Download 19x2 - 13x + 31 - 12x 2

Perform the indicated operation:
1. 19x2 - 13x + 31 - 12x2 - 24x - (16x2 - 27x + 25)
=19x2 - 13x + 31 - 12x2 - 24x - 16x2 + 27x – 25
=19x2 - 12x2 - 16x2- 13x - 24x + 27x + 31– 25
=-9 x2- 10x + 6
2. 7xy2(5x3 – 4x2y2 + 3xy4)
=7xy2(5x3) - 7xy2(4x2 y2) + 7xy2(3xy4)
=35x4y2 - 28x3y4 + 21x2y6
3. (13x + 5)(9x - 13)
=13x·9x - 13x·13 + 5·9x - 5·13
= 117x2-169x+45x-65
=117x2 - 124x - 65
4. (25x - 12)2
=(25x)2 - 2·25x·12 + 122
=625x2 - 600x + 144
5. (13a + 15b)(13a - 15b)
=(13a) 2 - (15b) 2
=169a2 – 225b2
6. (25x4 - 35x3 + 45x2) / (5x2)
= (5x2·5x2 - 5x2·7x + 5x2·9)/(5x2)
=(5x2)( 5x2 – 7x + 9)/(5x2)
=5x2 – 7x + 9
7. (9.63 x 1035)(8.56 x 10-26) answer in scientific notation
=9.63 x8.56 x 1035x 10-26
=82.4328 x 109
=8.24328 x 1010
8.
2x / (x + 5)
-
150 / (x2 - 25) +
=2x(x-5) / [(x + 5) (x-5)]
-
3x / (x – 5)
150 / (x2 - 25) +
[3x(x+5)] / [(x – 5) (x+5)]
=(2x2-10x)/( x2 - 25) - 150/(x2 - 25) + (3x2+15x)/(x2 - 25)
=(2x2-10x- 150 + 3x2 + 15x)/ (x2 - 25)
=( 5x2 + 5x - 150)/(x2 - 25)
=5(x2 + x - 30)/(x2 - 25)
=[5(x+6)(x- 5)]/[(x-5)(x+5)]
=(5x+30)/(x+5)
9.
x / (x - y) -
y / (x + y)
= [x(x + y)] / [(x - y)(x + y)]
=(x2 + xy)/ (x2 - y2) -
-
[y(x - y)] / [(x + y) (x - y)]
(xy – y2)/( x2 - y2)
=(x2 + xy - xy + y2)/ (x2 - y2)
=(x2 + y2)/ (x2 - y2)
10.
5 / [sqrt(5) + sqrt(7)]
–
7 / [sqrt(5) – sqrt(7)]
=5[sqrt(5) – sqrt(7)]/[ sqrt(5) + sqrt(7)][ sqrt(5) – sqrt(7)] – 7[sqrt(5) + sqrt(7)]/ [sqrt(5) –
sqrt(7)][ sqrt(5) + sqrt(7)]
=[5sqrt(5) –5 sqrt(7)]/(5-7) - [7sqrt(5) + 7sqrt(7)]/(5-7)
=[5sqrt(5) –5 sqrt(7) - 7sqrt(5) - 7sqrt(7) ]/(-2)
=[-2sqrt(5) – 12sqrt(7)] /(-2)
=sqrt(5) + 6sqrt(7)
Solve the equations for x.
11.
(2x – 3)2 = 7
2x-3=sqrt(7) or 2x-3=-sqrt(7)
2x=3 + sqrt(7) or 2x=3 - sqrt(7)
x=[3 + sqrt(7)]/2 or x=[3 - sqrt(7)]/2
12.
125x2 = 49
x2=49/125
x=7/(5sqrt5) or x=-7/(5sqrt5)
x= (7sqrt5)/25 or x=(-7sqrt5)/25
13.
8x2 + 6x - 5 = 0
(2x-1)(4x+5)=0
2x-1=0 or 4x+5=0
x=1/2 or x=-5/4
14.
5x2 – 4x – 3 = 0
X={-(-4)+/-sqrt[(-4) 2-4·5·(-3)]}/(2·5)=[4+/-sqrt76]/10
X=(2 + sqrt19)/5 or x=(2 - sqrt19)/5
15. 24x2 + 32x - 96 = 0
3x2 + 4x – 12=0
X={-4 +/- sqrt[42 - 4·3·(-12)] }/(2·3)= [-4 +/- sqrt(160)]/6=[-4 +/- 4sqrt(10)]/6
X=(-2 + 2sqrt10)/3 or x=(-2 - 2sqrt10)/3
16. 4.56x2 + 7.89x – 7.65 = 0 answer in decimal form
X={-7.89 +/- sqrt[7.892 - 4·4.56·(-7.65)] }/(2·4.56)
= [-7.89 +/- sqrt(201.7881)]/9.12
=[-7.89 +/- 14.21]/9.12
X=0.69 or x=-2.42
17. x2 = 6 – 3x
x2 + 3x -6=0
x={-3 +/- sqrt[32 - 4·1·(-6)] }/(2·1)=[-3+/-sqrt33]/2
x=(-3 + sqrt33)/2 or x=(-3 - sqrt33)/2
18. x / (x + 7) = 3x / (x – 1)
- 24 / (x2 + 6x - 7)
x2 + 6x – 7=(x+7)(x-1)
the LCD for the denominators is (x+7)(x-1)
multiply both sides by (x+7)(x-1)
x(x - 1)=3x(x + 7) – 24
x2-x=3x2+21x-24
x2+11x-12=0
(x+12)(x-1)=0
x=-12 or x=1
when x=1, the fraction 3x/ (x-1) and 24/(x2 + 6x - 7) is undefined, so it is not a solution.
So the solution to the equation is x=-12
19. Jim made a 350 mile trip in his car at a certain speed.
made the trip in one hour less time.
If he had gone 10 mph faster, he could have
Find his speed.
Let x represent his speed.
The time he made a 350 mile trip is 350/x hour.
If he had gone 10 mph faster, the speed is (x+10) mph, then the time he made a 350 mile trip is
350/(x+10) hour, which is 1 hour less. So we can make an equation:
350/x - 350/(x+10)=1
Multiply both sides by x(x+10):
350(x + 10) - 350x=x(x + 10)
x2 + 10x - 3500=0
x={-10 +/- sqrt[102 - 4·1·(-3500)] }/(2·1)=[-10 + /- sqrt14100]/2= -5+/-5sqrt141
x=54.37
Jim’s speed is 54.37 mph
20. The Monahan’s garden is 20 feet by 30 feet. They wish to lay a uniform border of pine bark
around the garden.
How large a strip should they lay if they only have enough bark to cover 420
square feet? (…and don’t tell me to buy more pine bark… )
let x represent the width of the border
the overall dimensions of border and garden is: (2x+20)feet by (2x+30)feet
the area of the garden is 20 * 30 = 600 sq/ft
The total area of border & garden is (420 + 600) sq ft, which can also expressed as: (2x+20)(2x+30).
So here is the equation:
(2x+20) * (2x+30) = 600 + 420
4x2 + 100x + 600=1020
X2 + 25x -105=0
(x+26)(x-1)=0
X=1 or x=-26(thrown out)
So the strip should be 1 foot.