Answer:
The value of x=9 and value of y= -7
Step-by-step explanation:
We need to solve the matrix equation for x and y
We are given:
![\left[\begin{array}{cc}-2x&6\\1&-8\\\end{array}\right] +2\left[\begin{array}{cc}5&-1\\y&6\\\end{array}\right] =\left[\begin{array}{cc}-8&4\\-13&-13\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-2x%266%5C%5C1%26-8%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%2B2%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%26-1%5C%5Cy%266%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-8%264%5C%5C-13%26-13%5C%5C%5Cend%7Barray%7D%5Cright%5D)
First multiply 2 with terms inside the matrix
![\left[\begin{array}{cc}-2x&6\\1&-8\\\end{array}\right] +\left[\begin{array}{cc}10&-2\\2y&12\\\end{array}\right] =\left[\begin{array}{cc}-8&4\\-13&-13\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-2x%266%5C%5C1%26-8%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D10%26-2%5C%5C2y%2612%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-8%264%5C%5C-13%26-13%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Now adding matrices on left side
![\left[\begin{array}{cc}-2x+10&6-2\\1+2y&-8+12\\\end{array}\right] =\left[\begin{array}{cc}-8&4\\-13&-13\\\end{array}\right]\\\left[\begin{array}{cc}-2x+10&4\\1+2y&4\\\end{array}\right] =\left[\begin{array}{cc}-8&4\\-13&-13\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-2x%2B10%266-2%5C%5C1%2B2y%26-8%2B12%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-8%264%5C%5C-13%26-13%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-2x%2B10%264%5C%5C1%2B2y%264%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-8%264%5C%5C-13%26-13%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Now both sides are equal , so we can say that
Solving equations and finding values of x and y
Finding value of x
Finding value of y
So, value of x=9 and value of y= -7
Answer:
n(n+1)(n+5)/3
Step-by-step explanation:
there is no value, as we don't know n.
but we can create a summary formula/ function definition :
this is the sum for k = 1 to n of k×(k+3)
k×(k+3) = k² + 3k
so, the overall sum splits into the sum of k² for k=1 to n, and the sum of 3k for k=1 to n.
and the sum of 3k is 3 times the sum of k for k=1 to n.
Σk² for k=1 to n = [n(n+1)(2n+1)]/6
Σk for k=1 to n = n(n+1)/2
3×Σk for k=1 to n = 3×n(n+1)/2
so, we have a function formula
n(n+1)(2n+1)/6 + 3n(n+1)/2 = n(n+1)(2n+1)/6 + 9n(n+1)/6 =
= n(n+1)(2n+1+9)/6 = n(n+1)(2n+10)/6 = n(n+1)(n+5)/3
So I went ahead and divided up the figure so that you would understand what I'm going to tell you. Let's start with the red rectangle.
The distance from point R to point I is 6 units and the distance from Point R to point S is 5 units. 6*5 = 30 so that red rectangle has an area of 30 units
Now let's calculate triangle AVI. Area of a triangle is Base * Height. The base is 1 and the height is 5 which means the area of triangle AVI is 5.
Next, triangle ALT. From Point A to point L is 4 unit. From Point L to point T is 3 units. 4*3 is 12. So triangle ALT has an area of 12.
Triangle TSI. From Point T to point L is 3 units. From Point L to X is 2. Triangle TSI has an area of 6.
Now we add all of them up. 30+5+12+6 = 53. In total, RSTUV has an area of 53
Factor by grouping because there are 4 Terms
Answer: 165in^{2}[/tex]
Step-by-step explanation:
rectangle : L x W
= 8 x 15
= 120in
triangle: A = 
=
=45in
total area: 120+45= 
