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kompoz [17]
3 years ago
9

Find the length of the second base of a trapzoid with one base measuring 12 feet a height of 4 feet and a area of 58 square feet

Mathematics
1 answer:
Strike441 [17]3 years ago
6 0
Equation:
b1+b2 x h / 2 = 58
12+ b2 x 4 / 2 = 58
12+b2 x 4 = 116
12 + b2 = 29
b2 = 17 feet is the length of the second base 
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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

7 0
3 years ago
If f(x)=3x^2 and g(x)=4x^3, what is the degree of (f*g)(x)?
Westkost [7]
3x^2 * 4x^3 = 12x^5

Answer is degree 5
3 0
3 years ago
Read 2 more answers
Which is the graph of the sequence defined by the function f(x + 1) = Three-fifthsf(x) when the first term in the sequence is 37
nadezda [96]

Answer: On a coordinate plane, 4 points are plotted. The points are (1, 375), (2, 225), (3, 135), (4, 81).

Step-by-step explanation:

We have the relation:

f(x + 1) = (3/5)*f(x)

such that the first term is 375

Then:

f(1) = 375.

Using the above relation, we have that:

f(1 + 1) = f(2) = (3/5)*f(1) = (3/5)*375 = 225

Then we have the pair (2, 225)

The next term is:

f(2 + 1) = f(3) = (3/5)*f(2) = (3/5)*225 = 135

Then we have the pair (3, 135)

the next term is:

f(3 + 1) = f(4) = (3/5)*f(3) = (3/5)*135 = 81

Then we have the pair (3, 81)

Then the correct option is the first one; On a coordinate plane, 4 points are plotted. The points are (1, 375), (2, 225), (3, 135), (4, 81).

9 0
3 years ago
Read 2 more answers
4(x-4)-3x=10 what is the answer
max2010maxim [7]

Answer:

26

Step-by-step explanation:

4(x-4)-3x=10

  • Rule = a(b + c) = ab + ac
  • Rule = a(b - c) = ab - ac

4(x-4) = 4x - 16

4(x-4)-3x=10

4x - 16 - 3x = 10

x - 16 = 10

x -16 +16 = 10 +16

x = 26

Hope this helps ^-^

6 0
3 years ago
Write 245,800,000 in scientific notation.
Olenka [21]

Answer:

2.485x10^8

Step-by-step explanation:

3 0
2 years ago
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