Answers
9514 1404 393
Explanation:
The length CD can be found from the Pythagorean theorem.
CF² + CD² = DF²
2² + CD² = (2√10)²
CD² = 40 -4 = 36
CD = √36 = 6
From here, any of several methods could be used to find the area of ΔDEF.
One of them is to subtract the areas of the triangles that are not ΔDEF from the area of the rectangle ABCD.
area ABCD = bh = (6 cm)(5 cm) = 30 cm²
area ΔADE = 1/2bh = 1/2(4 cm)(5 cm) = 10 cm²
area ΔBEF = 1/2bh = 1/2(2 cm)(3 cm) = 3 cm²
area ΔCDF = 1/2bh = 1/2(6 cm)(2 cm) = 6 cm²
Then the area of interest is ...
area ΔDEF = area ABCD -area ΔADE -area ΔBEF -area ΔCDF
area ΔDEF = (30 -10 -3 -6) cm²
area ΔDEF = 11 cm²
__
Alternate solution
If we define A as the origin of a coordinate system, then the coordinates of the vertices of ΔDEF are ...
D(0, 5), E(4, 0), F(6, 3)
The area can be computed as half the absolute value of the sum of the determinants of 2×2 matrices consisting of adjacent points.
[tex]A=\dfrac{1}{2}\left|\left|\begin{array}{cc}0&5\\4&0\end{array}\right|+\left|\begin{array}{cc}4&0\\6&3\end{array}\right|+\left|\begin{array}{cc}6&3\\0&5\end{array}\right| \right|\\\\=\dfrac{1}{2}|(0-20)+(12-0)+(30-0)|=\dfrac{1}{2}(22) = \boxed{11}[/tex]
_____
Additional comment
The solution using coordinates is effectively equivalent to the computation of the area of trapezoid ABFD, less the areas of triangles EBF and AED.
Related Questions
Alec types
3
5
of a paragraph in
2
3
minute. If he continues at the same rate, what fraction of a paragraph can Alec complete in 1 minute?
Alec types
3
5
of a paragraph in
2
3
minute. If he continues at the same rate, what fraction of a paragraph can Alec complete in 1 minute?
Answers
Answer:
He can type 4.5/5 of a paragraph
Step-by-step explanation: Because there are 60 seconds in a mintune right. 2/3 of an hour=40 seconds. 1.5/5=20 seconds and 60 seconds=4.5/5
What is the distance between the points (12, 6) and (−8, 6) on a coordinate plane? *
4 units
12 units
6 units
20 units
Answers
Answer:
im pretty sure it is "4 units"
Step-by-step explanation:
Help me with this pls
Answers
Answer:
C
Step-by-step explanation:
What is m∠1 ? I need help.
Answers
Answer:
*update* 99
Step-by-step explanation:
Carla e Ana foram tomar sorvete e gastaram r$ 23,00 dividido a conta em partes iguais, quanto cada uma pagou ? Gente me explica como faz a conta não só resposta por favor
Answers
Answer:
each of them has to pay $11.5 individually
Step-by-step explanation:
The computation of the amount paid by each one is shown below:
As carla and Ana gone for an icecream and the bill is $23 that should be divided equally
So here the carla should pay
= $23 ÷ 2
= 11.5
And, Ana should pay
= $23 ÷ 2
= $11.5
Hence, each of them has to pay $11.5 individually
Estimate the line of best fit using two points on the line.
A. y= -3/2x + 12
B. y= 3/2x + 12
C. y= -2/3 + 12
D. y= 2/3 + 12
Answers
Answer:
?
Step-by-step explanation:
Answer: c
Step-by-step explanation:
A p e x
plz help i can not figure this out
Answers
Answer: 30 cubic units
Step-by-step explanation:
Since the base has a volume of 2x3 or 6 and he plans on making the height 5 we must mutliply the base by height to get the new voulme so 6*5=30
Please help as quickly as possible, this is Algebra 1!
Answers
Answer:
First-term is 7
The second term is 14
and the third term is 28
i think so im not 100%
A bag contains 42 red, 45 green, 20
yellow, and 32 purple candies. You
pick one candy at random. Find the
probability that it is green or yellow.
Answers
Answer:
65/139 fraction form
0.47 decimal form
Answer:
Step-by-step explanation:
Total sample space , n (s) = 139
no of green candies , n (g) = 45
no. of yellow candies , n (y) = 20
Probability that is green or yellow is
P( g or y) = P(g) + P(y)
= n(g) / n(s) + n (y) / n(s)
= 45 / 139 + 20 / 139
= 65 / 139
hope it will help :)
PLZ I NEED HELP
i really need help on this or i will fail!!!
Answers
Answer:
A
Step-by-step explanation:
If you have the point (3,5) x = 3 and y = 5
x + 1 = 3 + 1. 3 + 1 = 4
The point (4,5) is one unit to the right of (3,5) so (x+1,y) would move one to the right
Questions:
PQ is a straight line.
Diagram NOT
accurately drawn
(126% )
(a)
Work out the size of the angle marked xº.
(b) (i) Work out the size of the angle marked yº.
Give reasons for your answer.
Answers
Answer:
the answer is up u can see it if u want explanation u can message me here
It angle relationship and show work??
Answers
Answer:
m<x=146
Step-by-step explanation:
its a supplementary angle, meaning both angles add up to 180.
So we subtract 34 from 180 which is 146.
180-34=146
The equation 7h=63 can be used to find how many hours h a person needs to work to earn $63 at $7 per hour. How many hours does a person need to work to earn $63?
HELPPP ME QUICKLY I HAVE TO SHOW MY WORK ALSO
Answers
Answer:
The equation 7h=63 can be used to find how many hours h a person needs to work to earn $63 at $7 per hour. How many hours does a person need to work to earn $63?
Step-by-step explanation:
The equation 7h=63 can be used to find how many hours h a person needs to work to earn $63 at $7 per hour. How many hours does a person need to work to earn $63?
Answer:
9 hours
Step-by-step explanation:
7h=63
divide both sides by 7 to get 9
7h/7=h
63/7=9
h=9
PLEASE ANSWER
What is the perimeter of the parallelogram?
Answers
Answer:
Perimeter = 44.8
Step-by-step explanation:
Perimeter = 2(13.4 + 9) = 44.8
In a survey of 3,200 people who owned a certain type of car, 1,920 said they would
buy that type of car again. What percent of the people surveyed were satisfied with the car?
% of the people surveyed were satisfied with the car
Answers
Answer: 60%
Step-by-step explanation: 1920/3200=.6 .6 in a percentage is 60%
hey guys its my bday and i don't have time to do work rn but I need the answer for this. I will give brainly away
Answers
Do you ever subtract using the z-score?
A) yes
B) no
C) sometimes
Answers
t/12 = 4
solve for the solution
Answers
Then t=12*4=48
The following can be decomposed in ????
Answers
Answer:
Triangle & semicircle
Step-by-step explanation:
Write two numbers that multiply to the value on top and add to the value on bottom.
Answers
Answer:
14+9 14×9that is the answer
Help due in 15 mins!
Answers
Answer:
Step-by-step explanation:
1
Proving Two Triangles Are Congruent: What additional is needed to prove that ABC = DBF using the SAS congruence theorem?
Answers
Answer:
the answer is the side length of ab and db
Answer: D on edge
Step-by-step explanation:
How far up the house would a ladder be resting if it is 25 ft long and 3 ft
away from the house? Round to the nearest tenth if necessary.
5.3 ft
21 ft
24.8 ft
25.2 ft
Answers
Answer:
C
Step-by-step explanation:
The last one is absurd. You can't have a ladder reaching higher than itself. The question is a Pythagorean problem.
Givens
a = 3
b = ?
c = 25 feet
Formula
a^2 + b^2 = c^2
Solution
3^2 + b^2 = 25^2
9 + b^2 = 625 Subtract 9 from both sides.
b^2 = 625 - 9
b^2 = 616 Take the square root of both sides.
b = sqrt(616)
b = 24.8
Please answer this correctly and do not guess or put random stuff. I will report if you do so.
Answers
Explanation: The graph shows a linear relationship.
The following are the ages (years) of 5 people in a room:
17, 21, 15, 15, 25
A person enters the room.
The mean age of the 6 people is now 25.
What is the age of the person who entered the room?
Answers
Answer:
57 years
Step-by-step explanation:
total=25*6=150
17+21+15+15+25+x=150
93+x=150
x=150-93
x=57
Answer:
age=57
Step-by-step explanation:
ages=17 21 15 15 25 ?
17+21+15+15+25=93(old mean)
17+21+15+15+25+?=25(new mean)
25(new mean)*6(number of numbers)=150
?=150-93=57
= 57
6) Find the value of x.
AKLM-ACDE
4x + 5
E
D
55
L
132
108
M M
K
Answers
Answer:
55 ? i think
Step-by-step explanation:
i just had the same question
A truck travels 333 km in 6 hours. What is the truck’s speed for that trip?
Answers
Answer:
55.5 km
Step-by-step explanation:
speed=distance/time
55.5= 333/6
Answer:
55.5 km per hour
Step-by-step explanation:
The simple formula is D_S-T
D is at the top for Distance
S is down to the left for speed
And T to the right as Time
Its simple so just take
Distance: 333km
Time: 6 hrs
333÷5=55.5/1
Is 2,-2,3,-2,7,-2,11,-2 a function
Answers
Answer:
Step-by-step explanation:
D
Write the recursive formula for this sequence: 3, 1, -1, ... *
Answers
Answer:
the answer is 5-2n please do you get it
HELP ILL GIVE BRAINLIEST what shape is the base??
Answers
Answer:
rectangle
Step-by-step explanation:
it's width is 6
it's length is 12
it couldn't be a square