60 points if you answer them all! answer ! 10. write the inequality correctly: the difference of x and 12 is more than 15 11. write the inequality correctly: the product of -3 and a number is at most 21. 12. cole makes $11 dollars an hour working at chic-fil-a. he wants to make at least $400 this month. write and solve an inequality to determine how many hours he needs to work to obtain his goal. 13. lucy is an avid horseback-rider. this year, she purchased a new safety riding helmet for $150 and continues taking lessons at $50 per lesson. her parents say that she cannot spend more than $500 on her sport this year. write an inequality that represents lucy's horseback-riding expenses for this year. 14. your class hopes to collect 275 cans of food or more for the annual food drive. there were 145 donated the first week and 80 more the second week. choose the inequality that describes this situation. let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass your goal. 15. kara buys tickets to her favorite concert for her and her friends. she has at most $175 to spend on concert tickets. each ticket costs $45 plus a service fee of $5. write and solve an inequality to determine how many tickets she can buy.

10. (x-12) > 15

11.  -3n ≤12

12. 400 ≤ 11*h

36.36 hours

13.     500 ≥ 150 + n * 50

14.  275≤ 145 + 80 +c

15.   175≥ 45*n +5n  

She can only buy 3 tickets  ( no partial tickets)

Step-by-step explanation:

10. Write the inequality correctly: The difference of x and 12 is more than 15  

Difference is subtraction   more than  is >

(x-12) > 15

11. Write the inequality correctly: The product of -3 and a number is at most 21.

Product is multiplication and  at most means ≤

-3n ≤12

12.  Wages = hours worked * rate

   400 = hours * 11

He wants to make at least 400

400 ≤ 11*h

Divide each side by 11

400/11 ≤h

36.36 hours

13.  Total cost = helmet + number of lessons*rate

          She can spend no more than 500

  500 ≥ 150 + n * 50

14.  Total cans = cans first week + cans second week + cans third week

We want  275 cans or more

275≤ 145 + 80 +c

15.   Cost of concert = cost of ticket * number of tickets + fee * number of tickets

It cannot cost more than 175

       175≥ 45*n +5n   (     assuming a service fee per ticket)

Combine like terms

175≥ 45*n +5n

 175≥50n

Divide by 50

175/50 ≥50n/50

3.5 ≥ n

She can only buy 3 tickets  ( no partial tickets)

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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