Sanjeet paid $32.85 for a file and 3 identical pens.Leon paid $83.50 for 2 such files and 8 such pens.Find the cost of 1 pen.

Step-by-step explanation:

Given are

Sides of the triangle measure 4 units, 6 units, and 7.21 units.

We need to compute the area of a circle whose circumference matches the triangle's perimeter.

The triangle's perimeter corresponds to the circle's circumference.

4 + 6 + 7.21 = 2πr, where r is the radius of the circle.

r = 2.73 units

Circle's area is:

or

A = 24 square units

Thus, the circle’s area is 24 square units.

(a) The multiplicative inverse of 1234 (mod 4321) is x so that 1234*x ≡ 1 (mod 4321). We can apply Euclid's algorithm:

4321 = 1234 * 3 + 619

1234 = 619 * 1 + 615

619 = 615 * 1 + 4

615 = 4 * 153 + 3

4 = 3 * 1 + 1

Now we will express 1 as a linear combination of 4321 and 1234:

1 = 4 - 3

1 = 4 - (615 - 4 * 153) = 4 * 154 - 615

1 = 619 * 154 - 155 * (1234 - 619) = 619 * 309 - 155 * 1234

1 = (4321 - 1234 * 3) * 309 - 155 * 1234 = 4321 * 309 - 1082 * 1234

This reduces to

1 ≡ -1082 * 1234 (mod 4321)

Thus, the inverse is

-1082 ≡ 3239 (mod 4321)

(b) Since both 24140 and 40902 are even, their GCD cannot equal 1, indicating no inverse exists.

Here’s a counterexample: consider

Select the subsets in the following manner:

It's accurate that and and that , but

Answer:

Step-by-step explanation:

We are provided with the information that

Function f is decreasing as it moves from quadrant 2 to quadrant 1, tending towards y=0

It intersects the y-axis at the point (0,6) and goes through (1,2).

Function g(x) also approaches y=0 in quadrant 2, but increases in quadrant 1.

It passes through (-1,2) and crosses the y-axis at (0,6).

Reflection across y-axis:

The transformation rule is identified as

Applying this rule, we derive

Then, by substituting

for x=-1

for x=0

Consequently, holds true.