John Anderson bought a home with a 10.5% adjustable rate mortgage for 30 years. He paid $9.99 monthly per thousand on his origin

Answer:

a) The first inequality is 100 + 55x > 150 + 51x;

b) The final inequality results in x > 12.5

c) Sal's mother will need to use the second phone for at least 13 months.

Step-by-step explanation:

a) Let x represent the number of months.

1. The first phone is priced at $100, with a monthly fee of $55 for unlimited use, leading to a total cost of $(100 + 55x) for x months.

2. The second phone costs $150 with a monthly fee of $51 for unlimited use, resulting in a total of $(150 + 51x) for x months.

3. For the second phone to be cheaper, we set up the inequality:

150 + 51x < 100 + 55x

which simplifies to

100 + 55x > 150 + 51x

b) Now solve this:

55x - 51x > 150 - 100

4x > 50

so x > 12.5

c) This means Sal's mother has to retain the second phone for at least 13 months (since x > 12.5).

Answer:

1) (2.2, -1.4)

2) (1.33, 1)

Detailed solution:

Question 1)

We are provided with two linear equations representing lines, and we need to find the intersection point that solves the system.

The lines given are:

Line 1 equation:

This line passes through points (0, 2.5) and (2.2, -1.4).

Line 2 equation:

The second line goes through (0, -3) and (2.2, -1.4).

According to the graph and data, the solution to the system is the coordinate where both lines intersect.

The solution to a system of linear equations is the coordinate pair common to both lines, i.e., the intersection point.

Here, both lines share the point (2.2, -1.4), indicating it is their intersection and the solution.

Therefore, the solution for question 1 is (2.2, -1.4).

Question 2)

The equations given are:

y = 1.5x - 1               Equation 1

y = 1                           Equation 2

The method of substitution can be used to find the solution.

Replacing y from Equation 2 into Equation 1 gives:

1 = 1.5x - 1

Add 1 to both sides:

2 = 1.5x

Dividing both sides by 1.5 yields:

x = 2/1.5

x = 1.33

y = 1

Thus, the solution of the system is (1.33, 1).

Response:1 and 2

Step-by-step Explanation:

Provided data

Volume required

For the initial cylinder

For the second cylinder

For the third cylinder

For the fourth cylinder

Thus, cylinders and meet the requirement as they remain under

Reducing

9x + -31 = 43

Rearranging the components:

-31 + 9x = 43

Finding the solution

-31 + 9x = 43

Isolating the variable 'x'.

Shift all terms with x to one side,

Add '31' to both sides of the equation.

0 + 31 + 9x = 43 + 31

Summing up similar items:

-31 + 31 = 0

0 + 9x = 43 + 31

9x = 43 + 31

Summing similar items:

43 + 31 = 74

9x = 74

Split each side by '9'

x = 8.222222222

Simplifying

x = 8.222222222