4×+7y=-12 __ -4x-y=-12 ________ 0x+6y=-24 , so you eleminated by it self 6y/6=-24/6 , you get : y=-4 and then you plug in 4x+7(-4)=-12 , that's your answer 4x-28 =-12 , you divided in both side 4x=-12+28 , 4x=16 , and then x=16/4 =4 , so x=4
The equation to represent the area of the triangle would be:
y = 1/2(x²) - (7/2)x
The equation to represent the perimeter of the triangle would be:
y = 3x - 6
The solutions to the system would be (12, 30) or (1, -3). The only viable solution is (12, 30).
Explanation
The area of a triangle is found using the formula
A = 1/2bh
For our triangle, b = x and h = x-7, so we have:
A = 1/2(x)(x-7)
A = 1/2(x²-7x)
A = 1/2(x²) - (7/2)x
We will replace A with y, so we have:
y = 1/2(x²) - (7/2)x
The perimeter of a triangle is found by adding together all sides, so we have:
P = (x-7) + x + (x+1)
Combining like terms we get:
P = 3x - 6
We will replace P with y, so we have:
y = 3x - 6
Since both equations have y isolated on one side, it will be easy to use substitution to solve the system:
3x - 6 = 1/2(x²) - (7/2)x
It's easier to work with whole numbers, so we will multiply everything by 2:
6x - 12 = x² - 7x
We want all of the variables on one side, so we will subtract 6x:
6x - 12 - 6x = x² - 7x - 6x
-12 = x² - 13x
When solving quadratics, we want the equation equal to 0, so we will add 12:
-12+12 = x² - 13x + 12
0 = x² - 13x + 12
This is easy to factor, as there are factors of 12 that sum to -13; -12(-1) = 12 and -12+-1 = -13:
0 = (x-12)(x-1)
Using the zero product property, we know that either x-12=0 or x-1=0; therefore x=12 or x=1.
Putting these back into our equation for perimeter (the simplest one) we have:
y = 3(12)-6 = 36-6 = 30; (12, 30);
y = 3(1) - 6 = 3 - 6 = -3; (1, -3)
We cannot have a negative perimeter, so the only viable solution is (12, 30).
Answer:
- 32, - 26, - 20, - 14
Step-by-step explanation:
To find the first 4 terms , substitute n = 1, 2, 3, 4 into the rule
a₁ = 6(1) - 38 = 6 - 38 = - 32
a₂ = 6(2) - 38 = 12 - 38 = - 26
a₃ = 6(3) - 38 = 18 - 38 = - 20
a₄ = 6(4) - 38 = 24 - 38 = - 14
Simply state that it is a parallelogram according to the parallelogram theorm. If you need the segments here's an example (A ≈ B and C ≈ D) thats it!
Answer:
0.0048828125
Step-by-step explanation:
35/7168= 0.0048828125
