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3 years ago

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There were 60 people on a bus. After 3 stops, the number of people decreased to 48. What was the percent of decrease in the numb

er of people on the bus?
A. 12%
B. 20%
C. 24%
D. 25%

2 answers:

JulsSmile [24]3 years ago

8 0

12% was decrease in the number of people in the bus

faltersainse [42]3 years ago

3 0

Answer:

I believe its 12%

Step-by-step explanation:

60-48=12 so 12%

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Step-by-step explanation:

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Step-by-step explanation:

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Use the quadratic formula to solve x^2 -3x - 5 = 0. Round to two decimal places.

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Answer:

$\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}$

$x=\frac{3+\sqrt{29}}{2},\:x=\frac{3-\sqrt{29}}{2}$

Step-by-step explanation:

Given the equation

$x^2\:-3x\:-\:5\:=\:0$

solving with the quadratic formula

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}$

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=1,\:b=-3,\:c=-5$

$x_{1,\:2}=\frac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \left(-5\right)}}{2\cdot \:1}$

$x_{1,\:2}=\frac{-\left(-3\right)\pm \sqrt{29}}{2\cdot \:1}$

separating the solutions

$x_1=\frac{-\left(-3\right)+\sqrt{29}}{2\cdot \:1},\:x_2=\frac{-\left(-3\right)-\sqrt{29}}{2\cdot \:1}$

solving

$x=\frac{-\left(-3\right)+\sqrt{29}}{2\cdot \:\:1}$

$=\frac{3+\sqrt{29}}{2\cdot \:1}$

$=\frac{3+\sqrt{29}}{2}$

also solving

$\:x=\frac{-\left(-3\right)-\sqrt{29}}{2\cdot \:\:1}$

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$=\frac{3-\sqrt{29}}{2}$

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$x=\frac{3+\sqrt{29}}{2},\:x=\frac{3-\sqrt{29}}{2}$

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3 years ago

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A(t)=.892t^3-13.5t^2+22.3t+579 how to solve this

Minchanka [31]

Answer:

t = (5 ((446 sqrt(3188516012553) - 827891226)^(1/3) - 204292 (-1)^(2/3) (3/(413945613 - 223 sqrt(3188516012553)))^(1/3)))/(223 6^(2/3)) + 1125/223 or t = 1125/223 - (5 ((-2)^(1/3) (223 sqrt(3188516012553) - 413945613)^(1/3) - 204292 (-3/(413945613 - 223 sqrt(3188516012553)))^(1/3)))/(223 6^(2/3)) or t = 1125/223 - (5 ((827891226 - 446 sqrt(3188516012553))^(1/3) + 204292 (3/(413945613 - 223 sqrt(3188516012553)))^(1/3)))/(223 6^(2/3))

Step-by-step explanation:

Solve for t over the real numbers:

0.892 t^3 - 13.5 t^2 + 22.3 t + 579 = 0

0.892 t^3 - 13.5 t^2 + 22.3 t + 579 = (223 t^3)/250 - (27 t^2)/2 + (223 t)/10 + 579:

(223 t^3)/250 - (27 t^2)/2 + (223 t)/10 + 579 = 0

Bring (223 t^3)/250 - (27 t^2)/2 + (223 t)/10 + 579 together using the common denominator 250:

1/250 (223 t^3 - 3375 t^2 + 5575 t + 144750) = 0

Multiply both sides by 250:

223 t^3 - 3375 t^2 + 5575 t + 144750 = 0

Eliminate the quadratic term by substituting x = t - 1125/223:

144750 + 5575 (x + 1125/223) - 3375 (x + 1125/223)^2 + 223 (x + 1125/223)^3 = 0

Expand out terms of the left hand side:

223 x^3 - (2553650 x)/223 + 5749244625/49729 = 0

Divide both sides by 223:

x^3 - (2553650 x)/49729 + 5749244625/11089567 = 0

Change coordinates by substituting x = y + λ/y, where λ is a constant value that will be determined later:

5749244625/11089567 - (2553650 (y + λ/y))/49729 + (y + λ/y)^3 = 0

Multiply both sides by y^3 and collect in terms of y:

y^6 + y^4 (3 λ - 2553650/49729) + (5749244625 y^3)/11089567 + y^2 (3 λ^2 - (2553650 λ)/49729) + λ^3 = 0

Substitute λ = 2553650/149187 and then z = y^3, yielding a quadratic equation in the variable z:

z^2 + (5749244625 z)/11089567 + 16652679340752125000/3320419398682203 = 0

Find the positive solution to the quadratic equation:

z = (125 (223 sqrt(3188516012553) - 413945613))/199612206

Substitute back for z = y^3:

y^3 = (125 (223 sqrt(3188516012553) - 413945613))/199612206

Taking cube roots gives (5 (223 sqrt(3188516012553) - 413945613)^(1/3))/(223 2^(1/3) 3^(2/3)) times the third roots of unity:

y = (5 (223 sqrt(3188516012553) - 413945613)^(1/3))/(223 2^(1/3) 3^(2/3)) or y = -(5 (-1/2)^(1/3) (223 sqrt(3188516012553) - 413945613)^(1/3))/(223 3^(2/3)) or y = (5 (-1)^(2/3) (223 sqrt(3188516012553) - 413945613)^(1/3))/(223 2^(1/3) 3^(2/3))

Substitute each value of y into x = y + 2553650/(149187 y):

x = (5 ((223 sqrt(3188516012553) - 413945613)/2)^(1/3))/(223 3^(2/3)) - 510730/223 (-1)^(2/3) (2/(3 (413945613 - 223 sqrt(3188516012553))))^(1/3) or x = 510730/223 ((-2)/(3 (413945613 - 223 sqrt(3188516012553))))^(1/3) - (5 ((-1)/2)^(1/3) (223 sqrt(3188516012553) - 413945613)^(1/3))/(223 3^(2/3)) or x = (5 (-1)^(2/3) ((223 sqrt(3188516012553) - 413945613)/2)^(1/3))/(223 3^(2/3)) - 510730/223 (2/(3 (413945613 - 223 sqrt(3188516012553))))^(1/3)

Bring each solution to a common denominator and simplify:

x = (5 ((446 sqrt(3188516012553) - 827891226)^(1/3) - 204292 (-1)^(2/3) (3/(413945613 - 223 sqrt(3188516012553)))^(1/3)))/(223 6^(2/3)) or x = -(5 ((-2)^(1/3) (223 sqrt(3188516012553) - 413945613)^(1/3) - 204292 ((-3)/(413945613 - 223 sqrt(3188516012553)))^(1/3)))/(223 6^(2/3)) or x = -(5 ((827891226 - 446 sqrt(3188516012553))^(1/3) + 204292 (3/(413945613 - 223 sqrt(3188516012553)))^(1/3)))/(223 6^(2/3))

Substitute back for t = x + 1125/223:

Answer: t = (5 ((446 sqrt(3188516012553) - 827891226)^(1/3) - 204292 (-1)^(2/3) (3/(413945613 - 223 sqrt(3188516012553)))^(1/3)))/(223 6^(2/3)) + 1125/223 or t = 1125/223 - (5 ((-2)^(1/3) (223 sqrt(3188516012553) - 413945613)^(1/3) - 204292 (-3/(413945613 - 223 sqrt(3188516012553)))^(1/3)))/(223 6^(2/3)) or t = 1125/223 - (5 ((827891226 - 446 sqrt(3188516012553))^(1/3) + 204292 (3/(413945613 - 223 sqrt(3188516012553)))^(1/3)))/(223 6^(2/3))

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