Answer:
(x, y) = (1, 1/3)
Step-by-step explanation:
The x-coefficient in the first equation is -2 times that in the second equation, so adding twice the second equation to the first will eliminate x:
(4x -9y) +2(-2x +3y) = (1) +2(-1)
-3y = -1 . . . . simplify
y = 1/3 . . . . . divide by -3
The y-coefficient in the first equation is -3 times the y-coefficient in the second equation, so adding 3 times the second equation to the first will eliminate y:
(4x -9y) +3(-2x +3y) = (1) +3(-1)
-2x = -2 . . . . . . simplify
x = 1 . . . . . . . . . divide by -3
The solution is (x, y) = (1, 1/3).
It is because both the dividend and the divisor are multiplied by 10, 100, 1000, or some other power of ten.
Answer:
2, 16
Step-by-step explanation:
(5,28) it's the correct answer
9514 1404 393
Answer:
72
Step-by-step explanation:
The triangles are said to be similar. (ΔNPQ ~ ΔRSQ) That means corresponding sides have the same ratio:
NP/RS = NQ/RQ = PQ/SQ = 24/32 = 21/28 = 3/4
This ratio, or scale factor, also applies to the perimeters of the two triangles.
perimeter NPQ / perimeter RSQ = 3/4
Using the given expressions for the perimeters, we have ...
(7x +2)/(10x -4) = 3/4
We can solve this equation in the usual way to find the value of x. Then we can use that value to find the perimeter of ΔNPQ.
4(7x +2) = 3(10x -4) . . . . . multiply both sides by 4(10x -4)
28x +8 = 30x -12 . . . . . eliminate parentheses
20 = 2x . . . . . . . . . . . add 12-28x to both sides
10 = x . . . . . . . . . . . divide both sides by 10
The perimeter of ΔNPQ is ...
7x +2 = 7(10) +2 = 72
The perimeter of triangle NPQ is 72 units.
