Evaluate the following expression when n=6. -6|n+3|

A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the

Alexandra [31]

Answer:

length=53 in

width= 23 in

Step-by-step explanation:

First, we know that each corner has now a square of 6 in long, so the heigth of the box will be of this size (as you can see in the picture attached). Then, the length and the width of the box would be the same as the piece, but with 12 in less. Therefore the equations to solve the problem are:

$h=6 in\\w=x-12\\l=x+30-12\\l=x+18\\\\V: volume of the box\\V=6*(x-12)*(x+18)\\2706=6x^{2}+36x-1296\\0=6x^{2}+36x-4002\\\\$

We factorize the 6 and we get:

$0=x^{2}+6x-667\\$

Finally we solve for x, and we get the initial dimensions of the piece of metal:

$x=23$ $l=30+x=30+23=53 in\\w=x= 23 in$

7 0

3 years ago

What are the coordinates of the point on the directed line segment from (-6, -6)(−6,−6) to (9, -1)(9,−1) that partitions the seg

GrogVix [38]

Answer:

(0, -4)

Step-by-step explanation:

The coordinates of the points from which the directed line segment extends = (-6, -6) to (9, -1)

The ratio the required point partitions the line = 2 to 3

The formula for finding the coordinate of a point that partitions a line AB into a ratio 'a' to 'b', where the coordinates of, A = (x₁, y₁) and B = (x₂, y₂) is given as follows;

$\left(\dfrac{a}{a + b} \times (x_1 - x_2)+ x_1, \ \dfrac{a}{a + b} \times (y_1 - y_2)+ y_1 \right)$