Part 1:
Given that triangle EFG is similar to triangle LMN, this means that the ratio of the measures of any two sides of triangle EFG is equal to the ratio of the measures of the corresponding sides of triangle LMN.
From the figure shown
FG / EG = MN / LN
⇒ 4 / 7 = 2 / LN
⇒ LN = 7 * 2 / 4 = 14 / 4 = 3.5
Therefore, LN = 3.5
Part 2:
<span>Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Thus, </span>if<span> m∠A = m∠D. The other fact that would guarantee that the triangles are similar is that m∠C = m∠F.
This is because if </span><span>m∠A = m∠D and </span><span>m∠C = m∠F, then </span><span><span>m∠B = m∠E and thus satisfies the triangle similarity condition.
</span>Part 3:
</span><span>Given
that the two triangles shown are congruent, one way to verify
that the corresponding angles of the two triangles are congruent is to place one of the triangle on top of the other to see if the corresponding angles of both triangles coincide.
This can be achieved by translating triangle 2 up by 2 units, and to the left by 6 units.
Part 4:
Given that t</span><span>rapezoid ABCD and trapezoid JKLM are similar.
From the naming of the trapezoids, the order of the naming of any similar object corresponds to the order of their similarity.
Thus, side AB corresponds to side JK, side AC corresponds to side JL and so on.
Therefore, the side that corresponds to side AB is side JK.</span>
Answer:
24 in all
Step-by-step explanation:
1,100/45=24
25+20=45
The answer is C: the average reading speed of the science fiction novel.
If x is her reading speed for the historical fiction novel, and her reading speed for the sci-fi novel is just two pages more than that of the historical fiction novel, then the equation to find out how fast she reads the science fiction novel would be x + 2, as you’re adding 2 to the reading speed of the historical fiction book (x)
Point D, as shown i the figure, is the intersection of the angle bisectors. This point is the Incircle, or the center of the inscribed circle.
All 3 angle bisectors meet at D, so drawing the angle bisector of C is useless. (Thus step 4 is not the one).
Since we have the center of the inscribed circle, we want to open the compass so that it touches all 3 sides at one point only, that is, we want the 3 sides to be tangent to this circle.
The segments joining the tangency points and D are 3 radii of the circle. We know that a radius is perpendicular to the tangent it touches.
Thus, we need to draw an altitude from D to any of the sides.
Answer: 1
Answer: 289 units
Step-by-step explanation:
Given the following :
Inventory (I) = 180
Lead time (L) = 7 days
Review time (T) = 2 weeks = 14 days
Demand (D) = 20
Standard deviation (σ) = 5
Zscore for 95% probability = 1.645
Units to be ordered :
D(T + L) + z(σT+L)
(σT+L) = √(T + L)σ²
= √(14 + 7)5²
= √(21)25
= 22.9
D(T + L) + z(σT+L) - I
20(14 + 7) + 1.645(22.9 + 7) - I
= 420 + 49.1855 - 180
= 289.1855
= 289 quantities
