A ______________ is a relation that assigns exactly one output value to one input value
2 answers:
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Answer:
The theater has 32 rows
Step-by-step explanation:
The rule of the sum of n terms of an arithmetic sequence is S =
(a + l), where
- a is the first term
- l is the last term
- n is the number of the terms
∵ The number of seats per row follows an arithmetic sequence
∵ The first row has 26 seats
∴ a = 26
∵ The last row has 150 seats
∴ l = 150
∵ The theater seats are 2,816
∴ S = 2,816
→ Substitute these values in the rule of the sum above to find n
∵ 2,816 = (26 + 150)
∴ 2,816 = (176)
∴ 2,816 = 88n
→ Divide both sides by 88
∴ 32 = n
∵ n represents the number of the rows
∴ The theater has 32 rows
Answer:
tan (C) = 2.05
Step-by-step explanation:
Given:
A right angled triangle CDE right angled at ∠D.
Side CD = 39
Side DE = 80
Side CE = 89
We know, from trigonometric ratios that, the tangent of any angle is equal to the ratio of the opposite side to the angle and the adjacent side of the angle.
Therefore, tangent of angle C is given as:
Plug in the given values and solve for angle C.This gives,
Therefore, the measure of tangent of angle C is 2.05.
Given the triangle
PQR
with points
P(8,0)
Q(6,2)
R(-2,-4)
And the triangle
P'Q'R'
with points
P'(4,0)
Q'(3,1)
R'(-1,-2)
Part A. Scale factor
Using the vertex
P( 8, 0)
P'(4,0)
the dilatation factor is given by
The triangle has a dilatation factor of 1/2
Part B:
P''Q''R'' after using P'Q'R' reflected about the y axis
to make a reflection over the y axis
coordinates (x,y) turn into coordinates (-x,y)
as follows
Then triangle P''Q''R'' has coordinates
P''(-4,0)
Q''(-3,1)
R''(1,-2)
Part C:
PQR is congruent to P''Q''R''?
Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.
Then the triangles are not congruent
