All categories

4 years ago

Y=x2 +6x-2

Mathematics

1 answer:

alisha [4.7K]4 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

The equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

y = x² + 6x - 2

To complete the square

add/ subtract ( half the coefficient of the x- term )² to x² + 6x

y = x² + 2(3)x + 9 - 9 - 2

= (x + 3)² - 11 ← in vertex form

with (h, k) = (- 3, - 11 )

Turning point = (- 3, - 11 )

You might be interested in

Factorise: x³ + 32x + 20.

LenKa [72]

Answer:

cant be factored

Step-by-step explanation:

7 0

3 years ago

There are 3 islands A,B,C. Island B is east of island A, 8 miles away. Island C is northeast of A, 5 miles away and northwest of

Nostrana [21]

Answer:

The bearing needed to navigate from island B to island C is approximately 38.213º.

Step-by-step explanation:

The geometrical diagram representing the statement is introduced below as attachment, and from Trigonometry we determine that bearing needed to navigate from island B to C by the Cosine Law:

$AC^{2} = AB^{2}+BC^{2}-2\cdot AB\cdot BC\cdot \cos \theta$ (1)

Where:

$AC$ - The distance from A to C, measured in miles.

$AB$ - The distance from A to B, measured in miles.

$BC$ - The distance from B to C, measured in miles.

$\theta$ - Bearing from island B to island C, measured in sexagesimal degrees.

Then, we clear the bearing angle within the equation:

$AC^{2}-AB^{2}-BC^{2}=-2\cdot AB\cdot BC\cdot \cos \theta$

$\cos \theta = \frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC}$

$\theta = \cos^{-1}\left(\frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC} \right)$ (2)

If we know that $BC = 7\,mi$ , $AB = 8\,mi$ , $AC = 5\,mi$ , then the bearing from island B to island C:

$\theta = \cos^{-1}\left[\frac{(7\mi)^{2}+(8\,mi)^{2}-(5\,mi)^{2}}{2\cdot (8\,mi)\cdot (7\,mi)} \right]$

$\theta \approx 38.213^{\circ}$

The bearing needed to navigate from island B to island C is approximately 38.213º.

8 0

3 years ago

The annual interest rate of Mike's savings account is 4.8%, and simple interest is calculated monthly. What is the periodic inte

Reptile [31]

The correct option will be: d. 0.4%

For finding the periodic interest rate , we need to divide the annual interest rate by the number of times interest calculated in a year.

Here, the simple interest is calculated monthly, that means the number of times interest calculated in a year will be 12.

Annual interest rate is 4.8%

So, the periodic interest rate = $\frac{4.8}{12}= 0.4$ %

5 0

3 years ago

Read 2 more answers

Thomas bought 80 tickets for rides at an amusement park. Each ride cost five tickets, Thomas has been on X right so far. Select

dsp73

Answer:

A. 80-5x

Step-by-step explanation:

Let the number of rides be represented by = x

Thomas bought 80 tickets for rides at an amusement park. Each ride cost five tickets, Thomas has been on x right so far.

The number of rides Thomas has been on so far= 5 × x = 5x

The expressions to show the number of tickets that Thomas has left is written as:

80 - 5x

Option A is the correct option.

3 0

3 years ago

Read 2 more answers

Write 2 expressions that represent the areas of 4 triangles

arsen [322]

2-9x and 17x - 8x +2

4 0

3 years ago