The line 2x + 3y = 8 meets the curve 2x^2 + 3y^2 =110 at the points A and B. Find the coordinates of A and B.

extra: This is the first time I’ve seen this type of question without a diagram. Pls help!

Answers

Answer 1

Answer:The cordinates of A and B are (-3.8, 5.2) and (7, -2).

Step-by-step explanation:From (1), we get x = (8 - 3y) / 2 ––(3)

Substitute (3) into (2),

2 [(8 - 3y) / 2]² + 3y² = 110

(8 - 3y)² + 3y² = 220

15y² - 48y - 156 = 0

Therefore y = 5.2, then x = (8 - 3×5.2) / 2 = -3.8

OR y = -2, then x = [8 - 3×(-2)] / 2 = 7

Answer 2

Answer:

The coordinates are A. (-3.8, 5.2) and B. (7, -2).

Step-by-step explanation:

At A and B the coordinates satisfy both equations so we solve simultaneously using substitution:

2x^2 + 3y^2 = 110

2x + 3y = 8

From the above equation

x = (8 - 3y)/2

So substituting for x in the first equation:

2 [(8-3y)/2]^2 + 3y^2 = 110

(8-3y)^2 / 2 + 3y^2 = 110

Multiply through by 2:

(8 - 3y)^2 + 6y^2 = 220

64 + 9y^2 - 48y + 6y^2 - 220 = 0

15y^2 - 48y - 156 = 0

3(5y^2 - 16y - 52) = 0

(5y - 26)(y + 2) = 0

y = 26/5, 2

y = 5.2,  -2.

So substituting in 2x + 3y = 8

When y = -2:

2x - 6 = 8

2x = 14

x = 7.

When y = 5.2

2x + 3(5.2) = 8

2x = 8 - 15.6 = -7.6

x = -3.8.


Related Questions

Write an equation in point-slope form of the line that passes through the point (-6,6) and has a slope of m=3/2

Answers

Answer:

y=3/2 x+15

Step-by-step explanation:

All the edges of the object in the diagram are equal in length. The object is cut by a vertical plane containing A and B and bisecting two of the horizontal edges. What is the shape of the cross-section resulting from the cut?.

Answers

The shape of the cross-section resulting from the cut is Rhombus.

Given that,

All the edges of the object in the diagram are equal in length.

The object is cut by a vertical plane containing A and B and bisecting two of the horizontal edges.

We have to determine,

What is the shape of the cross-section resulting from the cut?

According to the question,

All the edges of the object in the diagram are equal in length.

The length of all edges is equal in the rhombus.

The object is cut by a vertical plane containing A and B and bisecting two of the horizontal edges.

When the midpoints of all the four sides of a rhombus are joined with each other, you will obtain a rectangle whose length and width will measure half of the value of the prime diagonal.

Moreover, the area of the rectangle formed in this case will be half of the rhombus.

Hence, The shape of the cross-section resulting from the cut is Rhombus.

For more details refer to the link given below.

https://brainly.com/question/18660021

Answer: C. A rhombus

Step-by-step explanation:

What is the equation for the line in slope-intercept form?

Answers

Answer:y=4x+4

Step-by-step explanation:

3,080 feet = ____ miles. Answer as a proper fraction or as a whole or mixed number

Answers

Answer: 3080/5280 or (simplified) 7/12

Explanation:
There are 5280 feet in one mile so 3080/5280 is equal to 3080 ft/ 1 mile.

7/12 is equal to 3080/5280 when simplified.
Conversion a mixed number 3 3/
4
to a improper fraction: 3 3/4 = 3 3/
4
= 3 · 4 + 3/
4
= 12 + 3/
4
= 15/
4


To find a new numerator:
a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/
4
= 12/
4

b) Add the answer from previous step 12 to the numerator 3. New numerator is 12 + 3 = 15
c) Write a previous answer (new numerator 15) over the denominator 4.

Three and three quarters is fifteen quarters
Conversion a mixed number 2 2/
5
to a improper fraction: 2 2/5 = 2 2/
5
= 2 · 5 + 2/
5
= 10 + 2/
5
= 12/
5


To find a new numerator:
a) Multiply the whole number 2 by the denominator 5. Whole number 2 equally 2 * 5/
5
= 10/
5

b) Add the answer from previous step 10 to the numerator 2. New numerator is 10 + 2 = 12
c) Write a previous answer (new numerator 12) over the denominator 5.

Two and two fifths is twelve fifths
Multiple: 15/
4
* 12/
5
= 15 · 12/
4 · 5
= 180/
20
= 9 · 20/
1 · 20
= 9
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(180, 20) = 20. In the following intermediate step, cancel by a common factor of 20 gives 9/
1
.
In other words - fifteen quarters multiplied by twelve fifths = nine.

Bernie had $30 in his bank account. Today, he withdrew d dollars but tomorrow he will
bank account after tomorrow.
deposit $15. Write an expression to represent how much money Bernie will have in his

Answers

Answer:

Step-by-step explanation:

Bernie had $30 in his bank account.

Today he withdrew $d

Now he has = $30 — $d

Because from $30 he took away $d that’s why $d have to subtract from the $30.

Tomorrow he’ll deposit $15 and that will be added up with current balance $30 —$d.

So, the expression to represent how much money Bernie will have in his bank account is $30 —$d + 15

i need help plzzzzz be a good mon,woman

Answers

The graph is symmetric when X=40

The revenue earned when the shovel is sold for $20 is the same when the shovel is sold for $60.

Hope this helps! :)

Can somebody help me pleaseeeeee

Answers

The answer:  a° = 180° - 62° = 118°    ,     b° = 62°  ,     c° = (180° - 62°) ÷ 2 = 59°

Ok done. Thank to me :>

Write the equation of the line that is parallel to the line y=−14x−3 through the point (4,4).

Answers

Hello there! :)

Parallel lines have the same slope, so if one line has a slope of -14, then the line parallel to it has a slope of -14 as well.

We are also given a point that the line passes through.

That's enough information to find the equation of the line.

First, we write the equation in point-slope form, which looks like so:

y-y1=m(x-x1)

y1 is the y-coordinate of the point, m is the slope of the line and x1 is the x-coordinate of the point.

y-4=-14(x-4)

y-4=-14x+56

y=-14x+60

Hence, that's the equation. Hope it helps.

~A lonely teen who helps others with a smile

-Grace

Good luck.

Please help meeeeeeeeeeeeeeeeeee

Answers

Answer:

[tex]\frac{3^{12}}{3^{10}}[/tex]

Step-by-step explanation:

+ or x you plus the indices

- or divide you minus the indices

so 3^8 x 3^4 would be 3^12

and 3^2 x 3^8 would be 3 ^10

In the rectangle below,

Answers

Answer:

EI = FI and EG is twice the length of EI. Try setting up algebraic equations 3x + 8 = 6x -4 to find the value of x. Then substitute it back into the equation to find the length.

Step-by-step explanation:

Domain and Range of {(0,2), (2,4), (-1,1)}

Answers

Domain = {-1, 2, -1,0,1,2}
Range = {0,1,4)

Which statement is true about the equation f(x)=g(x) given f(x)=2x+3 and g(x)=x^2? please help

Answers

Answer:

x=3 and x=-1

Step-by-step explanation:

If f(x)=g(x), then 2x+3=x^2:

x^2-2x-3=0

(x-3)(x+1)=0

x=3 and x=-1

We can conclude that the statement:

There are values of x for which f(x) = g(x)" is true.

What is a function?

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

To determine which statement is true about the equation f(x) = g(x) given f(x) = 2x + 3 and g(x) = x²,

We can substitute the expressions for f(x) and g(x) into the equation and simplify:

f(x) = g(x)

2x + 3 = x^2

Now we have a quadratic equation.

We can rearrange it to standard form and solve for x using the quadratic formula:

x² - 2x - 3 = 0

a = 1, b = -2, c = -3

x = (-b ± √(b² - 4ac)) / 2a

x = (2 ± √(16)) / 2

x = (2 ± 4) / 2

x = -1 or x = 3

Therefore,

The equation f(x) = g(x) is true for some values of x, namely x = -1 and x = 3.

Thus,

Based on this, we can conclude that the statement "There are values of x for which f(x) = g(x)" is true.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ2

Simplify:

-5x - 2(3x - 7) + 4(3x - 5) - (6x -9)

Answers

Answer:

7x+3

Step-by-step explanation:

-5x+6x+14+12x-20-6x+9

combine like terms

7x+3

Given that D, E, and F are the midpoints of their respective sides, which of the following is a true statement?

Answers

Answer:

I'm pretty sure its the 1st one.

Step-by-step explanation:

Jack was the science Museum in sabotage the recycling plant had an average speed of 26KM/H. Sometime later Aaliyah love traveling in the opposite direction with an average speed of 57KM/H. After Jack had traveled for four hours they were 332KM a part. How long did Aaliyah travel?

Answers

Off topic, I like your username :] good luck with whomever answers though <33

3) Find the square root of these numbers by division method . 24336





I want full answer

Answers

Ans : 156 Hope you understand
Note : to find the squareroot of any number follow the steps : find the log ( lowest common factor )

In mosquito, more itchy bites are dominate to less itchy bites. If a male mosquito with a heterogeneous, more itchy bite mates with a less itchy, homologous female, what will the offspring likely be like?

4 Points Total:

Key (assign letters and traits) 1

Correct Punnet square 1

Correct phenotype 1

Correct prototypes 1

Answers

Answer:

a rash

Step-by-step explanation:

Which is the better buy? Explain.
Cereal
Price
$4.32
12-ounce box
16-ounce box
$5.44

Answers

For this problem, you have to find out how much each cereal costs per ounce. So you must divide each price by the amount of cereal you get and compare:
$4.08/16oz=$0.255/oz

Can you find the unit price ($/oz) of the remaining 2? You will then compare. The lowest value is the best buy!
the 16 ounce box is a better deal because it shows .34 cents per ounce while the other is .36 cents per ounce

a train goes 25 kilometers in 45 minutes, how fast would it go in 27 minutes?

Answers

Answer:

15km

Step-by-step explanation:

45mins = 25km

1 min =25/45

=5/9

27mins=5/9×27

=15km

1) -64÷16+[12x{6÷(16÷10-2)}] ​

Answers

Answer:

= -30[tex]x^{6}[/tex]-4

i hope that helps and is right

If that is a multiplication sign then it is -184

if that is an x then it would be -4 -180x

HELP PLEASE...........

Answers

Answer:

  B. slope -5, y-intercept (0, 7)

Step-by-step explanation:

The y-intercept is the first (x, y) pair shown in the table: (0, 7). (This eliminates choices C and D.)

The slope is ...

  change in y / change in x

  (-13 -7) / (4 -0) = -20/4 = -5 . . . slope

This matches choice B.

Need help l don’t understand new topic

Answers

7x - 2 = 5x + 14

7x - 5x = 14 + 2

2x = 16

x = 16/2

x = 8

______

Hope it helps ⚜

Answer:

x = -8

Step-by-step explanation:

[tex]7x - 2 = 5x + 14 \\ 5x - 7x = 14 + 2 \\ - 2x = 16 \\ \frac{ - 2x}{ - 2} = \frac{16}{ - 2} \\ x = - 8[/tex]

Bu sorunu nasil olur?
how can i solve this problem?

Answers

Answer:

i can't see your handwriting


I need helpppopppppppppppp

Answers

try it use your brain you can do it

Step-by-step explanation:

im not sure how to explain

Answer the ones you want to. Answer at least one.

Have no idea how to do this. Please help I beg you.

Answers

Answer:

I will answer one of them! Let's do... number 2.

Step-by-step explanation:

Conjecture: Each number increases by 5 each time.

I NEED HELP
Find the value

Answers

Answer:

7 and 2?

Step-by-step explanation:

i think because f(2) : f(x)= 5+2x = 7

PLEASE HELP WILL GIVE BRAINLIEST

5. Laura just became a personal trainer and is finalizing her pricing plans. One plan is to charge
$55 for the initial consultation and then $41 per session. Another plan is to charge $50 for the
consultation and $46 per session. Laura realizes that the two plans have the same cost for a
certain number of sessions. How many sessions is that? What is that cost?

Answers

Answer:

Step-by-step explanation:

Tod did not want the answer?

Jane went to get her hair cut and colored before Christmas. The hair stylist told her it would cost $80, but Jane wanted to leave a 15% tip how much would her tip amount be how much will it cost her including the tip

Answers

Answer:

12$ tip together is will be 92$

Step-by-step explanation:

I need the answers to a b c and d PLZ DUE AT 11:59PM ITS 9:23PM

Answers

Answer:

do u even still need the answer its been aweek since you asked it and it was due that same day

Step-by-step explanation:

NEED ANSWERS PLEASEEE! PROGRESS REPORTS GO IN SOON.

Answers

Answer:

1. they both are the same length and diameter, the difference is thw diameter is a different direction.

2. 4 cm

3. EB and 8 cm

Step-by-step explanation:

Diameter is the length of the circle aross, hope this helps!

Other Questions
Given that [tex] log_{4}(y - 1) + log_{4}( \frac{x}{2} ) = z \: \: and \: log_{2}(y + 2) + log_{2}(x) = z - 1 \: show \: that \: {y}^{2} = 1 + {8}^{z} \: and \: find \: the \: values \: of \: y \: and \: x [/tex]when z = 1 convert 8.4 10^16 molecules of CO2 to moles Identify a difference in the facts of Baker v. Carr (1962) and Wesberry v. Sanders (1964) that affected the impact of the Supreme Courts decision. Daniel is going to buy a pizza.He can choose one pizza variety, one extra topping and one pizza size.He can choose from23 different pizza varieties18 different extra toppingsThe total number of ways Daniel can choose the pizza variety, the one extra topping and thepizza size is 3726Work out the number of different pizza sizes that Daniel can choose from. Help me plsJin is an accountant who works for the national government, auditing the tax returns of large corporations. The pathway of the Government and Public Administration cluster that Jin works in is:Question 13 options:Public Management and Administration.Revenue and Taxation.Foreign Service.Planning. Explain why the formation of sand is a physical change. can someone help me i really need it is it true that playing badmenton help you to become a better person? Create 5 word problems on gcf using prime factorization. Jimez has $27 in his pocket. Which is the least number of bills that he can have, assuming he could possibly have $1, $5, $10, and $20. (A) 3 (B) 4 (C) 5 (D) 8 If one worker can lay 10 bricks every hour, and one bandit steals 3 bricks every hour, then how long would it take 8 workers and 5 bandits to lay 1400 bricks? Jeremiah's barber charges $20 for a haricut. The barber is increasing his prices by 40%. What will Jeremiah have to pay the barber the next time he gets a haircut? (waffle king asks you a question)take the blue pill and become a pancake ortake the red pill and become the pancake with holes ya this person is a bot be carefulcharissa2 1. An is a circulation of a convection cycle of air. Which part of the computer coordinates all computer operations and performs arithmetic and logical operations on data Grade 4c left their school at7:30 am for their trip to the market. They return at 10:45 am how much time did they spend onthe trip? Please make an essay on how did texas almost fail as a spanish colony? Please define processor When creating facial proportions like Rembrandt did, what two things will you need to use?aForm and patternObLine and shadingCPattern and shadingOdVariety and form