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
Vanya drove 405 miles in 9 hours. Chuy drove 350 miles in 7 hours. Alfredo drove 330 miles in 6 hours. Who was driving at the fa
Novosadov [1.4K]

Answer:

350 miles in 7 hours

Step-by-step explanation:

  1. find

if 9=405

1=v(represent with a variable

2. do the same for the others and select the highest number

7 0
3 years ago
A rock is dropped off a 500-foot cliff. After 1 second the rock is traveling 32 feet per second then after 4 seconds the rock st
kozerog [31]

Answer:

<u>A. The equation describing the relationship between speed and time is:</u>

<u>s = 32t</u>

<u>Ordered pairs of the form (speed, time) are:</u>

<u>(32, 1)</u>

<u>(64, 2)</u>

<u>(96, 3)</u>

<u>(128, 4)</u>

<u>B. </u>

<u>Using s = 32t, we have:</u>

<u>s = 32 * 5 = 160 feet per second</u>

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Height of the cliff = 500 feet

Speed after one second = 32 feet per second

Speed after four seconds = 128 feet per second

2. Assume the relationship between time, t, and speed, s, is linear and write an equation describing the relationship. Use ordered pairs of the form (speed, time)

The equation describing the relationship between speed and time is:

s = 32t

Ordered pairs of the form (speed, time) are:

(32, 1)

(64, 2)

(96, 3)

(128, 4)

3.  Use the equation to determine the speed of the rock 5 seconds after is dropped.

s = 32t

s = 32 * 5 = 160 feet per second

Note: Same answer to question 14436233, answered by me today.

4 0
3 years ago
Equation of slope 4, through (7,2)
Crazy boy [7]
Y - y₁ = m(x - x₁)
 y - 2 = 4(x - 7)
 y - 2 = 4(x) - 4(7)
 y - 2 = 4x - 28
   + 2          + 2
      y = 4x - 26
5 0
3 years ago
Write in y= mx + b form: a line through (-3,1) having the same y-intercept as the graph of x-2y=-4
MariettaO [177]

Step-by-step explanation:

Aight, so the same intercept

- 2y =  - 4 - x =  =  =  >  \\ y =  \frac{1}{2} x + 2

m=½

y =  \frac{1}{2} x + b =  =  =  >  \\ now \: let \: us \: replace \: the \: point \\ 1 =  \frac{1}{2} ( - 3) + b =  =  =  >  \\  \frac{5}{2}  = b

soooo

y =  \frac{1}{2} x +  \frac{5}{2}

7 0
2 years ago
Please answer this question I need it i. Vertex and standard form.
Brums [2.3K]

Equation :

This parabola is facing downwards and highest point of the parabola is it's vertex.

Highest point is (-2,2)

so the vertex is (-2,2)

The graph is passing through (-1,0)

Equation in vertex form is

y = a(x - h) {}^{2}  + k

0 = a( - 1 + 2) {}^{2}  + 2 \\ 0 =a (1) {}^{2}  +2 \\  0 = a + 2 \\ a =  - 2

Substitute back in Equation

y =  - 2(x  + 2) {}^{2}  + 2

the graph has two x intercepts -1 and -3

that means (x+1) and (x+3) are the factors

multiply factors to get the equation in standard form

-2(x + 1)(x + 3) = 0 \\ -2(x {}^{2}  + x + 3x + 3) = 0 \\  -2( x {}^{2}  + 4x + 3) = 0

-2x^2-8x-6=0

4 0
2 years ago
Other questions:
  • Clayton places tiles that spell the word time in a bowl. He draws one tile from the bowl and then without replacing it, draws an
    14·2 answers
  • The height and sides of a triangle are four consecutive integers. the height is the first integer, and the base is the third int
    11·1 answer
  • How many different books did the children read
    5·1 answer
  • The height of a rectangle, in which a= 10x^2 ft^2 base is 2x ft
    6·1 answer
  • Which of the following could be the equation of the graph shown below? click all that apply.
    10·2 answers
  • Soda A cost $1.49 per 28 oz. bottle vs. $0.95 per 21 oz.
    6·1 answer
  • What is the range of the graph?
    9·1 answer
  • PLEASE HELP!! <br><br> I COULDNT PAY ATTENTION IN CLASS TODAY
    11·1 answer
  • To the nearest whole number, what is the distance<br> between the points M(-5, 7) and L( 9, 12)?
    10·1 answer
  • 6 7 8 only 8th grade math
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!