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bonufazy [111]
2 years ago
5

Explain how the following terms are related: linear relationship, proportional relationship,

Mathematics
1 answer:
Alex777 [14]2 years ago
3 0
Numbers are related in all of them
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assume the substance has a half-life of 11 years and the initial amount is 126 grams.How long will it be until only 15 % remains
Mumz [18]
(126) times (1/2 to the x/11 power) = 15% times 126

(1/2) to the x/11 power = 0.15

Take the log of both sides :

(x/11) times log(1/2) = log(0.15)

Multiply both sides by 11 :

'x' times log(1/2) = 11 x log(0.15)

Divide both sides by " log(1/2) " :

x = 11 x log(0.15)/log(1/2) = <em><u>30.107 years</u></em> (rounded)

That's the time it takes for <em><u>any-size</u></em> sample of this substance
to decay to 15% of its original size.


5 0
2 years ago
What is 6y-3X=-18 written in slope-intercept form?
Schach [20]

Answer: B

Step-by-step explanation:

6 0
2 years ago
Whats the slope of (2,-5),(-6,5)​
Makovka662 [10]
The slope of the line with the points (2,-5) and (-6,5) is 5/-4 (or 10/-8).
3 0
2 years ago
The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotation
7nadin3 [17]
<span>It could be C. If the blade spends twice in a minute, it would be 30 seconds. 30=2pi/B=pi/15. </span>
6 0
2 years ago
Read 2 more answers
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
2 years ago
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