Answer:
D) 65
Step-by-step explanation:
The formula for direct variation is
y = kx
where k is the constant of variation.
If we know y=32.5 and x=5, we can substitute in to calculate k
32.5 = k * 5
Divide each side by 5
32.5/5 = k
6.5 = k
So the equation is
y = 6.5k
Given x =10
y = 6.5*10
y = 65
Answer:
C. T is not one-to-one because the standard matrix A has a free variable.
Step-by-step explanation:
Given

Required
Determine if it is linear or onto
Represent the above as a matrix.
![T(x_1,x_2,x_3) = \left[\begin{array}{ccc}1&-5&4\\0&1&-6\\0&0&0\end{array}\right] \left[\begin{array}{c}x_1&x_2&x_3\end{array}\right]](https://tex.z-dn.net/?f=T%28x_1%2Cx_2%2Cx_3%29%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-5%264%5C%5C0%261%26-6%5C%5C0%260%260%5Cend%7Barray%7D%5Cright%5D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx_1%26x_2%26x_3%5Cend%7Barray%7D%5Cright%5D)
From the above matrix, we observe that the matrix does not have a pivot in every column.
This means that the column are not linearly independent, & it has a free variable and as such T is not one-on-one
Answer: (use distributive property then add the like terms)
3(2p + 4) - (3p - 4) = 43
6p + 12 - 3p - 4 = 43
3p - 8 = 43
Answer:
76cm^2
Step-by-step explanation:
Separate the shape into two different rectangles. Then add the area of the rectangles together.
4 x 4 = 16
6 x 10 = 60
16 + 60 = 76