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

2.87x7.8
need answer

Answers

2.87 x 7.8
= 22.386
Hope this helps!
Answer:
2.87 * 7.8
= 22.386

9. On a standardized test where the results are distributed normally, Elliete scored a 246. If the mean score was
a 182 with a standard deviation of 36, then what is Elliete's percentile rank (percent less than or equal to 246)
rounded to the nearest whole percent? Explain how you arrived at your answer.

Answers

Elliete's percentile rank is 96% for a score less than or equal to 246

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation[/tex]

Given that μ = 182, σ = 36

For x ≤ 246:

[tex]z=\frac{246-182}{36}=1.78[/tex]

From the normal distribution table:

P(x ≤ 246) = P(z < 1.78) = 0.9625 = 96%

Elliete's percentile rank is 96% for a score less than or equal to 246

Find out more on z score at: https://brainly.com/question/25638875

The equation `F=\frac{9}{5}C+32` relates temperature measured in degrees Celsius, `C`, to degrees Fahrenheit, `F`. Determine whether there is a proportional relationship between `C` and `F`. Explain or show your reas

Answers

Answer:

No, a Celsius temperature is not proportional to its equivalent Fahrenheit temperature.

Step-by-step explanation:

The formula is

F=(9/5) C+ 32

F increases as C increases and F decreases as C decreases, but the relation is not a direct proportionality.

In mathematics, a direct proportion has the form

y=mx

where m is a constant.

If the formula had been F=(9/5) C, it would have been a direct proportion.

However, the addition of the + 32 term makes the formula no longer a direct proportion

2. You have 7 folders and you want to put the same number of pages in each folder.
a. If you have a total of p pages, how many pages will be in each folder?
b. Evaluate your expression to calculate the number of pages in each folder if you have 147 pages or
245 pages.

Answers

Answer:

  a. p/7

  b. 21; 35

Step-by-step explanation:

To find the number of pages in each folder, divide the number of pages by the number of folders.

a. There will be p/7 pages in each folder.

b. 147 pages will result in 147/7 = 21 pages in each folder

  245 pages will result in 245/7 = 35 pages in each folder

socks cost $2 per pair. the cost of n pairs $2n. john says that the cost of 6 pairs is $26 and the cost of 7 pairs is $27. is this correct? what did john do wrong?​

Answers

Answer:

John is incorrect. He did not multiply.

Step-by-step explanation:

If a pair of socks cost $2, then the total cost of the socks if you buy n pairs is $2n. In the expression 2n, the 2 is the dollar amount and the n is the number of pairs.

1 pair is $2.

2 pair are $4.

3 pair are $6.

4 pair are $8.

5 pair are $10.

6 pair are $12.

7 pair are $14.

13 pair are $26.

There is no way to spend $27 on these socks.

25 pair are $50.

Hopefully, you can use logic, your prior knowledge of making purchases of multiple items and also algebra to see you must multiply the number of items you're buying times the cost per item.

6 pair are $12 and 7 pair are $14. John is wrong. He did not multiply.

Trignometry plzz helpppp asappp

Answers

Answer:

[tex]x\approx4.5[/tex]

Step-by-step explanation:

In relation to ∠U, we are given the triangle's opposite side and adjacent side. Therefore, we should use the tangent function to determine the opposite side:

[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]

[tex]tan(34^\circ)=\frac{x}{6.7}[/tex]

[tex]6.7tan(34^\circ)=x[/tex]

[tex]x=6.7tan(34^\circ)[/tex]

[tex]x\approx4.5[/tex]

What is the correlation coefficient of y=2.6x+43.1?

Answers

Answer:

\mathrm{X\:Intercepts}:\:\left(-\frac{431}{26},\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:43.1\right)

Step-by-step explanation:

!!!NEED ANSWERS ASAP!!!! simplify 15 ÷ 3 +2 x 10

Answers

Answer:

70

Step-by-step explanation:

because 15 divided by 3 is 5+2=7 and 7 x 10=70

What is solution for 7y+9+6y=46

Answers

Answer:

combine like terms

7y + 6y

 13y + 9

Step-by-step explanation:

here is the solution

13y + 9

z/3 <= 3
solve for z

Answers

Answer:

assuming <= is less than or equal to

then z/3 is less than or equal to 3

z had to be less than 9

HELP!!!!!
M list the sides of ABC in order from shortest to longest

Answers

Question:

M list the sides of ABC in order from shortest to longest

Answer:

Sum of angles in a triangle = 180

Angles A + B + C = 180

80 + 3x + 5 + 5x - 1 = 180

3x + 5x = 180 - 80 - 5+1

8x = 96

x = 96/8

x = 12

So angle A = 80, B = 3x + 5 = 3*12 + 5 = 36 + 5 = 41, C = 5x - 1 = 5*12 - 1 = 60 - 1= 59

Angle A = 80, B = 41, C = 59

So the smallest side is the side facing the smallest angle and the largest side is the side facing the largest angle.

So from the smallest to biggest side:

AC < AB < BC

Arigatou gozaimasu!!

-16+5w=-1
solve for w

Answers

Answer:

w=3

Step-by-step explanation:

-16+5w=-1 .       add 16 to both sides

5w=15 .   divide both sides by 5

w=3

W=3
5w= -1 + 16
5w = 15
5 x 5 x 5 = 15

Which of these shapes have an area

Answers

I pretty sure the answer is c

Answer:

Shape 2 and 3

Step-by-step explanation:

shape 1 is not enclosed so it cannot have area

how many liters of a 30% antifreeze solution need to be added to 10 L of a 57% antifreeze solution to get 50% antifreeze solution. round to two decimal places.

Answers

50% decimal places hope it helps

A fishbowl has a capacity of 192 fluid ounces. How many quarts is that?

Answers

Answer:

hope this helps

Step-by-step explanation:

192 fl oz. = 6 quarts

to get this you divide the fluid ounces by 32.

You can answer the ones you want to. At least one.


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

Answers

Answer:

Step-by-step explanation:

5a.) It starts with two at time one and increases by one each time

5b.) x+1

6.) Formula: (2/3)(x-1)+1, the fifth term would be (2/3)*(5-1)+1= 11/3

7a.) I will leave you to make the table. n+2 is wrong because it's increasing by 2 blocks each time

7b.) 2n+1

8a.) x²

8b.) just draw a 6x6

8c.) 12²=144

Roger ran eight laps around a ¼ mile track during PE on Monday.How many feet did Roger run in completing eight laps

Answers

Answer:

10560 feet

Step-by-step explanation:

you're welcome :)

PLEASE HELP‼️‼️ILL MARK BRAINLYEST ‼️‼️I MEAN IT PLEASE ‼️‼️‼️‼️‼️‼️‼️15 POINTS PLEASE ‼️‼️
Given the two similar triangles below, which proportion is not true?

Answers

Answer:

1. Yes;   2. Yes ;     3. No;       4. Yes

Step-by-step explanation:

The proportion will have to be read the same way.  For example top Δ bottom  to the lower Δ bottom (locate in the same place)

14/21 = 6 /9     Yes  because the top Δ bottom to lower Δ bottom = top side to  

                         lower same side

13.5/21 = 9/ 14   Yes    because the same two sides to the same two sides in

                                     the lower Δ  

9/13.5 = 6 21      No   because top Δ side to lower Δ same location  but the

                                  second one top Δ side to the lower bottom

14 /6 =  21/6      Yes   because top Δ bottom to top side = lower Δ bottom to

                         lower side (in the same place)

Adding this so you can give the other dude the brailyist

HELP PLEASE!!! NEED NOW

Answers

Answer:

12

Step-by-step explanation:

HELPP EASY MATH FOR Y GUYS IM 5 GRADE

Answers

Answer:

Step-by-step explanation:

for number 8.) 14+8b
for number 9.) 9r-45

-33 less than or equal to -4x + 3

Answers

Step-by-step explanation:

-33 ≤ -4x + 3

Group like terms

4x ≤ 3 + 33

4x ≤ 36

Divide both sides by 4

4/4x ≤ 36/4

x ≤ 9

Final answer: x ≤ 9

Hope this helps.

Solve for x please help me ****

Answers

Answer:

x =10

Step-by-step explanation:

In a parallelogram, opposite sides are congruent

QT = RS

2x - 10 = x

Add 10 to both sides

2x = x + 10

subtract 'x' from both sides

2x -x = 10

x = 10

PLEASE HELP!!!!!!.....

Answers

Answer:

x=2

Step-by-step explanation:

hope this helps! :D

to everyone reading this: have a miraculous day!! <3

Answer:

x=2

Step-by-step explanation:

..............

✌️❤️✌️

Solve the system of linear equations by substitution: (SHOW UR WORK)
y=-x
y=3x-4

Answers

Answer:

x=1

y=-1

Step-by-step explanation:

they have already isolated y in both equations

label both equations

y=-x............1

y=3x-4........2

sub 1 into 2

-x=3x-4

-x-3x=-4

-4x=-4

x=1........ 3

sub 3 into 1

y=-(1)

y=-1

Add 3 5/6+(−1 1/6). Write your answer as a mixed number in the simplest form.

Answers

The result of 3 5/6+(−1 1/6) is 2 2/3.

INTRODUCTION

The definition of a fraction is that the division of two integers by the number being divided is called the numerator and the divisor is called the denominator.

Kinds of Fractions:

a. Mixed fractions, for example: 1⅘, 2½, 3⅔, etc.b. Common fractions, for example: , , , etc.c. Percent fractions, for example: 50%, 2%, 6%, etc.d. Decimal fraction, for example: 0.50

DISCUSSION

3 5/6+(−1 1/6)

= 23/6 + (-7/6)

= 23/6 - 7/6

= 16/6

= 8/3

= 2 2/3

Conclusion:

So, The result of 3 5/6+(−1 1/6) is 2 2/3.

Learn more:

mampir ke indo :v

Example of Fraction Problem: https://brainly.co.id/task/14280048Example of Fraction Subtraction Problem: https://brainly.co.id/task/23345402Material about fractional equations: https://brainly.co.id/task/3304077

______

Answer Details:Grade: 4 Elementary SchoolSubject: MathMaterial: Chapter 6 -ShardsCategorization Code: 4.2.6

Keywords: Subtract mixed fractions.

[tex]2\frac{2}{3}[/tex] is the simplest form of expression  [tex]3\frac{5}{6} +(-1\frac{1}{6} )[/tex]

What is Fraction?

A fraction represents a part of a whole.

Fractions are three types proper fraction, improper fraction and Mixed fraction.

The given expression is [tex]3\frac{5}{6} +(-1\frac{1}{6} )[/tex]

Three five by six plus minus one one by six.

Let us convert mixed fraction to improper fraction and solve

[tex]3\frac{5}{6} +(-1\frac{1}{6} )[/tex]

(18+5)/6 -(6+1)/6

23/6-7/6

Now take LCM as 6

(23-7)/6

Sixteen by six

16/6

Eight by three

8/3

[tex]2\frac{2}{3}[/tex]

To learn more on Fractions click:

https://brainly.com/question/10354322

#SPJ2

Please help y=30x - 30x^2 - 72

Answers

Answer:

  a.  4, 6

  b.  -72

  c.  (5, 3)

  d.  Graph A

Step-by-step explanation:

a.

To answer these questions, it is useful to start by factoring the equation.

  y = -3x² +30x -72 . . . . given

  y = -3(x² -10x +24) . . . . factor out leading coefficient

  y = -3(x -4)(x -6)

The x-intercepts are the values of x that make the factors zero:

  x = 4, 6

__

b.

The y-intercept is the constant in the equation: -72.

__

c.

We know the x-coordinate of the vertex is the midpoint between the x-intercepts: (4+6)/2 = 5. The y-coordinate can be found by evaluating y at that x-value.

  y = -3(5 -4)(5 -6) = -3(1)(-1) = 3

The vertex is (5, 3).

__

d.

The graph that has the correct vertex and x-intercepts is Graph A.

Find the slope-intercept equation of the line
that passes through (5, -3) and has a
slope of -1/2

Answers

Answer:

y = -1/2x - 1/2

Step-by-step explanation:

lmk if you want an explanation

The length of a rectangle is 3 less than twice the width. If the perimeter is 18 cm, what is the area? Show your work and solve using either substitution or elimination.

Answers

Answer:

Step-by-step explanation:

1) "The length of a rectangle is three more than twice the width." This can be written in a math sentence as  

L = 2W + 3

 where "twice the width" is 2W and "three more" is just adding 3.

 2) "Perimeter is 36 inches". Recall the formula for the perimeter of a rectangle

 P = 2W + 2L

  set the formula to 36 and that gives us our second equation: 36 = 2W + L

then use substitution do solve

(-5,-2),(-7,r) if m=5/9 what is r? slope

Answers

Answer:

r = -28/9

Step-by-step explanation:

use slope formula of (y₂-y₁) / (x₂-x₁)

5/9 = [r - (-2)] / [-7 - (-5)]

5/9 = (r+2) /-2

cross-multiply to get:

-2(5) = 9(r+2)

-10 = 9r + 18

-28 = 9r

r = -28/9

Carol has some dimes and quarters. If she has 31 coins worth a total of $4.30, how many of each type of coin does she have?

Answers

Answer:

23 Dimes and 8 Quarter.

Step-by-step explanation:

Important info:

31 Coins worth a total of $4.30

Note:

Dimes = .10

Quarters = .25

10 Dimes = 1.00

4 Quarter = 1.00

Question to Answer:

How many of each type of coin does she have?

Solution:

Lets get rid of the .30 cent in $4.30 so

.30 = 3 Dimes

Now $4.00,

4.00-1.00 of quarter

=

3.00 and 4 quarter..

Right now we have 3 Dimes and 4 Quarter = $1.30.

And that 7 Coins worth of $1.30.

3.00-2.00= 1.00 and 20 Dimes so now we have

23 Dimes and 4 Quarter.

And that add up to 27.

1.00-1.00 of Quarter = 4 Quarter.

so 31 worth a total of $4.30.

So that's 23 Dimes and 8 Quarter.

Check Work:

23 Dimes = $2.30 and 8 Quarter = $2.00

$2.30 + $2.00 = 4.30

Hence, The Correct Answer is 23 Dimes and 8 Quarter.

~[ RevyBreeze }~

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