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Elodia [21]
3 years ago
10

What would be the sum (total) of 1 quarter note + 2 Half notes?

Mathematics
1 answer:
trapecia [35]3 years ago
3 0

Answer:

5/4 (In terms of fours)

Step-by-step explanation:

1/4+1/2+1/2

5/4

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Find the values of x for which the combined function h(x) =f(x)/g(x) is undefined if f(x) = 5x + 1 and g(x) = x2 - 9.
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Hello : 
<span>the function h(x) =f(x)/g(x) is undefined : x²-9 =0
(x-3)(x+3)=0
x-3=0 or x+3=0
</span><span> the values  : </span>x=3 or x= -3
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Write an equation for a quadratic function that has x intercepts (-3, 0) and (5, 0)
Blizzard [7]

Answer:

One possible equation is f(x) = (x + 3)\, (x - 5), which is equivalent to f(x) = x^{2} - 2\, x - 15.

Step-by-step explanation:

The factor theorem states that if x = x_{0}  (where x_{0} is a constant) is a root of a function, (x - x_{0}) would be a factor of that function.

The question states that (-3,\, 0) and (5,\, 0) are x-intercepts of this function. In other words, x = -3 and x = 5 would both set the value of this quadratic function to 0. Thus, x = -3\! and x = 5\! would be two roots of this function.

By the factor theorem, (x - (-3)) and (x - 5) would be two factors of this function.

Because the function in this question is quadratic, (x - (-3)) and (x - 5) would be the only two factors of this function. In other words, for some constant a (a \ne 0):

f(x) = a\, (x - (-3))\, (x - 5).

Simplify to obtain:

f(x) = a\, (x + 3)\, (x - 5).

Expand this expression to obtain:

f(x) = a\, (x^{2} - 2\, x - 15).

(Quadratic functions are polynomials of degree two. If this function has any factor other than (x - (-3)) and (x - 5), expanding the expression would give a polynomial of degree at least three- not quadratic.)

Every non-zero value of a corresponds to a distinct quadratic function with x-intercepts (-3,\, 0) and (5,\, 0). For example, with a = 1:

f(x) = (x + 3)\, (x - 5), or equivalently,

f(x) = x^{2} - 2\, x - 15.

6 0
2 years ago
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