Answers
Answer:
area = 1/2(AC)(BD)yes; BE can be found using the Pythagorean theoremyesStep-by-step explanation:
1.Triangles ADB and CDB are congruent, so each is half the total area. The area of ADB is ...
A = 1/2bh
A = 1/2(DB)(1/2AC) = 1/4(DB)(AC)
The area of the kite is twice this value:
A = 1/2(DB)(AC)
__
2.In order to use the formula derived in part 1, we need to know the length of BE. That can be found using the Pythagorean theorem:
BE² +AE² = AB²
We know that AE = 1/2AC, so the desired dimension is ...
BE = √(AB² -(1/4)AC²)
Then the area of the kite is ...
area = 1/2(DB)(AC)
area = (1/2)(AC)(ED +√(AB² -(1/4)AC²)
__
3.Given three sides of a triangle, the area of it can be found using Heron's formula. If you have not yet seen that in your geometry class, you can always use the Pythagorean theorem and some algebra.
As before, we need to know the lengths of the diagonals. One is given. The other can be found considering the Pythagorean relations:
AD² = AE² +DE²
AB² = AE² +BE²
BE +DE = BD . . . . the sum of the horizontal diagonal lengths
Subtracting the second equation from the first gives ...
AD² -AB² = DE² -BE²
Using the third to write an expression for DE, we get an equation for BE:
AD² -AB² = (BD -BE)² -BE²
AD² -AB² = BD² -2BD·BE +BE² -BE²
(AB² +BD² -AD²)/(2BD) = BE
Substituting this into the original second equation, we can find AE, hence the area of the kite.
AE² = AB² -((AB² +BD² -AD²)/(2BD))²
Which means the kite area is ...
area = BD·AE = BD√(AB² -((AB² +BD² -AD²)/(2BD))²)
area = (1/2)√(4·AB²·BD² -(AB² +BD² -AD²)²
This area formula demonstrates it is possible to find the area of the kite given the three lengths AB, BD, DA.
_____
Additional comment
We have no doubt that the area formula of Part 3 can be rearranged to match Heron's formula. Here, we're interested in demonstrating area can be found.
Related Questions
can I have help pls
Answers
Answer:
D. II only
Step-by-step explanation:
The square root equations will each have only one real solution. (Sometimes, there is an extraneous solution if the variable is also found outside the radical.)
The rational equation will result in a quadratic when it is simplified. It will have two real solutions.
Only equation II will have two real solutions.
The area of an 17-cm-wide rectangle is 357 cm2. What is its length?
The length is
cm.
Answers
Given :-
The area of a rectangle is 357 cm².It's breadth is 17cm .To Find :-
The length of the rectangle.Solution :-
Here the area of the rectangle is 357cm² . As we know that the area of rectangle is ,
→ Area = length * breadth
On substituting the respective values ,
→ 357 cm² = 17cm * length
→ length = 357cm²/17cm
→ length = 21cm
Hence the length of the rectangle is 21cm.
I hope this helps.
Refer to the attachment!
Use the model below to calculate
2
3
×
3
4
.
A rectangle is shown divided into 3 rows and 4 columns. 3 of the 4 columns are shaded blue.
A.
3
12
or
1
4
B.
12
12
or
1
C.
4
12
or
1
3
D.
6
12
or
1
2
Answers
Answer:
D
Step-by-step explanation:
i already did the test
Answer:
d
Step-by-step explanation:
28 less than twice a number is equal to the number. What is the number?
Answers
Answer:
x = 28
Step-by-step explanation:
2x - 28 = x
-2x -2x
- 28 = - x
/-x /-x
28 = x
x = 28
Julia pays $4.56 to ship a package that weighs 8 ounces. What is the cost to ship one ounce?
Answers
Answer:
1.7543859649. . . . . . . .. .
Answer:
$0.57
Step-by-step explanation:
$4.56/8 = 0.57
so the cost to ship one ounce is $0.57
Solve the proportion 3/4 = 9/x
Answers
Cross-multiply.
3/4 = 9/x
3 * x = (9) * (4)
3x = 36
Divide both sides by 3.
3x/3 = 36/3
x = 12
The locations of three fish relative to the water's surface are - 17 feet, - 10 feet, and -19 feet.
There is also a bird flying 12 feet above the water. Which distance has the least absolute value?
Answers
Answer:
-10
Step-by-step explanation:
I think you are asking which is the least distance from 0 which would just be -10
12. What number is 20% less than 60?
Answers
The amount rupees 48 is 20% less than rupees 60.
Answer:
48
Step-by-step explanation:
Step 1: Multiply 20 by 0.6
20 × 0.612Step 2: Subtract 12 from 60.
60 - 1248A restaurant owner washed 87 kilograms of vegetables, some spinach and some carrots. The spinach came in 5-kilogram bags and the carrots came in 7-kilogram bags. The owner washed 15 bags of vegetables in all. How many bags of each kind did he wash?
Answers
Answer:
9 bags pf spinach, 6 bags of carrots
Step-by-step explanation:
x bags of spinach, y bags of carrots,
x + y = 15 (1)
weight of spinach = 5 * x, weight of carrots = 7 * x
5x + 7y = 87 (2)
From (1) y = 15 - x
Sub it into (2):
5x + 7(15 - x) = 87
5x + 105 - 7x = 87
2x = 105 - 87 = 18
x = 9
y = 15 - x = 15 - 9 = 6
So 9 bags pf spinach, 6 bags of carrots.
Your family is going on vacation to Disney. It will cost your family $987 to travel there, plus $150 per day for tickets into the park. What is the greatest number of days you can stay at Disney while staying within their $3500 budget?
Answers
Answer:
They can stay 16 days.
Step-by-step explanation:
3500 - 987 = 2,513
2,513 divided by 150 = 16.7
*They can't stay 16.7 days, so you have to round down. Rounding up will go out of their budget.*
Checking answer:
16 x 150 = 2,400
2,400 + 987 = $3,387
- I'm sure this isn't how your teacher wants you to solve it but this is just how I solved it, I hope this helps!
Step-by-step explanation:
Equation: 987 + 150x = 3500
x represents the number of days the family is staying at the park.
Solve.
Subtract 987 from both sides:
[tex]150x = 2513[/tex]
Divide each side by 150:
[tex]x= 16.75[/tex]
16.75 is decreased to 16, it's impossible to stay for 16.75 days.
The family can stay in the park for 16 days.
(PLEASE HURRY! will award brainliest)
Solve for x. Show your work.
Answers
Answer:
x = 8
Step-by-step explanation:
12 : 36
1 : 3
the distance is 3×, so
x = 26 ÷ 3
= 8
It takes 20 minutes for a cow to be milked by a milking machine.
How many cows can be milked in 6 hours?
Answers
Answer:
18 cows can be milked in 6 hours
Step-by-step explanation:
hrs.=3
GIVING BRAINIEST IF CORRECT!!!
Farmer Taja needs a field for her horses to graze. She found a field that has a width of x+4. The length of the field is more than twice the width. What is the area of the field Taja found?
Answers
Given :
w = x + 4L = 3+ 2(w) = 3 + 2 (x + 4)Solution:
Area = L × WArea = [3 + 2 (x + 4) ]× x + 4Area = [3 + 2x + 8] × x + 4Area = [2x + 11] × x + 4Area = 2x² + 11x + 8x + 44Area = 2x² + 19x + 44hope it helped!
.
Solve the equation -8(x + n) = x for n.
Answers
Answer:
-x/8 - x
Step-by-step explanation:
Answer:
n = -(9/8)x
Step-by-step explanation:
Solve for n:
-8(x + n) = x-8x - 8n = x-8n = 9xn = -(9/8)x-Chetan K
A rock is thrown upward with an initial velocity of 16ft/sec from an initial height 5ft. How much time does it take for the rock to hit the ground?
A. -0.25sec
B. 0.5sec
C. 1.25sec
D. 1.5sec
Answer: C
Answers
The amount of time it would take for the rock to hit the ground is 1.25 seconds.
Given the following data:
Initial velocity = 16 ft/secHeight = 5 ft.Scientific data:
Acceleration due to gravity (g) = 9.8 [tex]m/s^2[/tex]To determine the amount of time it would take for the rock to hit the ground, we would apply the parabolic function:
How to calculate the time.Mathematically, the parabolic function is given by this formula:
[tex]h(t) = -16t^2 +ut+h_0[/tex]
Where:
U is the initial velocity.a is the acceleration.[tex]h_0[/tex] is the height.t is the time.Substituting the given parameters into the formula, we have;
[tex]0 = -16t^2 +16t+5\\\\16t^2-16t-5=0\\\\(4t+1)(4t-5)=0[/tex]
Taking the positive value of t, we have:
[tex]4t-5-0\\\\4t=5\\\\t=\frac{5}{4}[/tex]
t = 1.25 seconds.
Read more on time here: brainly.com/question/24728358
Huang buys 3 shirts that each cost the same amount, a pair of pants that cost $12, and he pays with a $100 bill. Which expression represents the amount of change Huang should receive? Select three options.
100 – (12(3x))
100 – (3x+12)
(100 – 12) – 3x
(100 – 12)(x+x+x)
100 – (x+x+x) – 12
Answers
Answer:
B, C, E
100 - (3x+12)
(100 - 12) - 3x
100 - (x+x+x) - 12
Step-by-step explanation:
they are all saying the same thing, just rearranged and the last one is 3x expanded
Hunter and Christopher were analyzing the graph shown . Both students identified the function to be represented by the, d=13h-75, where d is the amount of money in a checking account and h is the number of hours worked. Hunter explained the equation represented an original amount of $75 that decreased $13 for every hour. Christopher disagreed. He interpreted the equation as a person who was in debt $75 earned $13 every hour.
Answers
Using linear function concepts, it is found that Christopher is correct.
What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can be interpreted as the initial value.In this problem, the function is:
[tex]d = 13h - 75[/tex]
Considering the description of the output d as the amount of money in a checking account and of the input h as the number of hours worked, we have that:
For each hour worked, the person earns $13.Considering taxes, the person starts at a debt of $75.Hence, Christopher is correct.
You can learn more about linear function concepts at https://brainly.com/question/24808124
A 12 sided die is rolled, find the probability of rolling a number greater than 4
Answers
Answer:
probability of rolling a number greater than 4
= 12/4 = 3
p(4) = 3
Mark as brainlest. Hope it helps...
Please help! 25 points
Answers
Answer: Look at explanation
Step-by-step explanation:
32 = 2 x 2 x 2 x 2 x 2
27 = 3 x 3 x 3
16 = 2 x 2 x 2 x 2
No as 32 can be broken down to 8 and 4 and not just pime and not prime
The price of a technology stock has risen to $9.77 today. Yesterday's price was $9.68. Find the percentage Increase. Round your answer to the nearest tenth of a percent.
Answers
Difference in price / original price
9.77 - 9.68 = 0.09
0.09/9.68 = 0.00929
Move two decimal points to the right = 0.9%
7. 65 out of 105
Simplify
Answers
Answer:
13/21
Step-by-step explanation:
65/105 = 13/21
NEED HELP!!
can someone please help me this work? I am so confused with this math problem. Thank you
Answers
Answer:
SOH CAH TOA
Little triangle first - hypotenuse is 4, now we used this info help us find the opposite.
Opposite & Hypotenuse - Sin
Sin(45) = O/H
Sin(45) = O/4
x 4 both sides, to get Opposite
Opposite = 4 x Sin(45)
= 2 root 2
= 2.8284.......
Big Triangle next,
Opposite is 2.8284......
Y is the adjacent
Opposite & Adjacent - Tan
Tan (30) = O/A
Tan(30) = 2.8/A
x A
A x Tan(30) = 2.8
÷Tan(30)
A = 2.8 ÷ Tan(30)
A= 2 root 6
A= 4.8989...
So, y is 5 to 1 significant figure
Or
Y = 4.9 to 1d.p
(Haven't rounded anything in my calculation, even though it's shown that way, in my workings. So, you can follow along)
Hope this helps!
help find circumference pls
Answers
Answer: 62.8
Step-by-step explanation:
2 x 3.14 x 10
Answer:
62.83
Step-by-step explanation:
2 x 3.14 is approx 62.83185 or 62.83
if im wrong let me know please.
8.If 20 is 50% of a number, what is the number
Answers
50% of 40= 20
Percentage
100:50 x 20 = 40
how do you do this as i get 42
46-2⁴÷(3-1)
Answers
Answer:
38
Step-by-step explanation:
[tex]46 - {2}^{4} \div (3 - 1) \\ 46 - 16 \div (2) \\ 46 - 8 \\ = 38[/tex]
first calculate whats in the brackets.
then divide
and lastly subtract
Brainliest if correct
Answers
Answer:
x=9
Step-by-step explanation:
Using the second equation (y=54), we can substitute 54 for y to solve for x...
y=6x
54=6x
Divide both sides by 6
x=9
Answer:
x = 9
Step-by-step explanation:
Since y = 54
54 = 6x
Divide both sides of the equation by the same term
54/6=6x/6
Simplify
x = 9
[RevyBreeze]
PLEASE HELP ME PLEASE
Answers
Answer:
0.75 lb potato salad = $2.22
Step-by-step explanation:
If 1 pound of potato salad = $2.96
Then 0.75 pounds of potato salad = 0.75 x 2.96 = 2.22
NEED HELP ASAP
Which statement correctly explains the association in the scatter plot?
Answers
Answer:
Negative relationship
Step-by-step explanation:
It is going in a negative direction.
Pls mark brainliest :)
work out the area of the shape
Answers
Answer:
45cm^2
Step-by-step explanation:
we have two shapes in the diagram a square and a triangle so we find the area of each of them and add them together
finding the area of a square
we have area= s×s
area = 7×5
area = 35cm^2
finding the area of a triangle
1/2 ×b×h
1/2×4×5
area = 10cm^2
so we add together
total area = 35+ 10
area = 45cm^2
Answer is linked below.
Answers
Answer:
- 7x² + 12x - 9Step-by-step explanation:
Given:
A = 3x² - 7x + 8B = x² + 8x - 3C = - 5x² - 3x + 2Find B + C - A:
B + C - A = x² + 8x - 3 + (- 5x² - 3x + 2) - (3x² - 7x + 8) = x² + 8x - 3 - 5x² - 3x + 2 - 3x² + 7x - 8 =(1 - 5 - 3)x² + (8 - 3 + 7)x + (-3 + 2 - 8) = - 7x² + 12x - 9A = [tex]3x² - 7x + 8[/tex]
B = [tex]x² + 8x - 3[/tex]
C = [tex]-5x²-3x + 2[/tex]
Lets find B + C - A :
→ [tex]B + C - A[/tex]
→ [tex]x² + 8x - 3+ (- 5x²-3x + 2)-(3x² - 7x + 8)[/tex]
→ [tex]x² + 8x - 3-5x² - 3x + 2-3x² + 7x - 8[/tex]
→[tex] (1-5-3)x² + (8 -3 + 7)x+ (-3 + 2 - 8)[/tex]
→ [tex]- 7x² + 12x - 9[/tex]