1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
m_a_m_a [10]
2 years ago
15

Find the coordinates where the line x+y=3 and the curve x^2+3y=27 intersect

Mathematics
1 answer:
mart [117]2 years ago
6 0
<h2>Solving System of Equations by Eliminations</h2>

<h3>Answer:</h3>

(6,-3) and (-3,6)

<h3>Step-by-step explanation:</h3>

The xy-coordinates of intersection between the graphs of two equations are just the xy-values that satisfies both equation.

Let's find the coordinates with the given system of equations:

x +y =3

x^2 +3y = 27

First let's rewrite one of the equations to make some eliminations. The easiest way that I can think of is to multiply both sides of x +y =3 by 3 so when we subtract it from x^2 +3y = 27 the y t terms are eliminated.

x +y =3 \\ 3(x +y) = 3(3) \\ 3x +3y = 9

Subtracting \bold{3x +3y = 9} from \bold{x^2 +3y = 27}:

3x +3y -(x^2 +3y) = 9 -27 \\ 3x +3y -x^2 -3y = 9 -27 \\ -x^2 +3x (3 -3)y = 9 -27 \\ -x^2 +3x + 0y = -18

We can disregard the term with 0 as its coefficient so the result is -x^2 +3x = -18.

Now we can solve the value of x with the resulting equation.

-x^2 +3x = -18 \\ x^2 -3x = 18 \\ x^2 -3x +(\frac{3}{2})^2 = 18 +(\frac{3}{2})^2 \\ ( -\frac{3}{2})^2 = 18 +\frac{9}{4} \\ ( -\frac{3}{2})^2 = \frac{72}{4} +\frac{9}{4} \\ ( -\frac{3}{2})^2 = \frac{81}{4} \\ x -\frac{3}{2} = ±\sqrt{\frac{81}{4}}

Solving for the positive square root:

x -\frac{3}{2} = \sqrt{\frac{81}{4}} \\ x -\frac{3}{2} = \frac{9}{2} \\ x = \frac{9}{2} +\frac{3}{2} \\ x = \frac{12}{2} \\ x = 6

Solving for the negative square root:

x -\frac{3}{2} = -\sqrt{\frac{81}{4}} \\ x -\frac{3}{2} = -\frac{9}{2} \\ x = -\frac{9}{2} +\frac{3}{2} \\ x = -\frac{6}{2} \\ x = -3

We have two x-values that satisfy both of the equation. We also have two respective y-values that satisfy both of the equation. This all means that both equations intersect twice.

Let's solve for the corresponding y-values of each of the x-values with x +y =3.

Solving \bold{y} with \bold{x = 6}:

6 +y = 3 \\ y = 3 -6 \\ y = -3

Now we know that both equations intersect at (6,-3).

Solving \bold{y} with \bold{x = -3}:

-3 +y =3 \\ y = 3 +3 \\ y = 6

Now we know that both equations also intersect at (-3,6)

You might be interested in
If anyone can help me I’ll give all my points to u..
balu736 [363]

Answer: 12x squared

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
What is the slope of the line (-3,0) and (1,-6)
iren2701 [21]

Answer is provided in the image attached.

6 0
3 years ago
Fill in the space to complete to equality:<br><br> 3v-v²=v(__)
levacccp [35]

Answer:

3v-v² = v(3-v)

Step-by-step explanation:

Use distributive property on the right side of the equality.

6 0
3 years ago
Describe the graph of the function f(x) = x3 − 11x2 + 36x − 36. Include the y-intercept, x-intercepts, and the end behavior.
jenyasd209 [6]
The function is f(x)=x^3-11x^2+36x-36.

To find the x-intercepts, we need to factorize the function. A very good idea is to first try the factors of 36:

f(1)=1-11+36-36, not 0

f(2)=8-44+72-36=-36+72-36=0. Here we have our first root (2).

Now we cad divide f(x) by (x-2) which will give us a quadratic expression, which we can factorize easily (if the discriminant is non negative).

We can also try some other factors of 36. Indeed we can check that 

f(3)=27-99+108-36=135-135=0, 
and
f(6)=216-396+216-36=0.

Thus, f(x)=(x-2)(x-3)(x-6). Note that if we expanded the right hand side expression, the constant term would be the product of the constants 2, 3, 6.

This is the reason why in the first place we looked at the factors of 36 for the possible zeros of f(x).


Thus, the x-intercepts are (2, 0), (3, 0), (6, 0), or 2, 3, 6. 

The y-intercept is f(0), which is -36.


Note that f(0)<f(2) because f(0)=-36 and f(2)=0. This means that at the left side, the graph is coming from - infinity. Similarly, 

we can check that f(10)=1000-1100+360-36=224> f(6). That is, to the right of our rightmost root, the graph is getting larger.

Thus, the end behaviors are: the graph goes to + infinity as x goes to + infinity, 

and it goes to minus infinity as x goes to - infinity.
7 0
3 years ago
SOMEONE PLEASE HELP ME BEFORE I FAIL
Viefleur [7K]

Answer:

4/40

Step-by-step explanation:

you can reduce this to 1/10

multiplying 4 by both 1 and 10 will give you the fraction 4/40 both can be divided by 4 and that's how it can reduce to the 1st fraction (1/10)

8 0
2 years ago
Other questions:
  • Need a word problem for -1/2 x 12
    12·1 answer
  • Find the average rate of change of f on the interval [10, 60]. (round your answer to the nearest integer.)
    5·1 answer
  • How do you answer this?
    10·1 answer
  • 4/5 = 28/x <br><br> x= <br> i need to know what x =
    14·1 answer
  • 7. Consider the inequality below. PART A: Select all values of x that make the inequality true. *
    7·1 answer
  • I need the fully simplified slope-intercept form
    7·1 answer
  • Esmeralda works in the snack bar at the movie theater. She serves popcorn in two sizes, small and giant. The dimensions of the s
    11·1 answer
  • PLSSSSS HELPPPPPP ASAPPPPP
    11·1 answer
  • Please please please help no link no links no links
    5·1 answer
  • What is the following expression?<br><br>12-3×(8-5)<br><br>will give brainliest :)​
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!