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Daniel [21]
3 years ago
10

What is the explicit formula for this sequence?-6 -1 4 9 14​

Mathematics
1 answer:
kogti [31]3 years ago
4 0
The answer is B, (plus 5)
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Help with this please.
Ivanshal [37]

Answer:

  • True
  • True

Step-by-step explanation:

This question asks you to compare the coordinates of the vertex of each function.

__

The vertex of the function is its minimum, the point where the graph stops decreasing and starts increasing. It is the lowest point on the graph.

<h3>f(x)</h3>

The vertex is (-4, -1). The minimum is -1, located at x = -4.

<h3>g(x)</h3>

The vertex is (1, -25). The minimum is -25, located at x = 1. We know this is the minimum because there are no g(x) values that are lower (more negative).

<h3>comparison</h3>

The minimum of f(x), -1, is greater than the minimum of g(x), -25. TRUE

The x-value of f(x) at its minimum, -4, is less than the x-value of g(x) at its minimum, 1. TRUE

8 0
2 years ago
Number 27.
atroni [7]
<h3>Answer:</h3>

none of these has "no solution"

<h3>Explanation:</h3>

A. The solution is (8/3, 3)

B. The second equation is -1/2 times the first, so these describe the same line. The system has an <em>infinite number of solutions</em>.

C. The solution is (-4, -2)

D. The solution is (4, -2)

E. The second equation is 2 times the first, so these describe the same line. The system has an <em>infinite number of solutions</em>.

_____

A system of equations will have "no solution" when it describes parallel lines—lines that do not intersect. In standard form, such equations are recognizable by their different constants. For example,

  • 3x -4y = -4
  • 3x -4y = 20 . . . . . . 20 is different from -4

have different constants, so the equations describe parallel lines.

We could multiply one of these by -2 and the system would still be "inconsistent"—having no solution.

  • 3x -4y = -4
  • -6x +8y = -40
5 0
3 years ago
If A(-5,7), B(-4,-5), C(-1,-6) and D(4,5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.
MrMuchimi
After plotting the quadrilateral in a Cartesian plane, you can see that it is not a particular quadrilateral. Hence, you need to divide it into two triangles. Let's take ABC and ADC.

The area of a triangle with vertices known is  given by the matrix
M = \left[\begin{array}{ccc} x_{1}&y_{1}&1\\x_{2}&y_{2}&1\\x_{3}&y_{3}&1\end{array}\right]

Area = 1/2· | det(M) |
        = 1/2· | x₁·y₂ - x₂·y₁ + x₂·y₃ - x₃·y₂ + x₃·y₁ - x₁·y₃ |
        = 1/2· | x₁·(y₂ - y₃) + x₂·(y₃ - y₁) + x₃·(y₁ - y₂) |

Therefore, the area of ABC will be:
A(ABC) = 1/2· | (-5)·(-5 - (-6)) + (-4)·(-6 - 7) + (-1)·(7 - (-5)) |
             = 1/2· | -5·(1) - 4·(-13) - 1·(12) |
             = 1/2 | 35 |
             = 35/2

Similarly, the area of ADC will be:
A(ABC) = 1/2· | (-5)·(5 - (-6)) + (4)·(-6 - 7) + (-1)·(7 - 5) |
             = 1/2· | -5·(11) + 4·(-13) - 1·(2) |
             = 1/2 | -109 |
<span>             = 109/2</span>

The total area of the quadrilateral will be the sum of the areas of the two triangles:

A(ABCD) = A(ABC) + A(ADC) 
               = 35/2 + 109/2
               = 72
8 0
3 years ago
please answer asap! A couple plans to have 5 children. The gender of each child is equally likely. Design a simulation involving
dimulka [17.4K]

Step-by-step explanation:

The gender of a child which is either a boy or a girl is determined by the XX-chromosomes, or XY-chromosomes.

Since the couple plan to have 5 children, the chance of a child being a boy is equal to the chance of it being a girl - the chances are 50/50.

What we do to achieve our aim is to run a simulation that would add an X or Y to an X for all 5 children.

Doing this 125 times, we obtain the number of trials we desire.

For each trial, we get for each child, C:

C1: X + (X or Y)

C2: X + (X or Y)

C3: X + (X or Y)

C4: X + (X or Y)

C5: X + (X or Y)

Since the chance of having an X is equal to the chance of having a Y, they equal probability, which is 0.5 for each.

6 0
2 years ago
What is Question I (if m&lt;EBF = 117°, fine m&lt;ABE)​
Natasha_Volkova [10]

Answer:

m∠ABE = 27°

Step-by-step explanation:

* Lets look to the figure to solve the problem

- AC is a line

- Ray BF intersects the line AC at B

- Ray BF ⊥ line AC

∴ ∠ABF and ∠CBF are right angles

∴ m∠ABF = m∠CBF = 90°

- Rays BE and BD intersect the line AC at B

∵ m∠ABE = m∠DBE ⇒ have same symbol on the figure

∴ BE is the bisector of angle ABD

∵ m∠EBF = 117°

∵ m∠EBF = m∠ABE + m∠ABF

∵ m∠ABF = 90°

∴ 117° = m∠ABE + 90°

- Subtract 90 from both sides

∴ m∠ABE = 27°

4 0
3 years ago
Read 2 more answers
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