Think of factor pairs of 9.
9 = 9 × 1 (sum is 10)
9 = 3 × 3 (sum is 6)
Your numbers are 3 and 3.
We say that there are
![x](https://tex.z-dn.net/?f=x)
girls. We equate the two expressions for the amount of sweets in the packet to get:
![6x-4=5x+3](https://tex.z-dn.net/?f=6x-4%3D5x%2B3)
Subtracting 5x from both sides and adding 4 to both sides, we see that:
![x=7](https://tex.z-dn.net/?f=x%3D7)
Since there are 7 girls, we have 7*6-4=38 sweets, using the first expression of the amount of sweets. To check our answer, we examine the second expression for the amount of sweets, for a result of 7*5+3=38 sweets. Since both of these amounts are equal, our answer seems to be correct. Thus, there are 38 sweets in a packet.
Answer:
1.-3, 2.1/3=3
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Answer:
![FL= \frac{a (\sqrt{3} + 1)}{\sqrt{2} }](https://tex.z-dn.net/?f=FL%3D%20%5Cfrac%7Ba%20%28%5Csqrt%7B3%7D%20%2B%201%29%7D%7B%5Csqrt%7B2%7D%20%7D)
Step-by-step explanation:
As given in figure 1 below:
FK = a, m∠F = 45° and m∠L = 30°
Construction: Draw an altitude KE from point K on FL.
Now, In ΔFEK,
FE = EK (Sides opposite to equal angles of a triangle)
Let FE = EK = x
Now, using pythagoras In ΔFEK,
![(a)^{2} = (x)^{2} + (x)^{2}](https://tex.z-dn.net/?f=%28a%29%5E%7B2%7D%20%3D%20%28x%29%5E%7B2%7D%20%2B%20%28x%29%5E%7B2%7D)
![(a)^{2} = 2x^{2}](https://tex.z-dn.net/?f=%28a%29%5E%7B2%7D%20%3D%202x%5E%7B2%7D)
![x = \sqrt \frac{a^{2} }{2} = \frac{a}{\sqrt{2} }](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%20%5Cfrac%7Ba%5E%7B2%7D%20%7D%7B2%7D%20%3D%20%5Cfrac%7Ba%7D%7B%5Csqrt%7B2%7D%20%7D)
∴ FE = EK = ![\frac{a}{\sqrt{2} }](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B%5Csqrt%7B2%7D%20%7D)
Now in ΔEKL, EK = ![\frac{a}{\sqrt{2} }](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B%5Csqrt%7B2%7D%20%7D)
Using trigonometry ratio,
TanФ = Altitude\ Base
![Tan \theta = \frac{KE}{EL}](https://tex.z-dn.net/?f=Tan%20%5Ctheta%20%3D%20%5Cfrac%7BKE%7D%7BEL%7D)
Tan 30° = ![\frac{a/\sqrt{2} }{EL}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%2F%5Csqrt%7B2%7D%20%7D%7BEL%7D)
![\frac{1}{\sqrt{3} } = \frac{a}{\sqrt{2} EL}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D%20%3D%20%5Cfrac%7Ba%7D%7B%5Csqrt%7B2%7D%20EL%7D)
![EL = \frac{\sqrt{3}a}{\sqrt{2} }](https://tex.z-dn.net/?f=EL%20%3D%20%5Cfrac%7B%5Csqrt%7B3%7Da%7D%7B%5Csqrt%7B2%7D%20%7D)
Now FL = FE + EL
FE =
and ![EL = \frac{\sqrt{3}a}{\sqrt{2} }](https://tex.z-dn.net/?f=EL%20%3D%20%5Cfrac%7B%5Csqrt%7B3%7Da%7D%7B%5Csqrt%7B2%7D%20%7D)
∴ ![FL = \frac{a}{\sqrt{2} } + \frac{\sqrt{3}a }{\sqrt{2} } = \frac{a (\sqrt{3} + 1)}{\sqrt{2} }](https://tex.z-dn.net/?f=FL%20%3D%20%5Cfrac%7Ba%7D%7B%5Csqrt%7B2%7D%20%7D%20%2B%20%5Cfrac%7B%5Csqrt%7B3%7Da%20%7D%7B%5Csqrt%7B2%7D%20%7D%20%3D%20%5Cfrac%7Ba%20%28%5Csqrt%7B3%7D%20%2B%201%29%7D%7B%5Csqrt%7B2%7D%20%7D)