if 3x+4y=11 and xy=2 solve simultaneously​

Answers

Answer 1

Answer:

(1, 2 ) and ([tex]\frac{8}{3}[/tex], [tex]\frac{3}{4}[/tex] )

Step-by-step explanation:

3x + 4y = 11 → (1)

xy = 2 ( divide both sides by y , y ≠ 0 )

x = [tex]\frac{2}{y}[/tex] → (2)

Substitute x = [tex]\frac{2}{y}[/tex] into (1)

3([tex]\frac{2}{y}[/tex] ) + 4y = 11

[tex]\frac{6}{y}[/tex] + 4y = 11 ( multiply through by y )

6 + 4y² = 11y ( subtract 11y from both sides )

4y² - 11y + 6 = 0

Consider the factors of the product of the y² term and the constant term which sum to give the coefficient of the y- term

product = 4 × 6 = 24 and sum = - 11

The factors are - 8 and - 3

Use these factors to split the y- term

4y² - 8y - 3y + 6 = 0 ( factor first/second and third/fourth terms )

4y(y - 2) - 3(y - 2) = 0 ← factor out (y - 2) from each term

(y - 2)(4y - 3) = 0

Equate each factor to zero and solve for y

4y - 3 = 0 ⇒ 4y = 3 ⇒ y = [tex]\frac{3}{4}[/tex]

y - 2 = 0 ⇒ y = 2

Substitute these values into (2)

y = 2 : x = [tex]\frac{2}{2}[/tex] = 1 ⇒ (1, 2 )

y = [tex]\frac{3}{4}[/tex] : x = [tex]\frac{2}{\frac{3}{4} }[/tex] = 2 × [tex]\frac{4}{3}[/tex] = [tex]\frac{8}{3}[/tex] ⇒ ( [tex]\frac{8}{3}[/tex], [tex]\frac{3}{4}[/tex] )


Related Questions

Mountain ranges often appear on the edges of continents. What theory does this support?

Mountains were formed when Earth’s crust cooled and Earth shrank.
Mountain ranges were formed when continents collided.
Mountain ranges did not exist millions of years ago.
Mountain ranges were formed only by glaciers.

Answers

Answer: Its B!

Step-by-step explanation:

i just got it right :)

Answer: b. Mountain ranges were formed when continents collided.

Step-by-step explanation:

divide £64 in the ratio 3:5

Answers

Answer:

64/1 . 5/3

320/3

106.666666?

Answer:

£24 and £40

Step-by-step explanation:

To divide into the ratio of 3:5, we can start by dividing into 8 parts - as 3+5=8, then do 3 parts and 5 parts to achieve the ratio.

£64 / 8 = £8

3 * £8 = £24

5 * £8 = £40

I need help with this, it's due today. *i'll give brainliest if you answer all of them*

Answers

Answer:

1. x = 13

2. a = 15

3. y = 3

4. g = -24

5. z = 5.57

6. h = 7.5

7. b = 5.8

8. w = -4.5

13. 29 chapters

14. 23.7 pounds

Step-by-step explanation:

hope this helps! :D

Help please.

A canine's body temperature is considered to be normal if it is 101 degrees Fahrenheit with an absolute deviation of 1.5 degrees Fahrenheit.
A. write an absolute value inequality that represents the normal temperature range. B.solve the inequality. what is the normal temperature range?

Answers

Answer: 101°F

Step-by-step explanation: A canine's body temperature is considered to be normal if it is 101°F with an absolute deviation of 1.5°F. a) Write an absolute value inequality

4x^2 - 3 when x= -10

Answers

Answer:

397

Step-by-step explanation:

1. To evaluate this expression, we plug in the value of x and simplify.

[tex]4x^2 - 3[/tex] [tex]4(-10)^2 - 3[/tex] [tex]4(100)-3[/tex] [tex]400-3[/tex] [tex]397[/tex]

Therefore, the answer is 397.

determine the measurement of segment XV​

Answers

Answer:

Segment XV is equal to 24 mm

Step-by-step explanation:

Both triangles are clearly congruent, both having the same type of angles as well as angle LKJ and angle VKW having the same angle measure, 21 degrees. Lastly, if you were to take out segment JL and WV, the triangles would fold the same. All of this leads to segment XV being the same as segment KL which leads it to be 24 mm. (Sorry if this is confusing, just trying to explain how my brain understood the problem. If you need me to elaborate more let me know).

There are 377 toys that Janet collected at the carnival. She wants to put them in 12 bags. After she splits them into bags, how many toys does she have left to give to her little brother?

Answers

Answer:

D. 31 toys

Step-by-step explanation:

377   ÷   12 =

31.41666666666667

given:

377 toys

12 bags

to find:

how many toys she'll have left to give her little brother.

solution:

[tex] \frac{377}{12} [/tex]

[tex] = 31.4166666667[/tex]

[tex]nearest \: whole \: number = 31[/tex]

hence, she'll have 31 toys left to give her little brother.

answer= option D

Describe how the graph of y= 2x is the same and different from the graph of y=2x+8

Answers

Answer:

They are the same because they have the same slope, 2. and they are different because they different y-intercepts, 0 and 8.

Step-by-step explanation:

Your equations y=mx+b

m is your slope, both 2 and

b is your y-intercept, 0 for your first one because it doesn't have any, and 8 for your second one.

Help pls ?? I just need this one question ):

Answers

Answer:

9 should be the greatest common factor. (I think) because 3b² =9b

12b⁴=48b

Answer:

3*(4b^4-b^2)

Step-by-step explanation:

you are looking for the greatest number who can be divided by the number(3) and the other number(12) , the greates common factor here is 3

and then take out the 3

so 3*(4b^4-b^2)

This is a list of ingredients for making a cake for 8 people.
Ingredients for 8 people
200 g flour
190 ml cream
60ml milk
4 eggs
Work out the amount of each ingredient needed to make a cake for 4 people

Answers

Answer:

100g flour

95ml cream

30ml milk

2eggs

Step-by-step explanation:

You just half them all

helpppppp mememeememememememememeemem

Answers

Answer:

Step-by-step explanation:

1.

area of triangle=1/2×12×5=30 in²

2.

obtuse scalene triangle.

Answer:

Step-by-step explanation:

1/2×12×5=30 in²

obtuse scalene triangle

Suppose a candy bar weighs ounces. How much does a pack of bars weigh?

Answers

Answer: it ways ounces?????????????

Step-by-step explanation:

a÷b when a = 2 and b = 1/2

Answers

Answer:

4

Step-by-step explanation:

a ÷ b = 2 ÷ 1/2 = 2 × 2/1 = 4

the total surface area of an cube is 294cm2 work out the volume of the cube

Answers

Answer:

343 cm³

Step-by-step explanation:

V = 343 cm³

Surface A = 294 cm²

Suppose that $2000 is placed in an account that pays 2% interest compounded each year. Assume that no withdrawals are made from the account.

Answers

The amount in the account after 1 year is $2,040.00

The amount in the account after 2 years is $2,080.80

What is future value of a single cash flow?

The future value of a single cash flow like the $2,000 is the future equivalent worth of the initial amount when interest earned is added to it.

The future value in this case can be determined as shown thus:

FV=PV*(1+r)^N

FV=unknown future value

PV=initial investment=$2000

r=interest rate=2%

N=years of investment , 1 and 2 years respectively

FV after one year:

FV=$2000*(1+2%)^1

FV=$2,040.00

FV after  two years:

FV=$2000*(1+2%)^2

FV=$2,080.80

Find out more about future value on:https://brainly.com/question/25545513

#SPJ1

Full question:

Suppose that $2000 is placed in an account that pays 2 % interest compounded each year. Assume that no withdrawals are made from the account.

Find the amount after one year. Find the amount after two years

5x + 7y = 5 10x + 14y = 10 solve by elimination​

Answers

multiply the first equation by -2

The answer is:

x= 46/5

y= 5/7

solve pls brainliest

Answers

Answer:2 3/4 for mixed                11/4 for  improper

Step-by-step explanation:

I need help i have no clue what to do!

Answers

Answer:

-2x-6y= -14 (i)

-6x-2y= -26 (ii)

Multiply eq (i) by 3

-6x-18y= -42 (iii)

-6x-2y= -26 (ii)

Subtract eq (iii) from ii

-6x -18y = -42

+6x+2y = +26

_______________

0 - 16y = -16

●y= 1

Put y =1 in eq 1

-2x -6 (1) = -14

-2x = -14 + 6

-2x = -8

●x =4

x=4 y=1

BRAINLIST PLS

Slope of parallel and perpendicular lines

Answers

Answer:

-1

Step-by-step explanation:

They already did the opposite reciprocal for you.

They have it in the form  now.

To find b you just enter (x,y)=(8,1).

Let's do that.

Subtract 2 on both sides:

b=-1

Write an equation for the line in the given form.

Contains the points (5, 2) and (8, 11); slope-intercept form

Answers

Answer:

y = 3x-13

Step-by-step explanation:

First find the slope

m = (y2-y1)/(x2-x1)

   = ( 11-2)/(8-5)

    = 9/3

    =3

Then using slope intercept form

y= mx+b

Using one of the points and the slope

2 = 3(5) +b

2 = 15 +b

2-15 = b

-13 =b

y = 3x-13

What is the point slope and slope intercept of this graph below

Answers

Answer:

Line is y = -3x + 3

Slope = -3

y-intercept = 3

Step-by-step explanation:

Slope is the movement up or down, and left or right. Y-intercept is the point in which the line crosses the y-axis. In slope-intercept form (y=mx+b), m represents the slope, while b represents the y-intercept.

So since the line crosses the y-axis at positive 3, that will be the y-intercept. Now if we go from that very same point, and do rise/run, we'd move downwards 3 units and to the right 1 unit, to get our slope of -3/1 (it's written as just -3 though).

So now we plug it in: y = -3x + 3

Hope this helps you :)

What is an equation of the line that passes through the points (-6, -2) and
(-3, 2)?

Answers

Answer:

y = (4/3)x - 2/3

Step-by-step explanation:

From (-6, -2) to (-3, 2) we see the x-component changing by 3 units and the y-component by 4 units.  Thus, the slope of this new line is

m = rise / run = 4/3.  

Let's focus on the point (-3, 2).  Here x = -3 and y = 2.  Plugging these three values into the slope-intercept form of the equation of a line, we get:

2 = (4/3)(2) + b.

Then 2 = 8/3 + b, or 6/3 = 8/3 + b.  Thus, b = 6/3 - 8/3, or -2/3.

The equation of the desired line is y = (4/3)x - 2/3

Answer:y=4/3x+6

Step-by-step explanation:

A ship leaves a port and travels 21km on a bearing of 32 and then 45km on a bearing of 287 calculate its distance from the port and the bearing of the port from the ship

Answers

Answer:

  44.5 km on a bearing of 134.1°

Step-by-step explanation:

A suitable vector calculator will tell you the location of the ship from port is ...

  21∠32° +45∠287° = 44.5∠-45.9°

The bearing of the port is in the reverse direction, so 180° added to this:

  180° +(-45.9°) = 134.1°

The distance from port is 44.5 km. The bearing of the port is 134.1°.

_____

Additional comment

The distance from port is perhaps most easily found using the Law of Cosines. It is the third side of a triangle with sides 21 and 45. The included angle is (287° -(180° +32°)) = 75°. The distance is then ...

  c = √(a² +b² -2ab·cos(C)) = √(21² +45² -2·21·45·cos(75°)) ≈ √1976.83

  ≈ 44.5 km

The angle between the 32° bearing and the bearing from the port to the ship can be found using the Law of Sines.

  B = arcsin(b/c·sin(C)) = arcsin(45/44.5sin(75°)) ≈ 77.9°

so, the bearing angle from the ship to the port is ...

  180° +(32° -77.9°) = 134.1°

__

Bearings are measured clockwise from north. A diagram can be helpful.

A non-proportional timetion is represented by y-2x.
7 which table represents this function?
с
3
4.
A
13
15
17
9
12
16
4
79
15
D
B
im
4
3
2
9
23
30
13
4.

Answers

Answer:

The numbers appear random.  Are there two columns?  I can't decipher the list.  

Step-by-step explanation:

Plot the function and see if any of the points fall on the line.  See attachment.

Is the function y-2x = 7  ??  { I see y-2x.7}

y = 2x + 7

The tape diagram below represents 100%.
100%
?
What percent is represented by the shaded area?
%

Answers

Answer:

60% is the answer also give me brainliest plss

(04.01 MC) Which set of points includes all of the solutions for y = negative four fifths times x plus two?line going through 0 comma 2 and 5 comma negative 2 Group of answer choices (15, 10), (0, 2), and (−10, 10) (−10, 10), (−5, 6), (0, 2), (5, −2), (10, −6) (x, y) for all real numbers (x, negative four fifths times x plus two) for all real numbers

Answers

The solutions of a function are the true values of the function

The solutions are: (0,2), (5,-2), (-10, 10) and (-5,6)

The function is given as:

[tex]\mathbf{y = -\frac 45 x + 2}[/tex]

From the question, we understand that the line of the equation passes through points (0,2) and (5,-2)

This means that:

(0,2) and (5,-2) are solutions of the equation

Other possible solutions include (-10, 10) and (-5,6)

This is true because, when these values are substituted in the equation, the result of the equation is true

Hence, the true options are:

(0,2), (5,-2), (-10, 10) and (-5,6)

Read more about solutions of equations at:

https://brainly.com/question/545403

I need help with both A and B please I will give brainliest

Answers

Answer:

You have A correct and I think B, is the second one

Step-by-step explanation:

You already have A correct as I solved the problem quickly (if you want a explanation I can give one) then the second one for B makes sense as it explains the same problem that was correct on question A. If you want more of a explanation I can give one

Could someone help me with these all these questions below
And no file please.
Use the information below to answer the questions:
Hastings 45 km Dover 108 km
Brighton 22 km Coventry 209 km
London 77 km Birmingham 172 km

1. How far is Hastings to the nearest 10 km?
2. How far is Brighton to the nearest 10km?
3. How far is London to the nearest 100km?
4. How far is Dover to the nearest 100km?
5. Approximately how far would you travel if you drive to London and then to Coventry?
6. Approximately how far would you have travel if you drive to Brighton, London and then Birmingham?

Answers

Answer:

1. 50km 2. 20 3. 100km 4. 100 5. 300 (rounded to the 100's) or 290 (rounded to the 10's) 6. 270 (to the nearest 10's) 300 (to the nearest 100's)

Step-by-step explanation:

1.

45

5=>5

Answer 50

2.

22

2<5

Answer 20

3.

77

7>5

Answer 100

4.

108

0<5

Answer 100

5.

Answer 300 or 290

(Based on the answer above)

6.

300 or 270

(Based on the answer above)

please help me answer this question

Answers

9514 1404 393

Answer:

  D.  -17%

Step-by-step explanation:

The change from March to April is (April - March) = (100 -120) = -20. As a fraction of the March bill, that is ...

  -20/120 = -1/6

As a percentage, that change is ...

  -1/6 × 100% ≈ -16.667% ≈ -17%

The electric bill changed by about -17% from March to April.

_____

Additional comment

Water went up 4%; groceries went up about 14%, and restaurant changed by -15%.

The percentage change is found by ...

  % change = ((new amount)/(original amount) -1) × 100%

Above, we have rearranged this to ...

  % change = ((new amount) -(original amount))/(original amount) × 100%

How do you Find cross products with multiplication?
I will give 500 pts and Brainliest!

Answers

Answer:

A cross product is an form from an vector multiplication, performed in between for two vectors from a different kinds or nature. An vector may have both magnitude also direction. So we can multiply two or more vectors for crossing a product also a dot product. The resultant vector is an perpendicular to a plane having the two add vectors.

Step-by-step explanation:

Sorry if I am wrong!!!!

Answer:

between for two vectors from a different kinds or nature. i think

brainliest???

Step-by-step explanation:

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