1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Over [174]
3 years ago
12

In trapezoid ABCD AC is a diagonal and ∠ABC ≅ ∠ACD. Find AC if the lengths of the bases BC and AD are 14m and 28m respectively.

Mathematics
1 answer:
krek1111 [17]3 years ago
8 0

Answer:

AC = 14 sqrt(2) = 19.80    

Step-by-step explanation:

Below is the diagram showing you how this has been set up. The figure is a trapezoid which means BC and AD are parallel. AC is a transversal of the parallel lines.

Givens

  • <ABC = <ACD                          
  • ABCD  is a trapezoid
  • BC = 14
  • AD = 28
  • AC is a transversal of BC and AD

Solution

  • <ABC = <ACD                Given
  • <DAC = <ACB                Alternate interior angles.
  • ΔACB ≅ΔDAC               AA
  • <BAC = <ADC                Angles of similar triangles are equal
  • AC /28 = 14/AC              Form a proportion from corresponding sides
  • AC*AC = 14 * 28             Cross multiply the proportion. Combine
  • AC^2 = 392                    Express as prime factors.
  • AC^2 = 7*7*2*2*2           Take the square root of both sides
  • sqrt(AC)^2 = sqrt(7*7*2*2*2)
  • AC = 7*2 * sqrt(2)
  • AC = 14 sqrt(2) = 19.80    

You might be interested in
What equation do you get when you solve z-m=z+bx for x
Sonbull [250]
Z-m=z+bx

z-m-z=z+bx-z

-m=bx

bx=-m

bx/b=-m/b; b=0

x=-m/b; b=0
5 0
3 years ago
Three less than two times a number is 55. What is the number ?
Aloiza [94]
29
2x29=58-3 =55
3-2x (x=29) =55
29x2=58-3
5 0
3 years ago
Read 2 more answers
For all values of x<br> f(x) = 3x + 2<br> Find f-¹(-12)
Novosadov [1.4K]

Answer:

-4.67

Step-by-step explanation:

first find f^-1(x)

let f(x)=y

y=3x+2

3x=y-2

x=y-2/3

Therefore f^-1(x)=x-2/3

Now f^-1(-12)=-12-2/3

=-14/3

=-4.67

8 0
2 years ago
Coach Taylor wants to know the total practice time if he has the players warm up for 15 min
mrs_skeptik [129]
18 mins it is ! I think your missing the question tho
8 0
3 years ago
Find the sum of the series.
ch4aika [34]

Answer:

as per my point to view you can use a L.C.M so you can get the answer or you can try using a exponent way like 5by 1 as n value is 1 so it may give yoh answer

6 0
3 years ago
Read 2 more answers
Other questions:
  • The least common multiple of 2 5 6 9?
    13·2 answers
  • What does the following expression mean? F (-3)=8
    11·1 answer
  • Find the 5th term of the sequence defined by the give rule. f(n) = n²+ 5. A step by step explanation with answer would be greatl
    12·1 answer
  • Please help me with this one guys
    13·1 answer
  • A man mixed 2 teaspoons of sugar into his large coffee but then added one more teaspoon of sugar because it was not sweet enough
    10·1 answer
  • Simplify completely x2 + 4x - 45/x2 +10x+9 and find the restrictions on the variable.
    13·1 answer
  • Find the unit rate and slope of the graph (ignore what I put down)
    15·1 answer
  • D(−5, –3) and E(9, –3)<br> Find the distance between the points without graphing.
    10·2 answers
  • https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-geometry-topic/cc-6th-volume-with-fractions/e/volume_with_fractions?
    12·1 answer
  • Which is the best step to do next to solve the equation by completing the square 9(x^2+49x=22-5x
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!