Answer:
1/10, 1/4, 2/5, 2/3.
Step-by-step explanation:
Convert the fractions into decimals.
2/5 = 0.4
2/3 ≈ 0.66666
1/4 = 0.25
1/10 = 0.1
Arrange from smallest to largest.
0.1, 0.25, 0.4, 0.6666
Change back to fraction form.
1/10, 1/4, 2/5, 2/3.
82 degrees and 98 degrees
First, find the original equation
180 = (x) + (x + 16)
Simplify: 180 = 2x + 16
Next, use the subtraction property of equality to subtract 16 from both sides
180 - 16 = 2x + 16 - 16
Simplify: 164 = 2x
Then, you can use the division property of equality to find the value of x
164/2 = 2x/2
Simplify: 82 = x
Now, we know that the first angle equals 82 degrees and that the second angle equals 98 degrees
Answer:
1) 2 and 6 ; 4 and 8 ; 1 and 5 ; 3 and 7
2) 3 and 6 ; 4 and 5
3) 1 and 8 ; 2 and 7
The diagonals are:
diagonal₁=2x+3y
diagonal₂=(x+8)+(2y+5)
We have to solve the following system of equations:
2x=3y
(x+8)=(2y+5)
We solve this system by substitution method:
2x=3y ⇒x=3y/2
(3y/2 +8)=2y+5
3y+16=4y+10
-y=-6
y=6
x=3y/2=3*6/2=9
we obtain the measure of the diagonals:
diagonal₁=2x+3y=2*9+3*6=18+18=36
diagonal₂=(x+8)+(2y+5)=(9+8)+(2*6+5)=17+17=34
Answer: The longest diagonal is 36 units.
