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ASHA 777 [7]
3 years ago
6

Geometry Proof - Thanks in advance for the help!

Mathematics
1 answer:
RideAnS [48]3 years ago
8 0

Answer:

Using reflexive property (for side), and the transversals of the parallel lines, we can prove the two triangles are congruent.

Step-by-step explanation:

  • Since AB and DC are parallel and AC is intersecting in the middle, you can make out two pairs of alternate interior angles<em>.</em> These angle pairs are congruent because of the alternate interior angles theorem. The two pairs of congruent angles are: ∠DAC ≅ ∠BCA, and ∠BAC ≅ ∠DCA.
  • With the reflexive property, we know side AC ≅ AC.
  • Using Angle-Side-Angle theorem, we can prove ΔABC ≅ ΔCDA.
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Identify the perimeter and area of a square with diagonal length 11in. Give your answer in simplest radical form. HELP PLEASE!!
Nataliya [291]

Answer:

  • Perimeter = 22*sqrt(2)
  • Area = 60.5 inches
  • D

Step-by-step explanation:

Remark

You need 2 facts.

  1. A square has 4 equal sides.
  2. It contains (by definition) 1 right angle but since we are not including and statement about parallel sides, it needs 4 right angles.

That means you can use the Pythagorean Theorem.

If one side of a square is a then the 1 after it is a as well.

Formula

  • a^2 + a^2 = c^2
  • 2a^2 = c^2

Givens

  • c = 11

Solution

  • 2a^2 = 11^2
  • 2a^2 = 121                    Divide by 2
  • a^2 = 121/2                  Take the square root of both sides
  • sqrt(a^2) = sqr(121/2)    
  • a = 11/sqrt(2)                Rationalize the denominator
  • a = 11 * sqrt(2)/[sqrt(2) * sqrt(2)]
  • a = 11 * sqrt(2) / 2

<em><u>Perimeter</u></em>

P = 4s

  • P = 4*11*sqrt(2)/2
  • P = 44*sqrt(2)/2
  • P = 22*sqrt(2)

You don't need the area. The answer is D

<em><u>Area</u></em>

  • Area = s^2
  • Area = (11*sqrt(2)/2 ) ^2
  • Area = 121 * 2 / 4
  • Area = 60.5


8 0
3 years ago
Which graph shows the solution to the system of linear inequalities? x – 4y &lt; 4 y &lt; x + 1 Image for option 1 Image for opt
slava [35]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

x-4y ----> inequality A

solve for y

-4y

4y>x-4

y> (x/4)-1

The solution of the inequality A is the shaded area above the dashed line

The slope of the dashed line is positive

The y-intercept is the point (0,-1)

The x-intercept is the point (4,0)

y< x+1 ----> inequality B

The solution of the inequality B is the shaded area below the dashed line

The slope of the dashed line is positive

The y-intercept is the point (0,1)

The x-intercept is the point (-1,0)

Using a graphing tool

The solution of the system of inequalities in the attached figure

7 0
3 years ago
Marcie can swim 20 laps in an hour. How many hours will it take her to swim 100 laps
Margarita [4]

Answer:

5 hours

Step-by-step explanation:

We can write a ratio

20 laps           100 laps

-------------- = --------------

1 hour            x hours

Using cross products

20x = 100

Divide by 20

20x/20 = 100/20

x = 5 hours

4 0
3 years ago
Read 2 more answers
The area of a square concrete slab is 20 square feet. Find the side length of the square concrete slab if the area is increase b
guapka [62]

The side length of the square concrete slab if the area is increased by 25% is 5feet

The formula for calculating the area of a square is expressed as:

A =  L² where:

L is the side length of the square

Given the area of the square concrete slab = 20 square feet

20 = L²

L =√20

If the area is increased  by 25%, new area will be:

An = 20 + (0.25*20)

An = 20 + 5

An = 25 sq.ft

Get the new length

An = Ln²

25 =   Ln²

Ln = √25

Ln = 5feet

Hence the side length of the square concrete slab if the area is increased by 25% is 5feet

Learn more here: brainly.com/question/11300671

7 0
3 years ago
the average speed of a race car is 240 km/h. if the race is 200 laps long with each lap being 4.02 km, how long will the race la
shtirl [24]
Each lap = 4.02 km
 200 laps x 4.02 = 804 km total

804 km / 240 km/h = 3.35 hours = 3 hours and 21 minutes

7 0
3 years ago
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