If 9x+2y^2−3z^2=132 and 9y−2y^2+3z^2=867, then x+y =


Answer 1


x + y = (1000)/(9)

Step-by-step explanation:

Step 1: Identify the approach:

With this problem, the general solution is to try manipulate given data and transform data into a new form, in which, the desired value (x + y) is on the left side and all of other components which do not contain x or y are on the right side.

Step 2: Analyze:

9x + 2y^(2) - 3z^(2) = 132\n9y - 2y^(2) + 3z^(2) = 867

Realize that in both equations, the 2y^(2) and 3z^(2) are in form of different signs. Then adding up corresponding sides of both equation can help eliminate these undesired components.

Step 3: Perform manipulation:

9x + 2y^(2) - 3z^(2) + 9y - 2y^(2) - 3z^(2) = 132 + 867


(9x + 9y) + (2y^(2) - 2y^(2)) +(3z^(2) - 3z^(2)) = 132 + 867


9(x + y) + 0 + 0 = 1000


x + y = (1000)/(9)

Hope this helps!


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Three Rivers publishes a catalog each year, last year it had 198 pages back and front. Weprint 150 copies. How much does it cost the college if a ream, 500 pages, cost

$7.40 each?




Step-by-step explanation:

We need to find how many ream was used in the printing forts, to determine how much the College spent.

The catalog is 198 pages, back and front, which means, 1 leaf will take 2 pages. Therefore, 99 pages were used in printing 1 copy of the catalog.

No of pages that were used in printing 150 copies = 150*99 = 14,850 pages.

If 500 pages = 1 realm, therefore,

14,850 pages = 14,850/500 = 29.7.

Since, it's a full team that is sold, let's approximate the number of reams bought to be 30 reams.

If 1 ream costs $7.40, therefore,

30 reams = 30*7.40 = $222

Final answer:

To calculate the cost of printing the catalogs, you need to calculate the total number of pages printed, convert that into the number of reams needed, and then multiply by the cost per ream. The total cost comes out to $444.


This problem involves simple multiplication and division to calculate the cost. The catalog has 198 pages and they print 150 copies, so the total number of pages is 198*150=29,700 pages. Every ream has 500 pages so you need 29,700/500=59.4 reams. But, you can't have a part of a ream, so you should round up to 60 reams. Then you multiply the number of reams by the cost per ream: 60 reams*$7.40/ream=$444. Therefore, the cost to the college is $444.

Learn more about Cost Calculation here:



Use the information given to answer the question. Triangle PQR undergoes a dilation by scale factor of 1/2 about vertex P to form triangle P’Q’R’PART A Which statement is true?


We can think of this dilation as this: if the center of dilation is P and the factor of dilation is k = 1/2, we can draw the image triangle as:

This way, the segments P'R' and P'Q' have half the length of PR and PQ respectively.

The segment RQ passes through the origin of coordinates. As no other image segment intersects with RQ, we know that no image segment passes through the origin of coordinates.


No segments of triangle P'Q'R' pass trhough the origin.

Use the following to answer questionsEmployment statistics in the US are often based on two nationwide monthly surveys: the Current Population Survey (CPS) and the Current Employment Statistics (CES) survey. The CPS samples approximately 60,000 US households and collects the employment status, job type, and demographic information of each resident in the household. The CES survey samples 140,000 non-farm businesses and government agencies and collects the number of payrolls jobs, pay rates, and related information for each firm.

a. What is the population in the CPS survey?

b. What is the population in the CES survey?



A. The population in the CPS survey are all US households.

B. The population in the CES survey are all the non-farm businesses and government agencies.

Step-by-step explanation:

A sample is the number of people from a whole population who actually participated in a survey. The population is the entire group of people whom the survey is meant to study. The sample is an off shoot of the population.

In the given question, the Current Population Survey is a study on the entire US households. Since every household cannot be interviewed because of the large population, a sample of 60,000 households is used.  The whole households in the United States thus form the population under study.

For the Current Employment Statistics survey, the goal is to understand employment statistics in all the non-farm businesses and government agencies. This is the population. Since the entire population cannot be studied, a sample of 140,000 is used.

2.Make up a new pair of numbers that would make
the same shade of green. Explain how you know
they would make the same shade of green.


9514 1404 393


  29, 145

Step-by-step explanation:

Any pair of numbers with a ratio of 1 to 5 can be used. Some possible pairs are ...

  3 : 15

  4 : 20

  29 : 145


The color depends on the ratio of blue to yellow paint. As long as that ratio is maintained, the color will be maintained.

5/32 × 64y/100 please help :,)


Answer:  y/10

Step-by-step explanation:  step 1 = simplify y/100

                                              step 2 = (5/32 x 64) x y/100

                                              step 3 = simplify 5/32

                                              step 4 = (5/32 x 64) x y/100

                                              step 5 = The answer is y/10

Solve F(x) for the given domain.F(x)= x2 + 3x-2
F(-1) =
a. -4
b. -6
C. 2.​



A. -4

Step-by-step explanation:

F(-1) means we must plug the number "-1" in for each x.

F(x) = x^2 + 3x - 2

F(-1) = (-1)^2 + 3(-1) - 2

= 1 - 3 - 2

= -4