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Zepler [3.9K]
3 years ago
8

What is the value of x in the diagram below?

Mathematics
2 answers:
Yuki888 [10]3 years ago
8 0

Answer:

18√2

____

√3

I checked this and got it right. I needed someone to explain to me so read the other persons lol. But this correct :)

Furkat [3]3 years ago
4 0
Hi, 
The answer will be \frac{ 18\sqrt{2} }{ \sqrt{3} } .

Now how is that, there is a rule for the right angled triangle which says:

cosθ = \frac{adjacent side}{hypotenuse} so, if we applied this rule on the lower triangle we can say: cos30°= \frac{9}{hypotenuse} and therefore the hypotenuse = \frac{9}{cos30} = \frac{18}{ \sqrt{3} } .

now in the upper triangle we will apply the same rule so,
cos45°=\frac{adjacent side}{hypotenuse}
and the adjacent side in the upper triangle is \frac{18}{ \sqrt{3} } and the hypotenuse is x.
so cos45°=\frac{( \frac{18}{ \sqrt{3} } )}{x} and then we can say 
x=\frac{ \frac{18}{ \sqrt{3} } }{cos45} = \frac{ 18\sqrt{2} }{ \sqrt{3} } .
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Answer:

Bag of windflower bulbs costs $8.50

Package of crocus bulbs costs $17.60

Step-by-step explanation:

Let $x be the price of one bag of windflower bulbs and $y be the price of one  package of crocus bulbs.

1. Mark sold 2 bags of windflower bulbs for $2x and 5 packages of crocus bulbs for $5y. In total he earned $(2x+5y) that is $105. So,

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2. Julio sold 9 bags of windflower bulbs for $9x and 5 packages of crocus bulbs for $5y. In total he earned $(9x+5y) that is $164.50. So,

9x+5y=164.50

3. You get the system of two equations:

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From the first equation

5y=105-2x

Substitute it into the second equation:

9x+105-2x=164.50

7x=164.50-105

7x=59.5

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So,

5y=105-2·8.5

5y=105-17

5y=88

y=$17.60

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