5 basic problems... Full answers w/ steps gets 10 points?

Question

1. A triangle has sides of length 5a centimeters, 3b centimeters, and 7a + 4 centimeters. What is the perimeter of the triangle?

2. Solve for x: 5x – 2x = 11 – 12x

3. Simplify: – 3/4 (4/5) + 5/7 ÷ 5/3

4. Solve the following equation for x

x – 1/2(2x – 4) = 6

5. Bradley Palmer State Park has a triangular piece of land on the border. The altitude of the triangle is 450 feet. The base of the triangle is 230 feet. What is the area of this piece of land?

Answer 1

2. 5x-2x=11-12x

        3x=11-12x

  12x+3x=11

       15x=11

          x=0.73

Answer 2

Problem 1:

perimeter = total of lengths of sides (having them all in the same unit of length)

= 5a + 3b + 7a+4

= 12a+3b+4 centimeters

Problem 2:

5x - 2x = 11 - 12x

Get the x-terms on the left side and the number term(s) on the right side. So add 12x to both sides.

5x - 2x + 12x = 11

15x = 11

x = 11/15

Problem 3:

3/4 (4/5) + 5/7 / 5/3

Do the multiplication and division parts first, and then the addition.

= 3/5 + (5/7 * 3/5)

= 3/5 + 3/7

= 21/35 + 15/35

= 36/35 = 1_1/35

Problem 4:

x - 1/2(2x - 4) = 6

x - x + 2 = 6

2 = 6

no solution

Problem 5:

area of a triangle = 1/2 * base * height (A=1/2*bh)

= 1/2 * 230 * 450

= 51,750 ft^2

Answer 3

1) 5a+3b+(7a+4)=12a+3b+4 there is no further known answers.

2) first, simplify the question to 3x=11-12x

since 1=1, and 1+1 = 1+1, you can add or subtract the same value to both sides of the equation. using this, you separate the x from the whole numbers. so you end up with 15x=11.

then, since 1=1, and 1*2=1*2, you can multiply or divide the same value to each side. get the 15 from x. you end up with x=11/15.

3) -3/4 (4/5) + 5/7 / 5/3. you must solve using the order P,E, MD, AS, where you multiply and divide before you can add. you end up with -3/5 + 3/7.

get a common denominator. in this one, just multiply 5 and 7. you then multiply the 3/5 by 7, and 3/7 by 5. you get 21/35+15/35. just add you get 36/35 or 1 1/35, whichever the teacher prefers.

4) first, you must distribute the -1/2 to the values in paranthesis. you end up with x-x+4=6.

as you can see, the x will never make any sense. if you go as far as you can, you end up with x=x+2. so there is no REAL solution. keep in that real, its essential.

5) write what you know. in triangles, A=1/2(BH). fill in the variables to get A=1/2(450 * 230). then use basic math skills to get that A=1/2(103,500). so this means that A, or area, is equal to 51,300 FEET. keep the feet in there- its essential.