Answer:
Step-by-step explanation:
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:
1.5789... is the interest rate
Step-by-step explanation:
200 down payment
1320. = 55 times 24 monrhs
----------
1520.00 total paid in 2 years
-1200. original price
---------
320. interest paid to finance company
Option b) 1960 is the total number of hours the electrician worked.
<u>Step-by-step explanation:</u>
It is given that, the full-time electrician will work 40 hours per week.
So, we need to know the total number of hours he could work in twelve months which is one year.
Therefore, one year has a total of 365 days.
<u>To find the number of weeks in twelve months :</u>
Number of weeks = Total days in one year / 7 days of week
⇒ 365 / 7
⇒ 52.14 (approximately 52 weeks)
The number of weeks in twelve months is 52 weeks.
Now, of this 52 weeks, the three weeks are given as vacation.
The total number of weeks the electrician worked = 52 weeks - 3 weeks
⇒ 49 weeks.
The electrician worked for 49 weeks.
To calculate the total number of hours he worked = 49 weeks × 40 hours
⇒ 1960 hours.
Therefore, the total number of hours the electrician worked is 1960 hours which is option b).
Answer:
B
) Negative
Step-by-step explanation:
Given the expression 3xy
when x>0 and y<0
The value of the expression 3xy will be negative.
This is because the product of a positive and negative number will always be negative.
For illustration,
Let x=5>0 and y=-5<0
3xy=3(5)(-5)=-75
NOTE:
