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andrey2020 [161]

4 years ago

7

Question: Michelle is making goodie bags for Christmas filled with chocolate and candy. Chocolates cost $2.50 per lb and candy c

ost $3.00 per lb. Michelle spent a total of $40 on 20 lbs of candy. How much of each kind of candy did she purchase ?

1 answer:

ehidna [41]4 years ago

4 0

The answer will be 80

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PLS HELP ME!!!!!!!! 99 POINTS

Amiraneli [1.4K]

Answer:

$\angle LKN=\arctan1.8\sqrt{97}\approx 86.77^{\circ}$

Step-by-step explanation:

Draw the second altitude MB (see attached diagram).

Quadrilateral HLMB is a rectangle, then LM = HB = 3 units.

Trapezoid KLMN is isosceles trapezoid (because KL=MN), thus

$KH = BN = \dfrac{KN-HB}{2}=\dfrac{13-3}{2}=5\ units\\ \\HN=HB+BN=3+5=8\ units$

Triangle LHN is right triangle, then by Pythagorean theorem,

$LN^2=LH^2+HN^2\\ \\89^2=LH^2+8^2\\ \\LH^2=89^2-8^2\\ \\LH^2=(89-8)(89+8)\\ \\LH^2=81\cdot 97\\ \\LH=9\sqrt{97}\ units$

Consider right triangle KLH. In this triangle,

$\tan\angle LKH=\{\tan\angle LKH\}=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{LH}{KH}=\dfrac{9\sqrt{97}}{5}=1.8\sqrt{97}\ units$

So,

$\angle LKN=\arctan1.8\sqrt{97}\approx 86.77^{\circ}$

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