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pashok25 [27]
3 years ago
10

state the domain, the range, and the intervals on which function is increasing, decreasing, or constant in interval notation

Mathematics
1 answer:
erma4kov [3.2K]3 years ago
8 0

Answer:

  • domain (-∞, ∞)
  • range (-∞, 4]
  • increasing (-∞, 0)
  • decreasing (0, ∞)
  • constant (only at x=0, not on any interval)

Step-by-step explanation:

The graph is of the equation y = -x^2 +4. It is a polynomial of even degree, so has a domain of all real numbers: (-∞, ∞).

The vertical extent of the graph includes y=4 and all numbers less than that:

  range: (-∞, 4]

The graph is increasing to the left of its vertex at x=0, decreasing to the right.

  increasing (-∞, 0); decreasing (0, ∞)

There is no interval on which the function is constant. It has a horizontal tangent at x=0, but a single point does not constitute an interval.

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and
\sqrt{ab^2} =b \sqrt{a}
\sqrt{ \frac{32}{5} } = \frac{ \sqrt{(4^2)(2)} }{ \sqrt{5} } = \frac{ 4\sqrt{2} }{ \sqrt{5} }
times whoe thing by \frac{ \sqrt{5} }{ \sqrt{5} }
\frac{4 \sqrt{10} }{5}


3 0
3 years ago
The difference between three times a number and seven is twenty. What is the number?
Mama L [17]

Answer:

9

Step-by-step explanation:

(9*3) = 27 which is 20 more than 7

6 0
3 years ago
In this diagram, which equation could you prove to be true in order to conclude that the lines are parallel?
Y_Kistochka [10]
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6 0
3 years ago
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What is the area of a triangle with vertices (3,0) (9,0) (7,6)
Nezavi [6.7K]

Answer:

The area of the triangle is of 21 units of area.

Step-by-step explanation:

The area of a triangle with three vertices (x_1,y_1),(x_2,y_2),(x_3,y_3) is given by the determinant of the following matrix:

A = \pm 0.5 \left|\begin{array}{ccc}x_1&y_1&1\\x_2&y_2&1\\1_3&y_3&1\end{array}\right|

In this question:

Vertices (3,0) (9,0) (7,6). So

A = \pm 0.5 \left|\begin{array}{ccc}3&0&1\\9&0&1\\7&7&1\end{array}\right|

A = \pm 0.5(3*0*1+0*1*7+1*9*7-0*7*1-0*9*1-3*1*7)

A = \pm 0.5*(63-21)

A = \pm 0.5*42 = 21

The area of the triangle is of 21 units of area.

5 0
3 years ago
Help please really don’t know what the answers is
Arturiano [62]

Answer:

No

Step-by-step explanation:

The Side-Angle-Side rule of congruence

two triangles are congruent if two sides and one included angle in a given triangle are equal to the corresponding two sides and one included angle in another triangle.

8 0
3 years ago
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