M IF THE VOLUME OF THE BOX BELOW IS
x3 + 6x2 + 9x + 4
AND THE WIDTH OF THE BOX IS x + 4,
THEN FIND THE LENGTH AND HEIGHT OF
THE BOX

The length of the box is (x + 1)

The height of the box is (x + 1)

Step-by-step explanation:

The given function representing the volume of the box is presented as follows;

V = x³ + 6·x² + 9·x + 4

The function representing the width of the box, W = x + 4

Therefore, we have;

(x³ + 6·x² + 9·x + 4)/(x + 4) = x² + 2·x + 1

x³ + 4·x²

     2·x² + 9·x + 4

     2·x² + 8·x

                  x + 4

Therefore, we have;

(x³ + 6·x² + 9·x + 4) = (x + 4) × (x² + 2·x + 1) = (x + 4) × (x + 1) × (x + 1)

(x³ + 6·x² + 9·x + 4) = (x + 4) × (x + 1) × (x + 1)

The width of the box = (x + 4)

The length of the box = (x + 1)

The height of the box = (x + 1).

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.