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11111nata11111 [884]
3 years ago
13

Can anyone show me the steps and answer?

Mathematics
1 answer:
valina [46]3 years ago
8 0

Answer:

  (-∞, 3) ∪ (3, 4) ∪ (4, ∞)

Step-by-step explanation:

<u>Steps</u>:

1. Read and understand the question. Here, you're being asked for the domain of a rational function, one with a 2nd-degree polynomial in the denominator. The domain is the set of x-values for which the function is defined.

2. Understand that the function will be undefined when the denominator is zero, so to answer the question, you must find the values of x that make the denominator zero.

3. Use any of the methods you have been taught to determine the zeros of the denominator polynomial. For this one, it is convenient to factor it:

  x² -7x +12 = (x -3)(x -4)

The values of x that make this zero are 3 and 4, so these values are excluded from the domain.

4. Write an expression in interval notation that includes all real numbers except 3 and 4. That is, you want to translate this to interval notation:

  (-∞ < x < 3) ∪ (3 < x < 4) ∪ (4 < x < ∞)

Using what you know about interval notation, you write it as ...

  (-∞, 3) ∪ (3, 4) ∪ (4, ∞)

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Lera25 [3.4K]

Answer:

A. y ≤ 1

Step-by-step explanation:

according to the graph, the coordinates of maximum value is (-3, 1) and besides the graph towards down, so, the range of the function is y ≤ 1

4 0
3 years ago
what positive number satisfies the condition that twice the number minus three times the reciprocal of the number is equal to 1?
marshall27 [118]
Solve:

"<span>twice the number minus three times the reciprocal of the number is equal to 1."
                                                     3(1)
Let the number be n.  Then 2n - ------- = 1
                                                       n

Mult all 3 terms by n to elim. the fractions:

2n^2 - 3 = n.  Rearranging this, we get 2n^2 - n - 3 = 0.

We need to find the roots (zeros or solutions) of this quadratic equation.

Here a=2, b= -1 and c= -3.  Let's find the discriminant b^2-4ac first:

disc. = (-1)^2 - 4(2)(-3) = 1 + 24 = 25.

That's good, because 25 is a perfect square.
                -(-1) plus or minus 5         1 plus or minus 5
Then x = ------------------------------ = --------------------------
                            2(2)                                  4

x could be 6/4 = 3/2, or -5/4.

You must check both answers in the original equation.  If the equation is true for one or the other or for both, then you have found one or more solutions.</span>
8 0
3 years ago
A car travels at an average speed of 56 miles per hour. How many miles does it travel in 4 hours and 15 minutes?
ivolga24 [154]
56*(4+15/60)

56*(240+15)/60

56*(255)/60

238 miles


8 0
3 years ago
Read 2 more answers
Find the distance between (6, -7), (3, -5) round your answer to the nearest tenth
saw5 [17]

Answer:

d ≈ 3.6 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2    }

with (x₁, y₁ ) = (6, - 7 ) and (x₂, y₂ ) = (3, - 5 )

d = \sqrt{(3-6)^2+(-5-(-7))^2}

   = \sqrt{(-3)^2+(-5+7)^2}

   = \sqrt{9+2^2}

   = \sqrt{9+4}

    = \sqrt{13}

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3 0
2 years ago
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Answer:

A, C, F

Step-by-step explanation:

4 0
3 years ago
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