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Sec 2s Substitute te giden values into cach formuul and solve for tha unknoun variable. 1. A: bh i A. 45 , b: à¹à¸£ (Area of a parallelogram.) 2. V Lwh L, 8, h 3 (valume of rectangular looy) Solve each rma tha speified variable. 2. Aab for b

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Sixta KovacekLv2

6 Sep 2019

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Need detailed help/answers/advice.1. A picture framer has a piece of wood that measures one inch wide by 50 inches long. She would like to make a picture frame as shown below, and uses all 50 inches of wood she has. Notice that x and y in our sketch below are the outside dimensions of the frame. The picture looks like a rectangle with the measurements 1 inch around all sides and it says that the length of the rectangle is Y and the width is X. A. Write an equation that expresses the required relationship between variables x, y, and the total length of the wood. I got 2(x+y)=50 B. Solve your equation from part (A) for y in terms of x. Got y=25-x C. Write an expression (i.e. a function) that gives the interior area of the frame as a function of its exterior height x. x^2+25x-50?? Confused on everything from here on out. D. Find the values of x that make the interior area of the picture frame equal to zero. Explain why this is the case in the context of the picture frame problem. Draw the frames that correspond to these two extreme conditions. E. Use your function to find the inside dimensions that will make this area a maximum. State also the maximum internal area of the picture frame. The second part of it goes like this: Now the picture framer would like to rework this problem for a piece of wood of arbitrary length L. [In PART I, L was 50 inches. Now L becomes a new variable so that we can generalize what we did in PART I for a piece of wood of any arbitrary length, L] A. Write an equation that expresses the required relationship between variables x, y, and the total length of the wood L. In PART I, you had a linear equation of the form ax+by = 50 where a and b were numbers. Now you will have a slightly more complicated equation involving x, y and L, i.e. your equation will have three variables, x, y, and L in it. B. Solve your equation from part (A) for y in terms of x and L. C. Use your answer to part (B) to write an expression (i.e. a function) that gives the interior area of the frame as a function of its exterior height x, and the wood length L. [The variable y will not appear in this equation] D. Use your function to find the inside dimensions that will make this area a maximum. Now each of your inside dimensions will depend on L, i.e. they will be functions of L.

sangriasalmon464

1. Evaluate the expression 2x - 2 for the value of x = -3

2. Factor: xsquare + 4x - 32 (x-4)(x+8) (x-4)(x-8) (x-4)(x-8) (x-16)

3. Factor: xsquare - 25 (x-5) (x+5)2 (x+5)(x-5) (x-5)(x-5)

4. Evaluate -u2v3 when u=4 and v=-2 128 64 32 -128

5. Using an online calculator, determine whether the value of x=7 is a solution of the equation. x Yes No

6. Explain why x=7 IS or IS NOT a solution of the equation. 7 + 1/x+2=8

7. Solve the equation and check your solution: -2 - 4x = 30

8. Solve the equation and check your solution: 67x - 24 = 3x + 8(8x - 3) 67 -3 -67 All real numbers

9. Solve the equation and check your solution. 5x/2 - x/6 = 14 10 6 7 9

10. Solve the quadratic equation by factoring: xsquare - 6x + 5 = 0 -1, 5 -1,-5 1,-5 1,5

11. The imaginary number i represents:

12. Find real numbers a and b such that the equation is true: a+ bi = 14 + 2i a=16, b=4 a=18, b=6 a=14, b=2 a=15, b=14

13. Find all solutions to the following equation. /4x - 8 = /4x + 9 x = -17/4 x=9 No solution x=-17

14. In a given amount of time, James drove twice as far as Rachel. Altogether they drove 120 miles. Write an equation to help find the number of miles driven by each. Use R as the variable to represent miles driven by Rachel and J for Jamesâ miles.

15. Karen works for $10 an hour. A total of 25% of her salary is deducted for taxes and insurance. She is trying to save $450 for a new set of tires. Write an equation to help determine how many hours she must work to take home $450 if she saves all of her earnings. Be sure to save the equation you write, as you will use it to answer the next question in this quiz. 10h - .25=450 10h + .25(10h)=450 h -.25 (10h)=450 10h - .25(10h)=450

16. Using the equation you wrote in the previous problem, find the actual amount of hours Karen must work to take home $450 if she saves all of her earnings. Show your work. 17. The length of a rectangular map is 15 inches and the perimeter is 50 inches. Find the width. Hint: Perimeter = width + length + width + length

18. Twice a number is added to the number and the answer is 80. Write an equation to solve this problem. 2n + n=80 2n = 80 2n + 80=n 80 + n=2n

19. If 4 is subtracted from twice a number, the result is 10 less than the number. Write an equation to solve this problem. Use n as the variable to represent the number.

20. Multiply the following binomials: (x + 5)(x - 5)

I would like to prove the last part (d).

Thank you