Amuseum borrows $2,000,000 at simple annual interest to purchase new exhibits. let x represent the amount borrowed at 7%, y represent the amount borrowed at 8.5%, and z represent the amount borrowed at 9.5%. set up a system of linear equations to determine how much is borrowed at each rate given that the total annual interest is $169,750 and the amount borrowed at 8.5% is four times the amount borrowed at 9.5%. you do not have to solve the system.

Step-by-step explanation:

Total amount borrowed by the museum is $2000000

Let x represent the amount borrowed at 7%

Let y represent the amount borrowed at 8.5%

Let z represent the amount borrowed at 9.5%.

The formula for simple interest is

l = PRT/100

Where

I = interest

P = principal

R = rate

T = time

For a Pincipal of $x borrowed at a rate of 7% and the time is 1 year,

the simple interest would be expressed as

I = (x × 7 × 1)/100 = 0.07x

Fora Principal of $y borrowed at a rate of 8.5% and a duration of 1 year, the simple interest would be expressed as

I = (x × 8.5 × 1)/100 = 0.085y

For a Principal of $z borrowed at rate of 9.5% and a duration of 1 year,

the simple interest would be expressed as

I = (x × 9.5 × 1)/100 = 0.095z

The total annual interest is $169,750 and the amount borrowed at 8.5% is four times the amount borrowed at 9.5%. This means that

y = 4z

The total annual interest would be expressed as

169750 = 0.07x + 0.085×4z + 0.095z

169750 = 0.07x + 0.34z + 0.095z

169750 = 0.07x + 0.435z

The museum borrowed $2,000,000 at simple annual interest. It means that

x + y + z = 2000000

Since y = 4z , then

x + 4z + z = 2000000

x + 5z = 2000000

So the equations are

x + 5z = 2000000

0.07x + 0.435z = 169750

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.