All categories

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.

You might be interested in

There are red, blue, and white buttons in a box. The ratio of the

vampirchik [111]

Answer:

680

Step-by-step explanation:

Ratio of red to white 4 : 7

Number of white = 280

White + red buttons = x

7x / 11 = 280

7x = 280 * 11

7x = 3080

x = 3080 / 7

x = 440

Number of red buttons 440 - 280 = 160

Number of red bottons ;

Blue + red buttons = x

3 : 2 ; blue : red

3 + 2 = 5 ;

2x / 5 = 160

2x = 160 * 5

2x = 800

x = 800 / 2

x = 400

Number of Blue buttons :

400 - 160 = 240

Total :

White + red + blue

280 + 160 + 240 = 680 buttons

5 0

3 years ago

Tod begins piano practice at 4:15 p.M. And ends at 5:50 p.M. How long does he practice

nikdorinn [45]

Answer:

95 minutes/1 hour and 35 minutes.

Step-by-step explanation:

Since there are 60 minutes in a hour you could convert it. Or you could just subtract 550 minutes by 415 minutes and get 95 minutes which is also 1 hour and 35 minutes.

Hope this helps

5 0

3 years ago

Andy and Christopher are measuring a liquid solution using graduated cylinders, Andy uses 3.5 liters of the liquid solution, and

Gre4nikov [31]

Answer:

$Ratio = 0.74$

Step-by-step explanation:

Represent

- Andy with A

- Christopher with C

$A = 3.5L$

$C = 2580mL$

Required

Determine the ratio of C to A

Ratio is represented as thus:

$Ratio = C:A$

Rewrite as fraction

$Ratio = \frac{C}{A}$

This gives

$Ratio = \frac{2580mL}{3.5L}$

Convert L to mL

$Ratio = \frac{2580mL}{3.5*1000mL}$

$Ratio = \frac{2580mL}{3500mL}$

$Ratio = \frac{2580}{3500}$

$Ratio = 0.73714285714$

$Ratio = 0.74$ --- Approximated

6 0

3 years ago

Nola was selling tickets at the high school dance. At the end of the evening she picked up the cash box and noticed a dollar lyi

Blizzard [7]

Answer:

The $1 belongs to the cash box

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine if the $1 belongs to the cash box or not

Represent singles with s and couples with c.

From the attachment, we have:

$s + c = 47$ --- total attendance

$5s + 4c =200$ --- ticket sold

Solve for s and c.

Make s the subject in (1)

$s = 47-c$

Substitute 47 - c for s in (2)

$5(47 - c) + 4c = 200$

Open bracket

$235 - 5c + 4c = 200$

$235 - c = 200$

$c = 235 - 200$

$c = 35$

This means that the total individual which makes up the couples are 35. This is not possible because couples are in 2's and the total should be an even number.

<em>So, we can conclude that the $1 belongs to the cash box</em>

4 0

3 years ago

Consider the following data set:

Komok [63]

Answer:

+5 Range; The range is now 25

Step-by-step explanation:

The original range would be calculated by subtracting 20 from 40, giving you 20 as the range. However, with the point 15 added, there would be a new lowest number, making the new range be 40-15, which is 25.

3 0

3 years ago