Karisha drew pentagon a on a coordinate grid. she then performed a rotation followed by a dilation with scale factor 5 to produce pentagon b. which is a true statement about the two pentagons? a. they are similar, but not congruent. b. they are neither congruent nor similar. c. they are similar and congruent. d. they are congruent, but not similar.

A.

Step-by-step explanation:

Rotation is a transformation that turns a figure about a fixed point. An object and its rotation image are the same shape and size, but the figures may be turned in different directions. So, rotation gives us two congruent pentagons.

Dilation is a transformation that produces an image that is the same shape as the original (similar to original), but is a different size. So, dilation gives us two similar pentagons.

A sequence of rotation and dilation produces pentagon that is similar to the initial, but not congruent.

In attached diagram you can see the pictorial representation:

A

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