Answer:
Given: In triangle ABC and triangle DBE where DE is parallel to AC.
In ΔABC and ΔDBE
[Given]
As we know, a line that cuts across two or more parallel lines. In the given figure, the line AB is a transversal.
Line segment AB is transversal that intersects two parallel lines. [Conclusion from statement 1.]
Corresponding angles theorem: two parallel lines are cut by a transversal, then the corresponding angles are congruent.
then;
and

Reflexive property of equality states that if angles in geometric figures can be congruent to themselves.
by Reflexive property of equality:
By AAA (Angle Angle Angle) similarity postulates states that all three pairs of corresponding angles are the same then, the triangles are similar
therefore, by AAA similarity postulates theorem

Similar triangles are triangles with equal corresponding angles and proportionate side.
then, we have;
[By definition of similar triangles]
therefore, the missing statement and the reasons are
Statement Reason
3.
Corresponding angles theorem
and
5.
AAA similarity postulates
6. BD over BA Definition of similar triangle
9x - 2y = 11 ... (i)
5x - 2y = 15 ... (ii)
Subtracting equation (ii) from (i) we get;
4x + 0 = -4
4x=-4 , x = -1
Replacing x = -1 in equation (i) we get;
9(-1) - 2y = 11
-9 - 2y = 11
-2y = 20
y = 20 ÷ -2 = -10
The solution to the system of equations is (-1,-10).
Answer:
k = 575
Step-by-step explanation:
let d be distance and h time.
Given d varies directly as h then the equation relating them is
d = kh ← k is the constant of variation
To find k use the condition d = 2875, h = 5, then
2875 = 5k ( divide both sides by 5 )
k = 575
Hi there!
We can use the following equation:

z = amount of standard deviations away a value is from the mean (z-score)
σ = standard deviation
x = value
μ = mean
Plug in the knowns for both and rearrange to solve for the mean:

Other given:

Set both equal to each other and solve:
