Find the ratio of 500and 1km

Consider the expression 17x+8x+35.Which of these mathematical statements could be used to accurately describe the given expressi

Mrac [35]

3. The product of seventeen and a number, increased by the product of eight and the same number, increased by thirty/five.
4. Seventeen times a number plus eight times the same number plus thirty five

5 0

3 years ago

Which line is parallel to a line that has a slope of 3 and a y-intercept at (0, 0)?

anyanavicka [17]

we know that

If two lines are parallel , then their slopes are the same

we will proceed to calculate the slope of each line to determine the solution.

The formula to calculate the slope m between two points of the line is equal to

$m=\frac{(y2-y1)}{(x2-x1)}$

case N 1) line AB

Let

$A(-4,3)\\B(4,3)$

substitute the values

$m=\frac{(3-3)}{(4+4)}$

$m=\frac{(0)}{(8)}$

$m=0$

$0\neq 3$

therefore

The line AB is not the solution

vase N 2) line FG

Let

$F(-3,-1)\\G(3,-3)$

substitute the values

$m=\frac{(-3+1)}{(3+3)}$

$m=\frac{(-2)}{(6)}$

$m=-1/3$

$-1/3\neq 3$

therefore

The line EG is not the solution

case N 3) line CD

Let

$C(-3,0)\\D(3,2)$

substitute the values

$m=\frac{(2-0)}{(3+3)}$

$m=\frac{(2)}{(6)}$

$m=1/3$

$1/3\neq 3$

therefore

The line CD is not the solution

case N 4) line HJ

Let

$H(-1,-4)\\J(1,2)$

substitute the values

$m=\frac{(2+4)}{(1+1)}$

$m=\frac{(6)}{(2)}$

$m=3$

$3=3$

therefore

The line HJ is the solution

therefore

the answer is the option

line HJ

7 0

3 years ago

Read 2 more answers

Show that the sets of upper-triangular and lower-triangular matrices are subspaces of F n,n . Call them U and L respectively. Wh

soldi70 [24.7K]

Answer:

dim L = dim U = $\frac{n(n+1)}{2}$

Step-by-step explanation:

We can do it only for the lower-triangular matrices, the case of the upper-triangular matrices is similar. We might caracterice nxn the lower-triangular matrices, as the nxn matrices $A=(a_{ij})$ such that the entry $a_{ij}=0$ if i<j.

Now let $A=(a_{ij})$ and $B=(b_{ij})$ be two lower triangular matrices, now if

$C=A+\lambda B$ for some $\lambda \in \mathbb{F}$

then the entry $c_{ij}$ of C is equal to

$c_{ij}=a_{ij}+\lambda b_{ij}$

Now, if i<j, it must hold that $a_{ij}=0 \quad \text{and} \quad b_{ij}=0$ . Therefore, if this is the case we must have that $c_{ij}=0$ and so we get that C is also a lower triangular matrix. This showa that L is closed under sum and scalar multiplcation, hence it is a linear subspace.

To find the dimension, note that all the entries of a lower-triangular matrix over the diagonal must be equal to zero. However, each entry of the matrix under the diagonal and in the diagonal might be any element of $\mathbb{F}$ , any entry that can be choosen add up to the dimension of L, we n such elemnts for the first column, (n-1) for the second column, (n-2) for the third column etc.... Therefore,