1. You have that:
- The<span> lengths of the bases are (6x-1) units and 3 units.
- The midsegment has a length of (5x-3) units.
2. To solve this exercise, you must apply the formula for calculate the length of the midsegment of a trapezoid, which is shown below:
Midsegment=Base1+Base2/2
As you can see, the midsegment is half the sum of the bases of the trapezoid.
3. When you substitute the values, you obtain:
(5x-3)=[(6x-1)+3]/2
4. Now, you can solve the problem by clearing the "x":
</span>
(5x-3)=[(6x-1)+3]/2
2(5x-3)=6x-1+3
10x-6=6x+2
10x-6x=2+6
4x=8
x=8/4
x=2
10 because it makes the most sense
<span>The definition of quadratic function is given by:
</span>

<span>
So the problem asks for two conditions:
<em>1. Write the quadratic function in factored form.
</em>
<em>2. The vertex has an x-coordinate of 3.</em>
Then the equation (1) must be written as follows:
</span>

<span>
To satisfy the two conditions:
So we are free to choose the value of one root, say:

Thus:
Finally,
the answer is:

The graph of this function is shown in the figure below.</span>
Step-by-step explanation:
<u>In isocseles triangle, base angles </u><u>are</u><u> equal</u> :
base angles are angle N and angle P:
angle N=angle P
3x+17=4x+2
4x-3x=17-2
x=15
<u>F</u><u>o</u><u>r</u><u> </u><u>a</u><u>n</u><u>g</u><u>l</u><u>e</u><u> </u><u>N</u><u>:</u>
subtitute x in angle N
=3(15)+17
=45+17
=62
<u>F</u><u>o</u><u>r</u><u> </u><u>a</u><u>n</u><u>g</u><u>l</u><u>e</u><u> </u><u>P</u><u>:</u>
subtitute x in angle P:
=4(15)+2
=60+2
=62
<u>F</u><u>o</u><u>r</u><u> </u><u>a</u><u>n</u><u>g</u><u>l</u><u>e</u><u> </u><u>O</u><u>:</u>
sum of all angles in a triangle is 180.
angle N +angle P+angle O=180
62+62+angle O=180
angle O=180-62-62
angle O=56
<u>N</u><u>o</u><u>t</u><u>e</u><u>:</u><u> </u><u>i</u><u>f</u><u> </u><u>y</u><u>o</u><u>u</u><u> </u><u>have</u><u> </u><u>any</u><u> </u><u>question</u><u> </u><u>l</u><u>e</u><u>t</u><u> </u><u>m</u><u>e</u><u> </u><u>k</u><u>n</u><u>o</u><u>w</u><u> </u><u>a</u><u>b</u><u>o</u><u>u</u><u>t</u><u> </u><u>i</u><u>t</u><u>.</u><u> </u><u>t</u><u>h</u><u>a</u><u>n</u><u>k</u><u>s</u>