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
Amy said 49 of her teammates got hits during a recent softball game. Which decimal represents this same amount?
A.
0.49
B.
0.444
C.
0.444
D.
0.49
Answers
please I need some help with both questions.
Answers
Step-by-step explanation:
which questions you were asking
Use the equation below to find y, if m=3 ,x=4 , and b=9
y=mx +b
Answers
Answer:
y = 21
Step-by-step explanation:
y = 3(4) + 9
= 12 + 9
= 21
5x-3 /4=2x+3
Pls help
Answers
Answer:
x=-5
Step-by-step explanation:
5x-3/4=2x+3
First, multiply by 4
5x-3=4(2x+3)
Next, distribute.
5x-3=8x+12
Subtract 5x
-3=3x+12
Subtract 12
-15=3x
x=-5
Hope this helps :D
You do reseprocal/cross multiplication
5x-3=4(2x+3)
5x-3=8x+12
5x-8x=12+3
-3x=15
x=15/-3
x=-5
Josh made $242 for 11 hours of work.
At the same rate, how much would he make for 7 hours of work?
Answers
Answer:
If 11hrs= $242
7hrs=7x242/100
154
Josh will made $154
Step-by-step explanation:
PLZ help me with this :(
Part 1: Simplify √250
Part 2: Classify the number above as rational or irrational
Level 3 (Proficient: 85%)
Part 1: Simplify √150x*5
Part 2: Is the follow expression rational or irrational and why? 2√4+7
Level 4 (Distinguished: 100%)
Part 1: Simplify 13√750x*5 y*8
Part 2: Create two unique expressions each involving 1 square root and at least 1 operation (adding, subtracting, multiplying, dividing). Make 1 results in a rational number and the other result in an irrational number. Explain your reasoning for both.
Answers
Explanation:
Level 2
Part 1: √250 would be simplified to 5√10, because you need to find two factors that equal 250. 25 multiplied by 10 are two factors that you can utilize. Because 25 is a perfect square, it could be reduced to 5. Because 10 isn't a perfect square, you leave it as a radical.
Part 2: √250 is an irrational number because it's a non-terminating decimal and you cannot convert it into a fraction, so it wouldn't be rational.
Level 3
Part 1: √150x^5 would be simplified to 5x^2√6x. Again, find two factors that equal the product, 150. 25 multiplied by 6 are two factors that are useable. Just like the first question, 25 is a perfect square, so it can be reduced to 5. 6 is not a perfect square, so you would leave as a radical. Now, moving onto x^5. You can factor out x^4, because it's a perfect square. x^4 can become x^2. Move x^2 next to 5 and x would be left in the radical with 6.
Part 2: It's rational because 2√4 is simply just 2 x 2 because √4 is a perfect square. 4+7=11. 11 can be converted into a fraction, so it wouldn't be irrational.
Level 4
Part 1: 13√750x*5 y*8 would be simplified to 65x^2y^4√30x. Find two factors that equal 750, which are 25 and 30. You know the drill, 25 is reduced to 5 and 30 stays as a radical. Multiply 13 and 5 to get 65. Factor out x^4 out of x^5 to get x^2. x^8 is a perfect square that can be reduced to x^4.
Part 2: Two unique expressions are 4√16+3 and 5√8 x 34. √16 is a perfect square, so it can become 4. 4 x 4 is 16 and 16 + 3 = 19. 19 is a rational number. 5√8 is irrational, so right off the bat, you'll know it's an irrational expression.
WHOEVER KNOWS HOW TO DO THIS ( in the picture above ) AND COULD GIVE ME ALL THE ANSWERS, ILL VENMO YOU $55 DOLLARS !!
FOR ALGEBRA
JUST DM ME ON INSTA :
VANESSACAMTON
Answers
Answer:
The answer would be -6x - 4 + -4. hope this is accurate!
Step-by-step explanation:
Choose a system and make a case for why you would
or would not choose to solve that system by substitution
Answers
Answer:
The method of solving "by substitution" works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other.
Step-by-step explanation:
[tex]\frac{1}{2} w -5\ \textless \ -2[/tex]
Answers
Help plzzzzzzzzzzzzzz
Answers
Answer:
∠P
Step-by-step explanation:
∠P is between NP and PE
What is the slope of the line?
pls help I need the answer
Answers
Answer:
the slope of a horizontal line is 0
I need help with my homework this is hard pls help thx!
z=m-x solve for x
Answers
Answer:
x = m - z
Step-by-step explanation:
z = m - x add x to both sides
z + x = m - x + x
z + x = m subtract z from both sides
z - z + x = m - z
x = m - z
Answer:
-z + m = x
Step-by-step explanation:
z = m-x
subtract the m from both sides
z-m = -x
you can't have a negative x so multiply everything by -1
-1(z-m = -x)
-z + m = x
HELP ASAP GIVING BRAINLIEST
Solve for x if the angles are adjacent supplementary angles. Use pencil and paper. Show how to check that your value of x is correct
Answers
Answer:
x=15
Step-by-step explanation:
srry if I'm wrong =(
Subtract -7x^2+4x+2 from x^2-3x
Answers
Answer:
-8x^2+x+2
Step-by-step explanation:
Find the square root of -36.
A-6
B 6
C Cannot be done
Answers
Answer: C) Cannot be done
Taking the square root of a negative number is not possible unless you involve complex numbers. If your teacher has not introduced that topic yet, then you just simply say "cannot be done" or something along those lines.
The schools says they will take the students to see the movie with more than 30% of the votes. Which type of movie will the 7th graders be seeing? Explain your reasoning.
7th grade movie votes:
drama-3
comedy-8
action-4
Work:
Fraction Drama:
Fraction Comedy:
Fraction Action:
Convert to Percent:
Answers
Now put that on the bottom for your fractions 3/15 8/15 4/15 because you need to find the percentage of the whole 7th grade.
Now to get each% divide the top number by the bottom.
3/15=.2
8/15=.53
4/15=.25
Then times each decimal by 100 to get the decimal converted to percentage.
So 53% voted for comedy.
If my current slope is 7 what is the perpendicular slope?
A- -7
B-7
C- -1/7
D- 1/7
Answers
Answer
-7
Step-by-step explanation:
opposite of 7
Althea traveled 280 miles at a speed of 70 miles/hour. How much time did she take to cover this distance?
Answers
dudee plz help will be given the brainlist if answered correctly
Answers
Answer:
hey im not actually here to help you, i just need points. thanks for the points
Step-by-step explanation:
HELP DUE TOMORROW ASAP BAINLYEST
Answers
Answer:
B is the correct answer
Step-by-step explanation:
3/12 = 1/4 = 0.25
Answer:
Step-by-step explanation:
(B)
What is the fifth term in the sequence 17.3, 34.3, 51.3, 68.3...?
A 77.7
B 85
C 85.3
D 89.7
Answers
The fifth term in the sequence would be C.
HELP PLEASEEEE<3!!!!
Answers
Answer:
a = b = 40°
Step-by-step explanation:
∠ a and 140° are adjacent and are supplementary , thus
a = 180° - 140° = 40°
a and b are alternate angles and are congruent, thus
b = a = 40°
Answer:
b=40 okkkkllllllkkkkkkkkkkkkkkkkkkkkkllllllkkkk
You get a student loan from the New Mexico Educational Assistance Foundation to pay for your educational expenses this year. Find the interest on the loan if you borrowed $5000 at 5% interest for 1 year
Answers
Answer:
500
Step-by-step explanation:
Plsss help I’ll give u brainlest and 10 points
Answers
Find the slope of (-1,4) and (5, 7)
Answers
Answer:
[tex]m=\frac{1}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-1, 4)
Point (5, 7)
Step 2: Find slope m
Substitute: [tex]m=\frac{7-4}{5+1}[/tex]Subtract/Add: [tex]m=\frac{3}{6}[/tex]Simplify: [tex]m=\frac{1}{2}[/tex]Write an explicit rule for the following sequence: 5, 9, 13, 17, 21.
Your answer:
A. a = 4
a = an-1 + 5
B. a = 5
a = an-1 + 4
C. an = 5n + 1
C. an = 4n + 1
Answers
*BRAINLIEST BRAINLIEST BRAINLIEST BRAINLIEST**
Determine whether or not each expression below is a perfect square. Explain why the expression is or is not a perfect square. If it is not a perfect square, find the perfect square that seems “closest” to the given expression and show how the perfect square can be adjusted to be the given expression.
1. A(x)=x^2+6x+13
2. A(x)=2x^2+8x+14
Answers
Step-by-step explanation:
These aren't a perfect square bec. 1 st and 3rd terms must be perfect square
A(X) = X^2+6X +13 be perfect square if 13 Changed to 9
= X ^2+6X +9
A(x)= 2X^2+8X +14 be perfect square
= 4X ^2+ 8X + 16
*will give brainliest*
While solving an equation, if the variable term becomes zero, and the equation makes a true statement, then the solution is (no solution, one solution, infinite solutions).
Answers
Point P is the center of the circle in the figure above. What is the value of x?
Answers
Answer:
x = 80°
Step-by-step explanation:
To find x, we need to create an equation.
Recall that the sum of all the 4 interior angles of a quadrilateral = 360°.
Therefore:
m<B + m<A + m<C + m<P = 360°
m<B = 20° (given)
m<C = 20° (given)
m<A = ½*x = x/2 (inscribed angle theorem)
m<P = (360 - x)°
Plug in the values and solve for x
[tex] 20 + \frac{x}{2} + 20 + (360 - x) = 360 [/tex]
[tex] 20 + \frac{x}{2} + 20 + 360 - x = 360 [/tex]
Collect like terms
[tex] 20 + 20 + 360 + \frac{x}{2} - x = 360 [/tex]
[tex] 400 + \frac{x}{2} - x = 360 [/tex]
Subtract 400 from each side
[tex] 400 + \frac{x}{2} - x - 400 = 360 - 400 [/tex]
[tex] \frac{x}{2} - x = -40 [/tex]
[tex] \frac{x - 2x}{2} = -40 [/tex]
[tex] \frac{-x}{2} = -40 [/tex]
Multiply both sides by 2
[tex] \frac{-x}{2} \times 2 = -40 \times 2 [/tex]
[tex] -x = -80 [/tex]
Divide both sides by -1
[tex] \frac{-x}{-1} = \frac{-80}{-1} [/tex]
[tex] x = 80 [/tex]
Help me pls ASAP thank you
