The pennant below is in the shape of an isosceles triangle. Determine and state the length of the base.

A. 24
B. 5
C. 10
D. 12

C. 10

Step-by-step explanation:

we know that

The height of an isosceles triangle divide the triangle into two equal right triangles.

so

Applying the Pythagorean Theorem at one triangle

solve for x

solve the quadratic equation by graphing

using a graphing tool

The solution is x=5

see the attached figure

therefore

The length of the base is

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

the answer is c. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀