Answer:
The equation of the function is;
y = |x-3| -3
Step-by-step explanation:
Here, we want to give the absolute-value function
For the minimum value to be -3, it means that k is negative
since the domain is the set of all real numbers, then we do not have any undefined value for the range y
So, the equation is ;
y = |x-3| - 3
A) Find KM∠KEM is a right angle hence ΔKEM is a right angled triangle Using Pythogoras' theorem where the square of hypotenuse is equal to the sum of the squares of the adjacent sides we can answer the
KM² = KE² + ME²KM² = 8² + (3√5)² = 64 + 9x5KM = √109KM = 10.44
b)Find LMThe ratio of LM:KN is 3:5 hence if we take the length of one unit as xlength of LM is 3xand the length of KN is 5x ∠K and ∠N are equal making it a isosceles trapezoid. A line from L that cuts KN perpendicularly at D makes KE = DN
KN = LM + 2x 2x = KE + DN2x = 8+8x = 8LM = 3x = 3*8 = 24
c)Find KN Since ∠K and ∠N are equal, when we take the 2 triangles KEM and LDN, they both have the same height ME = LD.
∠K = ∠N Hence KE = DN the distance ED = LMhence KN = KE + ED + DN since ED = LM = 24and KE + DN = 16KN = 16 + 24 = 40
d)Find area KLMNArea of trapezium can be calculated using the formula below Area = 1/2 x perpendicular height between parallel lines x (sum of the parallel sides)substituting values into the general equationArea = 1/2 * ME * (KN+ LM) = 1/2 * 3√5 * (40 + 24) = 1/2 * 3√5 * 64 = 3 x 2.23 * 32 = 214.66 units²
The conclusion that can be made given the slopes of the quadrilateral is that: since the slopes of the opposite sides are equal, the opposite sides are parallel, therefore the quadrilateral is a parallelogram. (Option A is correct).
<em><u>Recall:</u></em>
- The slopes of the opposite sides of a parallelogram are always parallel.
- When two lines have a slope that is equal, the lines are said to be parallel to each other.
The slopes given shows are:
-1/2, 3/2, -1/2, and 3/2
This implies that the quadrilateral has two pairs of equal sides that are parallel to each other.
- Therefore, the conclusion that can be made given the slopes of the quadrilateral is that: since the slopes of the opposite sides are equal, the opposite sides are parallel, therefore the quadrilateral is a parallelogram. (Option A is correct).
Learn more about parallelogram on:
brainly.com/question/3050890
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