angle abc is taken by a dilation with center p and scale factor 3 to angle a'b'c'.
the measure of angle abc is 21' what is the measure of angle a'b'c'?

21'

Step-by-step explanation:

We are given that angle ABC is dilated with center P.

Scale factor=3

Angle A'B'C' is formed after dilation of angle ABC.

Dilation: when a figure is dilated by scale factor a then, the figure shape does not change.

After dilation, the size of figure changes.

The initial figure and the figure obtained after dilation are similar in shape.

When two figures are similar then , the angles of one figure are  congruent to its corresponding angles in other figure and ratio of their corresponding sides are equal.

The measure of angle ABC=21'

After dilation by scale factor 3 then, the measure of angle A'B'C' remains=21'

Because the shape does not change in dilation transformation.

56

step-by-step explanation:

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: