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Semmy [17]
2 years ago
9

3n^2=6-17n I need Vertex form please.

Mathematics
1 answer:
nasty-shy [4]2 years ago
8 0

Answer:

3( n + \frac{17}{6} )² - \frac{361}{12} = 0

Step-by-step explanation:

3n² = 6 - 17n ⇔ 3n² + 17n - 6 = 0

3( n² + 2 × \frac{17}{6} n + ( \frac{17}{6} )² - ( \frac{17}{6} )² - 2 ) = 0

3( n + \frac{17}{6} )² - 3 × \frac{289}{36} - 6 = 0

3( n + \frac{17}{6} )² - \frac{361}{12} = 0

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Include work pleaseeeee
Angelina_Jolie [31]
Okay so to represent juice we are going to use X, and to represent water we are going to use Y.

We also know that the first two starting equations are:

6x + y = 135

4x + 2y = 110

We can re-arrange the first equation so that it equals y (for now), so it is going to end up looking like this:

y = -6x +135

Now you can take that equation and plug into either one of the starting two equations.  I chose the second equation.  We just substitute what y equals in for y in the equation, so we have:

4x + 2(135 - 6x) =  110

Now solve

4x + 270 -12x = 110

-8x + 270 = 110

Subtract 270 from both sides

-8x = -160

Now divide by -8 on both sides

x = 20

We can now confirm that juice costs $20

Now lets plug that into the equation where we solved for y, to get the actual value of y.

y = 135 - 6(20)

y = 135 - 120

y = 15

The price of water costs $15

From this we can conclude that the cost of juice is $20 and the price of water is $15

5 0
3 years ago
HELP ON A TEST
Strike441 [17]
First three. A, b, c.
The triangle is a right triangle.
The triangle is a Pythagorean triple.
The triangles hypotenuse is 39 inches.
7 0
3 years ago
last year, total sales for your grocery store were $10,342 with returns of $214 and discounts of $599. the linear feet of shelvi
kompoz [17]

Answer:

The answer would be A. $16.6 per linear foot


8 0
3 years ago
Read 2 more answers
Lines m and n are parallel and m&lt;1=140*<br> What is m&lt;7?
Arada [10]
m\angle 7=180-m\angle 5\\&#10;m\angle 5=m\angle 1=140\\&#10;m\angle 7=180-140\\&#10;m\angle 7=40
6 0
3 years ago
Triangle XYZ is shown, where n ≥ 5. Triangle X Y Z is shown. The length of side X Y is n + 4, the length of side Y Z is 2 n, and
motikmotik

Answer:

The longest side of the triangle is YZ, the shortest side is ZX, the largest angle is ∠X and the smallest angle is ∠Y.

Step-by-step explanation:

The lengths of the sides of the triangle XYZ are as follows:

XY = n + 4

YZ = 2n

ZX = n - 2

According to the triangle inequality theorem, the sum of two sides of a triangle is always greater than the third side.

Then,

XY < YZ + ZX ⇒ n + 4 < 2n + n - 2 ⇒ n + 4 < 3n - 2 ⇒ 2n > 6 ⇒ n > 3

YZ < XY + ZX ⇒ 2n < n + 4 + n - 2 ⇒ 2n < 2n + 2 ⇒ 0 < 2

ZX < XY + YZ ⇒ n - 2 < n + 4 + 2n ⇒ n - 2 < 3n + 4 ⇒ 2n > -6 ⇒ n > -3

It is provided that <em>n</em> ≥ 5.

Then the sides of the triangle are:

XY = n + 4 ≥ 5 + 4 = 9

YZ = 2n ≥ 2 × 5 = 10

ZX = n - 2 ≥ 5 - 2 = 3

So, the longest side of the triangle is YZ. And the shortest side is ZX.

The largest angle of a triangle is opposite to the longest side.

The angle opposite to YZ would be X. So, the largest angle is ∠X.

The smallest angle of a triangle is opposite to the shortest side.

The angle opposite to ZX would be Y. So, the smallest angle is ∠Y.

Thus, the longest side of the triangle is YZ, the shortest side is ZX, the largest angle is ∠X and the smallest angle is ∠Y.

6 0
3 years ago
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