7/3 divide 2/3 = 3 1/2
i had this question last year in a math test
For this case we must find an expression equivalent to 
. To solve we follow the steps below:
We apply distributive property to the terms within the parenthesis taking into account that 
:
We add common terms taking into account that equal signs are added and the same sign is placed:
Answer:
Option C
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:
2.25 yards per quilt
Step-by-step explanation:
if you add up all the numbers u get 58.5. then divide this by 26 to get 2.25
Answer:
Step-by-step explanation:
<u>Given the data set of 15 where:</u>
- Mean = 7
- Median = 6
- Mode = 5
- The minimum is 1 and the maximum is 10
<u>As per given we conclude</u>
- The set will have 7 numbers before 6 and 7 numbers after
- Sum of 15 numbers is 15*7 = 105
- The most used number is 5
a) <u>Possible set is:</u>
- 1, 5, 5, 5, 5, 5, 5, 6, 9, 9, 10, 10, 10, 10, 10
b) <u>Add number 20, the set will be:</u>
- 1, 5, 5, 5, 5, 5, 5, 6, 9, 9, 10, 10, 10, 10, 10, 20
<u>The mean is different as we have now more numbers with different sum:</u>
- (105 + 20)/(15 + 1) = 125/16 = 7.8125
<u>The median is different now and moves to the right as 20 added to the far right:</u>
<u>The mode stays same as still most used number is 5:</u>
