Answer:
m∠K = 37° and n = 31
Step-by-step explanation:
A lot of math is about matching patterns. Here, the two patterns we want to match are different versions of the same Law of Cosines relation:
- a² = b² +c² -2bc·cos(A)
- k² = 31² +53² -2·31·53·cos(37°)
<h3>Comparison</h3>
Comparing the two equations, we note these correspondences:
Comparing these values to the given information, we see that ...
- KN = c = 53 . . . . . . . . . . matching values 53
- NM = a = k . . . . . . . . . . . matching values k
- KM = b = n = 31 . . . . . . . matching values 31
- ∠K = ∠A = 37° . . . . . . . matching side/angle names
Abby apparently knew that ∠K = 37° and n = 31.
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<em>Additional comment</em>
Side and angle naming for the Law of Sines and the Law of Cosines are as follows. The vertices of the triangle are labeled with single upper-case letters. The side opposite is labeled with the same lower-case letter, or with the two vertices at either end.
Vertex and angle K are opposite side k, also called side NM in this triangle.
Answer:
19. x=28°
<E = 67°
20. x= 9°
<L = 25°
Step-by-step explanation:
19. Supplementary means that the angles will add to make a straight line, or they will add to = 180
<L+<E = 180°
4x+1°+3x-17°=180°
7x-16°=180°
7x=196°
x=28°
Measure of Angle E
<E = 3x-17° = 3(28°)-17° = 67°
20. Vertical angles are congruent, or equal to each other.
<L = <E
2x+7° = 4x-11°
2x+18° = 4x
18° = 2x
9° = x
x = 9°
<L = 2x+7° = 2(9°)+7° = 18°+7° = 25°
Answer:
479001600
Step-by-step explanation:
You will want to use 12!.
12*11*10*9*8*7*6*5*4*3*2*1=
479001600
Answer:
Perimeter ratio = 2:1
Area ratio = 4:1
Step-by-step explanation:
<u>Perimeter</u>
Perimeter of the smaller photo = 

inches
Perimeter of larger photo = 

inches
Ratio:
Perimeter of larger photo : perimeter of smaller photo = 

<u>Area</u>
Area of smaller photo = 

inches²
Area of larger photo = 

inches ²
Ratio
Area of larger photo : area of smaller photo = 

∴The ratio of the perimeters = 2:1, and the ratio of the areas = 4:1
Hope this helps :)