The pentagons ABCDE and JKLMN are similar. Find the length x of LM

Can anyone solve this question??? plss plsss its my request to all if any one can solve this question I will mark him/ her the b

almond37 [142]

Answer:

a) ∠EAB = 180° - 90° - 30° = 60°

∠EBA = 180° - 90° - 60° = 30°

a) ∠EBA = 30°

b) ∠DCA = 180° - 90° - 30° = 60°

∠EBA ≅ ∠DAC, ∠EAB ≅ ∠DCA, ∠AEB ≅ ∠CDA

ΔEBA ≅ ΔDAC because of the AAA postulate

c) EB ≅ DA, EA ≅ DC, AB ≅ CA

d) AB = CA given

sin ∠EAB = EB/AB (sin 60°) EB = (0.8660)AB

cos ∠EAB = EA/AB (cos 60°) EA = (0.5)AB

cos ∠DAC = AD/CA (cos 30°) AD = (0.8660)CA

sin ∠DAC = CD/CA (sin 30°) CD = (0.5)CA

ED = EA + AD

ED = (0.5)AB + (0.8660)CA

since AB = CA, ED = 1.366CA

since EB = (0.8660)AB and AB = CA, then EB = 0.866CA

since CD = 0.5CA,

EB + CD = 0.866CA + 0.5CA = 1.366CA

EB + CD = 1.366CA

1.366CA = 1.366CA

Proof: ED = EB + CD

7 0

3 years ago

Solve the system of equations algebraically. Verify your

xz_007 [3.2K]

Answer:

The solution is the point (0.5,-3)

Step-by-step explanation:

we have

$y=4x-5$ ----> equation A

$y=-3$ ----> equation B

Solve the system by substitution

Substitute equation B in equation A

$-3=4x-5$

Solve for x

Adds 5 both sides

$-3+5=4x$

$2=4x$

Divide by 4 both sides

$x=0.5$

therefore

The solution is the point (0.5,-3)

Verify your answer using the graph

using a graphing tool

Remember that the solution of the system of equations is the intersection point both graphs

The intersection point is (0.5,-3)

therefore

The solution is the point (0.5,-3)

see the attached figure

8 0

3 years ago

Read 2 more answers

3) Solve the system using substitution. Show all work. -4x + 3y = 23 y = -7x - 9

Rina8888 [55]

Answer:

x = -2

Step-by-step explanation:

-4x + 3y = 23

y = -7x - 9 // *-3

-4x + 3y = 23

-3y = 21x -27

+++++++++++++++++++

-4x = 21x + 50

-50 = 25x

x = -2

5 0

3 years ago

What are the real roots of 2x^3+9x^2+4x-15=0

klemol [59]

Well, luckily it is apparent that (x-1) is a root because when x=1 the equation is equal to zero. So we can divide the equation by that factor to find the other roots.

(2x^3+9x^2+4x-15)/(x-1)
2x^2 r 11x^2+4x-15
11x r 15x-15
15 r 0

(x-1)(2x^2+11x+15)=0

(x-1)(2x^2+6x+5x+15)=0

(x-1)(2x(x+3)+5(x+3))=0

(x-1)(2x+5)(x+3)=0

So the roots are x= -3, -2.5, 1

8 0

4 years ago

Which expression is equivalent to 5a+20? A: 5(5a+4). B: 5(a+4). C: 5(a+20). D: 5(a+1)

guajiro [1.7K]

Answer:

5(a+4)

Step-by-step explanation:

expression is equivalent to 5a+20

To get the equivalent expression we need to factor the given expression

5a+ 20

5a can be written as 5 * a

20 can be written as 5*2*2

WE can see that common factor is 5 for both 5a and 20

So GCF is 5

Now we factor out GCF 5

WE put 5 outside and write all the left of factors inside the parenthesis

5a +20

5 (a+2*2)

5(a+4)

4 0

4 years ago