Question

in ∆MQRand ∆MQR,MP=MQ is bisector OF PMQ.PROVE THAT ∆MPR CONGRUENT TO ∆MQR​
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Answer 1

Given: In ΔPQR, PA is the bisector of ∠QPR and PM ⊥ QR. To prove: ∠APM = 1212 (∠Q – ∠R) Proof: Suppose ∠APR = ∠1, ∠APM = ∠2 and ∠QPM = ∠3 ∠1 = ∠2 + ∠3 …(i) [As PA is the bisector of ∠QPR] In ΔPMR, ∠MPR + ∠PMR + ∠PRM = 180° (angle sum property of a triangle) ⇒ (∠1 + ∠2) + 90° + ∠PRM = 180° ⇒ (∠1 + ∠2) + ∠PRM = 90° …(ii) Similarly in ΔPQM, ∠3 + ∠Q = 90° …(iii) [As ∠PMQ = 90°] From (ii) and (iii), we get ∠1 + ∠2 + ∠PRM = ∠3 + ∠Q ⇒ ∠1 + ∠2 + ∠R = ∠3 + ∠Q ⇒ ∠1 + ∠2 – ∠3 = ∠Q – ∠R ⇒ (∠1 – ∠3) + ∠2 = ∠Q – ∠R (as ∠Q > ∠R) Using relation (i), we get ∠2 + ∠2 = ∠Q – ∠R ⇒ 2∠2 = ∠Q – ∠R ⇒ ∠2 = 1212 (∠Q – ∠R) ⇒ ∠APM = 1212 (∠Q – |_r)

Answer 2

Account A: Decreasing at 8 % per year

Account B: Decreasing at 10.00 % per year

The amount f(x), in dollars, in account A after x years is represented by the function below:

f(x) = 10,125(1.83)x

Account B shows the greater percentage

change

Step-by-step explanation:

Part A: Percent change from exponential

formula

f(x) = 9628(0.92)*

The general formula for an exponential

function is

y = ab^x, where

b = the base of the exponential function.

if b < 1, we have an exponential decay

function.

f(x) decreases as x increases.

Account A is decreasing each year.

We can rewrite the formula for an

exponential decay function as:

y= a(1 – b)”, where

1- b = the decay factor

b = the percent change in decimal

form

If we compare the two formulas, we find

0.92 = 1- b

b = 1 - 0.92 = 0.08 = 8 %

The account is decreasing at an annual rate of 8%. The account is decreasing at an annual rate of 10.00%.

Account B recorded a greater percentage change in the amount of money over the previous year.