Help me answer this question

2( 4x + 2) = 4x - 12(x-1)

aksik [14]

Answer:

$x=\frac{1}{2}$

Step-by-step explanation:

distribute 2 into (4x+2) and -12 into (x-1)

8x+4=4x-12x+12

combine like terms

8x+4=-8x+12

add -8x on both sides

8x+8x+4=12

16x+4=12

subtract 4 on both sides

16x=8

divide both sides by 16

x=1/2

hope this helps

8 0

3 years ago

Does anyone have the questions answered

nata0808 [166]

Answer:

no can you help me

Step-by-step explanation:

6 0

3 years ago

The base of a prism has n sides. Find the numbers of faces, edges, and

Harman [31]

Answers:

faces = n+2
edges = 3n
vertices = 2n

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Explanation:

Think of a hexagonal room with n = 6 walls, i.e. the floor is a hexagon with n = 6 sides. The floor and ceiling are parallel to each other, and congruent hexagons. That's 2 faces so far. Then we have another 6 faces to account for the walls. This gives 2+6 = 8 faces of a hexagonal prism.

In more general terms, a prism with a base of n sides will have 2 parallel and congruent base faces, and n walls or lateral faces. This gives n+2 total faces.

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Let's go back to the hexagonal prism. The floor has 6 sides to it, and so does the ceiling. We have 6+6 = 12 edges so far. Then we have another 6 edges where each of the rectangular walls meet up. That gives 12+6 = 18 edges total of this hexagonal prism room.

For any more general case, each base has n sides. That gives 2n sides so far for just the bases. Then add on another n for the lateral edges and we get 3n total edges.

--------------------------

Once again lets revisit the room with the hexagonal floor and ceiling. The floor has 6 vertices and the ceiling has the same vertex count. Therefore, this prism has 6+6 = 12 vertices.

For the general case, each base has n vertices. There are 2 such identical bases giving 2n vertices total.

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One way to check the answer:

We could use Euler's Polyhedron Formula which is

F+V-E = 2

where,

F = number of faces
V = number of vertices
E = number of edges

For the hexagonal prism we found

F = 8
V = 12
E = 18

Then notice how

F+V-E = 2

8+12-18 = 2

20-18 = 2

2 = 2

This confirms the formula works for a hexagonal prism.

Now let's check it for the more general case

We found earlier that,

F = n+2
V = 2n
E = 3n

So,

F+V-E = 2

n+2+2n-3n = 2

3n-3n+2 = 2

0n+2 = 2

0+2 = 2

2 = 2

This helps confirm the answer for any prism with the base of n sides.

4 0

2 years ago

Triangle ABC is equilateral. Find the height of BD

RideAnS [48]

Since ABC is equilateral, all 3 sides have equal length. side AC is 8 units since side BC is 8 units.

Line BD is placed in the middle, making D the midpoint of side AC.

knowing this information we can determine that the length of DC is 4 units (half of AC)

since triangle BDC is a right triangle, we can use the side lengths in the pythagorean theorem to find the length of BD

a²+b²=c² where a & b = legs of triangle , and c= hypotenuse (longest side)

we are given the hypotenuse and found one leg so we can plug our values into the equation to find the third

4² + b²= 8²

16 + b² = 64

b² = 48

b = $\sqrt{48}$

b= 4√3 or about 6.928 units

hope this helped

3 0

3 years ago

Find the distance between points (5,1) and (3,4) to the nearest tenth

Charra [1.4K]

Answer:

3.6 units (nearest tenth)

Step-by-step explanation:

distance formula

= $\sqrt{(x1 - x2)^{2} + (y1 - y2)^{2} }$

Thus, distance between the 2 points

= √[(5 - 3)² + (1 - 4)²]

= √[ 2²+ ( - 3)²]

= √13

= 3.6 units (nearest tenth)

5 0

3 years ago