Please help and explain.

Mathematics

1 answer:

Radda [10]2 years ago

7 0

Explanation:

Vertex form of a quadratic function is given by y = a(x - h)² + k

where

1) 'a' determines if parabola is stretched or compressed.

If a > 1 then graph is stretched by a factor of a.

If 0 < a < 1, then graph is compressed by a factor of a.

2) If a > 0 then graph opens upwards with a happy face. (minimum)

3) If a < 0 then graph opens downwards with a sad face. (maximum)

4) (h, k) is the vertex point

5) The axis of symmetry is x = h

While solving for y = 1(x - 4)² + 3

Identify following's:

Vertex: (h, k) = (4, 3)

Axis of symmetry: x = 4

Max/Min: As here a > 0, Minimum (4, 3)

Stretch/compression: a = 1, the graph is stretched by a factor of 1.

Direction of opening: As a > 0, the graph opens upwards.

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The price for each instructor will be the same at 3 hours. How I determined this answer:

First off, you need to add the initial price and hourly price for each person together, so you already know how much it will cost for 1 hour, including the initial fee. Here's how you do it:

Ieda: $11.00 (hourly price) + $8.50 (initial fee) = $19.50 (for 1 hour)

Thanh: $10.50 (hourly price) + $10.00 (initial fee) = $20.50 (for 1 hour)

Now that you have the price for 1 hour including the initial fee, now you need to find the price for each hour after that. Here's how I did that:

I created a graph that looked like this:

Hours: 1 2 3
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Thanh: 20.50 31.00 41.50

Here's how I figured out the price for each hour:

Ieda:

Hour 1 (including initial price):
$11.00 + $8.50 = $19.50
Hour 2 (excluding initial price): Only add the hourly price after Hour 1!
$19.50 + $11.00 = $30.50
Hour 3 (excluding initial price):
$30.50 + $11.00 = $41.50

Thanh:

Hour 1 (including initial price):
$10.50 + $10.00 = $20.50
Hour 2 (excluding initial price):
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Hour 3 (excluding initial price):
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I hope I was able to help you! :)

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3 years ago

Read 2 more answers

Solve the system by using a matrix equation.<br> --4x - 5y = -5<br> -6x - 8y = -2

evablogger [386]

Answer:

Solution : (15, - 11)

Step-by-step explanation:

We want to solve this problem using a matrix, so it would be wise to apply Gaussian elimination. Doing so we can start by writing out the matrix of the coefficients, and the solutions ( - 5 and - 2 ) --- ( 1 )

$\begin{bmatrix}-4&-5&|&-5\\ -6&-8&|&-2\end{bmatrix}$