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3 years ago

H(x) = x^2 + 2 - x g(x) = 4x + 5 find (h - g) (x/3)

Mathematics

1 answer:

Radda [10]3 years ago

3 0

Answer:

x^2 - 15x - 27

---------------------- (Answer C)

Step-by-step explanation:

(h - g)(x) is the difference between funcions h and g. Subtract g(x) from h(x) as follows:

x^2 + 2 - x

-(4x + 5)

-------------------

x^2 - 5x - 3 = (h - g)(x)

To find (h - g)(x/3), substitute x/3 for x in x^2 - 5x - 3 = (h - g)(x), obtaining:

(x/3)^2 - 5(x/3) - 3

We must expand this and then combine like terms:

x^2/9 - (5/3)x - 3

The LCD of these three terms is 9. The first term stays as is. The second term becomes (15/9)x. The third term becomes 27/9.

Combining these three terms, all with denominator 9, we get:

x^2 - 15x - 27

----------------------

This matches Answer C.

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Step-by-step explanation:

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3 years ago

Two angles of a triangle measure 22 and 53 what is the measure of the third angle

Musya8 [376]

The third angle is 105.
How do I know this?
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3 years ago

A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the flo

Arada [10]

Answer:

The parabolic shape of the door is represented by $y - 32 = -\frac{2}{49}\cdot x^{2}$ . (See attachment included below). Head must 15.652 inches away from the edge of the door.

Step-by-step explanation:

A parabola is represented by the following mathematical expression:

$y - k = C \cdot (x-h)^{2}$

Where:

$h$ - Horizontal component of the vertix, measured in inches.

$k$ - Vertical component of the vertix, measured in inches.

$C$ - Parabola constant, dimensionless. (Where vertix is an absolute maximum when $C < 0$ or an absolute minimum when $C > 0$ )

For the design of the door, the parabola must have an absolute maximum and x-intercepts must exist. The following information is required after considering symmetry:

$V (x,y) = (0, 32)$ (Vertix)

$A (x, y) = (-28, 0)$ (x-Intercept)

$B (x,y) = (28. 0)$ (x-Intercept)

The following equation are constructed from the definition of a parabola:

$0-32 = C \cdot (28 - 0)^{2}$

$-32 = 784\cdot C$

$C = -\frac{2}{49}$

The parabolic shape of the door is represented by $y - 32 = -\frac{2}{49}\cdot x^{2}$ . Now, the representation of the equation is included below as attachment.

At x = 0 inches and y = 22 inches, the distance from the edge of the door that head must observed to avoid being hit is:

$y -32 = -\frac{2}{49} \cdot x^{2}$