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3 years ago

In rectangle PQRS, PR = 18x – 28 and QS = x + 380. Find the value of x and the length of each diagonal.

Mathematics

1 answer:

chubhunter [2.5K]3 years ago

7 0

Answer:

x = 24, PR = 404, QS = 404

Step-by-step explanation:

PR and QS are both diagonals of the rectangle. The diagonals of a rectangle bisect each other and are of equal length. Thus, we can say:

PR = QS

18x - 28 = x + 380

Solving for x, we get:

18x - x = 380 + 28

17x = 408

x = 408/17

x = 24

Thus, PR = 18(24) - 28 = 404 and QS = 24 + 380 = 404

Third choice is right.

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3 years ago

An average of 145 people visited a 4-day exhibition on the first 3 days. Another 205 people visited the exhibition on the fourth

Alenkinab [10]

Answer:

160 visitors.

Step-by-step explanation:

Given:

An average of 145 people visited a 4-day exhibition on the first 3 days, <u>means here average people visited in 3 days is given 145.</u>

Average = 145

Number of people, n = 3

Another 205 people visited the exhibition on the fourth day.

To find:

What is the average number of visitors per day ?

Solution:

<u>First of all we will find total number of people visited in 3 days:-</u>

As we know:

$Average=\frac{Sum\ of\ observation}{number\ of\ observation}$

$145=\frac{Sum\ of\ observation}{3}\\$

Multiplying both sides by 3

$145\times3=\frac{Sum\ of\ observation}{3}\times3\\435=Sum\ of\ observations$

Thus, we found that total number of people visited in 3 days is 435 and as 205 people visited in fourth day, then total number of people increased to

435 + 205 = 640

Now, sum of total observations( total number of people ) = 640

And number of observation ( number of days ) = 4

Now, we will calculate average number of visitors visit per day :-

$Average=\frac{Sum\ of\ observation}{number\ of\ observation}$

$=\frac{640}{4} \\=160\ visitors$

Thus, the average number of visitors per day is 160 visitors.

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3 years ago