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pshichka [43]
3 years ago
8

Write the composite number for each prime factorization. You may wish to use a calculator.

Mathematics
1 answer:
tresset_1 [31]3 years ago
7 0

Only one of those is actually a prime factorization.  Demand better from your teacher.  Anyway, I think they're just asking us to take out the calculator and enter the multiplication into it.

5) 22 isn't prime, neither is 52.  Answer:  3432

6) 32 isn't prime.  Answer: 448

7) 33 isn't prime.  Answer: 165

8)  Finally a real prime factorization.  Answer: 106

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Apply The Remainder Theorem, Fundamental Theorem, Rational Root Theorem, Descartes Rule, and Factor Theorem to find the remainde
Over [174]

9514 1404 393

Answer:

  possible rational roots: ±{1/3, 2/3, 1, 4/3, 2, 3, 4, 6, 12}

  actual roots: -1, (2 ±4i√2)/3

  no turning points; no local extrema

  end behavior is same-sign as x-value end-behavior

Step-by-step explanation:

The Fundamental Theorem tells us this 3rd-degree polynomial will have 3 roots.

The Rational Root Theorem tells us any rational roots will be of the form ...

  ±{factor of 12}/{factor of 3} = ±{1, 2, 3, 4, 6, 12}/{1, 3}

  = ±{1/3, 2/3, 1, 4/3, 2, 3, 4, 6, 12} . . . possible rational roots

Descartes' Rule of Signs tells us the two sign changes mean there will be 0 or 2 positive real roots. Changing signs on the odd-degree terms makes the sign-change count go to 1, so we know there is one negative real root.

The y-intercept is 12. The sum of all coefficients is 22, so f(1) > f(0) and there are no positive real roots in the interval [0, 1]. Synthetic division by x-1 shows the remainder is 22 (which we knew) and all the quotient coefficients are all positive. This means x=0 is an upper bound on the real roots.

The sum of odd-degree coefficients is 3+8=11, equal to the sum of even-degree coefficients, -1+12=11. This means that -1 is a real root. Synthetic division by x+1 shows the remainder is zero (which we knew) and the quotient coefficients alternate signs. This means x=-1 is a lower bound on real roots. The quotient of 3x^2 -4x +12 is a quadratic factor of f(x):

  f(x) = (x +1)(3x^2 -4x +12)

The complex roots of the quadratic can be found using the quadratic formula:

  x = (-(-4) ±√((-4)^2 -4(3)(12)))/(2(3)) = (4 ± √-128)/6

  x = (2 ± 4i√2)/3 . . . . complex roots

__

The graph in the third attachment (red) shows there are no turning points, hence no relative extrema. The end behavior, as for any odd-degree polynomial with a positive leading coefficient, is down to the left and up to the right.

4 0
3 years ago
Rewrite this non-statistical question as a statistical question. How many minutes do I exercise each day?
stira [4]

Answer:

The statistical question should be

"how many minutes do I exercise on each day of the week" and "how many minutes do I exercise each day of the week whilst there is background music"

Step-by-step explanation:

Here we have the non statistical question, how many minutes do I exercise each day

We note that a statistical question is one in which there are are different variety answers, where the distribution and the inclination of the the answers is sought

Therefore, statistically, we should ask, "how many minutes do I exercise on each day of the week" or "how many minutes do I exercise each day of the week whilst there is background music".

8 0
3 years ago
5x+21+178/(x-7)<br> How do I solve for domain and range on this equation?
Luda [366]
The domain is easiest. You simply need to find the fractions, and exclude any X that makes the denominator zero. So in this case, your domain is everything except X=7.

For range, you are trying to find out what are the possible answers. Usually the best way to do this is to try x=infinity, and x=negative infinity, which here gives you answers of infinity and negative infinity. Since the function is almost continuous, I think your range is any real number.
3 0
3 years ago
What is the equation of a circle with center (-4,7) and a radius 6
s2008m [1.1K]

Answer:

( x +4)^2 + ( y-7)^2 = 36

Step-by-step explanation:

We can write the equation of a circle as

( x-h)^2 + ( y-k)^2 = r^2

where ( h,k) is the center and r is the radius

( x- -4)^2 + ( y-7)^2 = 6^2

( x +4)^2 + ( y-7)^2 = 36

7 0
3 years ago
Read 2 more answers
Mealworms are a healthy food for wild song birds. Adam buys a 3 oz container of mealworms for $7.35. Marco buys a 5 oz container
Artemon [7]

Answer: 5 oz

Step-by-step explanation:

you get more and for the price of 7.35 it’s not worth only getting three oz

3 0
3 years ago
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