its a sqaure so the angles are 90 degress each.
90 - 38 = 52
answer: C. 52
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:
24
Step-by-step explanation:
$2 divided by 4 equals 50 cents
50 cents per copy
$12 will get you 24 copies
Answer: Consistent and independent.
Step-by-step explanation:
We have the system of equations:
y = 4x - 4
y = -4x + 4.
Now, first let's define the terms used in the question.
consistent and independent: we have only one solution.
consistent and dependent: we have infinite solutions.
inconsistent: we do not have solutions.
Now, let's look at the system:
y = 4x - 4
y = -4x + 4.
Let's take the quotient between both the equations:
(y/y) = (4x - 4)/(-4x + 4)
1 = (4x - 4)/(-4x + 4)
let's see if we can solve this for x.
1*(-4x + 4) = 4x - 4
-4*x + 4 = 4x - 4
-4x - 4x = -4 - 4
-8*x = -8
x = -8/-8 = 1.
and to find the value of y, we can input this value of x in one of the equations:
y = 4*1 - 4 = 0.
Then we have only one solution, (1, 0).
(and will be the same if you input x in the other equation, as the right side is minus the right side of the first equation)
Then the system is consistent and independent.
