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
gladu [14]
3 years ago
12

The diagonals of rectangle nopq intersect at point r. if oq=2(x+3) and pr=3x-5, solve for x.

Mathematics
2 answers:
OverLord2011 [107]3 years ago
8 0
The diagonals of a rectangle are always congruent.  We have the whole length of OQ to be 2x + 6, and we have only half of NP.  Therefore, OQ = 2(PR).  2x+6=2(3x-5).  2x+6 = 6x-10.  16 = 4x so x = 4.  That means that each diagonal is 14 units long.
tatuchka [14]3 years ago
4 0

Answer:

x=4

Step-by-step explanation:

Please find the attachment.

We have been given that the diagonals of rectangle nopq intersect at point r.

We know that diagonals of rectangle are always congruent. Line segment oq is diagonal of our given rectangle.

We also know that diagonals of parallelogram bisect each other, so length of diagonal np will be two times pr.

np=2\times pr

np=2(3x-5)

Now, we will equate np with oq to solve for x as:

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

6x-10=2x+6

6x-10+10=2x+6+10

6x=2x+16

6x-2x=2x-2x+16

4x=16

\frac{4x}{4}=\frac{16}{4}

x=4

Therefore, the value of x is 4.

You might be interested in
Based on the data given in the picture, calculate the area of the car track...
Verizon [17]

Refer to the diagram below. We need to find the areas of the green and blue regions, then subtract to get the area of the orange track only.

The larger green region is composed of a rectangle of dimensions 200 meters by 4+42+4 = 50 meters, along with two semicircles that combine to make a full circle. This circle has radius 25 meters.

The green rectangle has area 200*50 = 10000 square meters. The green semicircles combine to form an area of pi*r^2 = pi*25^2 = 625pi square meters. In total, the full green area is 10000+625pi square meters. I'm leaving things in terms of pi for now. The approximation will come later.

The blue area is the same story, but smaller dimensions. The blue rectangle has dimensions 200 meters by 42 meters, so its area is 200*42 = 8400 square meters. The blue semicircular pieces combine to a circle with area pi*r^2 = pi*21^2 = 441pi square meters. In total, the blue region has area 8400+441pi square meters.

After we figure out the green and blue areas, we subtract to get the orange region's area, which is the area of the track only.

orange area = (green) - (blue)

track area = (10000+625pi) - (8400+441pi)

track area = 10000+625pi - 8400-441pi

track area = (10000-8400) + (625pi - 441pi)

track area = 184pi + 1600 is the exact area in terms of pi

track area = 2178.05304826052 is the approximate area when you use the pi constant built into your calculator. If you use pi = 3.14 instead, then you'll get 2177.76 as the approximate answer. I think its better to use the more accurate version of pi. Of course, be sure to listen/follow your teachers instructions.

4 0
3 years ago
The rabbit population in a certain area is 500% of last years population. There are 900 rabbits this year. How many were there t
12345 [234]

Answer:

180 rabbits

Step-by-step explanation:

<u><em>The correct question is</em></u>

The rabbit population in a certain area is 500% of last years population. There are 900 rabbits this year. How many were there last year?

we know that

900 rabbits represent 500% of last year population

Last year population represent 100%

so

using proportion

Find out how many rabbits represent a percentage of 100%

\frac{900}{500\%}=\frac{x}{100\%}\\\\x=900(100)/500\\\\x=180\ rabbits

7 0
3 years ago
WILL GIVE BRAINLIEST
Bezzdna [24]

Answer: D. (8, 4)

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Which is greater 1 1/10 or 1 1/12
RoseWind [281]
1 1/10
........................
3 0
3 years ago
Read 2 more answers
Enter the equation in standard form.<br> y = 5x - 1
kicyunya [14]

Answer:

-5x + 1y = -1

Step-by-step explanation:

move the 5x to the other side of the equal sign.

4 0
3 years ago
Other questions:
  • A class survey showed 8 out of 25 students had plans to travel over spring break.how many student out of the 400 students in the
    10·2 answers
  • X+a=3/4 I don't know how to solve this and I need someone to help explain it to me.
    5·1 answer
  • Solve for b.
    12·2 answers
  • 17-2/3-7(8-6)<br> How do I get the answer
    13·1 answer
  • Calculate the perimeter of this figure<br>to the nearest tenth.​
    15·1 answer
  • A group of friends went fishing. They each caught 20 fish but not all of them were keepers. Which person was able to keep 3/5 of
    5·1 answer
  • This is confusing i need help ;-;
    15·2 answers
  • Students arrived at the science museum at 1:15 P.M. They stayed at the museum for
    8·2 answers
  • Please help I’ll give Brainlist
    11·1 answer
  • Help please 75 points and brainliest
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!