Simon has a certain length of fencing to enclose a rectangular area. The function

What is the volume of the triangular prism? A triangular prism. The base of the triangular face is 5.4 centimeters and the heigh

IceJOKER [234]

Answer:

The volume of the triangular prism is 51.84 cm^3.

Step-by-step explanation:

The formula of the volume of a prism is:

V = Ah

where:

V = Volume of prism

A = Area of uniform cross-section or base of prism

h = Height of prism = 6 cm

We can substitute the information given in the problem into this formula.

To find A, we need to find the area of the triangular base.

A = bh / 2

where:

b = Base of triangle = 5.4 cm

h = Perpendicular height of triangle = 3.2 cm

We can substitute the information given in the problem into this formula.

A = ( 5.4 × 3.2 ) / 2

A = 17.28 / 2

A = 8.64 cm^2

Substitute the value of A into the original volume of a prism formula with the other information given in the problem.

V = Ah

V = ( 8.64 ) ( 6 )

V = 51.84 cm^3

7 0

4 years ago

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y <

shepuryov [24]

Answer:

See explanation

Step-by-step explanation:

You have to graph the system of inequalities presented as

$\left\{\begin{array}{l}y$

Part A:

1. Draw a dotted line $y=4x-2$ (dotted because the sign < is without notion "or equal to"). Select one of two regions by substituting the coordinates of origin into inequality:

$0$

Since this inequlity is false, the origin doesn't belong to the shaded region, so you have to shade that part which doesn't contain origin (red part in attached diagram).

2. Draw a solid line $y=-\frac{5}{2}x-2$ (solid because the sign ≥ is with notion "or equal to"). Select one of two regions by substituting the coordinates of origin into inequality:

$0\ge -\frac{5}{2}\cdot 0-2\\ \\0\ge -2$

Since this inequlity is true, the origin belongs to the shaded region, so you have to shade that part which contains origin (blue part in attached diagram).

The intersection of these two regions is the solution area.

Part B:

Plot point (-2,-2). Since this point doesn't belong to the solution area, this is not a solution of the system of two inequalities. You can check it mathematically - substitute x=-2 and y=-2 into the system:

$\left\{\begin{array}{l}-2$

Both inequalities are false, so (-2,-2) doesn't belong to the solution area.

3 0

3 years ago

Answer quick please.

pickupchik [31]

Answer:

4

1×2=2×2=4 so that is how the answer is reached

7 0

3 years ago

Read 2 more answers

Suppose that two teams are playing a series of games, each of which is independently won by team A with probability p and by tea

Lady_Fox [76]

Answer:

4 games played = 1/56

5 games played = 5/56

6 games played = 15/56

7 games played = 35/56

Step-by-step explanation:

The probability of each time winning is 0.5

So there are a couple of ways the series could go.

Team A could win all first 4 matches. We can depict this as A-A-A-A
Team A could win 4, while having lost 1. Lets depict this a A-B-A-A-A
Team A could win 4, while having lost 2. A-B-B-A-A-A
Team A could win 4, while having lost 3. A-B-B-B-A-A-A

These 4 possibilities could be repeated with B winning as well. It should be noted that these are the only ways for the series to end. We find the number of permutations of each possibility above to find their probability.

I advise you to study 'how to permute identical objects' for this.

These permutations are stated below:

1. 4!/4! = 1

2. $\frac{5!}{4! * 1!}$ = 5