x + y = 42, xy = 108 then what is x and y. Is there any (non-quadratic)formula for finding this instead of the process of elimination

Answers

Answer 1

Answer:

when x = 39.25, y = 2.75

when x = 2.75, x = 39.25

Step-by-step explanation:

use substitution method

x+y = 42 ------ (1)

xy = 108 ------ (2)

from (1) ,

x+y = 42

y = 42-x ------ (3)

substitute (3) into (2)

xy = 108

x( 42-x ) = 108

42x - x² = 108

-x² + 42x - 108 = 0

x² - 42x + 108 = 0

use the following formula to solve the value of x:

[tex]i) \: x = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \: \\ ii) \: x = \frac{ - b - \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

a = 1

b = -42

c = 108

[tex]i) \: x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

[tex]x = \frac{ - ( - 42) + \sqrt{( - 42) {}^{2} - 4(1)(108)} }{2(1)} [/tex]

[tex]x = \frac{42 + \sqrt{1764 - 432} }{2} [/tex]

[tex]x = \frac{42 + \sqrt{1332} }{2} [/tex]

[tex]x = \frac{42 + 6 \sqrt{37} }{2} [/tex]

[tex]x = 21 + 3 \sqrt{37} [/tex]

[tex]x = 39.25[/tex]

[tex]ii) \: x \: \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

[tex]x = \frac{ - ( - 42) - \sqrt{( - 42) {}^{2} - 4(1)(108} }{2(1)} [/tex]

[tex]x = \frac{42 - \sqrt{1764 - 432} }{2} [/tex]

[tex]x = \frac{42 - \sqrt{1332} }{2} [/tex]

[tex]x = \frac{42 - 6 \sqrt{37} }{2} [/tex]

[tex]x = 21 - 3 \sqrt{37} [/tex]

[tex]x = 2.75[/tex]

the 2 values of x are x = 39.25 and x = 2.75

substitute x = 39.25 into (3)

y = 42-x

y = 42-39.25

y = 2.75

substitute x = 2.75 into (3)

y = 42-x

y = 42-2.75

y = 39.25

when x = 39.25, y = 2.75

when x = 2.75, x = 39.25


Related Questions

Find the value of x

please help asap!!!​

Answers

Answer: 108

Step-by-step explanation:

x = 108

Help PLEASE. 15 pts

Which equations illustrate the zero property of multiplication? Select ALL that apply.
[tex] \frac{1}{3} \times 3 - 3 = 4[/tex]
[tex] \frac{1}{2} + 2 - 2 = \frac{1}{2} [/tex]
[tex]0 \times \frac{1}{9} \times 9 = 0[/tex]
[tex]x - 5 + 5 = x[/tex]
[tex] \frac{1}{3}(9 + 3) = 3 + 1 [/tex]

Answers

Answer:

0* 1/9*9=0

Step-by-step explanation:

The zero property of multiplication states that any non-zero number multiplied by zero will equal zero.

it can't be the first one, since there's no zero in it, and the answer isn't zero

it can't be the second one since there's no multiplication illustrated.

The third one is an option, since there is a zero and it's being multiplied by two non-zero numbers, and the answer is 0

the fourth one isn't an option since there's no multiplication

the fifth one isn't an option since there is no 0's there.

hope this helps!

A factory is going to hire 33 new employees. There are 79 applicants. Which
choice represents the ratio of new hires to applicants?

Answers

Answer:

33:79

Step-by-step explanation:

We are told that a factory is going to hire 33 new employees.

and the total applicants is 79

In this problem, we want to represent the situation as a ratio of new hires to applicants

Since the question says  new hires to applicants

Hence, the ratio will be

33 to 79

or

33/79, we can simplify this as

33:79

A fireman's ladder leaning against a house makes an angle of 50° with the ground. How long is the ladder if the ladder is 8 feet from the foot of the house?​

Answers

The ladder would be 12.4 feet hope that helps

B is between A and C. If AB = 2x + 1, BC = x, and AC = 22. Find AB.

Answers

Answer:

15

Step-by-step explanation:

AB + BC = AC

2x + 1 + x = 22

3x + 1    = 22

        3x = 22 -1

        3x = 21

         x = 21/3

   x = 7

AB = 2*7 +1

      = 14 + 1

      = 15

HELP ME PLEASE
Mr. Parke made snacks in separate gift bags. He gave one each to the 86 seventh grade students going on the field trip. Then he gave 17 bags to the students in Mrs. Mark's class for decorating the trophy cases. Next he gave 11 to the students in Mrs. Green's class for helping during the school play. Mr. Parke had 11 snacks left. How many snacks did he make?

Answers

Answer:

125 snacks

Step-by-step explanation:

just add every number

Answer:

125

Step-by-step explanation:

Jill spent half of the money she saved to buy a video game. To earn more money her parents let her wash the car and do other chores for $20. How much money did she have saved if she now has $50.

VALID ANSWERS ONLY OR YOU GET REPORTED.

Answers

Answer:

Step-by-step explanation:

She has $50 and before she earn $20 had $50-$20=$30

so she had $60

payed for video game $30 now has $30

earn from parents $20 now has $50

If she would not bye the video game she would have had $80 saved


The equation for line p can be written as y = 1/4x + 3. Line q includes the point (-1, 5) and is
perpendicular to line p. What is the equation of line q?

Answers

Answer:

[tex]y=-4x+1[/tex]

Step-by-step explanation:

To get this, use the following steps:

1) Knowing that line q is perpendicular to the line p, the slope of line q must be the negative reciprocal of the slope of line p. Thus the slope is [tex]-(\frac{1}{4})^{-1} = -4[/tex]

2) To find the equation, plug in the point given:

   [tex]5 = -4(-1) + b[/tex]

   [tex]b = 1[/tex]

3) The equation of line q is thus:

   [tex]y= -4x+1[/tex]

Whats the slope of (6,0) and (2,-2)

Answers

A. /3/2



Is the answer.

^^ this is the last oneeee

Answers

I believe the measurement of AB is 30 degrees

Answer:

30 degrees

Step-by-step explanation:

So a complete circle consists of 360 degrees but we are trying to find what ADB equals so we are going to subtract BDC and ADC from 360:

BDC = 150

The graph does not say what ADC equals so we are going to look at the graph and see that ADC is half of the circle so we are going to divide 360 by 2:

360/2 = 180

So ADC equals 180, since we know what ADC and BDC equal we are going to add them together and then subtract them from 360:

180 + 150 = 330

360 - 330 = 30

So ADB = 30 degrees

Hope this helps!

It takes Andre 4 minutes to swim 5 laps.

How many laps PER MINUTE is that? (round to two decimal places if needed)
can someone also show there work?

Answers

=> 4 minutes.........5 laps |:4
=> 1 minute....1,25 laps
=> 1,25 laps per minute

PLEASE HELO ME I NEED HDLP PLEASE

Answers

Answer:

what's that 120 which angle is that

Step-by-step explanation:

Triangle AGB has Angle AGB = 120° and AG = GB. (given)

Since it is isosceles, x = (180° - 120°)/2 = 30°.

-2(-g + 5)

someone please explain how to simplify then combine like terms

Answers

Answer:

2g-10

Step-by-step explanation:

-2(-g+5)  take the -2 and multiply each term in the ()

-2*-g= 2g  Two negatives multiplied turns it into a positive number

-2*5= -10

The answer is 2g-10

Car A is traveling east at a steady speed of 45 miles per hour. After 2 hours, it is 100 miles east of Johnstown


Car B is traveling east on the same road. it’s distance east of Johnstown is represented by the graph.


Where were the two cars in relation to each other when they began traveling?


A. Car B was 10 miles east of car A

B. Car A was 45 miles east of car B

C. Car A was 10 miles east of car B

D. Car B was 40 miles east of car A

Answers

Answer:

The correct option is;

A. Car B was 10 miles east of car A

Step-by-step explanation:

The given parameters are;

The speed of car A = 45 miles per hour

The direction of car A = East

The distance of car B from Johnstown after 2 hours = 100 miles east

The direction of Car B = East

The distance of car B from Johnstown is given on the graph

Therefore, the initial distance of car A from Johnstown when car A began driving is given as follows;

The initial distance, east, of car A from Johnstown = 100 - 2 × 45 = 10

∴ The initial distance, east, of car A from Johnstown = 10 miles

From the graph, the initial distance, east, of car B from Johnstown = 20 miles

Therefore, car B was 10 miles east of car A

Answer:

Car B was 10 miles east of car A

Step-by-step explanation:

can someone plz help i need to graph it and identify the x-intercept

Answers

Answer:

(-7/2,0) is the x intercept

Step-by-step explanation:

1. y+3 = -6/7x

2.  -3              -3 ....subtract 3 from both sides to isolate the variable y

y= =-6/7x -3 ....is your new equation

You graph it by putting your point on negative three and then counting 6 units down and 7 units right.

For the x intercept you set y to 0 and solve for x

0= -6/7x -3

+3               +3 ...to both sides

3= -6/7x .....divide both sides by -6/7

-7/2=x

put it in as a coordinate

HELP!! (30 points) and brainlist

Answers

1. 5.5 feet = 66 inches
2. 56.75 pounds = 908 ounces

Answer:

5.5 feet is 66 inches. and 56.75 pounds is 908 ounces

Step-by-step explanation:

Hope this helped you!! Give brainliest

A school group is planning a trip to Jacksonville, Florida. There are 29 people going on the trip. They have agreed to share the total cost of the trip equally. Let s equal each person’s share of the cost. What is each person’s share of the cost? Solve this problem any way you choose. bus cost 7,830$ the hotel cost 10,034$ the meal cost 812$ the event ticket cost 435$ the cost of eveyting is 19,111$

Answers

Answer:659

Step-by-step explanation:

someone please help me answer question in attachment..

Answers

Answer:

135*

Step-by-step explanation:

trust me

Daniel needs to order some new supplies for the restaurant where he works. The
restaurant needs at least 792 forks. There are currently 223 forks. If each set on sale
contains 15 forks, what is the minimum number of sets of forks Daniel should buy?

Answers

I think you would multiply 223 with 15 then divide that number with 792. That’s what I’m guessing

How many apples are there in a bag if there is a total of nine pieces of fruit

Answers

Answer:

9

Step-by-step explanation:

if their nine pieces nine apples

hope im right!

I think 9 because there nine pieces of fruit in the bag, hopefully I made sense !

Here is a triangle with the height on the side of the triangle. Use the formula: (1/2)*(Base)*(Height) to find the area of the triangle at the left.

Answers

(If one square on the graph = one centimeter)

b = 10cm

h = 10cm

Area

[tex] = \frac{1}{2} \times b \times \: h[/tex]

[tex] = \frac{1}{2 } \times 10 \times 10[/tex]

[tex] = \frac{1}{2} \times 100[/tex]

[tex] = 50 {cm}^{2} [/tex]

The table below represents a linear function f(x) and the equation represents a function g(x):



Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)

Part B: Which function has a greater y-intercept? Justify your answer. (4 points)

(10 points)

Answers

Answer:

Step-by-step explanation:

Part A

for f(x) slope between points (-1,-6) and (1,0)

m= y2-y1/x2-x1 = -6-0/-1-1 = -6/-2= 3

for g(x) slope m=4 because we compare to equation y=mx+b the given equation g(x)=4x-5

The slope of f(x) is 3 and the slope g(x) is 4 so the line of g(x) is steeper

part B

The y intercept for g(x) is  (0, -5)

The equation of f(x) can be found

y-y1 =m(x-x1) take any point for example point (1,0)

y-1 =3(x-0)

y=3x+1 so the y-intercept is at (0,1)

The y-intercept for f(x) is greater at y=1 then the one of g(x) at y=-5

HELP!! Who ever does all these problems gets a brainlist and 50 points

Answers

Answer:

760cm = 7.6m

2485m = 2.485km

3090g = 3.09kg

205ml = 0.205ml

It seems I only get 30 points, ah well.

G(n)=-11*4^n complete the recursive formula of g(n) g(1) g(n)=g(n-1)

Answers

-1 = 161,051
1x-1=-1
11^4= 161,051
I’m not sure

Answer:

-44

4

Step-by-step explanation:

Helppppppp pleaseeee

Answers

Answer:

-5

Step-by-step explanation:

a= -4 than 2 times-4. than be 8.and 4 square is -16. So it be 3+8-16 = -5

Answer:

27

Step-by-step explanation:

[tex]3-2a+a^2\\[/tex]

If a = -4 then just replace a with -4

[tex]3-2(-4)+(-4)^2\\3+8+16\\27[/tex]

Question 5
3 pts
A map has a scale of 2 inches = 3 miles. If two towns are nine inches apart on the map, how
far are they actually apart?
O 13.5 miles
O 6 miles
O 13.5 inches
O 54 miles
< Previous
Next

Answers

13.5

multiply the scale by 4 so
8 inches = 12 miles

then add on half to make it 9 inches
1 inch = 1.5 miles

add them together
9 inches = 13.5 miles

Solve the system of equations. (1 point)

2x − 5y = 3
x − 3y = 1

(4, 1)
(5, 2)
(7, 2)
(9, 3)

Answers

Answer:

The answer is (4, 1)

Step-by-step explanation:

I hope this helps have a good day.

4,1 is the answer!!!

Sarah said that 26÷8 is the same as/equal to 14÷4 and the answers are "3r2". What did Sarah do wrong? 5th grade math help fir my daughter. I think Sarah meant: 26÷8 is the same as or equal to 13÷4 instead of 14÷4 which is what she did wrong?

Answers

Answer:

Yes

Step-by-step explanation:

Yes, that is exactly what Sarah did wrong. Apparently, she tried to divide both the numerator and denominator in this problem by 2 (half) but divided the numerator incorrectly. 26 divided by 2 would equal 13 but Sarah mistakenly calculated it as 14 which would give her a totally different value when divided by the new denominator. If were to have divided correctly it would give her [tex]\frac{13}{4}[/tex] which is the same as [tex]\frac{26}{8}[/tex]

HELP ME PLEASE!!!
Martha states that –6 is a rational number. Which is a correct explanation for this statement?

The number –6 is the opposite of 6.

The number –6 is a negative integer.

The number –6 can be written as -6/1.

The number –6 is less than 0.

Answers

answer c, but then again i did this a while ago and my memory is cooky

PLZ HELP PLZ PLZ PLZZZZZ

Answers

Growing 10 inches in 2 years
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