Answer:
25 / 33
Step-by-step explanation:
(-1 2/3) / (-2 1/5)
(-5/3) / (-11/5)
Division is the same as the inverse of multiplication.
(-5/3) * (-5/11)
Multiply both numerators and multiply both denominators
(-5 *-5) / (3 * 11)
25 / 33
Answer:
389 and 3/4
Step-by-step explanation:
Just as an example, three consecutive integers might be 4,5,6.
If x is the least of these (4 in our example), then the other two integers would be x+1, and x+2.
Then the sum of our three integers is x + (x+1) + (x+2).
Addition is commutative so we can switch any two terms, and it is also associative so we can regroup any terms. This lets is rearrange things with all the "x" together and all the numbers together like this:
(x+x+x) + (1+2) OR 3x + 3
According to the problem, the sum is 126, so 3x+3 = 126.
3x = 123
x = 41 (which is the smallest consecutive integer)
Check our answer: 41 + 42 + 43 = 126.
Answer:
Step-by-step explanation:
1) Diagonal bisect the angles of Rhombus
∠CAB = ∠CAD
∠CAB = 71
2) ∠DAB = ∠CAB + ∠CAD
∠DAB = 71 + 71 = 142
In Rhombus, adjacent angles are supplementary
∠DAB + ∠ABC = 180
142 + ∠ABC = 180
∠ABC = 180 - 142
∠ABC = 38
3) In rhombus, opposite angles are congruent
∠ADC = ∠ABC
∠ABC = 38
In rhombus, diagonal bisect angles
∠BDC = (1/2)*∠ADC
∠BDC= 38/2
∠BDC = 19
4) Diagonals bisect each other at 90
∠DEC = 90
5) Diagonals bisect each other
BE = DE
BE + DE = DB
7x -2 +7x -2 =24 {add like terms}
14x - 4 =24
14x = 24+4
14x = 28
x = 28/14
x = 2 m
6) AB = 13m
BE = 7x - 2 = 7*2 -2 = 14 -2 = 12 m
In right angle ΔAEB, {use Pythagorean theorem}
AE² + BE² = AB²
AE² + 12² = 13²
AE² + 144 = 169
AE² = 169 - 144
AE² = 25
AE = √25
AE = 5 m
Diagonals bisect each other
AE = EC
AC = 2*5
AC = 10 m
7)Side = 13 m
Perimeter = 4*side
= 4*13
Perimeter = 52 m
8) d1 = AC = 10 m
d2 = DB = 24 m
Area = ![\frac{d_{1}*d_{2}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bd_%7B1%7D%2Ad_%7B2%7D%7D%7B2%7D)
![=\frac{10*24}{2}\\](https://tex.z-dn.net/?f=%3D%5Cfrac%7B10%2A24%7D%7B2%7D%5C%5C)
= 10 *12
= 120 m²