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
zzz [600]
3 years ago
11

the diagonals PR and QS of a rhombus intersect each other at point O. prove that 2(PQ) + 2(QR) + 2(RS)+ 2(PS) = 4 (2(OP)+2(OQ))

Mathematics
1 answer:
mamaluj [8]3 years ago
4 0

Answer:

It is proved that 2PQ + 2SR + 2QR + 2 PS = 4(2(OP)+2(OQ))

Step-by-step explanation:

In a rhombus, all sides are equal.

Thus, in this question;

PQ = SR = QR = PS

By inspection, QS is the same dimension as the four sides. So, QS = PQ

Thus, OQ = PQ/2

For OP, we can find it using Pythagoreas theorem since the angle that divides the diagonals is 90°

Thus;

|OP|² + |OQ|² = |PQ|²

Earlier, we saw that;OQ = PQ/2

Thus;

|OP|² + |PQ/2|² = |PQ|²

|OP|² = |PQ|² - |PQ/2|²

|OP|² = |PQ/2|²

Taking square root of both sides, we have;

OP = PQ/2

So,going back to the question, on the right hand side, we have;

4(2(OP) + 2(OQ))

Let's put,

PQ/2 for OQ and OP as gotten earlier

So,

4(2(PQ/2) + 2(PQ/2)) = 4(PQ + PQ)

Since PQ = SR = QR = PS, we can rewrite as;

4PQ + 4PQ = (PQ + SR + QR + PS) + (PQ + SR + QR + PS) = 2PQ + 2SR + 2QR + 2 PS

This is equal to the left hand side, so the equation is proved correct.

You might be interested in
A family buys 4 airline tickets online. The family buys travel insurance that costs $19 per ticket. The total cost is $752. Let
Ede4ka [16]

A. x = 752 / 4 - 19

B. 169

7 0
3 years ago
Read 2 more answers
Pleases solve this. I need help! At least the slope! Giving 75 points!
masha68 [24]

Answer:

Slope is 1/2. Used points 0,0 & 6,3

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Question 3
Katyanochek1 [597]

Answer:

oooooooooooooooooooooooooooooooooooooooooooooo

Step-by-step explanation:

5 0
2 years ago
Samir is trying to decide between two checking account plans. After researching plans at two banks, he finds that Unity Bank off
GREYUIT [131]

Answer:

The monthly compounded interest rate of 0.14% of Unity Bank is a better plan.

Step-by-step explanation:

<em>Step 1 : Write the formula for calculating a monthly compound interest rate and for calculating an annually compounded interest rate.</em>

Monthly compound interest rate = P(1+r/n)^nxt

<em>n=12 (number of months in a year)</em>

<em>t=1 (number of years)</em>

Annually compound interest rate = P(1+r/n)^nxt

<em>n=1 (because it is for 1 year only)</em>

<em>t=1 (number of years=1)</em>

<em>Step 2 : Lets assume that P is $100 in both banks and time is 1 year.</em>

<em>Step 3 : Lets substitute the values to find out which one is better.</em>

Monthly compound interest rate = P(1+r/n)^nxt

Monthly compound interest rate = 100(1+0.14/12)^12x1

Monthly compound interest rate = 114.93

114.93 - 100 = $14.93 per month

14.93 x 12 = $179.16 for 12 months or 1 year

Annually compound interest rate = P(1+r/n)^nxt

Annually compound interest rate = 100(1+1.6/1)^1x1

Annually compound interest rate = 260

260-100 = $160 for 1 year

Therefore, the monthly compounded interest rate of 0.14% of Unity Bank is a better plan.

!!

8 0
3 years ago
Read 2 more answers
Julio tenía 2/3 de una tablilla de chocolate en el recreo comió 1/5 que fracción de la tablilla le queda?
Furkat [3]

Answer:

7/15 de la tablilla de chocolate le va a quedar.

Step-by-step explanation:

2/3 se converte en 10/15

y 1/5 se converte en 3/15

Entonces le va a quedar 10/15-3/15 = 7/15 de la tablilla de chocolate.

5 0
3 years ago
Read 2 more answers
Other questions:
  • A line that passes throught the points (2,-3) and (b,7) is parallel to the line y=-2x+17. find the value of b
    11·1 answer
  • If a penny is tossed five times, what is the probability of all tails? a zero b 1/16 c 1/32 d larger than the probability of all
    12·1 answer
  • 13=78.0000000000000b
    14·2 answers
  • Which shows three hundred five million,two hundred eighty thousand, four hundred ninety-six written in standard form?
    11·1 answer
  • HELP ME PLZ PLZ PLZ!HELP ME PLZ PLZ PLZ!
    7·1 answer
  • Use similar triangles to find the value of x and y​
    8·2 answers
  • PLS HELP
    7·1 answer
  • Which scatterplot most likely has a line of best fit represented by y=-2x-1?<br>NO LINKS PLS
    7·2 answers
  • 8y - 3 = 37<br> What is y?
    8·2 answers
  • A water dispenser has a capacity of 20,000 milliliters. Use the facts to find how much this is in liters .
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!