Which expression represents the completely factored form of 2x3 + x2 - 8x - 4?a (x2 - 4)(2x + 1)
6 (x - 2)2(2x - 1)
0 (x - 2)(x + 2)(2x - 1)
d (x-2)(x + 2)(2x + 1)

Answer: C. 6 zebra fish, 5 neon tetras. Is $21.60

Step-by-step explanation:

1.85 • 6 = 11.10

2.10 • 5 = 10.50

11.10 + 10.50 = 21.60

$21.60

Final answer:

In solving the question, we establish two equations based on the condition provided, including the ratios among men, women, and children. Solving the equation, we find out that there were 270 people at the concert.

Explanation:

This question relates to the mathematical concept of ratio and proportion as well as fraction.

According to the question, 2/5 of the attendees at the concert were men and men outnumbered children by 45. First, let's make the number of children, x. So, the number of men will be x + 45. Because 2/5 of the total attendees were men, set up the equation: 2/5 * Total = x + 45.

There were 3 times as many women as children, thus the number of women will be 3x. So, the total number of people in the concert is the sum of the men, women, and children, which is (x + 45) + 3x + x. Simplifying this, we get 5x + 45 = Total. Therefore, if we substitute (x + 45) for 2/5 of the total in our original equation, we have 2/5 * (5x + 45) = x + 45. Solving this equation, we get x = 45.

So, if we substitute x=45 into our total equation, we get Total = 5(45) + 45 = 270. Therefore, there were 270 people at the concert.

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This involves creating some equations.

First, these are what the letters I used stand for:

c = children

w = women

m = men

x = total population

Then, we must make an equation for each statement.

2/5x = m (2/5 of the people are men)

3c = w (there are 3 times as many women than children)

45+c = m (there are 45 more men than children)

Now, let's start plugging in our numbers:

x = all the men, women, and children

2/5(m+w+c) = m

2/5 (45+c +3c + c) = m     [Now simplify]

2/5 (45 + 5x) = m       [Now Distribute]

2/5(45) + (2/5)(5x) = m

2c + 18 = m    [Above we stated that there were the same amount as men as c +45]

2c + 18 = 45 +c     [Now set equal to c]

2c (-c) +18 = 45 +c (-c)

c+18 (-18) = 45 (-18)

c = 27

Now that we know that there was 27 children, we can plug 27 in for c in the other equations.

MEN = 27 + 45

WOMEN = 3(27)

CHILDREN = 27

Now add those three answers to find your total!

Answer:

A vertex on polygon ABCD and its corresponding vertex on polygon AGHBGHCGHDGH are always equidistant from the line of reflection. Each of the four line segments (, for example) is perpendicular to and cut in half by the line of reflection, . This means that   is a perpendicular bisector of those line segments.

Step-by-step explanation:

Given:

Given that the two sides of the triangle are x, 4.0 and 5.6

We need to determine the range of possible sizes for the side x.

Range of x:

The range of x can be determined using the triangle inequality theorem.

The triangle inequality theorem states that, "if any side of a triangle must be shorter than the other two sides added together".

Thus, applying the theorem, we have;

Also, the the triangle inequality theorem states that, "the third side must be also larger than the difference between the other two sides".

Thus, we have;

Thus, the range of possible values for x are

Final answer:

In accordance with the triangle inequality theorem, the range for the length of the third side (x) in a triangle with sides of 4.0 and 5.6 is greater than 1.6 but less than 9.6.

Explanation:

In the field of Mathematics, specifically geometry, to find the range of possible lengths of a side of a triangle, you need to understand the triangle inequality theorem. The triangle inequality theorem states that the length of a side of a triangle must be less than the sum of the lengths of the other two sides, but more than the absolute difference.

Given you have two sides, 4.0 and 5.6, the possible length for side x should be less than (4.0 + 5.6 = 9.6) and greater than the absolute difference (5.6 - 4.0 = 1.6). So, the range for side x should be 1.6 < x < 9.6.

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