Twice the difference of a number and 6 is equal to three times te sum of the number and 4. find the number.

-24

Step-by-step explanation:

Let the unknown number be x , therefore ; The difference between the number and 6 implies x - 6

Also , twice their difference implies 2 ( x - 6 )

The sum of the number and 4 implies : x + 4

three times their sum implies : 3 ( x + 4 )

Combining all together , we have

2 ( x - 6 ) = 3 ( x + 4 )

Expanding , we have

2x - 12 = 3x + 12

collecting the like terms , we have

2x - 3x = 12 + 12

-x = 24

multiply through by -, we have

x = -24

Check :

2 ( x - 6 ) will give

2 ( -24 - 6 )

= 2 (-30)

= -60

3 ( x+4) will give

3 ( -24 + 4 )

= 3 ( -20)

= -60

Therefore:

2( x- 6 ) = 3 ( x + 4 )

answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

step-by-step explanation:

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.