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2 years ago

5x+2y=6 3y=2x+9 how many solutions does this problem have? No solution, one solution, or infinite solutions

Mathematics

1 answer:

Komok [63]2 years ago

8 0

Answer:

One solution

Step-by-step explanation:

First, organize the equations by moving y to the left hand side:

5x + 2y = 6, subtract 5x from both sides and we get: 2y=6-5x

3y = 2x + 9 is already done

Next, set the coeficcient of both y values equal to the least common multiple of 2 and 3 which is 6:

2y=6-5x multiply both sides by 3, 6y = 18-15x

3y=2x+9 multiply both sides by 2, 6y = 4x+18

Substitute y on both sides and we get 18-15x=4x+18

Simplify that and you get 19x=0, x equals 0, so there is one solution

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Please help me I need help please

MakcuM [25]

Answer:

p = 4

Step-by-step explanation:

Given equation:

$x^2+(p-3)y^2-4x+6y-16=0$

Standard equation of a circle:

$(x-a)^2+(y-b)^2=r^2$

(where $(a,b)$ is the centre of the circle, and $r$ is the radius)

If you expand this equation, you will see that the coefficient of $y^2$ is always one.

Therefore, $p-3=1$

$\implies p=1+3=4$

Additional information

To rewrite the given equation in the standard form:

$\implies x^2+y^2-4x+6y-16=0$

$\implies x^2-4x+y^2+6y=16$

$\implies (x-2)^2-4+(y+3)^2-9=16$

$\implies (x-2)^2+(y+3)^2=16+4+9$

$\implies (x-2)^2+(y+3)^2=29$

So this is a circle with centre (2, -3) and radius √29

3 0

2 years ago

Midpoint of (2,4) and (2, -7)

slega [8]

Step-by-step explanation:

soln:

let,

(x1,y1) =(2,4)

(x2,y2)=2,-7)

Now,

By midpoint formula,

×= x1+x2

= 2+2

=4

=2,,

And,

Y=y1+y2

=4-7

= -3

Hence ,

The mispoint between points (2,4) and (2,-7) is (2,-3 )

6 0

2 years ago

At a kennel, the ratio of dogs to cats was 4to9. if there were 64 dog s how many cats were there

hichkok12 [17]

Dogs. Cats.
4. To. 9

64. To. ?

I solved this by guess-timating, and i got it right. I know that 8*8=64 and 4*2=8 8*2=16, and i checked and got 16*4=64.
Since you do:

Dogs:4 * 16= 64
You have to do:
Cats:9 * 16= # of cats
And 9*16=144,

So there are 144 cats at the kennel

8 0

3 years ago

EASY! WILL MARK BRAINEST!! What is f(3) for the function f(x)=7x+5

Debora [2.8K]

Answer:

26 is the answer

Step-by-step explanation:

6 0

4 years ago

Multiply the polynomials. (2x^2 + 6x + 6)(3x – 2)

DaniilM [7]

Hey there! :)

Answer:

6x³ + 14x² + 6x - 12.

Step-by-step explanation:

Given:

(2x² + 6x + 6)(3x - 2)

Multiply each term in the first polynomial by both terms in the second:

3x( 2x² + 6x + 6) - 2(2x² + 6x + 6) =

6x³ + 18x² + 18x - 4x² - 12x -12 =

Combine like-terms:

6x³ + 14x² + 6x - 12.

6 0

4 years ago