ABCD is a rectangle in which AD = (2x + 1) cm and DC = (3x - 2) cm. PQRS is a trapezium in which PQ is parallel to SR, PQ = (x + 2) cm, SR = (5x − 8) cm and the shortest distance between PO and SR is (4x – 11) cm. The area of ABCD is twice the area of PQRS. Write down an equation in x to represent this information and show that it simplifies to 18x²89x + 68 = 0.​

Answer:

x = -8/3 and y = -49/3

Step-by-step explanation:

(Step 1) To solve using substitution, you first need to isolate a variable in one of these equations. I chose to isolate "y" in the following equation.

-8x + y = 5                                        <--- Original equation

y = 5 + 8x                                         <--- Add 8x to both sides

(Step 2) Now, substitute (5 + 8x) for "y" in the second equation.

5x - y = 3                                          <--- Original equation

5x - (5 + 8x) = 3                               <--- Substitute 5 + 8x for "y"

5x - 5 - 8x = 3                                  <--- Distribute (-) in the parentheses

-3x - 5 = 3                                        <--- Combine terms with "x"

-3x = 8                                              <--- Add 5 to both sides

x = -8/3                                             <--- Divide both sides by -3

(Step 3) Since you know the value of "x", plug it into one of the equations to solve for "y".

y = 5 + 8x                                         <--- Original (rearranged) equation

y = 5 + 8(-8/3)                                   <--- Plug (-8/3) for "x"

y = 5 - 64/3                                       <--- Multiply

y = 15/3 - 64/3                                   <--- Convert 5 into a fraction

y = -49/3                                           <--- Subtract

(Step 3.5) You can check your work by plugging "y" into the other equation to see if the answer for "x" is the same.

5x - y = 3                                             <--- Original equation

5(-8/3) - y = 3                                      <--- Plug (-8/3) for "x"

-40/3 - y = 3                                        <--- Multiply

-40/3 - y = 9/3                                     <--- Convert 3 into a fraction

-49/3 - y = 0                                        <--- Subtract both sides by 9/3

-49/3 = y                                             <--- Add both sides by "y"

The value of the system of equations is x = -8/3 and y = -49/3.

Answer:

The answer is 301 square inches.

Step-by-step explanation:

Answer:

-6 < x [tex]\leq[/tex] 6

Step-by-step explanation:

-5 < [tex]\frac{x-4}{2}[/tex] [tex]\leq[/tex] 1

Multiply all the sides by 2

-10 < x-4 [tex]\leq[/tex] 2

Add 4 to all the sides

-6 < x [tex]\leq[/tex] 6

Answer:

-6 < x < 6

Step-by-step explanation:

either way its still higher than -5 and lower than 1

Answer:

1 is c

2 is a

3 is a

Step-by-step explanation:

just solved them

Answer:

0

This is because for a number to be divisible by 9 all the digits should add up to a number divisible by 9. Since they already do you just put a 0.

Answer:

10

Step-by-step explanation:

Answer:

All of the above

Step-by-step explanation:

I'm not sure, but if you divide the number of people by each candidate, you'll get a value that the number of candidates will equal the number of people. I repeat I'm not sure of my answer.

Answer:

  11126

Step-by-step explanation:

The mean of a set of data is another name for its average. It is the sum of the data, divided by the number of numbers in the sum.

__

If you use a calculator to help you with the computation of the addition or division, you may as well use the calculator's "mean" function to do the job.

The mean of the given 6 values is their sum, divided by 6. The units of the mean are the same as those of the contributors.

  (1117 +1409 +675 +536 +1398 +1621)/6 = 6756/6 = 1126 . . . . degrees F

The mean of the data is 1126 °F.

Answer:

Step-by-step explanation:

Inequality:

The dot must start at -3 (-3b).

Which would be B.

Then, we solve this inequality:

Solve:

Answer:

1 - True

2 - False

3 - False

4 - True

Step-by-step explanation:

N/A

Answer:

His brother gets 8 apples

His friends gets 4 apples

He gets 12 apples

Step-by-step explanation:

brother: friend himself::total

2                1          3        2+1+3 = 6

He has a total of 24 apples

24/6 = 4

Multiply each term by 4

brother: friend himself::total

2*4           1*4        3*4        6*4

8                4          12           24

His brother gets 8 apples

His friends gets 4 apples

He gets 12 apples

Answer:

c

Step-by-step explanation:

Answer:

a. true

b. false

c. false

d. false

e. true

Step-by-step explanation:

a is true because the graph is measuring the weight of the box based on the number of cookies in it, and the box has weight even without cookies in it.

b is false because the slope of the line is 1/2, and each cookie weighs 1/4 oz.

c is false because there is an association between the number of cookies and the weight of the box.

d is false because that is the weight of one cookie, and doesn't take into account the weight of the box by itself.

e is true because the graph shows that at 13 cookies, the box weighs around 3.75 ounces.

Answer:

D

Step-by-step explanation:

because it's normal reasonal if it is wrong i will look for a better answer

Answer:

A. select all students who are currently in the chess club

Step-by-step explanation:

If the teacher randomly selects students, there is a greater chance that many don't play chess. But, if the teacher selects all the students who are currently in the chess club, most likely all of them play chess because they are in the chess club.

Answer:

the hieght is 9

Step-by-step explanation:

divide 162 by 6 and you should get 27 then divide 27 by 3

to check your answer multiply 9x6x3 and you are done!!!

Answer:

Write and solve a proportion to answer the question.

34 is 75% of what number?

34w= 12/16

w= what?

Can anyone please

Step-by-step explanation:

Answer:

45.33

Step-by-step explanation:

Answer:

A.) 15984.42cm^2/5088πcm^3

B.) 3466.56cm^2/1104πcm^2

Step-by-step explanation:

A.) fine the V of the cone and then cylinder then add them.

B.) The cone you have to find the LA (lateral area) to do that you would do is find S (slant) so you would do 12^2+16^2 which is 400 then u have to find the square root of it which is 20 which is that slant of the cone. After that you would do 12x20 which gives 240 that would be the LA of the cone.

Then you would find the LA of the cylinder which you have to do is 30x12 which is 360 then multiply it by 2 which gives 720.

Lastly you find the area of the base which in this case is a circle and that would be 144 add all of them then get the SA

Answer:

5 2/3 divided by 2 2/3 = 17/3 divided by 8/3 = 17/8 = 2 1/8 miles per hour

2 2/3 divided by 5 2/3 = 8/3 divided by 17/3 = 8/17 hours per mile

Step-by-step explanation:

Answer:

4 and 6

Step-by-step explanation:

10 and 8 leave a remainder so can't be equal number of booklet

Answer:

the answer is a, Charles Ives

Answer:

6

Step-by-step explanation:

-3 -1 +2 +8 = -4+10 = 6

Answer: 4

Step-by-step explanation:

first put 2 fingers up

then with the other hand put 2 more fingers up

then count and you get 4

or you could use a calculator

Answer:

1, 1, 17

Step-by-step explanation:

17 is a prime number. This means the only factors are 1, and 17. This means that since only 17, and 1 multiply to 17, to get a volume of 17 you can only use 1, and 17 (1, 1, and 17)

Answer:

720

Step-by-step explanation:

1 yard = 36 inches

20*36

720