Answer:
AAS(Angle-Angle-Side) postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent
In triangle RAS and triangle QAT
[Angle]
[Side] [Given]
By Base Angle Theorem states that in an isosceles triangle(i.e, AST), the angles opposite the congruent sides(AS =AT) are congruent.
⇒ 
[By base ∠'s of isosceles triangle are equal]
By definition of supplementary angles, if two Angles are Supplementary when they add up to 180 degrees.
, 
are supplementary and 
, 
are supplementary.
⇒
and
Two 
supplementary to equal
Since, 
then, we get;
[Angle]
then, by AAS postulates,
By CPCT[Corresponding Part of Congruent Triangles are equal]
Hence Proved!
Answer: 35 inches.
Step-by-step explanation:
We know that:
hypotenuse = 5*y in
cathetus 1 = (x + 8) in
cathetus 2 = (x + 3) in
The perimeter of the triangle is 76 inches, then:
5*y + (x + 8) + (x + 3) = 76
5*y + 2*x + 13 = 76
We also know that the length of the hypotenuse minus the length of the shorter leg is 17 in.
The shorter leg is x + 3, then:
5*y - (x + 3) = 17
Then we have the equations:
5*y + 2*x + 11 = 76
5*y - (x + 3) = 17
With only these two we can solve the system, first we need to isolate one of the variables in one of the equations, i will isolate x in the second equation.
x = 5*y - 3 - 17 = 5*y - 20
x = 5*y - 20
Now we can replace this in the other equation, we get:
5*y + 2*x + 11 = 76
5*y + 2*(5*y - 20) + 11 = 76
15*y - 40 + 13 = 76
15*y - 29 = 76
15*y = 76 + 29 = 105
and remember that the hypotenuse is equal to 5*y, then we want to get:
3*(5*y) = 105
5*y = 105/3 = 35
5*y = 35
Then te length of the hypotenuse is 35 inches.
Answer:
<em>A) Be sure the task is understood.
</em>
Step-by-step explanation:
The principle "Make sure the mission is understood, performed, and achieved."
<em>Another way we talk about this principle in the Navy is through the idea of "intrusive leadership." In some respects both "micromanagement" and "intrusive leadership" sound terrible. </em>
Think about certain great managers and leaders you have had in your career yet again. Probability are they will be the ones who asked you those difficult questions, too.
They moved everyone to new technical levels, and eye for detail. When you said you knew what you were doing or when you announced the progress of a project, they didn't necessarily take it to face value.
In music, polyphony is a texture consisting of two or more simultaneous lines of independent melody, as opposed to a musical texture with just one voice which is called <u>monophony</u>, and in difference from musical texture with one dominant melodic voice accompanied by chords which is called homophony.
Answer:
Step-by-step explanation:
a. P(Z > 1.12) = 1-N(1.12) = 1-0.8686431=0.1313569
b. <em>P(Z S-2.35)</em> => P(Z <= 2.35) = 0.009386706
(please check interpretation of question b)
c. <em>POSZ s 1.34)</em> => P(0 <= Z <= 1.34) = 0.9098773 - 0.5 = 0.4098773
(please check interpretation of question c)
d. P(-0.8 sz s 2.44) => P(-0.8 <= 2.44) = 0.9926564 - 0.2118554 = 0.780801
(please check interpretation of question d)
