Answer:
C
Step-by-step explanation:
Step 1: find BC
Given Triangles ABC and ADE are similar,
= 
BC = x DE
= 
x 9
= 6 cm
Step 2: use Pythagorean theorem to find AC and / or AE
Consider triangle ABC,
by Pythagorean theorem,
AB² + BC² = AC²
AC² = 6² + 8² = 100
AC = √100 = 10 (answer... we can see that C is the only one with AC=10.
Step 3: Verify.. even though we know that it is C because AC = 10, you can verify that the ansewer is correct by finding CE and confirming that CE=5
By using similar triangles ABC and ADE,
AC/AE = AB / AD
AE = AD/AB x AC = 12/8 x 10 = 15
CE = AE - AC = 15 - 10 = 5 (answer confirmed)
In a square, all sides are equal and all angles are equal.
So, the length of the side is only the height.
Therefore height can be:
1)The root of the area of square
2)The perimeter divided by 4
For
to be continuous at
, you need to have the limit from either side as
to be the same.
If
and
, then the limit from the right would be
, so the answer to part (1) is no, the function would not be continuous under those conditions.
This basically answers part (2). For the function to be continuous, you need to satisfy the relation
.
Part (c) is done similarly to part (1). This time, you need to limits from either side as
to match. You have
So,
and
have to satisfy the relation
, or
.
Part (4) is done by solving the system of equations above for
and
. I'll leave that to you, as well as part (5) since that's just drawing your findings.
The <em>second order</em> polynomial that involves the variable <em>x</em> (border inside the rectangle) and associated to the <em>unshaded</em> area is x² - 62 · x + 232 = 0.
<h3>How to derive an expression for the area of an unshaded region of a rectangle</h3>
The area of a rectangle (<em>A</em>), in square inches, is equal to the product of its width (<em>w</em>), in inches, and its height (<em>h</em>), in inches. According to the figure, we have two <em>proportional</em> rectangles and we need to derive an expression that describes the value of the <em>unshaded</em> area.
If we know that <em>A =</em> 648 in², <em>w =</em> 22 - x and <em>h =</em> 40 - x, then the expression is derived below:
<em>A = w · h</em>
(22 - x) · (40 - x) = 648
40 · (22 - x) - x · (22 - x) = 648
880 - 40 · x - 22 · x + x² = 648
x² - 62 · x + 232 = 0
The <em>second order</em> polynomial that involves the variable <em>x</em> (border inside the rectangle) and associated to the <em>unshaded</em> area is x² - 62 · x + 232 = 0. 
To learn more on polynomials, we kindly invite to check this verified question: brainly.com/question/11536910
Answer:
79
Step-by-step explanation:
They have the same angle measure because the angles are corresponding angles.
