In the figure above, AB = AD, BC = CD, BE = 2, BC = 4, and AC = 10. What is the area of triangle ABD?
Answers
The properties of items in a question can be used to simplify the solution to the questions
The area of triangle ΔABD is 20 - 4·√3
The reason the above value for the area of ΔABD is correct is as follows:
The given parameters are;
AB = AD, BC = CD, BE = 2, BC = 4, AC = 10
Given that AB = AD, and BC = CD, we have that the figure ABCD is a kite
∴ AC is perpendicular to BD by properties of the diagonals of a kite
ΔBCE is a right triangle
By Pythagoras' theorem, [tex]\overline{CE}[/tex]² = [tex]\overline{BC}[/tex]² - [tex]\overline{BE}[/tex]²
Which gives;
[tex]\overline{CE}[/tex]² = 4² - 2² = 12
[tex]\overline{CE}[/tex] = 2·√3
Given that AC is the perpendicular bisector of BD, by the properties of a kite, we have;
BD = BE + DE, where BE = DE definition of bisected line
∴ BD = BE + BE = 2·BE
Area of a triangle = (1/2) × Base length × Height
AE = The altitude (height) of the ΔABD = AC - CE
∴ AE = 10 - 2·√3
BD = The base length of ΔABD = 2·BE (Length of BE = 2)
∴ BD = 2 × 2 = 4
The area of triangle ΔABD = (1/2) × BD × AE
∴ The area of triangle ΔABD = (1/2) × 4 × (10 - 2·√3) = 20 - 4·√3
The area of triangle ΔABD = 20 - 4·√3
Learn more about the properties of a kite here:
https://brainly.com/question/24110637
Related Questions
select each expression that is equivalent to 5(n + 4).
A. 5n + 4
B. 5n + 20
C. 15 + 5n + 5
D. 5(n + 3) + 5
E. 5n + 54
Answers
Answer:
B and C and D
Step-by-step explanation:
Answer:
The Answer is B. C. and D.
Step-by-step explanation:
You have to get everything on your list in 5 moves.
Can you do it?
Help please
Answers
목록에있는 모든 것을 5 개의 동작으로 가져와야합니다.
Need Help plz it has to be done now
Answers
Answer:
38 ft
Step-by-step explanation:
:)
Answer:
32ft
Step-by-step explanation:
Multiply 8 by 3 to get the area of the rectangle. Multiply 4 by 4 and then divide by two to get the area of the triangle.
Finally add them together to get 32ft
If asked to multiply 18 by 100 quicky, what is the short cut?
Answers
Answer: 18 x 100 = 1,800
Step-by-step explanation:
You take the 100 and you remove the 2 zeros and put them at the back of 18 to get your answer.
The graph shows the proportional relationship between rainfall during the growing season and seasonal growth of a type of plant. What does the point (8,6) represent? If the plants grew 12 mm one season, how much rain fell?
Answers
Answer/Step-by-step explanation:
✔️The point (8, 6) represents seasonal plant growth of 6 mm with 8 cm of rainfall during the growing season.
✔️To determine how much rain fell if the plants grew 12 mm one season, find the value of x (rainfall) when y (plant growth) = 12.
From the graph, when y = 12, x = 16.
This means that when the plant grew 12 mm, 16 cm of rainfall was recorded.
Therefore:
If the plants grew 12 mm one season, 16 cm rainfall fell.
Which of the following is NOT a rational number?
-4/7
3/5
(the symbol for pie)
2/3
Answers
Answer: (the symbol of pi)
Step-by-step explanation: Because if you divide each of those fractions only pi keeps in going without repeating itself.
Please help asap!! I will mark you as brainliest :)
Answers
Please explain I will also give BRAINLIEST
Answers
Answer:
read the step by step
Step-by-step explanation:
WARNING IM NOT POSTITIVE ITS RIGHT
a:how fast it will reach the ground
b:descending since they are going down
C:subtract a number by 1500
Line t has a slope of -9/2 line u is parallel to t what is the slope of u
Answers
Answer:
the slope of the parallel line would also be -9/2
Step-by-step explanation:
Find the cost of erecting a 6 m by 4 m rectangular garden shed that is 2 m high if
the metal sheeting costs shs58,500 per square metre.
Answers
Answer:
2320000
Step-by-step explanation
work out the perimeter first 6+4 times 2= 20
20 time 2m high=40
40 times 58000= 2320000
solve 28m+21=413 thanks!
Answers
Answer:
14
Step-by-step explanation:
28m + 21 = 413
28m = 413 - 21
= 392
m = 392/28
= 14
Therefore m is 14 :)
Answer:
14
Step-by-step explanation:
28m+21=413
Subtract both sides by 21
28m=413-21
28m=392
m=14
A local fish market is selling fish and lobsters by the pound. The fish, f, costs $5.00 a pound, while the lobster, l, costs $8.00 a pound. The fish market sells 20.5 pounds and makes $131.00. How many pounds of fish and pounds of lobster did the market sell?
Answers
Given :
A local fish market is selling fish and lobsters by the pound. The fish, f, costs $5.00 a pound, while the lobster, l, costs $8.00 a pound. The fish market sells 20.5 pounds and makes $131.00.
To Find :
How many pounds of fish and pounds of lobster did the market sell.
Solution :
Let, pounds of fish sells are x.
So, pounds of lobsters sells are (20.5 - x) .
Total amount of spend = 5x + 8( 20.5 - x)
5x + 8( 20.5 - x) = 131
5x - 8x + 164 = 131
3x = 33
x = 11
Therefore, number of pounds of fish and lobsters are 11 and 9.5 pounds respectively.
Hence, this is the required solution.
-4-3(1-x)<7-2(x+2)
Its just this :)
Answers
Answer: the answer is x=12 and x=4
 Please create a graph to reflect the following situation:
Max is going to school. For the first 20 minutes he walks at a constant speed of 10 miles per hour. Then he gets to the bus stop and waits for the bus for another 5 minutes. Then he rides the bus for 10 minutes. The speed of the bus is 40 miles per hour.
Show graphically the distance Max has traveled to school over time since he has left his house.
Make sure you include the name of the graph, the labels and the scale on x- and y-axes; Please use graphing paper, pencil and a ruler. Please help me it’s due today I would love the help.
Answers
You show the time on the x-axes (from 0 to 35) and the distance on the y-axes (from 0 to 10).
You start at origin of coordinates. Then the graph rises linear until it reaches the point (20|3.3333...), then it is parallel to the x-axes (as he does not move) until it reaches (25|3.3333...). Then it increases again until it reaches (35|10).
Basically, it's linear all the time, while the slope of the graph varies in three different intervals. (Actually it wouldn't be linear as he doesn't move with the same speed all the time but we can't go more into detail based on the information we have, so we use average values.)
You can use the rule of three to find out how far he moves.
Is (-3,-9) a solution of the equation y = 3x ?
O YES
O NO
O NOT A SOLUTION
Answers
Answer:
Yes, (-3, -9) is a solution.
Step-by-step explanation:
y = 3x (-3,-9)
-9 = 3(-3)
-9 = -9
HELP! Which is a solution to the inequality y>2x-5?
a
(5,-5)
b
(0,0)
c
(0,-5)
d
(10,0)
Answers
Answer:
5, -5
Step-by-step explanation:
Which one should I choose
Answers
Answer: 9
Step-by-step explanation:
Since x=2 that means there should be 2 3s being multiplied since it’s 3 to the second power. So 3x3 which equals 9. If this answer helped please mark it brainliest!
Answer:
the last option, 9
Step-by-step explanation:
if x=2 then you would just plug x into the equation to get:
y=3^2 or 3 squared and that's just:
3x3 which is
9
So your answer would be 9
I hope this helps! blessings, have a lovely day/night, xo, nm :) <3
Find the slope and the y-intercept of the graph of y=−45x−2.
Answers
Answer:
Slope: -45
Y-intercept: -2
Step-by-step explanation:
The expression is written in slope-intercept form or y=mx+b.
mx is the slope and b is the slope intercept
PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((
Answers
Answer:
A and C
Step-by-step explanation:
m+5n(9−p)−6−rsquar(2.718282)d
Distribute:
=m+(5n)(9)+(5n)(−p)+−6+−2.718282adqr2su
=m+45n+−5np+−6+−2.718282adqr2su
Answer:
=−2.718282adqr2su−5np+m+45n−6
Can someone help me!!
Answers
Answer:
$642
Step-by-step explanation:
To calculate sales tax, you multiply the percentage by the price. In this case it would be 600 x 0.07 which is 42. Then you add them together which would be 600 plus 42 which equals 642.
Please answer the question below
Answers
Answer:
50 i think
Step-by-step explanation:
An online store that sells baseballs and bats offers free shipping on any order of $20 or more. The baseballs cost $1 each and the bats
cost $8 each. The inequality below shows the number of baseballs, 2, and bats, y, that a person can buy to get free shipping.
x+8y > 20
Which of the following ordered pairs are solutions to this inequality? Select all that apply.
Answers
Answer:
What are the answers?
Step-by-step explanation:
Carina spent a total of $5.27 buying a pineapple for $3.40 and some tomatoes that were on sale for $0.85 per pound
To determine the number of pounds of tomatoes that she bought, x, Carina wrote and solved the equation as shown
below.
3.40+0.85x=5.27
0.85X= 8.67
X= 10.2 pounds
Where, if anywhere, did Carina make an error?
Answers
Answer:
Carina made an error in the beginning.
Step-by-step explanation:
Carina didn't do the inverse operation of adding 3.40. She added it to the 5.27 when she shouldve subtracted it. x=2.2 lbs. Hope this helps!
Anwser ( C )
C: Carina should have divided 8.67 by 0.85.
Took the test. Hope this helps
will make brainleist find the value of ar in the figure below if re is parallel to bc show your work
Answers
The value of the variable x is 5. Then the value of length AR will be 2.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The triangle ΔABC is given.
There is a line segment RE which is parallel to the BC.
Then the triangle ΔABC and triangle ΔARE will be the similar triangles.
Then the ratio of the corresponding side will be constant.
(x – 3) / (x – 1) = 5 / 10
2(x – 3) = x – 1
2x – 6 = x – 1
x = 5
Then the value of AR will be
AR = x – 3
AR = 5 – 3
AR = 2
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ1
curved surface area of half cylinder
Answers
Answer:
curved surface area of half cylinder is
Step-by-step explanation:
πr2h
Answer:
Area of half cylinder is
Step-by-step explanation:
πr2h
Which graph represents to equality y<-1+2x
Answers
The third graph (bottom left corner)
You can draw the linear liner first as the equation y=-1+2x, then fill up the space. Since it is less than, the shaded area is lower than the line
Approximately 6.5x10^7 people fly commercially in the United States each month. Approximately how many fly commercially each year?
Answers
The number of people that travel commercially each year is 7.8 x 10^8.
How many fly commercially each year?The number of people that travel commercially each year is represented in scientific notation. Scientific notation is used to compress larger numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
In order to determine the number of people who flew commercially each year, multiply the number of people who flew each month by 12.
Number of people who fly commercially each year = 6.5x10^7 x 12
= 78 x 10^7
= 7.8 x 10^8
To learn more about scientific notation, please check: https://brainly.com/question/5756316
#SPJ1
PLEASE ANSWER ASAP!!!!!!!!!
A ball is dropped from a certain height. The function below represents the height f(n), in feet, to which the ball bounces at the nth bounce.
f(n) = 9(0.7)n
What does the number 9 in the function represent?
A) Number of times the ball was dropped.
B) Height from which the ball was dropped.
C) Height to which the ball will bounce at the nth bounce.
D) Number of times the ball bounces at the nth bounce.
Answers
Answer:
c
Step-by-step explanation:
The area of a rectangle a=1(w) is represented by the expression 24x6y15. If the width of the rectangle is 2x3y9, what is the length of the rectangle
Answers
Answer:
Length of rectangle is: [tex]Length=12x^3y^6[/tex]
Step-by-step explanation:
The area of rectangle = [tex]24x^6y^{15}[/tex]
Width of rectangle = [tex]2x^3y^9[/tex]
We need to find length of rectangle
The formula used is: [tex]Area=Length\times Width[/tex]
Putting values and finding length
[tex]Area=Length\times Width\\24x^6y^{15}=Length\times 2x^3y^9\\Length=\frac{24x^6y^{15}}{2x^3y^9} \\Length=12x^{6-3}y^{15-9}\\Length=12x^3y^6[/tex]
So, Length of rectangle is: [tex]Length=12x^3y^6[/tex]
Find the product of 51 and -2.5. Use the distributive property to rewrite and solve. The first step is done for you. 51(-2.0) + 51(-0.5) What is the next step in using the distributive property to solve this equation?
Answers
Answer:
-12.75
Step-by-step explanation:
Find the product of 51 and -2.5. Use the distributive property to rewrite and solve.
The next step using Distributive property is to expand the brackets
5.1 × 2.5
Step 1: Distributive property
51(-2.0) + 51(-0.5)
Step 2: Expand the brackets
-10.2 + -2.55
Step 3
- 12.75
Answer:
-12.75
The next step using Distributive property is to expand the brackets
5.1 × 2.5
Distributive property
51(-2.0) + 51(-0.5)
Expand the brackets
-10.2 + -2.55
- 12.75