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weeeeeb [17]
3 years ago
13

Organize the following expressions from greatest to least by number of terms: (2 points) I. 6x2 II. 18x2 + 5ab − 6y III. 8a − 5

IV. 4x3 + 3x2 − x − 4 II, III, IV, I IV, II, I, III III, II, I, IV IV, II, III, I
Mathematics
1 answer:
Mnenie [13.5K]3 years ago
5 0
The last answer is correct, or IV, II, III, I. We can tell because we can see the amount of terms in each expression. In expression IV, there are 4 terms (4*3 + 3*2 - x - 4), expression II has 3 terms (18*2 + 5ab - 6y), expression III has 2 terms (8a - 5), and expression I has 1 term. (6*2)
Hope that helped =)
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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:

\mathbf{y = ax^2 + bx + c}

So, we have:

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

\mathbf{b = \frac{1}{4}}

Recall that:

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

So, we have:

\mathbf{x = -\frac{1/4}{2 \times -1/640}}

\mathbf{x = \frac{1/4}{1/320}}

This gives

\mathbf{x = \frac{320}{4}}

\mathbf{x = 80}

Hence, the axis of the symmetry of parabola is: \mathbf{x = 80}

Read more about parabola at:

brainly.com/question/21685473

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Please help!!!!!<br>Solve the equation 5(2y - 1) - 2(3y)= 1<br>​
-Dominant- [34]

Answer:

y = 3/2

Step-by-step explanation:

5(2y - 1) - 2(3y) = 1

First we use distributive property:

10y - 5 - 6y = 1

because 5 × 2y = 10y

and -2 × 3y = -6y

Now we combine the like terms:

4y -5 = 1

because 10y - 6y = 4y

Now we have to send the -5 to the other side. (when we send it to the other side it becomes positive because right now it is negative)

4y = 1 + 5

Again we combine the like terms:

4y = 6

(because 5 + 1 = 6)

Now we have to send the 4 to the other side because we need to get the y value. (when we send it to the other sidr it will be divided)

y = 6/4

and we simplify:

y = 3/2

And we cannot simplify or do anything else. So that is the answer.

Hope that helped!

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We can not round it to the tenths because it already is rounded to the tenths.
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