Answers
Given:
In triangle ACD, BE||CD, AB = 20 cm, BC = 5 cm, CD = 18 cm, AE = 26 cm.
To find:
(a) The length of ED.
(b) The length of BE.
Solution:
In triangle ABE and ACD,
BE||CD, so angle ABE and angles ACD are corresponding angles. So, their measure are equal.
[tex]m\angle ABE=m\angle ACD[/tex] (Corresponding angles)
[tex]m\angle BAE=m\angle CAD[/tex] (Common angle)
Now,
[tex]\Delta ABE\sim \Delta ACD[/tex]
Corresponding sides of similar triangles are proportional.
[tex]\dfrac{AB}{AC}=\dfrac{BE}{CD}=\dfrac{AE}{AD}[/tex]
(a)
[tex]\dfrac{AB}{AC}=\dfrac{AE}{AD}[/tex]
[tex]\dfrac{20}{20+5}=\dfrac{26}{AD}[/tex]
[tex]\dfrac{20}{25}=\dfrac{26}{AD}[/tex]
[tex]0.8=\dfrac{26}{AD}[/tex]
Isolate AD.
[tex]0.8AD=26[/tex]
[tex]AD=\dfrac{26}{0.8}[/tex]
[tex]AD=32.5[/tex]
Now,
[tex]AD=AE+ED[/tex]
[tex]32.5=26+ED[/tex]
[tex]32.5-26=ED[/tex]
[tex]6.5=ED[/tex]
Therefore, the length of ED is 6.5.
(b)
[tex]\dfrac{AB}{AC}=\dfrac{BE}{CD}[/tex]
[tex]\dfrac{20}{25}=\dfrac{BE}{18}[/tex]
[tex]0.8=\dfrac{BE}{18}[/tex]
Multiply both sides by 18.
[tex]14.4=BE[/tex]
Therefore, the length of BE is 14.4.
Related Questions
Triangle Deff is shown below. 110°, e, d, f, 135°
Answers
Answer:
Step-by-step explanation:
a° + 110° = 180° [Linear pair of angles]
a = 180° - 110°
a = 70°
b° + 135° = 180° [Linear pair of angles]
b = 180° - 135°
b = 45°
a + b + c = 180° [Triangle sum theorem]
45° + 70° + c = 180°
c = 180° - 115°
c = 65°
Therefore, a triangle similar to DEF will have an angle that measures 45 degrees, an angle that measures 70 degrees and an angle that measures 65 degrees.
What is the slope of the line that passes through the points (2, -3) and (5, 1)?
Answers
Answer:
The slope is 4/3 :)
Step-by-step explanation:
f(x) = 3x² + 4x – 6
g(x) = 6x3 – 5x2 – 2
Find (f – g)(a).
Answers
Step-by-step explanation:
(-6x^3+8x^2+4x-4)
option D is correct answer
Answer:A
Step-by-step explanation:
PLEASE HELP ME
Solve for X and Z
Answers
9514 1404 393
Answer:
x = 1z = 11Step-by-step explanation:
If we assume that the segment marked (2x+1) is a midsegment, then it is half the length of the parallel base:
2(2x+1) = 8x-2
4x +2 = 8x -2 . . . . eliminate parentheses
4 = 4x . . . . . . . . . . add 2-4x to both sides
1 = x . . . . . . . divide by 4
__
The above assumption makes the two segments marked with z-expressions be the same length:
3z = z +22
2z = 22 . . . . . . subtract z
z = 11 . . . . . . . . . divide by 2
The values of X and Z are 1 and 11, respectively.
I NEED HELP
I don’t know what to do!!
Answers
2.A
3.d
4.B
Hope this helps!
Brainliest?
Is okay if no !
A pizza company sells a small pizza for $6. Then it charges $2 per topping. What equation corresponds to this scenario? (20 points)
Answers
Answer:
A
Step-by-step explanation:
Matt read 65 pages in 50 minutes. He reads at a constant rate.
How many pages can Matt read per minute?
Answers
Answer:
78
Step-by-step explanation:
Can you give me brainliest please
Answer:
Give somuchcringe321 brainliest
Step-by-step explanation:
A pair of shorts regularly cost $35 are on sale for 20% off what is the price of the shorts?
Answers
Write the correct order of letters to the finish line Example ABCGH
Answers
Solve for r.
r/-4 = 250
Answers
Answer: r= -1000
Step-by-step explanation:
Solve for r by simplifying both sides of the equation, then isolating the variable
Answer:
-1000
Step-by-step explanation:
-4 x 250 = -1000
-1000/-4= 250
PLZ MARK BRAINLIEST
have a great day! :)
kyler wanted to pay no more than$ 0.62 per litter of orange juice. if he purchased 12 litters for $7.58. Did he pay under $0.62?
Can someone please answer this quickly i'll give 16 pts
its based on unit rates
Answers
Answer:
No he payed $0.63 per liter.
Step-by-step explanation:
Okay to solve this you would divide the price payed by the number of liters purchased. So 7.58/12. When we divide this, we get 0.631666667. Rounded this is 0.63. So no he did not pay 0.62.
PLEASE HELP ASAP IT'S DUE TODAY Use the graph of the function below to answer the questions that follow.
Answers
Answer:
So for..
a. from: 2 to: 4
b. from: 0 to: 2 ( I believe this one, may be incorrect- sorry if so)
c. from: 6 to: 10 ( I believe also for this one, sorry if incorrect)
d. from: 5 to: 6 ( I beleive- that is what it looks like- sorry if incorrect)
e. They are staying at a constant rate, not changing, at rest...
Hope this helps!
-10 = -0.2k
k = ?
solve for k
Answers
-10/-0.2 =50
so 50=k
Answer:
-10 = -0.2k
we multiply both sides by 5
-50 = -k
k = 50
Step-by-step explanation:
A company is desinging a square prism. Its height is 3 yarss longer than a side of its base. The volume of the prism must be 20 cubic yards. Write a representative function for the volune of the solid..
Answers
Answer:
[tex]a^{2} (a+3) = 20\\OR\\a^3 +3a^2 -20 = 0[/tex]
Step-by-step explanation:
Given that:
There is a square prism which has height equal to 3 yards longer than that of the base of the prism.
Let the base of prism = [tex]a[/tex] units
As per question statement:
Height, [tex]h = (a+3)[/tex] units
Volume of the prism = 20 cubic yards
Now, we have to find a representative function that will represent the volume of the solid.
First of all, let us have a look at the formula for volume of a prism.
[tex]V = B\times h[/tex]
Where, [tex]B[/tex] is the area of base and
[tex]h[/tex] is the height of prism.
And the base is a square, whose area will be represented as:
[tex]B = Side \times Side[/tex]
Now, putting the values in the formula for Volume:
[tex]V = a^2(a+3) = 20\\OR\\a^3+3a - 20 =0[/tex]
Express the interval shown on the number line in inequality notation.
Answers
Answer: x < -3 or x > 5
Step-by-step explanation: Interval notation shows the values of x. X is less than -3, or greater than 5.
Mrs. Wilson tells you that the next test is worth 100 points and contains 38 problems. Multiple-choice questions are worth 2 points each and word problems are worth 5 points. How many of each type of question are there
Answers
Answer:
30 mcq and 8 word problems
plz mark as brainliest
Help!! Thank u and please
Answers
Answer:
150
Step-by-step explanation:
z^2. (x-y)
(5)^2. (9-3)
25. 6
150
MULTIPLE QUESTIONS FOR 100 POINTS IF CORRECT YOU WILL GET BRAINLIEST!!! PLEASE HELP
1. Do Charlotte's calculations make sense? Why or why not? Make sure to address each step in your answer and use complete sentences to explain your reasoning.
2. Charlotte is redecorating the master bedroom in her house. She has purchased a new bedroom set and also plans to paint the room and put in new flooring. The room is rectangular, with dimensions of 16 feet (length) by 13 feet (width). The walls in the room are 9 feet tall, and the room contains two doors and two windows.
Charlotte has decided to put new carpet in the bedroom. The carpet she chose costs $1.85 per square foot, not including the cost of labor or other related materials. She was given the following information by the local flooring store where she is purchasing the carpet.
She is required to purchase a piece of carpet that includes a 3-inch overlap on all sides. Labor and material costs will relate to the area of this piece.
The labor costs are $23 per hour, per person.
A two-person carpet crew can lay 50 square feet of carpet each hour.
The crew that will complete the job at Charlotte's house will be a four-person crew.
There is an additional $75 fee to cover the cost of equipment, materials, and supplies.
What are the dimensions of the piece of carpet that Charlotte must purchase? Note: Express your answer as a decimal number and do not round.
Length:
feet; Width:
feet.
3. Charlotte is redecorating the master bedroom in her house. She has purchased a new bedroom set and also plans to paint the room and put in new flooring. The room is rectangular, with dimensions of 16 feet (length) by 13 feet (width). The walls in the room are 9 feet tall, and the room contains two doors and two windows.
Charlotte has decided to put new carpet in the bedroom. The carpet she chose costs $1.85 per square foot, not including the cost of labor or other related materials. She was given the following information by the local flooring store where she is purchasing the carpet.
She is required to purchase a piece of carpet that includes a 3-inch overlap on all sides. Labor and material costs will relate to the area of this piece.
The labor costs are $23 per hour, per person.
A two-person carpet crew can lay 50 square feet of carpet each hour.
The crew that will complete the job at Charlotte's house will be a four-person crew.
There is an additional $75 fee to cover the cost of equipment, materials, and supplies.
Recall that the area of a rectangle is found by multiplying the length and width of the rectangle. What is the area of the piece of carpet that Charlotte must purchase? Note: Express your answer as a decimal number and do not round.
_____ square feet
Answers
I hope this helped!
Answer:
Yes, they do make sense because the amount of square feet is equal to the amount of money needed to make the purchase in the mathematical abbreviations.
Step-by-step explanation:
what is 5square times 34 times 10square.
Answers
Answer:
85,000
Step-by-step explanation:
(5 square) *34* (10 square)
Need help please!!!!
Answers
Answer:
15/x-2
Step-by-step explanation:
Cant attach the photo but you use a division table
What is 100 - 10 x 3
Answers
Two and a half hours later than 3:30 is
What is it??
Answers
Answer:
1 o'clock
Step-by-step explanation:
plz brainliest!
Answer:
6:00
Step-by-step explanation:
3:30+2:30=6:00
If that's what u mean
combine like terms -21a + 16a
A. -5a
B. 5a
Answers
Answer:
-5a
Step-by-step explanation:
-5a
Answer: b
Step-by-step explanation:
solve the system of equations. 2x + 7y =3
x = -4y
x =
y =
Answers
Answer:
x = 3/2−7y/2
Step-by-step explanation:
hope this is correct
I will give BRAINLIEST!!! Please answer as soon as possible
Answers
Answer:
2 c ( 7c + 1 )
Step-by-step explanation:
because 14 and 2 go into the table of 2
you first find out what number in table 2 go into 14 in this case 7 times 2 and then you find what number in the time table 2 give you 2 so it's 2 times 1. because it's c squared you can't not put both c inside due that would not be factorizing due that it's common and it does not have to be common.
so the answer will be 2c(7c+1)
Find the Mean,
3, 9, 13, 8, 10, 2
Mean
can someone help me?
Answers
Answer:
7.5
Step-by-step explanation:
3 + 9 + 13 + 8 + 10 + 2 = 45
There are 6 numbers so we divide 45 by 6
45/6 = 7.5
Gabriel works at a snack bar that sells drinks for $3, hot dogs for $5, and t-shirts for $15. In the last hour, Gabriel sold $60 wroth of each of items. How many of each item did Gabriel sell?
Answers
Determine the center and radius of the following circle equation: x^2+y^2-8x+6y-75=0 x 2 +y 2 −8x+6y−75=0 Center: \big(( , \big)) Radius:
Answers
Answer:
Compare x^2 +y^2-8x-6y=75 with the general circle equation x^2+y^2 -2ax-2by+c=0
-2a =-8 And -2b=-6
a=4 b=3
c=-75
To find the radius use the equation
r^2=a^2+b^2-c
r^2=4^2+ 3^2-(-75)
r^2=25+75=100
r=10(radius is always positive)
Hence the center is (4,3) and radius 10
Step-by-step explanation:
what is 5+5 plssssssssssssss!!!!! i need it now!!!!!!!!!!!! plsssssssssssssssssss
Answers
Answer:
Hmmmmmmmmm I think it’s 10....?
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
PLEASE HELP I WILL MARK BRAINLY
Answers
Answer:
The answer is C
Step-by-step explanation:
We apply the given formula: y= 2x + 1.
0 x 2 = 0 + 1 = 1, so A is incorrect.
1 x 2 = 2 + 1 = 3, C is the only one with 3 as the second number, so C is correct