James has t toy cars and Paul has 13 more. How many cars will James have if Paul gives him half of his cars?

2x + 4

To represent 2x + 4, the following is required:

2 positive x-tiles corresponding to 2x.

4 positive unit tiles for the value of 4.

3x + (-1)

To illustrate 3x + (-1), you will need:

3 positive x-tiles to depict 3x.

1 negative unit tile to signify (-1).

Rotational symmetry indicates that an object appears unchanged when rotated.

Upon examining the figures, option B might seem plausible, but observe that the edges vary in length—rotating it will not align perfectly with its original position.

Options C and D are eliminated as they lack any symmetrical characteristics; no matter how they are turned, they appear different.

This leaves option A as the only choice: if you rotate this figure by 180 degrees, its appearance remains unchanged.

Consequently, the figure possessing rotational symmetry is A.

Answer:

Step-by-step explanation:

Let’s consider that the amount deposited, C dollars, generates r% simple interest each year.

After a span of t years, the value of the deposited C dollars reaches D dollars; our task now is to formulate a relationship using these variables to find t.

We can express this relationship through the simple interest formula:

⇒

⇒

⇒

Thus, this yields the formula for t. (Answer)

Answer:

Step-by-step explanation:

We apply the exponential decay formula, which is represented as

A = P(1 - r)^t

Where

A signifies the car's value after t years.

t denotes the number of years.

P is the initial car value.

r signifies the decay rate.

Based on the provided information,

A = $2700

P = $20300

n = 2004 - 1997 = 7 years

Therefore,

20300 = 2700(1 - r)^7

20300/2700 = (1 - r)^7

7.519 = (1 - r)^7

Taking logarithms on both sides leads to

Log 7.519 = 7 log(1 - r)

0.876 = 7 log(1 - r)

Log (1 - r) translates to 0.876/7 = 0.125

By applying inverse logarithm, it results in

10^log1 - r equals 10^0.125

1 - r = 1.33

Thus, r = 1.33 - 1 = 0.33

We now have the expression

A = 20300(1 - 0.33)^t

A = 20300(0.67)^t

Thus, in 2007,

t = 2007 - 1997 = 10 years

The projected value equals

A = 20300(0.67)^10

A = $370