What is length of BC ?
1 answer:
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Let x refers to the Month numbers
And y refers to Number of births
There is 5 steps to find the quadratic function that models the data.
First step ⇒ <span>Plot <span>the data pairs (<span>x<span>, <span>y<span>) in a coordinate plane.
which are the blue circles in the attached figure
Second step ⇒ </span></span></span></span></span></span><span>Draw <span>the parabola you think best fits the data.
Which is the red function in the attached figure.
</span></span><span><span>Third step ⇒</span> Estimate <span>the coordinates of three points on the
<span> parabola, which are (2, 108), (4, 68), and (6, 75).</span>
</span></span><span><span>which are the black squares in the attached figure</span>
Fourth step ⇒ </span><span>Substitute <span>the coordinates of the points into the<span> model <span>
y <span>= <span>ax<span>2 <span>+ <span>bx <span>+ <span>c
<span> to obtain a system of three linear equations.</span>
4a + 2 b + c = 108 ---------(1)
</span></span></span></span></span></span></span></span></span></span></span><span><span>16a + 4 b + c = 68 ---------(2)</span>
36a + 6 b + c = 75 ---------(3)
Fifth step ⇒ </span><span>Solve <span>the linear system.
By using the calculator
a = 5.875 , b = -55.25 , c = 195
So, the</span></span><span> quadratic model for the data is ⇒ y = 5.875 x²- 55.25 x + 195
============================================
T</span><span>o predict the number of births for month 8
substitute with x = 8 ⇒ y = </span><span>5.875 * 8²- 55.25 * 8 + 195 = 129</span>
And y refers to Number of births
There is 5 steps to find the quadratic function that models the data.
First step ⇒ <span>Plot <span>the data pairs (<span>x<span>, <span>y<span>) in a coordinate plane.
which are the blue circles in the attached figure
Second step ⇒ </span></span></span></span></span></span><span>Draw <span>the parabola you think best fits the data.
Which is the red function in the attached figure.
</span></span><span><span>Third step ⇒</span> Estimate <span>the coordinates of three points on the
<span> parabola, which are (2, 108), (4, 68), and (6, 75).</span>
</span></span><span><span>which are the black squares in the attached figure</span>
Fourth step ⇒ </span><span>Substitute <span>the coordinates of the points into the<span> model <span>
y <span>= <span>ax<span>2 <span>+ <span>bx <span>+ <span>c
<span> to obtain a system of three linear equations.</span>
4a + 2 b + c = 108 ---------(1)
</span></span></span></span></span></span></span></span></span></span></span><span><span>16a + 4 b + c = 68 ---------(2)</span>
36a + 6 b + c = 75 ---------(3)
Fifth step ⇒ </span><span>Solve <span>the linear system.
By using the calculator
a = 5.875 , b = -55.25 , c = 195
So, the</span></span><span> quadratic model for the data is ⇒ y = 5.875 x²- 55.25 x + 195
============================================
T</span><span>o predict the number of births for month 8
substitute with x = 8 ⇒ y = </span><span>5.875 * 8²- 55.25 * 8 + 195 = 129</span>
Answer:
One Triangle = 2.09 in²
Two Triangles = 4.18 in²
Rectangle = 17.48 in²
Total area of whole trapezoid = 21.66 in²
Step-by-step explanation:
Since it was not clarified which region is shaded we will just find the area of each individual part of the shape.
Let's start with the triangles.
1. To find the area of a triangle, the formula is . It is given that the base of one triangle is equal to 1.1 in and the height is equal to 3.8 in., so in the equation, it would look like:
in²
2. So now that we know one triangle is equal to 2.09 in², we now know that the other triangle is equal to the same area. To find the total of the two triangles you need to multiply the area by 2:
in²
Moving on to the rectangle...
1. To find the area of the rectangle we need to use the formula base times height or b x h. It is given that the height is 3.8 in while the length is 4.6 in. So in the equation it would look like:
in²
Now to find the total area of all shapes combined...
1. To do this, we just need to add up all the areas we found, so...
17.48 + 4.18 = 21.66 in²