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just olya [345]
3 years ago
9

A landscaping business bought 8 rose bushes and 15 daylilies for $193. They went back later and bought 3 more rose bushes and 12

daylilies for $117. How much does each daylily cost?
Mathematics
1 answer:
pantera1 [17]3 years ago
6 0

Answer:

Each daylilies  cost $7

Step-by-step explanation:

Step one:

let roses be x

and daylilies be y

so

8x+15y=193--------------1

also

3x+12y=117--------------2

we can solve equations 1 and 2 by substitution

8x=193-15y

x=(193-15y)/8

put x= (193-15y)/8  in 3x+12y=117

3((193-15y)/8)+12y=117

(579-45y)/8+12y=117

579-45y=8(117-12y)

579-45y=936-96y

collect like terms

579-936=-96y+45y

-357=-51y

divide both sides by -51

y=-357/-51

y=7

Hence each daylilies  cost $7

put y=7 in eqn 1

8x+15(7)=193

8x+105=193

8x=193-105

8x=88

x=88/8

x=11

rose cost $8

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sin2x =12/13

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STEP - BY - STEP EXPLANATION

What to find?

• sin2x

,

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Given:

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Let h be the hypotenuse.

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\begin{gathered} \cos 2x=(\frac{3}{\sqrt[]{13}})^2-(\frac{2}{\sqrt[]{13}})^2 \\  \\ =\frac{9}{13}-\frac{4}{13} \\ =\frac{5}{13} \end{gathered}

Hence, cos2x = 5/13

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\tan 2x=\frac{2\tan x}{1-\tan ^2x}=\frac{2(\frac{2}{3})}{1-(\frac{2}{3})^2}=\frac{\frac{4}{3}}{1-\frac{4}{9}}=\frac{\frac{4}{3}}{\frac{9-4}{9}}=\frac{\frac{4}{3}}{\frac{5}{9}}=\frac{4}{3}\times\frac{9}{5}=\frac{4}{1}\times\frac{3}{5}=\frac{12}{5}

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\tan 2x=\frac{\sin 2x}{\cos 2x}=\frac{\frac{12}{13}}{\frac{5}{13}}=\frac{12}{5}

Hence, tan2x = 12/5

Therefore,

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

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