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

Which of the following represents the GCF of 98 ab 3 and 231 a 3 ?

7 a
7 a 3
7
7 a 3b 3

Answers

Answer:

7a

Step-by-step explanation:

we know this, because there is no b in the second polynomial. Therefore, there cannot be a b in the answer. There is also no b^3 in the second polynomial, so there cannot be a ^3

Which point is located at
2.15?
PLEASE HELP IN 30 MINUTES

Answers

Answer:

it is a

Step-by-step explanation:

Answer:

a

Step-by-step explalan

How did immigration to the United States from Europe change between 1840 and 1850?
It decreased by half.
It decreased by a third.
It more than tripled.
It increased tenfold.

Answers

Answer:

it more than tripled

Step-by-step explanation:

I'm not sure if you need more but it requires me to type more to send the answer

Answer:

It more than tripled

Step-by-step explanation:

Right on Edge 2021

During hibernation, a garter snake’s body temperature never goes below 3 °C. Write an inequality that represents this situation.

Answers

Answer:

x ≥ 3*C

Step-by-step explanation:

what expression is equivalent to (2.1x+4.3) - (-3x-7)

Answers

The answer is 5.1x+11.3

Ana tiene ahorrados 30 €. Un fin de semana sale al cine con unos amigos y se gasta 7 €, le compra un regalo que le cuesta 12 € a una amiga y paga el billete de tren, que le supone 3 €. Si al llegar a casa su padre le da sus 15 € semanales, ¿cuánto le queda finalmente? (Plantear la solución como una única operación con enteros).

Answers

Answer:

A Ana le queda 23 €.

Step-by-step explanation:

La mejor estrategia para la resolución de este problema consiste en leer paso a paso y traducirlo en una serie de sumas y restas. Comenzamos:

1) Ana tiene ahorrados € 30:

[tex]x = 30\,EUR[/tex]

2) Un fin de semana sale al cine con unos amigos y se gasta € 7:

[tex]x = 30\,EUR-7\,EUR[/tex]

[tex]x = 23\,EUR[/tex]

3) Le compra un regalo que le cuesta € 12 a una amiga y paga el billete de tren, que le supone € 3:

[tex]x = 23\,EUR-12\,EUR-3\,EUR[/tex]

[tex]x = 8\,EUR[/tex]

4) Si al llegar a casa su padre le da sus € 15 semanales:

[tex]x = 8\,EUR + 15\,EUR[/tex]

[tex]x = 23\,EUR[/tex]

Si lo definimos como única operación con enteros, tenemos que:

[tex]x = 30\,EUR-7\,EUR-12\,EUR-3\,EUR+15\,EUR[/tex]

[tex]x = 23\,EUR[/tex]

A Ana le queda 23 €.

Evaluate g(x)=4 -3x when x=-3,0, and 5

Answers

Answer:

-11

Step-by-step explanation:

Ashley is a software saleswoman. Her base salary is $1,500, and she makes an additional $60 for every copy pf history is fun she sells. Let P represent her total pay (in dollars), and let N represent the number of copies of History is Fun she sells. Write an equation relating P to N. Then use this equation to find her total pay if she sells 23 copies of History is Fun

Answers

Answer:

2,880

Step-by-step explanation:

P + 60N = x

1500 + 60(23) = x

1500 + 1380 = x

2880 = x

if (x ➖ y)2=441 and xy=46 find the value of x2+y2​

Answers

Why didn’t you just take a picture?

What is the equation of this line in slope-intercept form? A. y=-4x+1 B. y=-1/4x+1 C. y=4x-1 D. y=4x+1. ​

Answers

Answer:

A (y= -4x+1)

Step-by-step explanation:

The ‘+1’ in the answer represents the point at which the line cuts the y axis (it crosses the y axis at +1)

The -4x comes from finding the gradient of the line which is done by using the formula (y2-y1)/(x2-x1) which will give you -4

please answers this​

Answers

Answer:

shusidvxxosbsbzbz

Step-by-step explanation:

usjzkdofjfbf

Answer:

50 degree for X look at pic attached

Can somebody plz help answer this word problem (showing the steps to get answer) thanks!


WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :DDDDDD

Answers

Answer:

528 cookies

Step-by-step explanation:

3 hours 55 minutes

=3×60+55

=235 and

235-215 ( for preheating minutes)

220

So

20 minutes…=48 cookies

1. ". =48/20 "

220 ". =48/20×220 "

=12/5×220 "

= 528 "

Answer:

well im not sure but i got 220

Step-by-step explanation:

so you convert the 3 hours and 55 minutes into minutes so

3*60=180

180+55=235

235-15=220

(for the preheating part)

220/48=4.583333333

4.583333333*48=(about)220  (actual number is 219.999999984)

so 220 cookies

two irregular pentagons are constructed so that every side has length of 1 unit. Does this necessarily mean that these figures are congruent with one another

Answers

Answer:

la repuedta es la tila idnjxnfozmsuzndybdjsnshsbsb

can someone help me with these two problems please!!!!!

Answers

Answer:

The question at the top is:

Factor  

x 2 + 2 x − 63

using the AC method.

( x − 7 ) ( x + 9)

WHICH THE ANSWER IS (B)

The question at the bottom is:

Factor  

x 2 + 18 x + 80

using the AC method.

( x + 8 )  ( x + 10 )

WHICH IS ANSWER (C)

Step-by-step explanation:

Hope this helped! :)

In a recent survey 5/8 of the Siamese cat said that they didn't mind having a lap up water from a bowl but another 3/16 admitted they would have preferred to use a straw instead of 39 of the Siamese cats gave one of these two answers how many were surveyed in total make sure your answer is fully reduced

Answers

Answer:

48 Siamese cats were surveyed

Step-by-step explanation:

Let x represent the total number of surveyed Siamese cats.

Since 5/8 of the Siamese cat said that they didn't mind having a lap up water from a bowl , hence:

Number of cats who lapped = (5/8)x

Also, 3/16 admitted they would have preferred to use a straw:

Number of cats who used straw = (3/16)x

Taking into consideration that 39 of the Siamese cats gave one of those two answers:

(5/8)x + (3/16)x = 39

(13 / 16)x = 39

x = 39 * 16 / 13

x = 48

48 Siamese cats were surveyed

Give the equation of the line in
slope intercept form.
y = [?]x + []
Enter the number that belongs in the green box.
Enter

Answers

Answer:

y = 3x - 2

Step-by-step explanation:

The equation of a line is y = mx + c where m is the slope of the line and c is the y-intercept. I will be calculating the slope of the line using the points (1, 1) and (2, 4).

Slope = [tex]\frac{rise}{run}[/tex]

          = [tex]\frac{4-1}{2-1}[/tex]

          = 3

Based on the graph, the y-intercept is (-2) so the equation of the line is:

y = 3x - 2

The slope is y= 3x-2 is correcttt

At right is the tunnel entrance that runs through
Castle Hill in Budapest, Hungary.



-a If the maximum height of the tunnel is the
same as its maximum width, 9.8 meters,
determine a quadratic model to represent
the tunnel
-b State a geometric model that could be used to
represent a truck passing through the tunnel.
-c If a typical truck has a width of 2.62 m,
determine the height limitation that should
be put on these trucks if they are going to
travel through the tunnel safely. State any
assumptions that you made and be sure to
show all of the steps in your solution.
-d Because its length is almost 350 meters,
a truck stopped in the tunnel would need
enough room for the passenger door to open
fully. Suppose a truck with a width of 2.6 m
and height of 3.4 m is stuck in the right lane
of the tunnel by the center line. The top of
the driver's door is 0.2 m below the top of the
truck, and the door opens 0.8 m to the side.
Show that the door can open fully, showing
all of your steps.
-e Determine how close to the side of the tunnel
the truck could be in d be and still be able to
open the passenger door.
-f Describe some issues/concerns that you
think architects take into account when
modelling a tunnel before its construction
End of document​

Answers

Answer:

My buddy what's popping??

Step-by-step explanation:

Those coming from the Pest end had to walk round the Castle Hill on the Buda side to be able to proceed northwards. On 10 February 1853, four years after the completion of the Chain Bridge, the building of a tunnel leading through the hill was started to the plans of Adam Clark. On 6 March 1856, the tunnel was opened for foot traffic, and on 30 April 1857 also for motor traffic. Being 350 meters in length, it leads through under the Buda Castle to the other side of the hill. Its length is approximately identical to that of the Chain Bridge, prompting anecdotes according to which the tunnel has only been built so that in rainy weather, the Chain Bridge can be shoved in and be protected from wet conditions. The entry of the tunnel at its Chain Bridge end was also fittingly designed in classicist style.

Answer:

At right is the tunnel entrance that runs through Castle Hill in Budapest, Hungary.-a If the maximum height of the tunnel is the same as its maximum width, 9.8 meters, determine a quadratic model to represent the tunnel-b State a geometric model that could be used to represent a truck passing through the tunnel.

Step-by-step explanation:

b. Sonya says that her profit is increasing 4 times as
fast as Kirsten's profit. Do you agree? Explain.
Lesson 8 Compare Functions

Answers

Answer:

No, I beleive that her profits are only 3 times as much as Kirsten's profits.

Step-by-step explanation:

9 3/5 as a improper fraction

Answers

Answer:

48/5

Step-by-step explanation:

hope it helps!

......

HELP PLZ!! WILL MAKR BRAINLIEST

Answers

Answer:

See below

Step-by-step explanation:

The y-intercept is -5.5 as per graph

Taking two random points from the graph to find the slope:

(-1, -6) and (1, -5)

Use slope formula: m = (y2 - y1)/(x2 - x1)

m = (-5 - (-6))/(1 - (-1)) = 0.5

The line in slope-intercept form is (y = mx + b)

y = 0.5x - 5.5

or

y = 1/2x - 11/2

Answer:

i don’t think I understand.

Step-by-step explanation:

Please provide an explanation with your answer, thank you!

Answers

Answer:

the answer is c. because the awnser is 47.5 and round upto the nearest whole number si 50

Step-by-step explanation: if the yard stick is  3ft and the shadow is 4ft that means the shadow of the stick is 1ft longer than the stick itself.

so if the shadow of the flag pole is 20ft than you -1 and get 19 as shown "20 - 1 = 19" then it said the rope needs to be 2.5 times as long as the pole so you multply 19 by 2.5 as shown "19 x 2.5 = 47.5" round up its 50ft. so there you go hope it helped let me know

Which fraction is equivalent to 2/4

Answers

Answer: 1/2

Step-by-step explanation:

2/4=1/2

Answer: Yes, 1/2, ,2/4, and 4/8 are all equal because if they are all one half, then they are equal.

Step-by-step explanation:

I need help with this question! Will mark brainliest :)

Answers

Answer:

hiii

your answer is option d

HOPE IT HELPS YOU OUT PLEASE MARK IT AS BRAINLIEST AND FOLLOW ME PROMISE YOU TO FOLLOW BACK ON BRAINLY.IN

answer: y= 20x+30

Step-by-step explanation:

it says they charge 20$ per hour and x is the amount of hours.

30$ is charged as the registration fee at the beginning only.

WILL MARK YOU BRAINLIEST ANSWER 1-3 plz

Answers

Answer:1)52

2)13

3)22

Step-by-step explanation

The answer to each part is mentioned below -

P = 72RU = 16SU = 22

What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is a kite TSVU as shown in the image.

{ 1 } -

UT = ST = 20

Perimeter of ΔSUT will be -

P = ST + TU + SU

P = 20 + 16 + 16 + 20

P = 72

{ 2 } -

Perimeter of ΔSUV will be -

P = SV + SU + VU

38 + 26 + VU = 102

VU = 38

ΔSUV ≅ ΔRUV

RU = SR = 16

{ 3 } -

ΔSUV ≅ ΔRUV

SR = RU

4x - 1 = x + 8

4x - x = 8 + 1

3x = 9

x = 3

SU = SR + RU

SU = 4x - 1 + x + 8

SU = 12 - 1 + 3 + 8

SU = 22

Therefore, the answer to each part is mentioned below -

P = 72RU = 16SU = 22

To solve more questions on kites, visit the link below -

brainly.com/question/1041084

#SPJ5

Select the values that make b≥-3 true

Answers

Answer:

-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10+

Step-by-step explanation:

and anything above 10 would be true

Write the slope-intercept form of the equation that is described below.

Through (-3, 3) and perpendicular to y = 1/3x + 5

What is the equation:

Answers

Answer:

3=-3*-3+b

3=9+b

-9 on both sides

-6=b

y=-3x-6

*-3 because the opposite of 1/3 is -3*

What is the value of X?

A: 125
B: 110
C: 35
D: 55

Answers

Answer:

The value of X is 35

Step-by-step explanation:

If I’m not right I apologize

Select yes or no to indicate whether each of the ordered pairs is most likely a solution to the equation represented by the graph.

Answers

Answer:

No

No

Yes

Step-by-step explanation:

-1/4 is the only correct solution to the equation represented by the graph.

Help 9th grade math please please please

Answers

Answer:

A.) This system has no solutions.

Step-by-step explanation:

y = 1/2x + 4

-1/2x + y = -5

-1/2x + (1/2x + 4) = -5

4 = -5

The system has no solutions, if we graph it, we get that it has the same slope with two different y-intercepts, these two are parallel. These two points will never meet at a point.

Answer:

use the relationship between coefficients of a pair of linear equations for no solutions i.e. a1/a2 equal to b1/b2 not equal to c1/c2 .

Here, a is coefficient of x and b is coefficient of y and c is constant term in both equation but make sure that you put the values of a1,a2,b1,b2,c1 and c2 after converting both equation in the form ax+by+c=0 with proper sign and here y=1/2(x) +4 is equation 1 and other is equation 2

PLEASE HELP I WILL GIVE BRAINLIEST ANSWER! What is y-5/3=1?????

Answers

Answer:

Y =1 is a good answer for this question.

This is your perfect answer
Other Questions
Complete the sentence it is very important for the medical assistant to When meeting with a patient while filling out the electronic record Please help soon! Thanks! Solve for x Rachel's gym charges a one-time registration fee of $45 and a monthly fee of $39. Whichfunction can be used to find y, the total charges at this gym for x months?Fy= 45x +39Gy=6x +39Hy=39x +6jy=39x + 45 What was Mississippian society like in Georgia prior to contact with Europeans? why are women so precious ? How did the status of free blacks change in preparation for Louisiana's application for statehood I GIVE BRAINLEIST!!!!! How does kinetic energy naturally flow; from hot to cold or cold to hot? Which of the following traits is found in major depression A ps4 uses uses 8.8 watts when on stand by mode. If electricty in your area costs 0.10$ kwh, how much would this cost? 2x 10 = 4x solve for x A system in which patients pay doctors for health care is known as a:A. fee-for-service system.B. universal system,C. health maintenance organization,D. capitalist system. rewrite in standard form y-2=4/3(x-1) Kayla bought a book for $13 . She now has $47 . How much did Kayla have before she bought the book? Which of the given character development criteria will get your audience to empathize with your character?OA.motivationB.having a secretO c.vulnerabilityD.contradiction What do Endocrine Glands do? How do you write 7.3 x 10-1 in standard form? Jorge is sending a message to Thomas but would like a copy sent to his external email address as well. Jorge does not want Thomas to see this copy that was sent.Which mail field will Jorge use to achieve this goal?To:From:CC:BCC: In colonial America, who were the Sons of Liberty? if [tex]\frac{r + s}{x - y} = \frac{3}{4}[/tex] then [tex]\frac{8r + 8s}{15x - 15y}[/tex] equals Merry Christmas please help