Algebra 2 homework help?

Question

I wasn't in class today and my teacher sent me with 14 word problems to do and I'm completely confused. I think If I can figure out how to do a few, I'll be set, so here they are. If you could please walk me step-by-step on how to do it, and then the answer you got, I'd GREATLY appreciate it. (^2 denotes "squared")

1. A rectangle is 4 cm longer than it is wide, and its area is 117cm^2. Find the dimensions.

2. The area of a right triangle is 44m^2. Find the lengths of its legs is one of the legs is 3m longer than the other.

3. A rectangle is 15cm wide and 18cm long. If both dimensions are decreased by the same amount, the area of the new rectangle formed is 116cm^2 less than the area of the original. Find the dimensions of the new rectangle.

Answer 1

1. l * w = 117, l = w + 4

Substitute l into first equation:

(w + 4) * w = 117
w^2 + 4w - 117 = 0

Now use the quadratic equation.

Answer 2

Answer 1:
Let the width of the rectangle be x
Length = x + 4
Area = 117 sq. cm
x(x + 4) = 117
x^2 + 4x = 117
x^2 + 4x - 117 = 0
x^2 - 9x + 13x - 117 = 0
x(x - 9) + 13(x - 9) = 0
(x - 9)(x + 13) = 0
x = 9 or -13
x cannot be negative.
Therefore, x = 9 cm
Breadth = 9cm, Length = 13 cm

Answer 2:
Area = 44 m^2
Let the legs be x and x + 3
[x(x + 3)]/2 = 44
x(x + 3) = 88
x^2 + 3x - 88 = 0
x^2 - 8x + 11x - 88 = 0
x(x - 8) + 11(x - 8) = 0
(x - 8)(x + 11) = 0
x = 8m
x + 3 = 11m
The lengths of the legs are 8m and 11m.

Answer 3:
l = 18 cm
b = 15 cm
Area = lb
= 15*18
= 270 cm^2

New area = 270 - 116
= 154 cm^2

New length = 18 - x
New breadth = 15 - x

(18 - x)(15 - x) = 154
270 - 18x - 15x + x^2 = 154
x^2 - 33x + 270 = 154
x^2 - 33x = -116
x^2 - 33x + 116 = 0
x^2 - 29x - 4x + 116 = 0
x(x - 29) -4(x - 19) = 0
(x - 29)( x- 4) = 0
x = 4 or 29
x cannot be 29 because then, 18 - x will be negative.
So, x = 4
The sides of the new rectangle are:
18 - 4 = 14 cm
15 - 4 = 11cm

Answer 3

1. Use the formula Area = l x w (length times width).

A = lw
117 = (4+w)(w)
117 = w² + 4w
0 = w² + 4w - 117
a = 1 b = 4 c = -117

Use the quadratic formula to solve that. It's difficult to type it out, so here's the formula on Wikipedia:
http://en.wikipedia.org/wiki/Quadratic_Formula#Quadratic_formula

Replace "x" with "w".


2. A = 1/2(b)(h) <- that's the formula for a triangle's area
44 = 1/2 (x) (x+3) <- one leg is 3 longer than the other
44 = 1/2 (x² + 3x)
44 = 1/2x² + 3/2x
0 = 1/2x² + 3/2x - 44
a = 1/2 b = 3/2 c = 44

Once again, use the quadratic formula.


3. This one is a little harder. First, you'll have to use a variable for the area decreased- let's use "x". The problem lists TWO situations, so you should end up with two equations.

First equation: (15)(18) = area of original
(15)(18) = 270 cm2
Second equation:
(15-x)(18-x) = 270 - 116
(15-x)(18-x) = 154 <- use FOIL to multiply the parentheses
270 - 15x - 18x + x² = 154
x² - 33x + 270 = 154
x² - 33x + 116 = 0
a = 1 b = -33 c = 116

Again, use the quadratic formula.


I think I explained just about everything. Hope it helps.

Answer 4

After attempting to remedy project after project on yahooanswers, I truthfully think of maximum human beings dont study a lot if I provide them the solutions. Heres a very comparable project. basically fill interior the values out of your own project. (hint: you will could desire to apply the Quadratic formulation on the top!) Goodluck!!! question: The hypotenuse of a maximum appropriate triangle has a length of 13 cm. The sum of the lengths of the two legs is 17 cm. discover the lengths of the legs. enable a = length of one leg enable b = length of alternative leg we are advised that: a + b = 10.23 --> b = 10.23 - b [a million] The hypotenuse is 8.312. From Pythagorus: a² + b² = 8.312² [2] replace [a million] into [2]: a² + (8.312 - b)² = 169 This simplifies to: 2a² - 34a + one hundred twenty = 0 Divide by utilising 2: a² - 17a + 60 = 0 which factors: (a - 5)(a - 12) = 0 and has roots: a = 5, 12 replace into [a million] and get: b = 12, 5 The lengths of the legs are 5 and 12 cm.

Answer 5

1) x(x+4) = 117

x^2 + 4x = 117

x^2 + 4x + 4 = 121

(x+2)^2 = 121

x+2 = +-11 x = 9 9 by 13

2) 1/2 (x)(x+3) = 44

x^2 + 3x -88 = 0
(x+11)(x-8) = 0
x = 8 8 by 11

3) 15(18) = 270
270 - 116 = 154

(15-x)(18 - x) = 154
270 - 33x + x^2 = 154

x^2 - 33x - 116 = 0

Use quad formula

Answer 6

#1 x(x+4)=117
2x+4=117
-4
2x=113
/2
x=56.5


#2 ?????i don't get it--whats the height

#3 15x18=270
270-116=154
15-4=11
18-4=14
11x14=154

Answer 7

1.) Let: x= the short side
x+4 = long side
since area ='s length x width (short side x long side) we can say that x(x+4)= the area (which is 117)
no solve for x (reject negative answers as you will have to take a root) and then plug in x into x+4 for the long side... the same kind of process works for the rest of these too.