a2 + b2 = c2

52 + 132 = c2 52 + b2 = 132

25 + 169 = c2 25 + b2 = 169

194 = c2 b2 = 144

Square root 194 equals square root c squared. Square root b squared equals square root 144.

13.93 ≈ c b ≈ 12
Who is right?

Makenzie is correct,  13.93 ≈c

Step-by-step explanation:

the sides with determined lengths (see image) are A (13) and B (5). C however is not determined.

the correct equation would be to solve for c.

13² + 5² = c²

c ≈ 13.93

Clara solved for b and not c, which is incorrect.

180

step-by-step explanation:

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places