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).
If i read it right, it would just be 1 - 953. Depending on your grade (Around 3rd grade it would just be 952) Above that would be -952
Answer:
B). Graph B
Step-by-step explanation:
A Histogram is a graphic representation of data using bars varying in height as per the range of values.
In the given question, the second option correctly represents the data provided in the table using a histogram. It portrays the class ranging from 0.320 - 0.329 with an average of 1 in the first bar, from 0.330 - 0.339 with an average of 14 runs in the second bar, and moves so on till 0.360-0.369 correctly. The other options fail to portray the numerical distribution appropriately and hence, <u>option B</u> is the correct answer.
Answer:
a. 2 – 8 - [- 4 – (-6 + 3 -9)] X ( -10 ÷2) suprimir los signos de agrupacion
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given the function :
y=x³ - 3x² - 9x + 2. The largest and smallest values of the function at interval [-2, 4]
We substitute x values in the interval (-2 to 4) into the equation and solve for y
At x = - 2
y = (-2)³ - 3(-2)² - 9(-2) + 2 = 0
At x = - 1
y = (-1)³ - 3(-1)² - 9(-1) + 2 = 7
At x = 0
y = (-0)³ - 3(-0)² - 9(-0) + 2 = 2
At x = 1
y = (1)³ - 3(1)² - 9(1) + 2 = - 9
At x = 2
y = (2)³ - 3(2)² - 9(2) + 2 = - 20
At x = 3
y = (3)³ - 3(3)² - 9(3) + 2 = - 25
At x = 4
y = (4)³ - 3(4)² - 9(4) + 2 = - 18
Function is greatest at
