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Gnoma [55]
3 years ago
10

Drag each expression to the correct location on the table. Not all expressions will be used.

Mathematics
1 answer:
FrozenT [24]3 years ago
4 0

Answer:

The price of the ticket before tax - P

The amount of tax Jennifer pays- 0.08P

Jennifer's total amount for the ticket- P + 0.08P

Step-by-step explanation:

The price of the plane ticket is P dollars, before airport security tax. Here P is an independent variable.

An airport security tax of 8% is applied to the price of a plane ticket. So, the amount of airport security tax that Jennifer pays is 8% of the cost of her plane ticket, or 0.08P.

To find Jennifer's total amount for the plane ticket, add the price of the ticket before airport security tax and the amount of airport security tax Jennifer pays. So, the total amount of the plane ticket is P + 0.08P.

The table below shows the expressions matched to their meanings.

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Multiply (3x + 2) (4x-5)
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12x^2-7x-10

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Answer:

Step-by-step explanation:

Let the quadratic equation of the function by the points in the given equation is,

f(x) = ax² + bx + c

If the points lying on the graph are (-3, -10), (-4, -8) and (0, 8),

For (0, 8),

f(0) = a(0)² + b(0) + c

8 = c

For a point (-3, -10),

f(-3) = a(-3)² + b(-3) + 8

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For (-4, -8),

f(-4) = a(-4)² + b(-4) + 8

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Subtract equation (1) from equation (2)

(4a - b) - (3a - b) = -4 + 6

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From equation (1),

6 - b = -6

b = 12

Function will be,

f(x) = 2x² + 12x + 8

     = 2(x² + 6x) + 8

     = 2(x² + 6x + 9 - 9) + 8

     = 2(x² + 6x + 9) - 18 + 8

     = 2(x + 3)² - 10

By comparing this function with the vertex form of the function,

y = a(x - h)² + k

where (h, k) is the vertex.

Vertex of the function 'f' will be (-3, -10)

And axis of symmetry will be,

x = -3

From the given graph, axis of the symmetry of the function 'g' is; x = -3

Therefore, both the functions will have the same axis of symmetry.

y-intercept of the function 'f' → y = 8 Or (0, 8)

y-intercept of the function 'g' → y = -2 Or (0, -2)

Therefore, y-intercept of 'f' is greater than 'g'

Average rate of change of function 'f' = \frac{f(b)-f(a)}{b-a} in the interval [a, b]

                                                               = \frac{f(-3)-f(-6)}{-3+6}

                                                               = \frac{-10-8}{3}

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Average rate of change of function 'g' = \frac{g(b)-g(a)}{b-a}

                                                                = \frac{g(-3)-g(-6)}{-3+6}

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                                                                = 3

Therefore, Average rate of change of function 'f' is less than 'g'.

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