Point P is in the interior of ∠OZQ. If m∠OZQ = 125 and m∠OZP = 62, what is m∠PZQ?

Mathematics

1 answer:

aev [14]3 years ago

3 0

Answer:

Step-by-step explanation:

If point P is in the interior of ∠OZQ, then ∠OZQ = ∠OZP+∠PZQ. Given m∠OZQ = 125 and m∠OZP = 62, to get m∠PZQ, we will substitute the value of the angles given into the expression above as shown;

∠OZQ = ∠OZP+∠PZQ.

125 = 62 + ∠PZQ.

subtract 62 from both sides;

125 - 62 = 62 + ∠PZQ -62

63 = ∠PZQ

<em>Hence the angle m∠PZQ is 63°</em>

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Tristan is working two summer jobs, making $7 per hour babysitting and $19 per hour lifeguarding. Tristan must earn at least $21

rodikova [14]

Answer: 7bb +19 ll ≥210

Step-by-step explanation:

Hi, to answer this question we have to write an inequality:

The product of the number of hours he works babysitting (bb) and the amount he earns per hour (7); plus The product of the number of hours he works lifeguarding (ll) and the amount he earns per hour 19; must be higher or equal to the amount he must earn this week (210)

Mathematically speaking:

7 bb + 19 ll ≥210

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3 years ago

A valid license plate in Xanadu consists of two capital letters followed by three digits. How many valid license plates are poss

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The valid license plates are possible = 676,000 possibilities

<h3>What is permutation and combination?</h3>

In mathematics, there are two alternative methods for dividing up a collection of components into subsets: combination and permutation. The subset's components can be arranged in any sequence when used together. The subset's components are given in a permutation in a certain order.

<h3>According to the given information:</h3>

There is no prohibition on using the same letters or numbers more than once, therefore all 26 letters of the alphabet and all 10 numerals are permissible choices.

There are 26 options if the initial answer is A:

AA, AB, AC,AD,AE ...................................... AW, AX, AY, AZ.

There are 26 options if the initial answer is B:

BA, BB, BC, BD, BE .........................................BW, BX,BY,BZ

So,

The first letter can be one of 26 options, and the second letter can be one of 26 options. There are a variety of 2 letter combinations, including:

26 x 26 = 676

For the three digits, the same holds true.

The first, second, and third options each have ten options available:

10 × 10 × 10 = 1000

Thus, there are several options for a license plate with two letters and three digits:

26 x 26 x 10 × 10 × 10 = 676,000 possibilities.