Given: ∠ABC ≅ ∠DEF and ∠GHI ≅ ∠DEF Prove: m∠ABC = m∠GHI We are given that angle ABC and are congruent, and that angle GHI and an

Response:

To accumulate $7,500 in three years, the required one-time deposit is $4388.17

Step-by-step explanation:

Basic Financial Formulas

A commonly used formula for calculating present and future values is

Where FV represents the future value, PV denotes the present value, r signifies the interest rate, and n indicates the number of compounding periods. It’s essential to remember that r and n must correspond to the same compounding duration, e.g. r is compounded monthly while n is expressed in months.

The inquiry seeks to determine the PV necessary as a one-time deposit to achieve a future value of $7,500 in 3 years at an interest rate of 1.5% compounded monthly.

FV=7,500

r=1.5%=0.015

n=3*12=36 months

We have changed n to months since r is monthly compounded. The equation

must be arranged to isolate PV.

Response

Answer:

The scale factor equates to 3.

Detailed explanation:

Please refer to the provided image for clarity regarding this issue.

We know that

If two shapes are similar, then the ratio of their areas corresponds to the square of the scale factor.

Let

z -----> scale factor

x -----> area of polygon Q

y ----> area of polygon P

Thus, we have

so, we proceed with

Determining the area of polygon Q

The polygon Q can be divided into five distinct squares.

Refer to the additional figure N 2.

The area of polygon Q, which represents the total area of the five squares, is

Calculating the scale factor

Thus, we derive

By substituting the values, we find

Taking the square root of both sides results in

Thus,

The scale factor resolves to 3.