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musickatia [10]
2 years ago
5

Given: ABCD is a parallelogram and AC bisects BD. Prove: AB is congruent to BC.

Mathematics
1 answer:
earnstyle [38]2 years ago
3 0

Let's see

In ∆ABE and ∆CBE

  • BE=BE(Common side)
  • AE=EC[Diagonals of a parallelogram bisect each other]
  • <AEB=<BEC[90°]

So by

SAS congruence the triangles are congruent

AB=BC

  • Proved

Fact:-

It's already given AC is perpendicular to BD

  • It means diagonals are perpendicular to each other

According to general property of rhombus this parallelogram is also a rhombus.

So sides are equal hence AB =BC

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Solve the system of equations.<br> <img src="https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7By%3D220x-160%7D%20%5Catop%20%7By%3
Leni [432]

\begin{cases} y=220x-160\\ y=20x^2-400 \end{cases}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{\stackrel{\textit{\Large y}}{220x-160}~~ = ~~20x^2-400} \\\\\\ -160=20x^2-220x-400\implies 0=20x^2-220x-240 \\\\\\ 0=20(x^2-11x-12)\implies 0=x^2-11x-12 \\\\\\ 0=(x-12)(x+1)\implies x= \begin{cases} 12\\ -1 \end{cases}

\dotfill\\\\ x=12\qquad \qquad \stackrel{\textit{substituting on the 1st equation}}{y=220(12)-160}\implies y=2480 \\\\\\ x=-1\qquad \qquad \stackrel{\textit{substituting on the 1st equation}}{y=220(-1)-160}\implies y=-380 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (12~~,~~2480)\qquad (-1~~,~~-380)~\hfill

4 0
2 years ago
A company makes t-shirts and their research shows that that price and demand are related linearly: p = mx + b. They know that in
loris [4]

Answer:

P= -2x +46

Step-by-step explanation:

the relation between price and demand is

P= mx +b ........................1

when demand is 10 shirts price is $26

when demand is 20 shirts price is $6

firstly put P= 26 and x= 10 in 1

26= 10m + b.......................2

secondly put x= 20 and P= 6 in 1

6= 20m + b ............................3

solving  2 and 3 we get

m = -2

putting this value of m in either of 2 and 3 to get b

b= 46

so the final relation obtained by putting m= -2 and b= 46 in 1 we get

P= -2x +46

4 0
3 years ago
Answer pwease lol now
Anettt [7]

Answer:

D) y = 27 · (3)^x

Step-by-step explanation:

Replace x with the x values.

27 · (3)^-2 = 27 · 1/9 = 3

27 · (3)^-1 = 27 · 1/3 = 9

27 · (3)^0 = 27 · 1 = 27

27 · (3)^1 = 27 · 3 = 81

17 · (3)^2 = 27 · 9 = 243

D is your answer.

Hope this helps

5 0
2 years ago
How do I know when I need to use SSS or SAS in geometry? I'm having a lot of trouble understanding the difference and when to us
Pavel [41]
SSS = Side-Side-Side
If three sides of one triangle are congruent to three sides of another triangle then the triangles are congruent.


SAS  = Side-Angle-Side
If two sides and the included angle are equal to the corresponding parts of another triangle then the triangles are congruent.'
The angle must be formed by the two pairs of congruent, corresponding sides of the triangles. If the angles are not formed by the two sides that are congruent and corresponding to the other triangle's parts then you cannot use the SAS postulate.

you will notice that the main difference between the two postulates is that the SAS consists of an angle and the SSS does not.

hope this helps :)




7 0
3 years ago
What is the volume of the figure? PLEASE HELP ASAP NO LINKS
kotykmax [81]

Answer:

720 I think there is your answer from me

have a great day bye hop helps

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
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