Answer:
LF = PF given
ΔLFP is isosceles definition of isosceles triangle
∠FLP = ∠FPL isosceles triangle theorem: if two sides of a triangle are
congruent, then angles opposite those sides are
congruent.
LP = PL reflexive property
∠PDL = ∠LKP Perpendicular lines postulate (perpendicular lines form 90
degree angles)
ΔPDL ≅ ΔLKP AAS
LK = PD corresponding parts of congruent triangles are congruent
Answer:
right
Step-by-step explanation:
The sum of all three angle measures in a triangle will always equal 180 degrees. So, if you subtract 63 and 27 from 180 you will have your third angle measure, which is 90.
So now your 3 measures are 63, 27, and 90. Since one of the angles is a 90-degree angle, the triangle must be a right angle because a right angle has a measure of 90 degrees.
I hope this helps!
Answer:
You''ll have 3 boxes of eggs.
Step-by-step explanation:
1 x 3 = 3
It depends on how many eggs are in the box. If there were a dozen eggs then that would be thirty six.
I hope this helps!
Answer:
0.97
Step-by-step explanation:
Given that a homeowner has two smoke detector alarms installed, one in the dining room (adjacent to the kitchen) and one in an upstairs bedroom (above the kitchen). If cooking produces smoke in the kitchen, the probability of setting off the dining room alarm (D) is .95. The probability of setting off the bedroom alarm (B) is .40.
Both alarms are independent of each other.
Probability for smoke detection=P(any one alarm rings)
=P(Kitchen alarm sets off)+P(bed room alarm sets off)-P(Both sets off)
Since both are independent
P(Both) = 
Probability for smoke detection
= 0.95+0.40-0.38
=0.97
Answer:
<em>The shaded region has an area of 1400 square units</em>
Step-by-step explanation:
<u>Area of Compound Shapes</u>
We are given a shape and it's required to calculate its area. The shape can be divided into three rectangles as shown in the figure attached below.
The lengths of these rectangles are x, y, and z.
The value of x can be calculated as:
x = 60 - 15 - 10 = 35
Similarly:
y = 60 - 15 = 45
z = y = 45
The first rectangle has dimensions of x by 10, thus its area is:
A1 = 35*10 = 350
The second rectangle has dimensions of 60 by 10:
A2 = 60*10 = 600
The third rectangle has dimensions y by 10:
A3 = 55*10 = 450
The shaded area is:
A = 350 + 600 + 450 = 1400
The shaded region has an area of 1400 square units