Indira has 18 coins valued at $4.20. she has only quarters and dimes. Which augmented matrix can be used to determine the number

Response:

j = 21 and n = 14

Step-by-step breakdown:

We start with the equations:

6j + n/3 = 134

j/3 + n = 31

54j + 3n = 1206

j + 3n = 93

53j = 1113

j = 21

(21)/3 + n = 31

7 + n = 31

n = 14

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Answer:

P(t) = 1000e^(0.01155)t

Step-by-step explanation:

The population of the barangay can be modeled using the exponential function;

P(t) = P0e^kt

P(t) reflects the population after t years

P0 denotes the initial population

t indicates the time

With an initial population of 1000, we set P0 = 1000

Given that the population doubles every 60 years, at t = 60, it holds that P(t) = 2P0

Inserting that into the equation yields

2P0 = P0e^k(60)

2 = e^60k

Taking the natural logarithm of both sides

ln2 = lne^60k

ln2 = 60k

k = ln2/60

k = 0.01155

Inserting the determined k value and P0 into the function gives

P(t) = 1000e^(0.01155)t

Thus, the exponential model for the population of the barangay is

P(t) = 1000e^(0.01155)t

Answer with explanation:

In a two-dimensional plane, when the point (x,y) is transformed into polar coordinates (r,α)

1. The origin (0,0) corresponds to the pole.

2. When x=0 and y=0, it translates to the equation of the polar axis, which equals 0.

The two curves featured here exhibit the following symmetries:

1. Symmetry across four lines of the blade-shaped curve, including one along the polar axis at x=0 and y=0, and two along x=y and y=-x.

2. The Cardioid shape possesses one line of symmetry, found at x=0.

Characteristics of the polar graph include:

Option:

A. Symmetry about the line

B. Symmetry about the polar axis = 0