Ratio for 669 and 221

a) The area of a rectangle is calculated by multiplying the length by the width:
   A = l·w

This formula allows us to express the width in terms of area and length. By dividing A by l, we find
   A/l = w

We also recognize that the perimeter of a rectangle is the total length around it.
   P = l + w + l + w
   P = 2(l + w)
We aim to rewrite the perimeter formula to isolate l on one side, using the expression for w derived earlier.
   P = 2(l + A/l)

By substituting the known value for A, we can express p(l) as
   p(l) = 2(l + 25/l)
   p(l) = 2l + 50/l


b) For lengths exceeding widths, we have
   l > w
   l > A/l
   l² > A
   l > √A
   l > √25

This indicates that the domain of p(l) is
   l ∈ (5, ∞)..... meters

Define x as the first mile marker, thus x + 1 corresponds to the second mile marker. This can be expressed as x + (x + 1) = 561, which simplifies to 2x + 1 = 561. Therefore, 2x equals 560, leading to x being 280. Consequently, the first mile marker is 280, and the second mile marker is 281.

Answer:

The scenario is more accurately represented by the exponential model since the linear model suggests that the repayment amount could turn negative.

Step-by-step explanation:

There is a table with two columns and five rows. The first column is labeled months, with entries 6, 12, 18, 24, 30. The second column, which denotes the repayment amount (in dollars), contains the entries 2,700; 2,110; 1,110; 870; 220.

The remaining balance owed changes inconsistently after every six months.

This indicates that the regression cannot be linear, but is instead modeled by an exponential curve.

Consequently, the exponential model better represents the situation because the linear model indicates that the repayment amount will eventually be negative. (Answer)

Answer:

1) E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)   reflects across the x-axis

2) E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)     translates 5 units downward

3) E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)    reflects across the y-axis

4) E(4, 4), F(8, 3), G(10, 6), and H(8, 6)    translates 7 units to the right

Step-by-step explanation:

The vertices of quadrilateral ABCD are A(-3, 4), B(1, 3), C(3, 6), and D(1, 6).

1) E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

In this instance, the vertices share the same x-coordinates while their y-coordinates are opposites, indicating a reflection across the x-axis.

2) E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

In this case, the x-coordinates of the vertices remain constant, while the y-coordinates of EFGH are reduced by 5 units, indicative of a downward translation of 5 units.

3) E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

Here, the vertices share the same y-coordinates while the x-coordinates are opposites, representing a reflection across the y-axis.

4) E(4, 4), F(8, 3), G(10, 6), and H(8, 6)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

For this case, the y-coordinates for EFGH remain the same while the x-coordinates have increased by 7 units, showing a rightward translation of 7 units.

To address this problem, a straightforward table can be utilized to determine the amount of quarters and dimes:

 type of coin        I  Quantity of coin  I  Value of coin (in cents)
------------------------------------------------------------------------------------------------------
 dimes                I   x                        I  10x (since a dime equals 10 cents)
------------------------------------------------------------------------------------------------------
 quarters       I   18-x                   I   450-25x (given a quarter is 25 cents)


Following this, an equation can be formed:

10x + 450 - 25x = 420

-15x = -30

x = 2 dimes
18-x = 16 quarters