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Answer:

A) Maia had 1920 beads more.

B) Maia had 2544 beads at first.

Step-by-step analysis:

Let x denote the beads with Jenny and y for Maia.

The information provided states that Maia possesses 2064 beads more than Jenny, which can be represented mathematically as:

Additionally, after Maia made a necklace with 144 beads, she had five times more beads than Jenny.

This can also be formulated as an equation:

A) Since Maia had 2064 beads more than Jenny before using 144 beads, we calculate her final bead count by subtracting 144 from 2064.

Thus, Maia is left with 1920 beads more than Jenny.

B) To solve this system of linear equations, we will utilize the substitution method.

By inserting equation (1) into equation (2), we arrive at:

Now, let's divide our equation by 4.

Now, we'll substitute x=480 into equation (1) to isolate y.

Conclusively, Maia initially had 2544 beads.

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).

Let’s evaluate the provided pairs one by one.

A. ∠MKR and ∠OAR

In the diagram, it’s visible that the angle bisector of the right-angled vertices creates angles MKR and OAR.

Thus, they are congruent measuring 45°

B. ∠ONT and ∠MTN

From the diagram, MTN forms a right angle, while ONT is created by bisecting this right angle.

Hence, these angles are not congruent with ∠MTN at 90° and ∠ONT at 45°

C. ∠IRS and ∠MRO

In the diagram, MRO is a right-angle, while IRS results from the bisection of the right angle.

Accordingly, these angles are not congruent with ∠MRO equal to 90° and ∠IRS at 45°

D. ∠URC and ∠TRO

In the diagram, it’s shown that the angle bisector of the right-angled vertices forms angles URC and TRO.

Thus, they are congruent, both measuring 45°

Therefore, the pairs of congruent angles are

A. ∠MKR and ∠OAR and D. ∠URC and ∠TRO