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Evgen [1.6K]
3 years ago
8

The ratio of dogs to cats is 2 to 3. There are 15 pets total. How many dogs are there? How many cats are there?

Mathematics
1 answer:
ElenaW [278]3 years ago
6 0
So there are 2 dogs to every 3 cats (put into words)

in order to reach 15 total multiply both 2 and 3 by 3

2x3 = 6
3x3 = 9

so there are 6 dogs and 9 cats
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Find the y? 3x + 6y = 12
kari74 [83]

Could you give Brainliest please???

Answer:

y = 2 - 1/2x

Step-by-step explanation:

So we are given the equation 3x + 6y = 12 and are ask to find y.

To find y you must isolate it first.

3x + 6y = 12

(Subtract 3x to isolate the y term)

6y = 12 - 3x

(Divide both sides by 6 to isolate the variable)

y = 2 - 3/6x

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y = 2 - 1/2x

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Transforming quadratic graphs
rewona [7]

Answer:

f(x) = 3(x - 2)² + 4

OR  

f(x) = 3x² - 12x + 16

Step-by-step explanation:

Vertex form of a parabola:

  • y = a(x - h)² + k

Standard form of a parabola:

  • y = ax² + bx + c

Let's find the vertex of this parabola.

  • (h, k) → (2, 4)

In order to find the a-value (vertex form), let's use another point besides the vertex on the parabola.

Using (3, 7) for (x, y), let's substitute this point and the vertex (2, 4) for (h, k) into the vertex form equation and solve for a.

  • 7 = a[(3) - (2)]² + 4

Simplify using PEMDAS.

  • 7 = a(1)² + 4
  • 7 = a + 4

Subtract 4 from both sides.

  • a = 3

Now we have (h, k) and a of the vertex form.

  • y = a(x - h)² + k  → y = 3(x - 2)² + 4

In order to convert from vertex to standard form, simplify the equation by FOILing.

  • y = 3(x - 2)² + 4
  • y = 3(x² - 4x + 4) + 4

Distribute 3 inside the parentheses.

  • y = 3x² - 12x + 12 + 4

Combine like terms.

  • y = 3x² - 12x + 16

Therefore, we have the answer:

<u>Vertex form:</u>

  • f(x) = 3(x - 2)² + 4

<u>Standard form:</u>

  • f(x) = 3x² - 12x + 16
8 0
3 years ago
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