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2 years ago

Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range. y=-0.5x^2+0.7x-5.1

Mathematics

2 answers:

lianna [129]2 years ago

8 0

Answer:

The domain of the equation is all real number and the range of the equation is (-∞,-4.885].

Step-by-step explanation:

The given quadratic equation is

$y=-0.5x^2+0.7x-5.1$

Use a graphing calculator to sketch the graph of the quadratic equation.

The graph of given quadratic equation is shown below.

From the graph it is clear that it is a downward parabola and the vertex of the parabola is (0.7,-4.885).

The function is defined from all values of x, therefore the domain of the function is all real number.

The vertex of the parabola is (0.7,-4.885). It means the maximum value of the function is -4.885 and the value of y cannot be more than -4.885.

So, the range of the function is

$Range=\{y|y\leq -4.885\}$

Therefore the domain of the equation is all real number and the range of the equation is (-∞,-4.885].

blsea [12.9K]2 years ago

4 0

The graph below is on the scale of five and I hope it is helpful.

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Step-by-step explanation:

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N76 [4]

The simplification of the polynomial expression will give 3x² - 20x + 8.

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The polynomial expression is given as:

(5x² + 13x4) (17x² + 7x - 19) + (5x-7)(3x + 1)

= 5x² + 13x - 4 - 17x² - 7x + 19 + 15x² + 5x - 21x - 7

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Oliga [24]

Answer:

Part A)

The height of the water level in the rectangular vessel is 2 centimeters.

Part B)

4000 cubic centimeters or 4 liters of water.

Step-by-step explanation:

We are given a cubical vessel that has side lengths of 10cm. The vessel is completely filled with water.

Therefore, the total volume of water in the cubical vessel is:

$V_{C}=(10)^3=1000\text{ cm}^3$

This volume is poured into a rectangular vessel that has a length of 25cm, breadth of 20cm, and a height of 10cm.

Therefore, if the water level is h centimeters, then the volume of the rectangular vessel is:

$V_R=h(25)(20)=500h\text{ cm}^3$

Since the cubical vessel has 1000 cubic centimeters of water, this means that when we pour the water from the cubical vessel into the rectangular vessel, the volume of the rectangular vessel will also be 1000 cubic centimeters. Hence:

$500h=1000$

Therefore:

$h=2$

So, the height of the water level in the rectangular vessel is 2 centimeters.

To find how how much more water is needed to completely fill the rectangular vessel, we can find the maximum volume of the rectangular vessel and then subtract the volume already in there (1000 cubic centimeters) from the maximum volume.

The maximum value of the rectangular vessel is given by :

$A_{R_M}=20(25)(10)=5000 \text{ cm}^3$

Since we already have 1000 cubic centimeters of water in the vessel, this means that in order to fill the rectangular vessel, we will need an additional:

$(5000-1000)\text{ cm}^3=4000\text{ cm}^3$