If alpha and beta are the zeroes of the polynomial 6x2+x-2 find the value og alpha/beta + beta/alpha

Answers

Answer 1

Answer: $6x^2+x-2=6x^2+4x-3x-2=2x(3x+2)-1(3x+2)\n\n=(3x+2)(2x-1)\n\n3x+2=0\to x=-(2)/(3)\n\n2x-1=0\to x=(1)/(2)\n\n\alpha=-(2)/(3);\ \beta=(1)/(2)\n\n(\alpha)/(\beta)+(\beta)/(\alpha)=(-(2)/(3))/((1)/(2))+((1)/(2))/(-(2)/(3))=-(2)/(3)\cdot(2)/(1)-(1)/(2)\cdot(3)/(2)=-(4)/(3)-(3)/(4)\n\n=-(16)/(12)-(9)/(12)=-(25)/(12)=-2(1)/(12)$

$use\ Vieta's\ formula:\n\n(\alpha)/(\beta)+(\beta)/(\alpha)=(\alpha^2+\beta^2)/(\alpha\beta)=(\alpha^2+2\alpha\beta+\beta^2-2\alpha\beta)/(\alpha\beta)=((\alpha+\beta)^2-2\alpha\beta)/(\alpha\beta)=((\alpha+\beta)^2)/(\alpha\beta)-2\n\n\alpha+\beta=(-b)/(a);\ \alpha\beta=(c)/(a)\n\n((\alpha+\beta)^2)/(\alpha\beta)-2=(\left((-b)/(a)\right)^2)/((c)/(a))-2=(b^2)/(a^2)\cdot(a)/(c)-2=(b^2)/(ac)-2$

$6x^2+x-2\n\na=6;\ b=1;\ c=-2\n\n(\alpha)/(\beta)+(\beta)/(\alpha)=(1^2)/(6\cdot(-2))-2=(1)/(-12)-2=-2(1)/(12)$

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What are the possibilities of getting a total score that is prime, square and greater than 7?

Answers

See the solution in the pdf file attached. Please, let me know if it is satisfactory for you.

Calculate the following total weekly wages:a) 38 hours at $22.10 per hour, plus 2 hours at time-and-a-half
b) 37 hours at $18.32 per hour, plus 3 hours at time-and-a-half and 2 hours at double time

Answers

So we would multiply 22.10 times 38, which is $839.00, then multiply 22.10 times the two extra hours which is $44.20, and then you'll divide 22.10 in half to find out how much it would be in a HALF hour, which is $11.05, and add all of those answers and your final answer for A. would be $894.25.

We would do the same as above for B., but only 2 hours at double would be 4 hours, and your final answer would be $815.24.

I hope I helped! =D

1/2x +31/2y=
Please help I have only till 3 pm

Answers

Answer: $(x)/(2)$ + $(31y)/(2)$

Step-by-step explanation:

1) Combine multiplied terms into a single fraction.

$(1)/(2)$ x + $(31)/(2)$ ⋅ y

2) Multiply the equation by 1.

1x/2+ 31/2 ⋅ y

x/2 + 31/2 ⋅ y

3) Combine multiplied terms into a single fraction.

x/2 + 31/2 y

x/2 + 31y/2

4) Solution

x/2 + 31y/2

ladt month you used 125 minutes and your bill was $37.50. this month you used 175 minutes. how much was will your home phone bill be this month

Answers

Answer: $52.5

Step-by-step explanation:

Given : Last month you used 125 minutes and your bill was $37.50.

i.e. Charges for each minute used = $(37.50)/(125)=\$0.3$

i.e. it charges $0.3 for each minute home phone used.

If this month you used 175 minutes.

Then , your this month's home phone bill will be :-

$175*0.3=\$52.5$

Hence, you month home phone bill will be $52.5 .

so 37.50/125=0.3

0.3*175=52.5

so his bill is $52.50

PLEASE HELP!!!The equation for the line of best fit is shown below.

Y=5/6 x+ 10

Based on the line of best fit, if an employee works at a company for six years, how much vacation time will he or she accrue?
A.
20 days
B.
15 days
C.
13 days
D.
6 days

Answers

  y = ⁵/₆x + 10
  y = ⁵/₆(6) + 10
  y = 5 + 10
  y = 15
(x, y) = (6, 15)

The answer is B.

The charge of ISD from Biratnagar to Tokyo is Rs 125 for the first 3 minutes and Rs 15 for every additional 10 seconds. If a man made a call from Biratnagar to his friend in Tokyo and paid Rs 305, how long did he make a call

Answers

We know he talked for over 3 minutes since the total is 305 which is > 125 (the cost of 3 minutes). The remaining amount he paid is 305-125= 180. He was charged 15 per 10 seconds which amounted to 180. 180/15=12 which means he was charged 12 times. Each time charged it was because he took 10 seconds so in total he took 12x10= 120 second. That’s 2 minutes. The two minutes he was charged 15s plus the first 3 minutes he was charged 125 is 5 minutes. We can plug in the numbers to make sure we are right. If he talked for 5 minutes then we know for the first three he was charged 125 and the additional two he was charged 15s (s representing 10 seconds). We can put the 125 aside for now to figure out the 15s. If he took two minutes then he took 120 seconds. Divide that by 10 because he’s getting charged per 10 seconds not per second so that’s 12. 15(12) is 180. 125 + 180 is 305

*** he took five minutes talking on the phone***

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