At what point does the graph of 3x + 4y = 15 intersect the graph of x^2 + y^2 = 9? Express any non-integer coordinate as a common fraction.

Answers

Answer 1

Answer

12 and 36 and 13

Answer 2

If  you need an explanation;

let's first isolate x in 3x + 4y = 15 ---

x = (15 - 4y) / 3

now substitute as x in the second equation provided ---

((15 - 4y) / 3)^2) + y^2  = 9,

((15 - 4y) / 3)^2) +( 3y/3)^2  = 9,

((15 - 4y)^2 + (3y/3)^2)/3^2 = 9,

225 - 120y +25y^2/9 = 9,

225 - 120y +25y^2 = 81,

25y^2 - 120y + 144 = 0

we now solve using the quadratic formula  ---

[tex]y_{1,\:2}=\frac{-\left(-120\right)\pm \sqrt{\left(-120\right)^2-4\cdot \:25\cdot \:144}}{2\cdot \:25}\\=\frac{-\left(-120\right)\pm \sqrt{0}}{2\cdot \:25}\\=\frac{-\left(-120\right)\pm \sqrt{0}}{2\cdot \:25}\\\\= 12/5[/tex]

So then x = (15 - 4*12/5)/3 = 9/5. Our solution = (9/5, 12/5)


Related Questions

Select all of the rational numbers. (there can be more than one)

3^-1
square root of 12
square root of 9
-0.25
pi
0.6 (the six has a line over it)

Answers

Answer:

3^-1, square root of 9, -0.25, and 0.6

Step-by-step explanation:

Rational numbers are numbers that you can turn into fractions.

3^-1 = 0.3333333333... which is also known as 1/3

square root of 9 = 3, which can be written as 3/1

-0.25 can be written as -1/4

0.66666666... = 2/3

The numbers 3⁻¹ , sqrt(9), -0.25 and 0.6 are the rational numbers.

What is Number system?

A number system is defined as a system of writing to express numbers.

The rational numbers are those that can be expressed as a ratio of two integers.

3⁻¹ = 1/3, which is a rational number.

sqrt(12) = sqrt(4 x 3) = 2sqrt(3), which is irrational.

sqrt(9) = 3, which is a rational number.

-0.25 = -1/4, which is a rational number.

pi is irrational.

0.6 = 3/5, which is a rational number.

Hence, 3⁻¹ , sqrt(9), -0.25 and 0.6 are the rational numbers.

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The sales tax on a surfboard is $12. What is the percent of sales tax?
surfboard is 240$


The percent of sales tax is
____%

Answers

Answer:

it is a 5% sales tax

Step-by-step explanation:

12/240= 0.05

0.05 x 100 = 5%

Honestly I would do 240x10% and see what that gives you and if it’s lower than 12 keep raising or lowering the percentage that you’re multiplying by to figure it out yes it takes times. But the answer is 5%.

Isaac applied the steps below to find the product of (4.2)(–5.4). Step 1: (4.2)(–5.4) = (–5.4)(4.2) Step 2: = (–5.4)(4) + (–5.4)(0.2) Step 3: = (–21.6) + (–1.08) Step 4: = –22.68 Which step shows where Isaac applied the distributive property? Step 1 Step 2 Step 3 Step 4 will mark BRAINLIEST FOR QUICKEST CORRECT ANSWER

Answers

Answer:Isaac applied the distributive property in Step 2.

Answer:

a

Step-by-step explanation:

step shows where Isaac applied the distributive property

i need help with this

Answers

Answer:

im not good at math

Step-by-step explanation:

I have two questions and one will be on topic so please don't report.

1. Can someone give me a summary of Linear relationships? I still can't get a grip on it which is making me fail math.
&
2. Why do people report the memes on here? Like they are supposed to be left here and uplifting. Not deleted and forgotten just because.

Answers

Linear is basically a straight line on a graph and in a table when why changes it choice change the same amount through out for example 3,6,9,12,15 it’s by three if it’s like 2.1.3.3 it wouldn’t be linear bcuz it goes -1,+2,0

Fill in the missing fractions

Answers

Answer:

The second choice.

Step-by-step explanation:

1/5 = 20%

2/5 = 40%

3/4 = 75%

Answer:

The answer is the second option, X= 1/5, Y= 2/5, Z= 3/4

uuhhh help me out please?

Answers

First and third options are correct
A and c I’m pretty sure :)

Anika had 810 songs on her phone and then she discovered Broadway. This led to 130% increase in the number of songs she had on her phone. How many songs does she have on her phone now

Answers

810+130=940 sorry if I am wrong

Answer:

243

Step-by-step explanation:

that's I did was find what 130% of 810 was and I found it was 1053 so then I subtracted it by 810 to find 243

sorry if I'm wrong

Which model is NOT a function? (i accidentally clicked on b ignore that lol)

Answers

Answer:

C

Step-by-step explanation:

It's the only one where an x-axis has more than one y-axis.

I hope this explanation helps.

Question below answer asap please

Answers

Answer:

I think flip and rotate

D=A which means D gets to the spot where A is.

The answer would be D=A

Determine whether the graph represents a proportional relationship. (4 points)
A graph is shown. The x-axis is labeled from 0 to 9. The y-axis is labeled from 0 to 10. Four points are shown on the graph on ordered pairs 0, 0 and 1, 3 and 2, 6 and 3, 7. These points are joined by a line. The label on the x-axis is Number of pans. The title on the y-axis is Number of cakes.
Group of answer choices
A. Yes, it is a proportional relationship because the graph goes through the origin
B. Yes, it is a proportional relationship because the graph is a straight line
C. No, it is not a proportional relationship because the graph is not a straight line
D. No, it is not a proportional relationship because the graph does not go through the origin

Answers

Answer:

C. No, it is not a proportional relationship because the graph is not a straight line

Step-by-step explanation:

In 12 ½ minutes, Dulce read 50 pages.
a. On average, how many pages did she read per minute?
b. On average, how many minutes does it take to read one page?

Answers

Answer:

a. 4 pages per minute

b. one forth of a minute or 15 seconds

Step-by-step explanation:

a. divide total pages by minutes 50/12.5

b. divide minutes by pages 12.5/50

Which expressions are equivalent?

Answers

Answer:

A

Step-by-step explanation:

answer:

A :)

step by step explanation:

The population of Jacobtown is 14,312 and the population of Waltterville is 8,944. What is the combined population of Jacobtown and Waltterville?

Answers

Answer:

23,356

Step-by-step explanation:

You have to add 14,312 and 8,944 to get the total population.

The table below shows the amounts of cherry juice and soda used in each container of cherry soda. The ratio of cherry juice to soda is 1:r, where r is the unit rate. Use the table to determine r. (4 points) Cherry Juice (cup) Soda (cup) one-fourth 1 2 8 3 12
Group of answer choices
A. one-fourth
B. 4
C. 2
D. two-thirds

Answers

Answer:

is d i did the test c is wrong

Step-by-step explanation:

What is the solution to the proportion a/b = c/d?

Answers

Answer:

I hope this helps

Step-by-step explanation:

a/b=c/d

If we can simply multiply

we have!

a x d = c x b

= ad = cb

There are about 1.61 kilometers in 1 mile. Let x represent a distance measured in kilometers and y represent the same distance measured in miles. Write two equations that relate a distance measured in kilometers and the same distance measured in miles..

Answers

Answer:

1.61y=x

Step-by-step explanation:

1. 6 1 y = x is the answer

Find the number of the quadrant that contains the point (4,-3)

Answers

Answer:

Quadrant IV

Step-by-step explanation:

(+, +) -> Quadrant I

(-, +) -> Quadrant II

(-, -) -> Quadrant III

(+, -) -> Quadrant IV

Qu-lv. Hope get answer right

Please answer this question and answer correctly.

Answers

Answer:

C. 11

Work:

y=number of misses

x=number of scores

Points: 2x-0.5y=2(7)-0.5(6)=14-3=11

Hope this helps; please vote brainliest.

what is 5(​x​ + 2)+10 simlified?

Answers

Answer:

Step-by-step explanation:

5(X+2) =  5x +10 +10  5x=10-10=-20

-20/5=  -4

to be honest these might not be right but maybe 2

What is the surface area, in centimeters, of a cube with a side length, s, of cm?

Use the formula of surface area = 6s²

Answer: ⬜

Use / for a fraction. Example 1/2

Answers

Answer:

216cm

Step-by-step explanation:

i think that's right

Area is 6s^2 and that’s one side: a cube has 6 sides so the surface area is 6(6s^2) = 36s^2 cm

Jerry has a new job and earns a salary of $45,000. Victoria has a new job and earns a salary of $54,000. Jerry will receive a salary increase of $2,500 per year, and Victoria will receive a salary increase of $1,500 per year. Which equation can be used to find x, the number of years it will take Jerry to earn the same salary as Victoria?

A.) 45,000x + 2,500x = 54,000x + 1,500x

B.) 45,000x +2,500 = 54,000x + 1,500

C.) 45,000 + 2,500x = 54,000 + 1,500x

D.) 45,000x + 2,500x = 54,000x + 1,500

Answers

The answer is d I think
The answer to this question is d

Solve.
ASAP
90 = 5x + x

Answers

Answer:

15

Step-by-step explanation:

LEtS Do It PrOpeRly

90=5x+1x

90=6x

x=

[tex] \frac{90}{6} [/tex]

if we divide 90÷6=15

Wesley bought one T-shirt for $7.90 and another T-shirt for $12.40. What is the total amount he spent?
a. $20.30
b.$20
c.$4.50
d.$4
(brainliest included for correct answer)​

Answers

Answer:

20.30

Step-by-step explanation:

if you multiply 12.40 to 7.90 u will get 20.30

$20.30

7.90 plus 12.40 equals 20.30

A small motor boat can go 182 nautical miles at a steady speed in 13 hours. How far can it go in 1, 2,​ 3, 4, 5, 6, 7, 8, 9 and 10 hours.

Answers

Answer:

The answer is on google.

Step-by-step explanation:

400 i think if not correct me please

The vertex of the parabola described by the equation 3y=2x^2-16x+18 is (m,n). What is m+n?

Answers

Answer:

the aswer is 32

Step-by-step explanation:

The vertex of the parabola described by the equation 3y=2x^2-16x+18 is (m,n). the sum of m + n is 178/27.

To find the vertex of the parabola described by the equation 3y = 2x^2 - 16x + 18, we first need to put the equation in the standard form of a parabola, which is y = a(x - h)^2 + k, where (h, k) represents the vertex.

Let's begin by dividing the entire equation by 3 to simplify it:

y = (2/3)x^2 - (16/3)x + 6

Now, we need to complete the square to rewrite the equation in the form y = a(x - h)^2 + k:

y = (2/3)(x^2 - (8/3)x) + 6

Next, we need to find the value that completes the square for the expression inside the parentheses. To do that, we take half of the coefficient of x and square it:

(8/3) / 2 = 4/3

(4/3)^2 = 16/9

Now, we add and subtract 16/9 inside the parentheses:

y = (2/3)(x^2 - (8/3)x + 16/9 - 16/9) + 6

Now, we group the first three terms and factor the perfect square trinomial:

y = (2/3)((x - 4/3)^2 - 16/9) + 6

Next, distribute the (2/3):

y = (2/3)(x - 4/3)^2 - (2/3)(16/9) + 6

Now, simplify:

y = (2/3)(x - 4/3)^2 - (32/27) + 6

Finally, bring everything together:

y = (2/3)(x - 4/3)^2 + (142/27)

Now we can see that the vertex of the parabola is at the point (h, k) = (4/3, 142/27).

To find m + n, we simply add the x-coordinate (h) and the y-coordinate (k):

m + n = 4/3 + 142/27

To add these fractions, we need to find a common denominator, which is 27. Convert 4/3 to have a denominator of 27:

4/3 = (4/3) * (9/9) = 36/27

Now we can add the fractions:

m + n = 36/27 + 142/27

m + n = (36 + 142)/27

m + n = 178/27

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The length of the Titanic was 882 feet. Porter's history class is building a model of the Titanic. The model is 1/100 of the actual length of the ship. How long is the model?

Answers

Answer:

8.82 feet

Step-by-step explanation:

Explanation:

Let's set up the ratio. We know that the actual length of the ship was 882 feet and we want to know how long the model will be. We also have a ratio of 1 model length to every 100 actual length. So we can write this as:

Model length

Ship length

=

1 Model length

100 actual length

And we can drop in some numbers (I'll also put in the variable

x

to represent the length of the ship model):

x

882

=

1

100

Let's cross multiply to solve for x:

100

x

=

882

x

=

8.82

feet

8.82 is teh correct answer mark me as branlilest

PLEASE, I NEED HELP! I’M DOING AN ASSIGNMENT AND ITS DUE NEXT TUESDAY!

Answers

Answer: Study at least 2 hours a day



Step-By-Step-Solution: 1. Find notes on what you’re doing 2. Wright them down 3. Study them 4. Wallah you’re done you can thank me later :D

A number 5 is quadrupled and then decreased by f

Answers

Answer:

20-f

Step-by-step explanation:

Answer:

I believe it is 5^4 -f

Step-by-step explanation:

what is -3/4, -3, 0.75, -1.8, -3.5 ordered greatest to least i need the full order thx

Answers

Answer:

0.75, -3/4, -1.8, -3, -3.5

Step-by-step explanation:

Answer:

0.75, -3/4, -1.8, -3.5

Hope this helps :)

Step-by-step explanation:

-3/4 is also -0.75

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