In ΔLMN, the measure of ∠N=90°, ML = 97, NM = 65, and LN = 72. What ratio represents the tangent of ∠L?

The tangent of ∠L represents the ratio between side NM and side LN.

The value of this tangent is 0.9028

Step-by-step explanation:

The angle ∠N is 90°, so we have a right triangle. In a right triangle, the tangent of an angle represents the ratio between the opposite side of that angle and the adjacent side (the cathetus, not the hypotenusa) of that angle.

So, in the triangle LMN, the opposite side to the angle ∠L is NM, and the adjacent side is LN (ML is the hypotenusa, because it is the bigger side). The value of this tangent is:

tan(L) = NM / LN = 65 / 72 = 0.9028

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.