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3 years ago

The lodge at the Three Lakes Resort is offering the following two options for a holiday weekend.

1 answer:

7 0

so let be the x - the cost of one night´s lodging
and let be -the y - the cost of a meal
now solve them
so x is the meal and y night spend
puting values
3 x + 6 y = 132
3 x + 2 y = 109 / * (-1)
-----------------------------
3 x + 6 y = 132
-3 x - 2 y = - 109
-----------------------
4 y = 23
solving for y
y = 5.75
now for x
3 x + 34.50 = 132
3 x = 97.50
x = 97.50 : 3
so
x = $32.50
<span>The cost of one night´s lodging is $32.50.
hope it helps</span>

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Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P. Side QR= 5 m and diagonal QS

svet-max [94.6K]

Answer:

Given the statement: Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P.

Properties of Kite:

The diagonals are perpendicular

Two disjoint pairs of consecutive sides are congruent by definition of kite

One diagonal is the perpendicular bisector to the other diagonal.

It is given that: Side QR = 5m and diagonal QS = 6m.

Then, by properties of kite:

$QP = \frac{1}{2}QS$

Substitute the value of QS we get QP;

$QP = \frac{1}{2}(6)$ = 3 m

Now, in right angle $\triangle RPQ$

Using Pythagoras theorem:

$QR^2= RP^2 +QP^2$

Substitute the given values we get;

$(5)^2= RP^2 +(3)^2$

$25= RP^2 +9$

Subtract 9 from both sides we get;

$16= RP^2$

Simplify:

$RP = \sqrt{16} = 4 m$

Therefore, the length of segment RP is, 4m

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