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2 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]2 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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Read 2 more answers

PRECALCULUS HONORS HELP ME PLZ AND THANKS

Natalka [10]

Inequalities are used to show the relationship between unequal expressions

The set notation of (5) and (6) are: $\{x : -6 > x \ge -2\}$ and $\{x:-4 < x \ge 6\}$ .
See attachment for the graphs

The following should be notated when plotting the graph of an inequality

< and > are represented with open circles, while $\leq$ and $\geq$ are represented with closed circles
The arrows of and $\le$ point to the left, while the arrows of $>$ and $\geq$ point to the right.

So, we have:

$(a)\ -8 < x$

Rewrite as:

$x > -8$

The graph of $x > -8$ will point to the right, and it will use an open circle

$(b)\ -6 > x \ge -2$

Split the inequality:

$-6 > x$ and $x \ge -2$

It is not possible for -6 to be less than x and at the same time, x is greater than or equal to -2.

Hence. $-6 > x \ge -2$ cannot be represented on a graph

$(c)\ -4$

Split the inequality:

$-4 < x$ and $x \ge 6$

$-4 < x$ means that -4 is less than x or x is greater than -4.

So, we have:

$x > -4$ and $x \ge 6$

If $x > -4$ and $x \ge 6$ , then we make use of $x > -4$ because it contains more values of x.

The graph of $x > -4$ will point to the right, and it will use an open circle