The reason is the gotter of the right angle is 12
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).
$0.15x>$5.00
x>33.3333
So if she sends or receives more than 33 text messages, she will be paying more than $5.00.
Answer:
Hence x = 60 and y = 50
e = 85 degrees
f = 158 degrees
Step-by-step explanation:
1) The sum of the interiror angle of the triangle is equal to the exterior
Given
Interior angles = y and 70
Exterior angle = 120 degrees
According to the law;
y + 70 = 120
y = 120-70
y = 50°
Sum of angle in the triangle is 180
x + y + 70 = 180
x + 50 + 70 = 180
x + 120 = 180
x = 180-120
x = 60
Hence x = 60 and y = 50
2) The sum of angles on a straight line is 180 degrees
40 + 55 + e = 180
95 + e = 180
e = 180 - 95
x = 85 degrees
3) Sum of angle at a point is 360 degrees
Hence 130 + 36.8 + 35.2 + f= 360
130 + 72 + f = 360
202 + f = 360
f = 360 - 202
f = 158 degrees
Answer:
Step-by-step explanation:
the formula for a circle which would be C = 2 \pi r
The 9.5*3.14 divide by two so 14.915
and this rounded would be 15.0 or 14.9 not too sure just pick whatever
