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:
18/3
Step-by-step explanation:
Took the test
Answer:
Step-by-step explanation:
Given 
, start by squaring both sides to work towards isolating 
:
Recall 
and 
:
Isolate the radical:
Square both sides:
Expand using FOIL and 
:
Move everything to one side to get a quadratic:
Solving using the quadratic formula:
A quadratic in 
has real solutions 
. In 
, assign values:
Solving yields:
Only works when plugged in the original equation. Therefore, 
is extraneous and the only solution is 
Answer:
Multiply 4 x 2 and the add the P in the front like this:
P = 8
HOPE IT HELPS, BE SAFE :3
Answer:
Number of jars can be filled from 15kg of the salt = 468 or 469 jars (Approx.)
Step-by-step explanation:
Given:
Amount of salt containing in jar = 32 gram
Total amount of salt in jar = 15 kg
Find:
Number of jars can be filled from 15kg of the salt
Computation:
Total amount of salt in jar = 15 kg
Total amount of salt in jar (in grams) = 15 x 1000 g
Total amount of salt in jar (in grams) = 15,000 g
Number of jars can be filled from 15kg of the salt = Total amount of salt in jar (in grams) / Amount of salt containing in jar
Number of jars can be filled from 15kg of the salt = 15,000 / 32
Number of jars can be filled from 15kg of the salt = 468.75
Number of jars can be filled from 15kg of the salt = 468 or 469 jars (Approx.)
