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Answer:
ΔLMN ~ ΔLFG; scale factor 7/3
Step-by-step explanation:
The ratios of side lengths, shortest to longest are ...
FG : GL : LF = 24 : 36 : 42 = 4 : 6 : 7 (reduced)
MN : NL : LM = 56 : 84 : 98 = 4 : 6 : 7 (reduced)
The side ratios are the same, so ΔLMN ~ ΔLFG. The scale factor is ...
MN/FG = 56/24 = 7/3
Answer:
6 benches are needed
Step-by-step explanation:
3/4= 6/8
1/8 goes into 6/8, 6 times so,
6 benches are needed on the 3/4 mile trail
2/9=2.50
Allowence=2.50x9 divided by which gives you an answer of 11.25
Hope this helps you!
Answer:
x= 4
y= -5
Step-by-step explanation:
-2x+6y=-38 equation 1
3x-4y=32 equation 2
using equation 1 we have:
-2x+6y=-38
6y +38 = 2x
3y + 19 = x equation 3
using equation 3 in equation 2 we have:
3(3y + 19) - 4y = 32
9y + 57 -4y =32
5y = 32 -57
5y = -25
y= -25/5
y = -5
so we have:
3y + 19 = x
3(-5) +19 = x
x= 4
Step-by-step explanation:
We start with Left hand side
We know that csc(x) = 1/ sin(x)
So csc(2x) is replaced by 1/sin(2x)
Also we use identity
sin(2x) = 2 sin(x) cos(x)
4 divide by 2 is 2
Now we multiply top and bottom by sin(x) because we need tan(x) in our answer
We know that sinx/ cosx = tan(x)
Also 1/ sin(x)= csc(x)
so it becomes 2csc^2(x) tan(x) , Right hand side
Hence verified
