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saw5 [17]
3 years ago
6

Sienna is solving the quadratic equation by completing the square.

Mathematics
2 answers:
VladimirAG [237]3 years ago
6 0

Answer:  The correct option is (C) 3.

Step-by-step explanation: Given that Sienna is solving the quadratic equation by completing the square as follows:

3x2+9x-4=0\\\\\Rightarrow 3x^2+9x=4\\\\\Rightarrow a(x^2+3x)=4.

We are given to find the find the value of a.

We can see that in the second step of Sienna's solution, 3 is common in both the terms, 3x2 and 9x.

So, she took 3 out and then in the third step, the expression within the bracket remais x^2+3x.

Therefore, the complete steps are as follows:

3x2+9x-4=0\\\\\Rightarrow 3x^2+9x=4\\\\\Rightarrow 3(x^2+3x)=4.

Hence, the value of a is 3.

Thus, (C) is the correct option.

kari74 [83]3 years ago
4 0
3x^2 + 9x - 4
3x^2 + 9x = 4
3(x^2 + 3x) = 4

Therefore, a = 3
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A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh
Stella [2.4K]

A parabola is a mirror-symmetrical U-shape.

  • The equation of the parabola is \mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}
  • The focus is \mathbf{Focus = (80, -1760)}
  • The directrix is \mathbf{y = \frac{1}{640}}
  • The axis of the symmetry of parabola is: \mathbf{x = 80}

From the question, we have:

\mathbf{Vertex: (h,k) = (80,10)}

\mathbf{Origin: (x,y) = (0,0)}

The equation of a parabola is:

\mathbf{y = a(x - h)^2 + k}

Substitute the values of origin and vertex in \mathbf{y = a(x - h)^2 + k}

\mathbf{0 = a(0 - 80)^2 + 10}

\mathbf{0 = a(- 80)^2 + 10}

\mathbf{0 = 6400a + 10}

Collect like terms

\mathbf{6400a =- 10}

Solve for a

\mathbf{a =- \frac{1}{640}}

Substitute the values of a and the vertex in \mathbf{y = a(x - h)^2 + k}

\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}

The focus of a parabola is:

\mathbf{Focus = (h, \frac{k+1}{4a})}

Substitute the values of a and the vertex in \mathbf{Focus = (h, \frac{k+1}{4a})}

\mathbf{Focus = (80, \frac{10+1}{4 \times -\frac{1}{640}})}

\mathbf{Focus = (80, -\frac{11}{\frac{1}{160}})}

\mathbf{Focus = (80, -11\times 160)}

\mathbf{Focus = (80, -1760)}

The equation of the directrix is:

\mathbf{y = -a}

So, we have:

\mathbf{y = \frac{1}{640}} ----- the directrix

The axis of symmetry is:

\mathbf{x = -\frac{b}{2a}}

We have:

\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}

Expand

\mathbf{y = -\frac{1}{640}(x^2 -160x + 6400) +10}

Expand

\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x - 10 +10}

\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x }

A quadratic function is represented as:

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So, we have:

\mathbf{a = -\frac{1}{640}}

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Recall that:

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Central angles are shaped by an arc between the two points. When a central angle and the inscribed angle intercept the same arc, then the central angle would be the double of the inscribed angles while the inscribed angle will be half of the central angle.

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