In the figure above, AB = AD, BC = CD, BE = 2, BC = 4, and AC = 10. What is the area of triangle ABD?
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:
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Someone please help i can’t find the answer.
Answer:
f(3) = 4
Step-by-step explanation:
Give x = 3 in the interval x ≥ 1 then f(x) = x + 1 , and
f(3) = 3 + 1 = 4
Can you answer this question
Answer:
5/6= 0.83333333333
4/15= 0.266666666
3/5= 0.6
1 &3/4 = 1.75
1/3= 0.33333333
4/1000= 0.004
so the ones that are repeating decimals are:
5/6 , 4/15, and 1/3
Step-by-step explanation:
mary is 5 feet and 7 inches tall how tall is mary in inches?
After getting her close friends to follower her, she starts posting pictures her outfit each morning and gaining new followers. Her total number of followers is given by the functionF(p)=5p+8 where p
is the number of posts she's made. Based on this function, Okoye gains followers for every post she makes. After posting 10 times, she will have followers?
Answer:
58
Step-by-step explanation:
Replace the p in the function with 10. 5(10) + 8 = 58
с
16 km
12 km
Figure not drawn to scale
C =
Kilometers
Step-by-step explanation:
[tex](16)^{2} + (12)^{2} = 400 \\ \sqrt{400} \: = 20km[/tex]
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $53,150. The variable costs will be $12 per book. The publisher will sell the finished product to bookstores at a price of $24.50 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
Answer:
12x +53,150 = 24.5x (production cost = revenue )
53,150 = 12.5x (subtract 12x from both sides and then divide 53,150 by 12.5)
x= 4,252 books
Step-by-step explanation:
pls help answer quick and do NOT WASTE MY POINTS
Answer:
points waisted
Step-by-step explanation:
Answer:
Yeah its parallel
Step-by-step explanation:
I would waste your points, but nah. Anyways, its parallel
Points A' and B' are the images of points A and B after a 270 rotation about the origin. If the slope of line segment AB is -3, what is the slope of line segment A'B'? Put your answer in simplified fraction form with no spaces.
The slope of the line segment AB will change from -3 to 1/3 after a 270 degree rotation of the line segment
How to determine the slope of line segment A'B'information gotten from the question include
Points A' and B' are the images of points A and B after a 270 rotation
the slope of line segment AB is -3
Rotation is one of the movements that is under transformation it involves a movement about an axis.
With respect to the problem here, the axis of the rotation is the origin of the coordinates
The rotation will lead to formation of an image A'B' which is perpendicular to the preimage
The relationship between two slopes that are perpendicular to each other is
slope of line, m = -1/slope of the perpendicular line, m'
m' = -1/m
m' = -1/3
Learn more about slope of perpendicular line
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#SPJ1
which slopes could be the slopes of perpendicular lines?
1/2 and 2
8 and -1/8
2 and 2
1 and -1
0 and undefined
Answer:
0 and undefined
Step-by-step explanation:
Find the length of each arc.
Answer:
34/3 pi
Step-by-step explanation:
We can find the arc length by
s = r theta where theta is in radians
Change 255 to radians
255 * pi/180 = 17/12 pi
s = 8 * 17/12 pi
s = 34/3 pi
Jillian is selling boxes of cookies to raise money for her basketball team. The 10 oz. box costs $3.50, while the 16 oz. box costs $5.00. At the end of one week, she collected $97.50, selling a total of 24 boxes. The system of equations that models her sales is below.
x+ y= 24
3.50x + 5.00y = 97.50
Solve the system of equations. How many 10 oz. boxes were sold?
6
9
12
15
9514 1404 393
Answer:
15
Step-by-step explanation:
We see that x represents the number of 10-oz boxes sold. Then y=24-x is the number of 16-oz boxes sold. Substituting for y in the second equation gives ...
3.50x +5.00(24 -x) = 97.50
-1.50x +120 = 97.50
22.50 = 1.50x . . . . . . . add 1.50x -97.50
15 = x . . . . . . . . . . . . . . divide by 1.50
15 10-oz boxes were sold.
Answer:
The answer is D) 15 on edge
(have a nice day and brainiest pls)
Step-by-step explanation:
Which ordered pair is a solution of the equation?
y= 8x + 3
WChoose 1 answer:
А
Only (1, 11)
B
Only (-1,-5)
Both (1, 11) and (-1,-5)
Neither
Step-by-step explanation:
both (1,11)and (_1,_5)
1/8 + c = 4/5
what is c
Answer:
27/40
Step-by-step explanation:
You are buying a t-shirts for the math club members. The t-shirt company will charge you according to the amount of shirts you buy, where c(x) is the total cost and x, is the number of shirts. If you buy 10 or less shirts it cost 12 dollars per shirt, if between 11 and 50 it will cost 10 dollars per shirt, then if you buy more then 50 it will cost 8 dollars per shirt. What is your equation if you buy 9 shirts. *
Answer:
honestly I just need likes on this sorry i couldn't help.
Step-by-step explanation:
Help plzzzzzzzzzzzzzz
Answer:
∠E
Step-by-step explanation:
∠E is between PE and EN
5. Which of the following is a good strategy to solve this problem?
"Jane has saved $240 to spend on gifts this year. She is planning to spend $96.00 on gifts for her parents, $18.00 on gifts for each of her two brothers, and $44.00 on gifts for her grandmother. How much money will she have left after buying the gifts?"
A. draw a picture
B. make a list
C. write an equation
D. any of these would work
Answer:
C. or D.
Step-by-step explanation:
It depends on the person to be honest, however in this situation an equation is the best route.
Answer: C is the best as choice A is just plain out wrong.
James and Mary were both saving some of their lunch money to purchase a new skate board. James started off with only $7 and he will save 56
each week and Mary started off with $13 and she will save 57 each week. How much money will James and Mary have after 8 weeks?
Answer:
James: $455
Mary: $469
Step-by-step explanation:
Tell me if it is wrong I would like to know!
:)
Also I'm new on Brainly so don't go too hard on me if this is wrong plz.
(4x + 2y + 6) + (7x + 3y - 4) + (x - 2y + 1)
Can someone break this down step by step so i know how to do it please
thankyou .
Answer:
12x+3y+3
Step-by-step explanation:
Let's simplify step-by-step.
4x+2y+6+7x+3y−4+x−2y+1
=4x+2y+6+7x+3y+−4+x+−2y+1
Combine Like Terms:
=4x+2y+6+7x+3y+−4+x+−2y+1
=(4x+7x+x)+(2y+3y+−2y)+(6+−4+1)
=12x+3y+3
Answer:
12x + 3y + 3
General Formulas and Concepts:
Algebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define
(4x + 2y + 6) + (7x + 3y - 4) + (x - 2y + 1)
Step 2: Simplify
Combine like terms (x): 12x + 2y + 6 + 3y - 4 - 2y + 1Combine like terms (y): 12x + 3y + 6 - 4 + 1Combine like terms (Z): 12x + 3y + 3What is the relationship between two coplanar lines that are perpendicular to the same line?
Answer:
If two lines are perpendicular to the same line, then the two lines are parallel, and if two lines are parallel, then their slopes are equal
Step-by-step explanation:
Answer:
I'm sorry for this but I'll help you if you help me?
Mrs. Brown uses 1/4 package of graph paper for each class. She needs 1 1/2 packages to serve all of her classes. How
many classes does Mrs. Brown teach?
Answer:
I think the answer is 6 sorry if i'm wrong
Step-by-step explanation:
I dont know what I'm doin
Answer:
60 minutes
Step-by-step explanation:
Which relation is a function?
Question 1 options:
{(3,2), (5,8), (3,−4)}
{(−1,6), (−2,7), (−3,6)}
{(5,7), (12,−3), (5,6), (12,7)}
{(3,5),(3,6)}
Henry sells rings for $8 each. His expenses are $2.00 per ring, plus$90 for supplies. How many rings does he need to sell for his revenue to equal his expenses?
Answer:
12
Step-by-step explanation:
Answer:
yooooo lamarr over here cheating
Step-by-step explanation:
y = 2x²- 5x + 2
determine the x value for the vertex and whether this value is a maximum or a minimum
a. maximum at x = -1.25
b. maximum at x = 1.25
c. minimum at x = -1.25
d. minimum at x = 1.25
Answer: D
Explanation:
Use the vertex formula, -b/2a. Because the quadratic formula is ax^2+bx+c, -b would be 5 in this case and a would be 2 in this case. Plug the numbers in and you get 5/4. The AOS or vertex would be 5/4 or 1.25. Because the a-value is a positive in this equation, the parabola would have a minimum.
Choose the graph of this equation
helpppp i’ll give that crown thing
Answer:
N K Q
Step-by-step explanation:
Find the slope of the line passing through the points (-7, 8) and (5.-7).
Answer:
slope is 15/-12
Step-by-step explanation:
:)
how do i solve 9 divide by 10.034
Answer:
9/10.034=.89695037
Step-by-step explanation:
Answer:
= 1.114
Solution:
We have the equation:
10.034 ÷ 9 = 1.114
Calculated to 3 decimal places.
0 1. 1 1 4
9 1 0. 0 3 4
− 0
1 0
− 9
1 0
− 9
1 3
− 9
4 4
− 3 6
8
HOPES THIS HELPS YOU!!!
CAN YOU PLEASE MARK MINE AS BRAINLIEST????
A line with a slope of -7 passes through the points (-8, 7) and (-7, k). What is the value of
K?
Answer:
k = 0
Step-by-step explanation:
On the graph, the second point would be at (-7,0)
Answer:
k = 0
Step-by-step explanation:
We can find the answer to this question by using the slope equation:
[tex]\frac{y2 - y1}{x2 - x1}[/tex]
Let's define some variables:
[tex]\frac{k - 7}{-7-(-8)} = \frac{k-7}{1} = k- 7[/tex]
We know the slope is -7 so we can put k-7 equal to it and solve
[tex]k-7 = -7\\k = 0[/tex]
We find that k is equal to 0.
I hope this helps!!
- Kay :)