Mathematics, 22.04.2020 19:56 wyseguy8971

You are comparing phone plans. Q company charges a one time fee of $25 and then $3 per month. W company charges a one time fee of $60 and then $1 per month. How many months until the two companies have the same cost?

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Answer from: dairysoto9171

month one:

Q company = 31

W company = 61

month two:

Q company = 34

W company = 62

month three:

Q company = 37

W company = 63

month four:

Q company = 40

W company = 64

month five:

Q company = 43

W company = 65

month six:

Q company = 46

W company = 66

month seven:

Q company = 49

W company = 67

month eight:

Q company = 52

W company = 68

month nine:

Q company = 55

W company = 69

month ten:

Q company = 58

W company = 70

month eleven:

Q company = 61

W company = 71

month twelve:

Q company = 64

W company = 72

month thirteen:

Q company = 67

W company = 73

month fourteen:

Q company = 70

W company = 74

month fifteen:

Q company = 73

W company = 75

month sixteen:

Q company = 76

W company = 76

month seventeen:

Q company = 79

W company = 77

month eighteen:

Q company = 82

W company = 78

Step-by-step explanation:

month 16 is the answer

Answer from: Quest

Answer: f(x) = -2x^3 +3x^2 +11x -6see attachedan infinite number. since the magnitude of the leading coefficient is not specified, it may be any negative number. (we have chosen the smallest magnitude integer that makes all coefficients be integers.)step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.

Answer from: Quest

look at the picture.

$efgh\sim abcd\to2: 3$

ef : ab = 2 : 3

gf : cb = 2 : 3

gh : cd = 2 : 3

he : da = 2 : 3

∠a ≅ ∠e

∠b ≅ ∠f

∠c ≅ ∠g

∠d ≅ ∠h

$6: 3x=2: 3\to\dfrac{6}{3x}=\dfrac{2}{3}\to\dfrac{2}{x}=\dfrac{2}{3}\to2x=(2)(3)\to x=3$

use pythagorean theorem:

$a^2=8^2+(2\cdot3)^2\\\\a^2=64+36\\\\a^2=100\to a=\sqrt{100}\to a=10\ cm$

the length of the abcd trapezoid sides:

|ab| = 3 cm

|bc| = 10 cm

|cd| = 3(3) cm = 9 cm

|da| = 8 cm

the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm

the ratio of perimeters of the tarapezoids is equal 2 : 3.

$p_{efgh}: p_{abcd}=2: 3\to\dfrac{p_{efgh}}{p_{abcd}}=\dfrac{2}{3}$

substitute:

$\dfrac{p_{efgh}}{30}=\dfrac{2}{3}$ cross multiply

$3p_{efgh}=(30)(2)$ divide both sides by 3

$p_{efgh}=20\ cm$

$p_{abcd}=30\ cm\\\\p_{efgh}=20\ cm$

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