Answer:
Step-by-step explanation:
a) A square is a rectangle. True
Reason: Property of Rectangle: (i) Opposite sides are equal and parallel. (ii) Each angle is 90 (iii) Diagonals are equal and bisect each other.
A square hold all these properties. A square is a rectangle.
b) A polygon with 21 sides has 432 possible diagonals. False
Reason: Number of diagonals of a polygon = 
n --> number of sides of a polygon.
=
= 189 diagonals
c) All three angles in an Isosceles triangle are equal. False
Reason: In an isosceles triangle, two angles are equal.
If three angles are equal, then that is an equilateral triangle.
d) The measures of the exterior angles of a nonagon, a nine-sided figure, have a sum of 360°. True.
Reason: The sum of measures of the exterior angles of any polygon is 360
Answer:
The minimum number of cities we need to contact is 96.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence interval
, we have the following confidence interval of proportions.

In which
Z is the zscore that has a pvalue of
.
The margin of error is:

95% confidence interval
So
, z is the value of Z that has a pvalue of
, so
.
In this problem, we have that:







The minimum number of cities we need to contact is 96.
Answer:
The height of the projection will be (x - 5) feet.
Step-by-step explanation:
A projector displays an image on a wall. The area (in square feet) of the rectangular projection can be represented by (x² - 8x + 15).
Now to get the width and the height of the rectangular projection we have to factorize the expression (x² - 8x + 15).
Here, (x² - 8x + 15)
= x² - 3x - 5x + 15
= (x- 3)(x - 5)
Now, if the height of the projection is less than its width then, the height of the projection will be (x - 5) feet. (Answer)
Answer:
ASA
Step-by-step explanation:
In given triangle
Line BC = Line QR
Angle ABC = Angle PQR
Angle ACB = Angle PRQ
Computation:
Angle ABC = Angle PQR (Angle)
Line BC = Line QR (Side)
Angle ACB = Angle PRQ (Angle)
So,
ΔABC ≅ ΔPQR
By Angle Side Angle property
ASA
Answer with explanation:
In Δ ABC and ΔD BC
∠A=∠D-------Given
∠ABC=∠DCB-------Each being 90° given in the Diagram.
Side, BC is Common.
⇒⇒Δ ABC ≅ ΔD BC-------[AAS]
When two triangles are congruent , their areas are equal.
So, Area(ABC)=Area (DCB)
Option B :⇒ A AS