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
Anni [7]
3 years ago
15

How many real solutions does this system of equations have? x^2 + y^2 = 36

Mathematics
1 answer:
Vinvika [58]3 years ago
4 0

Answer:

C:  there are two real solutions

Step-by-step explanation:

x^2 + y^2 = 36 is the equation of a circle centered at the origin and with radius √36, or 6.  Even a rough sketch of this circle would enable you to visualize what is happening here.  

3x – y + 1 = 0 may be solved for y:  y = 3x + 1.  The y-intercept of this straight line is (0, 1).  Plot this point inside the circle of radius 6 mentioned above and then draw a straight line with slope m = 3 through it.  This line will intersect the circle in two places; they represent real solutions.

Alternatively, substitute 3x + 1 for y in x^2 + y^2 = 36:

x^2 + (3x + 1)^2 = 36, or

x^2 + 9x^2 + 6x + 1 = 36, or

10 x^2 + 6x + 1 - 36 = 0, or

10 x^2 + 6x - 35 = 0.  This is a quadratic equation.  We'll use the quadratic formula to find solutions which represent the intersections of this line with this circle:

The coefficients are a = 10, b = 6 and c = -35.  Thus, the discriminant is

b^2 - 4ac, or 6^2 - 4(10)(-35), or 1436.  

Because the discriminant is positive, we can safely conclude that there are two real solutions, that is, two different, real x-values, each representing the x-coordinate of a point of intersection of the circle and the line.

The correct answer to this prolem is C:  there are two real solutions.

You might be interested in
Volume of prisms just 3 problems
Vladimir79 [104]

Answer:

2.  18 cubic cm.

3. 27 cubic cm

5. 90 cubic m

Step-by-step explanation:

2. Triangular prism

So, we have a triangular prism with a width of 3 cm, a height of 1.5 cm and a length of 4.  We'll take the triangle shape as the base.

Like for any prism, the volume is the base multiplied by the height.

So, the area of the base is found with the regular formula: base x height:

so, 3 x 1.5 = 4.5 sq cm for the base.

Then we multiply the base by the length to get the volume: 4.5 x 4 = 18 cubic cm.

3. Trapezoidal prism

Again, first step is to calculate the area of the trapezoid shape, then multiply by its depth.

The area of a trapezoid is calculated with the formula:

A = h/2 * (a + b) where a and b represent the short and long sides respectively.

So, for our given trapezoid:

A = 1.5/2 * (2+4) = 0.75 * 6 = 4.5 sq cm.

Then we multiply the base area by the height to get the volume:

V = 4.5 * 6 = 27 cubic cm

5. Triangular prism 2

The best way to approach this one is to consider it's a triangle prism with a height of 3 cm, and use the triangle shape (with sides of 13 and 5) as the base.

But to calculate the area of that triangle we need to find out the missing length. Using Pythagore's theorem, we can easily find the length of the other side with the hypotenuse formula:

hypotenuse² = sideA² + sideB²

In our case, we have:

13² = x² + 5²

169 = x² + 25

x² = 144

x = 12

Now we can calculate the area of the triangle easily:

A = (b x h)/2 = (5 x 12)/2 = 30 sq m

Then multiply by the thickness of the prism....

V = 30 x 3 = 90 cubic m

4 0
3 years ago
Can somebody help me with this ?? :)
Alex777 [14]

Answer:

Your answer would be D, the equation is a function because it is a polynomial and all polynomials are functions.

Step-by-step explanation:

I like to remember that polynomials have no negative , fraction exponents and no division. In this case everything is positive so I knew it was a polynomial , and like the answer says all polynomials are functions !

Hope this helped

7 0
3 years ago
Solve:
drek231 [11]

The solutions to the inequalities are x >1 and x < 6

<h3>How to solve the inequalities?</h3>

The inequality expression is given as:

-2x + 5 < 3x + 10

Collect the like terms in the above inequality

-2x - 3x < 10 - 5

Evaluate the like terms

-5x < 5

Divide by -5

x >1

Also, we have

5(x - 2) <3x + 2

Open the bracket

5x - 10 < 3x + 2

Evaluate the like terms

2x < 12

Divide by 2

x < 6

Hence, the solutions to the inequalities are x >1 and x < 6

Read more about inequalities at

brainly.com/question/24372553

#SPJ1

5 0
1 year ago
Good morning can y’all help me
Ulleksa [173]

Answer:

rate of change

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Help pleaseeee ASAP just tell me the answer
iragen [17]

HEY MATE YOUR ANSWER IS HERE

★ GIVEN EQUATION ★

X + Y = 4

★ SOLUTION ★

LET VALUE OF X = 0 , 1 , 2 , 3 AND 4

WHEN X = 0

0 + Y = 4

Y = 4

WHEN X = 1

1 + Y = 4

Y = 3

WHEN X = 2

2 + Y = 4

Y = 2

WHEN X = 3

3 + Y = 4

Y = 1

WHEN X = 4

4 + Y = 4

Y = 0

NOW OUR 5 COORDINATES OF LINE X + Y = 4 ARE

A ( 0 , 4)

B ( 1 , 3 )

C ( 2 , 2)

D ( 3 , 1 )

E ( 4 , 0 )

THANKS FOR YOUR QUESTION HOPE THIS HELPS

can i have a brill

thank u

good luck

6 0
2 years ago
Other questions:
  • Write a function rule that represents each sentence c is 8 more than half of n
    15·2 answers
  • Three people toss a fair coin and the odd one pays for coffee. if the coins all turn up the same, they are tossed again. find th
    7·1 answer
  • What is the product of (3a + 2)(4a2 - 2a + 9)?
    8·1 answer
  • Julia went to buy Swedish Fish for a birthday party. One store had a 750g bag for $4.49 and and another store had a 425g bag for
    8·2 answers
  • Try This!!!!!!!!!!!!!!!!!!!!!!
    6·1 answer
  • Solve the equations 4× + 4 = 20. Write the problem on the sketch pad then solve the problem algebraically. I need shown work.
    11·1 answer
  • PLEASE HELP ME!!!!!!!!!!! NEED ANSWER IN LIKE 6 MINS!!!
    15·1 answer
  • en la tienda la cuquita vende queso cortado en trosos de diferentes pesos calculen presios y pesos para completar la infomacion
    6·1 answer
  • 9 apples and 9 bananas cost £2.43 altogether. The total cost of 2 apples and 3 bananas is £0.69. Calculate the cost of an apple
    13·2 answers
  • Kim drew the diagram below to find x, the length of the pole holding up the stop sign that is at an angle with the ground as sho
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!