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Pani-rosa [81]
3 years ago
11

Describe how to transform the quantity of the third root of x to the fourth power, to the fifth power into an expression with a

rational exponent. Make sure you respond with complete sentences
Mathematics
1 answer:
Novosadov [1.4K]3 years ago
8 0

Answer:

x^{\frac{20}{3} }

Step-by-step explanation:

To write: third root of x to the fourth power, to the fifth power into an expression with a rational exponent

Solution:

Exponent refers to the number of times a number is multiplied to itself.

Exponent is sometimes also known as power.

Third roots of x=x^{\frac{1}{3} }

Third root of x to the fourth power(x^{\frac{1}{3} })^4 =x^{\frac{4}{3} }

Third root of x to the fourth power, to the fifth power=(x^{\frac{4}{3} })^5= x^{\frac{20}{3} }

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I believe it’s 0.6% I just did 170/255
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Which description best fits the distribution of the data shown in the histogram?
s344n2d4d5 [400]
This is an approximately bell-shaped distribution. The highest bar is in the center, with height = 12. Just to its left and right are bars of heights 6 and 5. At the extremes are bars of heights 2 and 1.

If the highest bar was on the left, it would be skewed left (and if it was on the right, skewed right). A uniform distribution would more or less have the same height level over all the bars.
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Y=-x^2+6x-4<br> Find the Axis of Symmetry and the Vertex, Also solve the whole equation.
Inessa [10]

Answer:

1. <em>Axis of symmetry</em>: x = 3

2. <em>Vertex:</em> (3,5)

3. <em>Solution of the equation</em>:

<u />

  • x-intercepts:

               (3-\sqrt{5},0) \\\\(3+\sqrt{5},0)

  • y-intercept: (0, -4)

Explanation:

<u>1. Equation:</u>

    y=-x^2+6x-4

<u>2. </u><em><u>Axis of symmetry:</u></em>

That is the equation of a parabola, whose standard form is:

                 y=ax^2+bx+c

Where:    

                 a=-1;b=6;c=-4

The axis of symmetry is the vertical line with equation:

               x=-b/2a

Substitute  a=-1,\text{ and }b=6

          x=-6/[(2)(-1)]=-6/(-2)=3

Thus, the axis of symmetry is:

            x=3

<em><u>3. Vertex</u></em>

<em><u /></em>

The x-coordinate of the vertex is equal to the axys of symmetry, i.e x = 3.

To find the y-xoordinate, substitute this value of x into the equation for y:

               y=-x^2+6x-4\\\\y=-(3)^2+6(3)-4=-9+18-4=5

Therefore, the vertex is (3, 5)

<u>4. Find the x-intercepts</u>

The x-intercepts are the roots of the equation, which are the points wher y = 0.

        y=-x^2+6x-4=0

Use the quadratic equation:

       x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} \\\\x=\frac{-6\pm\sqrt{(-6)^2-4(-1)(-4)} }{2(-1)}\\\\x_1=3-\sqrt{5} \\\\x_2=3+\sqrt{5}

<u>5. Find the y-intercept</u>

<u />

The y-intercet is the value of y when x=0:

         y=-x^2+6x-4\\\\y=-(0)^2+6(0)-4=-4

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The height of a triangular window is 3 feet less than its base. The area the window is 20 ft.? find the dimensions of the window
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Plugging values in formula, we get

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\mathrm{Multiply\:both\:sides\:by\:}2

40=b\left(b-3\right)

40=b^2-3b

b^2-3b-40=0

Factoring quadratic, we get

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<h3>Therefore, base of the triangle = 8 feet and height = 8 -3 = 5 feet.</h3>
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