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motikmotik
2 years ago
7

Find the value of x. Round the length to the nearest tenth.

Mathematics
1 answer:
elena-s [515]2 years ago
4 0

Answer:

The answer is. 5 cause 40÷8=5

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Year 1960 1975 1990 2005 2020 (est.) Population P(t) 200,000 240,000 288,000 345,600 414,720 According to the data, what would t
Leno4ka [110]
The correct answer is Choice A) 367,274.

The chart for this data starts in the year 1960. We are looking for the population during year 2010. That is 50 years later.

To find the answer, just input 50 for t in the equation.

P(50) = 200(1.01223)^50
5 0
3 years ago
A circle with a diameter of 10 inches has a circumference of a square, what is the length of each side of the square? ​
Veronika [31]

The circumference is πd, and the diameter is 10, so the circumference is 10π. All sides of a square are equal, so the length of each side is 10π/4, which is 2.5π.

The length of each side of the square is 2.5π  

7 0
3 years ago
Plsssssss can someone help me
77julia77 [94]

Answer:

2^3 = 8

Step-by-step explanation:

2*2*2 = 8

16 - 8 = 8

8 / 2 = 4

4 + 9 = 13

13 may be your answer

5 0
2 years ago
Read 2 more answers
Find all the zeros of the equation x^4-6x^2-7x-6=0 Explain please.
Alina [70]
<h3>Answer:</h3>
  • zeros are {-2, 3, (-1±i√3)/2}
<h3>Step-by-step explanation:</h3>

I like to look at a graph of the function to see where the zeros might be. Here, there are x-intercepts at x=-2 and x=3. These can be factored out using synthetic division to find the factorization to be ...

... (x +2)(x -3)(x² +x +1) = 0

By completing the square, using the quadratic formula, or by looking at the graph of it, the complex roots of the quadratic factor can be found to be ...

... x = (-1 ±i√3)/2

_____

The second attachment shows my synthetic division. The first division takes out the root x=3 to give a quotient of x³ +3x² +3x +2. The second division takes out the root -2 to give the quotient of x² +x +1. (You can see that I tried -1 as a root first.)

The graph shows both the quartic and the quadratic factor of it. The latter has a leading coefficient of 1 and a vertex at (-1/2, 3/4), so you know the complex roots are -1/2 ±i√(3/4).

_____

<em>From the beginning</em>

There is only a very complicated formula for the roots of a quartic equation, so these are usually solved by machine or by some form of trial and error (iteration). There are some helps, like Descarte's Rule of Signs, and the Rational Root theorem.

Here, the former looks at the one sign change in the coefficients to tell you there will be 1 positive real root. Changing the sign of the odd-degree terms makes there be 3 sign changes, so there will be 3 or 1 negative real roots. Thus, we're assured at least two real roots, one of each sign.

We can look at the constant term to find the y-intercept to be -6. We can add the coefficients to find the value of the function is -18 for x=1, so the positive real root is larger than 1.

The Rational Root theorem says any rational roots will be factors of 6, the constant term. Choices are 1, 2, 3, 6. We have already eliminated 1 as a possibility, and we consider it unlikely that 6 will be a root. (The 4th power overwhelms the other terms in the function.) We tried 2 and found it doesn't work (this was before we graphed the function). The attached division result shows that 3 is a root, as does the graph.

Once you get down to a quadratic, you can find the remaining roots in the usual way. Because it is so simple to read them from the graph, we decided to graph the quadratic factor.

_____

<em>Comment on terminology</em>

"root" and "zero" are essentially the same thing when the function is equated to zero, as here. The terms refer to the value(s) of x that make the polynomial function evaluate to zero.

8 0
3 years ago
What is the volume of this triangular prism?
Liula [17]

Answer:

5676.16 cm^3

Step-by-step explanation:

The volume of any prism is given by the formula ...

V = Bh

where B is the area of one of the parallel bases and h is the perpendicular distance between them. Here, the base is a triangle, so its area will be ...

B = 1/2·bh

where the b and h in this formula are the base and height of the triangle, 28 cm and 22.4 cm.

Then the volume is ...

V = (1/2·(28 cm)(22.4 cm))·(18.1 cm) = 5676.16 cm^3

_____

You will note that this is half the product of the three dimensions, so is half the volume of a cuboid with those dimensions. Perhaps you can see that if you took another such prism and placed the faces having the largest area against each other, you would have a cuboid of the dimensions shown.

4 0
3 years ago
Read 2 more answers
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