Given klmn is a trapezoid, kl = mn, m<1 = m<2, lm/kn = 8/9, pklmn = 132. Find: the length of the legs
Answers
Answer:
The length of legs lm, mn, and lk is 32 while that of kn is 36.
Step-by-step explanation:
The diagram is attached in the answer.
As both the angles are equal thus the two forms isosceles triangles. This is true because the converse of base angle theorem is applicable here. The theorem clearly states that when a trapezoid is divided by the diagonal, it forms two set of angles where m<1=m<2 and m<lmk=m<nmk
This leads the two set of legs such as
[tex]\dfrac{lm}{kn}=\dfrac{8}{9}[/tex]
Or this could be written as
[tex]lm=8x\\kn=9x[/tex]
Now the remaining two sides are given as
[tex]lk=lm[/tex] as this form an isosceles triangle so
[tex]lk=8x[/tex]
Similarly
[tex]mn=lm\\[/tex]
Or
[tex]mn=8x[/tex]
Now the perimeter is given as
[tex]\text{perimeter}=lm+mn+kn+lk\\[/tex]
Here perimeter is given as 132 so this gives:
[tex]\text{perimeter}=lm+mn+kn+lk\\132=8x+8x+8x+9x\\132=33x\\x=\dfrac{132}{33}\\x=4[/tex]
So the four legs are of length as given below:
[tex]lm=8x=8\times 4=32\\mn=8x=8\times 4=32\\lk=8x=8\times 4=32\\kn=9x=9\times4=36[/tex]
So the length of legs lm, mn, and lk is 32 while that of kn is 36.
Related Questions
The height of a penny t seconds after being dropped down a well is given by the product
of (10 - 3t) and (10+ 31). Find the product and simplify.
Answers
I don’t know this ppl I need help lol
Answers
Answer:
15
Step-by-step explanation:
7. lawn chair: $15, 25% off, 6% tax
Answers
Answer:
$3.75 + 6% tax
$3.75
tax: $0.22
Total price with sales tax: $3.97
Step-by-step explanation:
Please help ASAP due 9:20, will give brainliest
Answers
Answer:
1) 1,095
Step-by-step explanation:
[tex]a^{2} +1300^{2} =1700^{2} \\ a^{2} =1700^{2} -1300^{2} \\ =2890000-1690000\\ =1200000[/tex]
[tex]a^{2} =1200000\\ a=\sqrt{1200000} \\ a=1095.4451[/tex]
round to 1,095
Answer:
The answer is 1
Step-by-step explanation:
[tex]a =\sqrt{c^{2} - {b^{2 } \\[/tex]
[tex]a = \sqrt{1700^2 - 1300^2}[/tex]
[tex]a = \sqrt{2890000 - 1690000}[/tex]
[tex]a = \sqrt{1200000}[/tex]
[tex]a = 1095.4451150103[/tex]
PLZZ HELP Me ASAP!!!!
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
The area is calculated as length × breadth
area = 2x(2x + 6) ← distribute
= 4x² + 12x
(b)
area = x(x + 4) ← distribute
= x² + 4x
(c)
shaded area = 4x² + 12x - (x² + 4x)
= 4x² + 12x - x² - 4x ← collect like terms
= 3x² + 8x
Write the equation of the line that passes through the points (4,1) and (-6,9). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answers
Answer:
Find the slope:
[tex]m = \frac{y2-y1}{x2-x1} = \frac{9 - 1}{-6 - 4} = -\frac{8}{10} = -\frac{4}{5}[/tex]Use point-slope form and one of the points:
y - y₁ = m(x - x₁)[tex]y - 1 = -\frac{4}{5}(x - 4)[/tex]ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
Answers
Answer:
-15u²
Step-by-step explanation:
[tex]-(4+11)u^{2} \\-15u^{2}[/tex]
same exponent so it can be added together
Please help me on this question I really need help. :,)
Answers
Answer:
a. (7, 27) Polly was incorrect.
b. (3, 1) Polly was correct.
Step-by-step explanation:
a.
y = 4x - 1
2x - y = -13
We can solve this by substitution. Our first equation gives us y. Plug that into our second equation for each instance of y.
2x - y = -13
2x - (4x - 1) = -13
First distribute the negative sign across the parentheses.
2x - 4x + 1 = -13
Combine like terms.
-2x + 1 = -13
-2x = -14
Divide both sides by -2.
x = 7
Now that we know x, plug its value into one of our original equations.
y = 4x - 1
y = 4(7) - 1
Solve.
y = 28 - 1
y = 27
Our solution is (7, 27).
Let's check our answer by plugging both values into one of our original equations.
2x - y = -13
2(7) - 27 = -13
Solve.
14 - 27 = -13
-13 = -13
Your solution is correct.
Polly's solution was (-2, -9), which is incorrect.
b.
3x + 6y = 15
-2x + 3y = -3
Let's solve this by elimination. To solve by elimination means to eliminate a variable from the equation.
We have 3x & -2x and 6y & 3y. Notice that 6 and 3 can be simplified easily. To eliminate y, we want to multiply each factor of the second equation by -2.
-2x + 3y = -3
-2(-2x + 3y = -3)
4x - 6y = 6
Write the equations together.
3x + 6y = 15
4x - 6y = 6
Now we can see that the y variable will cancel out.
Apply the elimination method.
3x + 6y = 15
4x - 6y = 6
________
7x = 21
Divide both sides by 7.
x = 3
Now that we know x, plug its value into one of our original equations.
3x + 6y = 15
3(3) + 6y = 15
Solve.
9 + 6y = 15
6y = 15 - 9
6y = 6
y = 1
Our solution is (3, 1).
Let's check our answer by plugging both values into one of our original equations.
-2x + 3y = -3
-2(3) + 3(1) = -3
Solve.
-6 + 3 = -3
-3 = -3
Your solution is correct.
Polly's solution was (3, 1), so she was correct.
Hope this helps!
The high temperatures for the last seven days are: High Temperatures: 81, 78, 83, 89, 80, 87, 78
Find the MODE of the temperatures.
Answers
Answer: 78
Step-by-step explanation:
The mode is the number that appears the most number of times. In this case the number 78 appears twice unlike the other numbers that only appear once. Hence, 78 is the mode :)
Answer:
78
Step-by-step explanation:
The mode is the value that appears most often in a set of data. The mode of a discrete probability distribution is the value x at which its probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled.
Find the length of BC .
72
54
40.5
108
Answers
value of n=72
Answer:
∆ABC~DEF
since the side of similar triangle are proportional
[tex] \frac{AB}{DE} = \frac{BC}{EF} [/tex]
[tex] \frac{54}{9} = \frac{n}{12} [/tex]
6×12=n
n=72
in the figure below, <1 measures (3x+20) and <2 measures x. what is the measure of <4?
Answers
Answer:
D. 140
Step-by-step explanation:
∠ 1 + ∠ 2 = 180
So:
(3x + 20) + x = 180
4x + 20 = 180
4x = 180 - 20
4x = 160
x = 160 / 4
x = 40
∠ 1 = ∠ 4
∠ 2 = ∠ 3
If ∠ 1 is equal to ∠ 4, just plug in for x and solve.
3x + 20 = 3(40) + 20 = 120 + 20 = 140
Erin is ordering a laptop computer. The computer costs $1,360.00, and there is a 6% sales tax.
What is the amount of sales tax Erin will owe for her computer?
Answers
Answer:
$81.6
Step-by-step explanation:
(1,360.00)(6%)=81.6
Find the hypotenuse of the triangle, the
distance between points (4, 4) and (-2,-2).
[?]
(4.4)
Enter the number that
6 goes beneath the radical
symbol
(-2,-2)
6
Answers
For this parallelogram (a) choose the best name and then (b) find the value of x and y.
Answers
Answer:
rhombus
3x + 6 = 90
3x = 84
x = 28
there is no y
1) ABC is a right-angled triangle.
AB = 50 cm.
Angle ABC= 24°
Work out the length of BC.
Give your answer correct to 1 decimal place.
Answers
Answer:
112.3
Step-by-step explanation:
At Food Lion, you can buy 3 bags of Takis for $4.99. What is the
price of one bag of Takis? (Round to the nearest cent)
Answers
Answer:
Step-by-step explanation:
price of one bag of Takis = $4.99/3 = $1.66333, which is approximately $1.66
subtract (5x + 3) - (x + 2)
Answers
What is the formula for the volume of a cylinder? (Use the word Pi instead of the symbol)
Answers
Answer:
pi x radius x 2 x height of the cylinder.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
In a circle with a 12-inch radius, find the length of a segment joining the midpoint of a 20-inch chord and the center of the circle.
x =
Answers
Answer:
X=295.6
Step-by-step explanation:
I took the test
Answer:
295.6
Step-by-step explanation:
(45 points)
(1) It takes 4 eggs for 5 waffles. How many more waffles can 6 eggs make?
(2) A 1-lb. mix will make 32 biscuits. How many ounces of mix are needed for 24 biscuits?
I NEED THIS ASAP!
Answers
Answer:
1). 6 eggs = 7.5 waffles 2). 8 ounces for 24 biscuits
Step-by-step explanation:
Por la comra de un televisor en 130 000 se ha pagado 1/4 al contado y el resto en 6 cuotas en igual valor cada una.
Answers
Answer:
Por la compra de un televisor en $ 130000 se ha pagado →1/4 del total al contado → el restante en 6 cuotas de igual valor .
el valor de cada cuota =?
Step-by-step explanation:
Para resolver el ejercicio se procede a realizar la operación indicada de calcular el valor de cada una de las 6 cuotas de igual valor, de la siguiente manera :
1/4 * $130000 = $ 32500
$ 130000 - $ 32500 = 97500 $ 97500 /6 = $ 16250
El valor de cada una de las 6 cuotas restantes es de $ 16250 .
Traingle ABC below has a rigth angle C and a hieght CD. If AC is 3 units long, and BC is 4, what is the lengtyh of CD
Answers
Answer:
5 units
Step-by-step explanation:
the length of CD can be determined using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
3² + 4²
= 9 + 16
= 25
the square root of 25 is 5
Louis will spend $755.00 on a new kitchen sink. He will use his credit card to withdraw
$800 cash to pay for the sink. The credit card company charges 4% interest on the
borrowed amount. How much will Louis owe?
$332
Answers
Answer:
332$?
Step-by-step explanation:
pls help me, im adding integers 40 points!!!!!!!!!
Use a number line to find each sum.
2 + 4
6 + (-7)
-6 + 6
Find each sum
-2 + (-7)
9 + (-9)
-12 + (-9)
91 + 28
-51 + (-9)
-8 + 72
Then a question.
Temperature At 7:30 A.M. on January 22,1943, the temperature was -4 °F in Spearfish, South Dakota. At 7:32 A.M. the temperature had risen 49 degrees. What was the temperature at 7:32 A.M.?
Answers
Answer:
1. 6
2. -1
3. 0
4. -9
5. 0
6. -21
7. 119
8. -60
9. 64
10. 45 degrees
Step-by-step explanation:
how do I find the volume?
Answers
Answer:
Width x length
Step-by-step explanation:
Find the width or how wide it is
Then find the length or how long it is
multiply those
solve for x
[tex]\frac{7}{x+4}[/tex] = 4
Give your answer as an improper fraction in its simplest form.
Answers
Answer:
-9/4 = x
Step-by-step explanation:
4 is the same as 4/1
this problem is a proportion which can be solved by cross-multiplying:
7 = 4(x+4)
7 = 4x + 16
-9 = 4x
-9/4 = x
Answer ASAP! Best Answer Will Be Awarded!
Answers
Answer:
B
Step-by-step explanation:
4x-8y=16
add 8y to both sides, so you get
8y+16=4x
then subtract 16 from both sides
8y=4x-16
divide by 8 on both sides
y=1/2x-2
The swimming pool shown is a right prism with concave hexagonal bases.... pls help
Answers
3 bottom sections:
10 x 20 = 200
5x 20 = 100
10 x 20 = 200
Bottom area = 200 + 200 + 100 = 500 square feet.
Short side: 3 x 20 = 60
Deep end wall : 6 x 20 = 120
Side wall : (24 x6) - (10x3) - (1/2 x 4x3) = 144-30-6 = 108
2 side walls: 108 x 2 = 216
Total area : 500 + 216 + 60 + 120 = 896 square feet
Divide total area by area of 1 gallon:
896/400 = 2.24 gallons
It will take 2.24 gallons of paint
An inequality is shown 1 < -18% 8 Which value of x makes the inequality true??
Answers
Answer:0.02
Step-by-step explanation:
The "Open" sign at Cenzo's flashes every 4 seconds. The "Open" sign at The Kettle flashes every 5 seconds and the "Welcome" sign at Centrella's Deli flashes every 6 seconds. If the signs are turned on and flash at the same time, how long will it take for them to flash at the same time again?
Answers
Find the lcm ( least common denominator)
4: 4,8,12,16,20,24,28,32,36,40,44,48,52,
56,60
5: 5,10,15,20,25,30,35,40,45,50,55,60
6: 6,12,18,24,30,36,42,48,54,60