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Linear-equations/486515: Write the slope-intercept equation for the line that passes through (-7, 6) and is perpendicular to -7x + 9y = -2
1 solutions

Answer 332562 by Gogonati(809) on 2011-08-26 16:39:10 (Show Source):

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We write the equation -7x+9y=-2 in the slope intercept form y=%287%2F9%29%2Ax-2%2F9

As we know perpendicular lines have reciprocal negatives slopes.
Therefore we must find the equation of a line with slope -9/7 through the point
(-7, 6). This equation is given by the formula y-y%5B0%5D=m%28x-x%5B0%5D%29

,
substituting we get: y-6=%28-9%2F7%29%28x%2B7%29

. Simplifying this equation we get:
y=%28-9%2F7%29x-3

, what is the required equation.

Linear-systems/483274: can someone please help me solve the following equations for x
1) 6/x+3=9x/x^2-9
2) sqrt2x+3=5
3) x^3-2x^2-x=2 given x=1 is one solution.
Thank you

1 solutions

Answer 330770 by Gogonati(809) on 2011-08-19 10:12:39 (Show Source):

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1) We write the equation in the simple way to find the LCD:
6%2F%28x%2B3%29=9x%2F%28x%2B3%29%28x-3%29

.Assuming x different from 3 and -3, multiply both
sides by (x+3)(x-3) and get: 6%28x-3%29=9x

<=>

<=>

.
2)

Squaring both sides we get:2x+3=25<=>2x=22<=>x=11.
3)Since x=1 is a solution the polynomial x%5E3-2x%5E2-x-2

is divisible by x-1
%28x%5E3-2x%5E2-x-2%29%2F%28x-1%29=x%5E2-x-2

<=>

x%5E3-2x%5E2-x-2=%28x-1%29%28x%5E2-x-2%29

To find the other roots we solve the quadratic equation:
x%5E2-x-2=0

<=>

. The solution set for the original equation
is:{-1, 1, 2}.

Equations/483305: 0=16x2-(-16x-(-4)

1 solutions

Answer 330768 by Gogonati(809) on 2011-08-19 09:48:27 (Show Source):

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Rewrite the equation without parentheses: 16x%5E2%2B16x%2B4=0

Divide both sides by 4: 4x%5E2%2B4x%2B1=0

. Now we solve the quadratic equation
by factoring: %282x%2B1%29%5E2=0

<=>

<=>

.
The solution is x=-1/2.

Expressions-with-variables/481620: Solve for x:
2^2x - 3 * 2^x - 40 = 0
1 solutions

Answer 329779 by Gogonati(809) on 2011-08-14 20:26:56 (Show Source):

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2%5E%282x%29-3%2A2%5Ex-40=0

, substituting 2%5Ex=y

we get the quadratic equation:
y%5E2-3y-40=0

. We solve this equation by factoring: %28y-8%29%28y%2B5%29=0

The roots are: {-5, 8}. Now we find the roots of original equation:
2%5Ex=8

<=>

and

<=>

, since the log of
negative numbers doesn't exist our equation has only one solution x=3.

Angles/481622: the area of the top of a triangular corner desk must be at least 7 sq. ft. if the base of the triangular desk topneeds to be four feet, what should the height be?
1 solutions

Answer 329778 by Gogonati(809) on 2011-08-14 20:13:01 (Show Source):

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Lets the height be x ft, then 7=4%2Ax%2F2

<=>

<=>

ft.

Geometry_Word_Problems/479591: the exterior angle of a triangle are 5x,3x and 4x.
Find the size of the smallest interior angle
1 solutions

Answer 328610 by Gogonati(809) on 2011-08-09 08:57:29 (Show Source):

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As we know the sum of exterior angels of a polygon is 360 degree.
Write the equation 5x+4x+3x=360, solving this equation we get x=30. The supplement of the biggest exterior angle is the smallest interior angle of the triangle. In our case the biggest exterior angle is 5*30=150 degree and the smallest interior angle will be: 180-150=30 degree.

Trigonometry-basics/479638: I need help with this identity. Thank you
1+sec(theta)/sec(theta)=sin^2(theta)/1-cos(theta)
I keep hitting a roadblock as I end up with 1+sec(theta)=1+cos(theta)(sec(theta)
1 solutions

Answer 328606 by Gogonati(809) on 2011-08-09 08:38:52 (Show Source):

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=

<=>

%281%2Bcos%28theta%29%29%281-cos%28theta%29%29=%28sin%28theta%29%29%5E2

<=>

1-%28cos%28theta%29%29%5E2=%28sin%28theta%29%29%5E2

<=>

1=%28sin%28theta%29%29%5E2%2B%28cos%28theta%29%29%5E2

The final equality is an well known identity.

Travel_Word_Problems/479634: A number less it reciprocal is 8/3. What is the number?
1 solutions

Answer 328603 by Gogonati(809) on 2011-08-09 08:26:06 (Show Source):

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Let the number be x. Its reciprocal is 1/x. Write the equation as we read.
x-1%2Fx=8%2F3

, solving this equation we get x=3.

logarithm/475755: x^log[x,sqrt(x+3)]
1 solutions

Answer 326254 by Gogonati(809) on 2011-07-29 11:59:43 (Show Source):

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x%5Elog%28x%2C+sqrt%28x%2B3%29%29=sqrt%28x%2B3%29

, by the definition of log.

Quadratic_Equations/475756: What is the discriminant and how do you find it if you are given a quadratic equation? For instance, if you have -x² + 12 + 20 = 0, what would the discriminant be? How many solutions would this equation have?

1 solutions

Answer 326250 by Gogonati(809) on 2011-07-29 11:41:58 (Show Source):

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The standard form of the quadratic equation is ax%5E2%2Bbx%2Bc=0

, where a, b, c
are real numbers and a is different from zero. The discriminant of the quadratic
equation is the expression b%5E2-4ac

the quadratic
equation has two real roots. If b%5E2-4ac=0

the quadratic equation has one
real root, and if b%5E2-4ac%3C0

the quadratic equation has not real solution.
Example:For the equation -x%5E2%2B12x%2B20=0

the discriminant is:
12^2-4(-1)*20=144+80=224>0, this equation has two real roots.

real-numbers/475759: May some one please help with this problem....12-(-3+4)-[4+(-2)]+2
1 solutions

Answer 326242 by Gogonati(809) on 2011-07-29 11:29:42 (Show Source):

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12-(-3+4)-[4+(-2)]+2=12-(+1)-(+2)+2=12-1-2+2=11

Equations/475757: I need exact and approximate solutions to three decimal places.
(x-1)^2=25
x=__
1 solutions

Answer 326238 by Gogonati(809) on 2011-07-29 11:26:30 (Show Source):

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%28x-1%29%5E2=25

, is equivalent to x-1=5

and

, solving these
two equations we get: x=6 and x=-4.
Answer:The solution set is {-4, 6}.

Polynomials-and-rational-expressions/475752: use the dofference of squares rule to factor the following expression 36x^8-9y^4
show all work please and thank you
1 solutions

Answer 326236 by Gogonati(809) on 2011-07-29 11:21:16 (Show Source):

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Radicals/470631: A cylinderical can is designed to hold a volume of 1000 cm3.
If the radius is increased by 25%, what is the corresponding decrease in height so the volume is still 1000 cm3?
Could you please show all the steps?
1 solutions

Answer 322844 by Gogonati(809) on 2011-07-15 13:41:54 (Show Source):

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The volume of the cylindrical cane is given by the formula: V=pi%2Ar%5E2%2Ah

.
Since the volume does not change we can write:
pi%2Ar%5E2%2Ah%5B1%5D=pi%2A%28.25%29%5E2%2Ar%5E2%2Ah%5B2%5D

<=>

%.
Answer:If the radius is increased by 25% the height is decreased by 6.25%.

Rectangles/470666: the perimeter of a rectangle is 40ft. The ratio of the width to length is 2:3. How do you find the length and the width?
1 solutions

Answer 322838 by Gogonati(809) on 2011-07-15 13:20:43 (Show Source):

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Let the width be x ft, then the length will be 20-x ft. Since the ratio
W%2FL=2%2F3

, we write the equation: x%2F%2820-x%29=2%2F3

. Solving this equation
we get: 3x=40-2x

<=>

<=>

.
Answer:The width of the rectangle is 8 ft, and the length 20-8=12 ft.

Exponential-and-logarithmic-functions/470281: 1. Find the domain of the composite function f◦g . Please show all of your work.
f(x) = x + 6; g(x) = 7/x+7
Will someone help me with this problem? thank you.
1 solutions

Answer 322587 by Gogonati(809) on 2011-07-14 10:27:11 (Show Source):

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First we get the composite function: f%28g%28x%29%29=7%2F%28x%2B7%29%2B6

<=>

f%28g%28x%29%29=%287%2B6%28x%2B7%29%29%2F%28x%2B7%29

<=>

f%28g%28x%29%29=%286x%2B49%29%2F%28x%2B7%29

.
This function is defined for x+7≠0 or x≠-7, and its domain will be:
( -infinity

, -7)U (-7, infinity

Travel_Word_Problems/470271: A boy traveling by a canoe can go downstream 6 miles per hour and upstream 2 miles per hour. How fast can he go in still water, and what is the rate of the current?
1 solutions

Answer 322584 by Gogonati(809) on 2011-07-14 10:15:18 (Show Source):

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Let the rate of the current be x miles per hour.The speed of the canoe downstream will be: 6-x, and upstream 2+x.Since the rate of the current does not change we write: 6-x=2+x, solving this equation we get x=2 miles per hour, is the rate of change of the current.
Answer:On still water the canoe travel 6-2=4 or 2+2=4 miles per hour, and the rate of the current is 2 miles/h.

Bodies-in-space/470267: If the total surface area of a right circular cylinder is 104π square meters, and a radius of the base is 4 meters long, find the height of the cylinder.
1 solutions

Answer 322580 by Gogonati(809) on 2011-07-14 09:54:07 (Show Source):

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The total surface area of the cylinder is given by the formula:
A=2%28pi%2Ar%5E2%2Bpi%2Ar%2Ah%29

, where h is the height and r the radius.
Substituting our values for A, r and h we have:
104%2Api=2%28pi%2A4%5E2%2Bpi%2A4%2Ah%29

, solving this equation for h we get:
h=%2852%2Api-16%2Api%29%2F%284%2Api%29

<=>

<=>

Rectangles/470268: the perimeter of a rectangle is 18 feet and the area of the rectanggle is 20 feet what is the width of the rectangle?
1 solutions

Answer 322578 by Gogonati(809) on 2011-07-14 09:41:24 (Show Source):

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Half of the perimeter is 9 feet and its equal L+W=9. Let the W=x, then L=9-x, and the area is equal A=LxW, substituting we get:
20=x%289-x%29

write this equation in standard form x%5E2-9x%2B20=0

, and solve
it by factoring %28x-5%29%28x-4%29=0

. Set to zero each factor to find the roots:
x-5=0 <=> x=5, and x-4=0 <=> x=4.
Answer:The width of the rectangle is 4 feet and its length 5 feet.

Trigonometry-basics/468308: How do I stop my butt from pooping?
1 solutions

Answer 321329 by Gogonati(809) on 2011-07-08 12:06:12 (Show Source):

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It's so easy, Don't eat.

Geometry_Word_Problems/468269: the total number of angles in the two regular polygons is 13, while the total number of the diagonals is 25. how many angles are there in each of the polygons?
1 solutions

Answer 321327 by Gogonati(809) on 2011-07-08 12:00:50 (Show Source):

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This problem is undefined because on the regular polygons the number of angles is always greater than the number of diagonals.

Length-and-distance/468314: find the area of a sector with a central angle of 270 and the radius of 11.5m round to the nearest
1 solutions

Answer 321323 by Gogonati(809) on 2011-07-08 11:46:50 (Show Source):

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To find the area of a sector we use the formula: A=%28pi%2Ar%5E2%2Atheta%29%2F360

, where

degree is the central angle. Substituting we get:
A=%28pi%2A%2811.5%29%5E2%2A270%29%2F360

, the area is about A=312 square meters.

Exponential-and-logarithmic-functions/468306: Suppose you invest $130 at 4% compounded continuously.
a. Write an exponential function to model the amount in your investment account.
b. Explain what each value in the function model represents.
c. In how many years will the total reach $600? Show your work.
1 solutions

Answer 321321 by Gogonati(809) on 2011-07-08 11:33:30 (Show Source):

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The compounding continuously formula is: A%28t%29=P%2Ae%5E%28rt%29

, where P is the
initial investment, r is the interest rate, and t the amount of time in years the
investment is held. To find in how many years the initial investment of $130 will
reach $600, we substitute in our formula A(t)=600, and get:
600=130%2Ae%5E%28.04t%29

, solving this equation we get: 60=13%2Ae%5E%28.04t%29

<=>

, taking the natural logarithms of both sides, we have
ln%2860%2F13%29=.04t

, and final t=%28ln%2860%2F13%29%29%2F.04

or t=38 years.

Quadratic_Equations/468307: solve by the substitution method.
8x+7y=9
-3x+y=22
1 solutions

Answer 321319 by Gogonati(809) on 2011-07-08 11:12:38 (Show Source):

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From the second equation isolate y: y=3x+22. Substitute this value for y in the first equation:8x+7(3x+22)=9, solving this linear equation we get:29x=-145, and
final x=-145/29. Plugging x=-145/29 in the equation y=3x+22 we get: y=3(-145/29)+22,
and final y=7.
Answer: the solution of our system is the ordered pair (-145/29, 7).

Evaluation_Word_Problems/468132: 22.
Solve the following inequalities for x. Be sure to include a written check in your answer:

x
- + 4 > 0
3

23. -2x < 6

Solve the problems below. Be sure to include a check of your answer. (Remember, for or solutions you will need to check two values. )
24. | x-1 | < 4

25. | 2x + 5 | > 7

26. | 3 - x | = 20
1 solutions

Answer 321223 by Gogonati(809) on 2011-07-07 19:03:31 (Show Source):

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22) x/3+4>0<=>x/3>-4 <=> x>-12.
23)-2x<6 <=> x>-3.
24) abs%28x-1%29%3C4

is equivalent to two inequalities: -4 -3 25) abs%282x%2B5%29%3E7

is equivalent to two inequalities:1)2x+5<-7 <=> x<-6, and
2)2x+5>7 <=> x>1.
26) abs%283-x%29=20

is equivalent to two equations: 3-x=20 <=> x=-17, and
3-x=-20 <=> x=23.

Graphs/468148: the equation of the line passing through (-1,2) and perpendicular to y=3x=4
1 solutions

Answer 321212 by Gogonati(809) on 2011-07-07 18:44:41 (Show Source):

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As we know two lines are perpendicular if and only if their slopes are negative
reciprocals of one another m%5B1%5D=-1%2Fm%5B2%5D

Since the equation of one line is y=3x-4, its slope is m%5B1%5D=3

The slope of the perpendicular line will be 3%2Am%5B2%5D=-1

<=>

Now we write the equation of the line that passes through (-1, 2), and has the
slope m%5B2%5D=-1%2F3

: y-2=-1/3(x+1), converting it in the standard form we get:
3y-6=-x-1 <=> x+3y=5 or in slope-intercept form y=-%281%2F3%29x%2B5%2F3

Problems-with-consecutive-odd-even-integers/468147: 3 times an odd integer is 12 more than the next consecutive odd integer
1 solutions

Answer 321208 by Gogonati(809) on 2011-07-07 18:27:08 (Show Source):

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Let the odd integer be n the next consecutive will be n+2. Write the equation as we read: 3n=(n+2)+12, solving this equation we get n=7, and the next consecutive
odd integer will be 9.

test/468124: Short Answer: Simplify the following expression; express in terms of i.
√-36

1 solutions

Answer 321207 by Gogonati(809) on 2011-07-07 18:21:33 (Show Source):

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sqrt%28-36%29=sqrt%286%29%5E2%2Asqrt%28-1%29=6i

. Remember that sqrt%28-1%29=i

Inequalities/467568: solve this?Let −4 ≤ x ≤ 5 and a ≤ 2x + 1 ≤ b.(a) Find the largest possible value of a.
a =
(b) Find the smallest possible value of b.
b =
1 solutions

Answer 320850 by Gogonati(809) on 2011-07-06 11:33:39 (Show Source):

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Multiply by 2 both inequalities and get: -8≤2x ≤10, adding 1 on both inequalities we get:-7≤2x+1≤11 Comparing our final inequalities with the inequalities a≤2x+1≤b, we conclude that the largest possible value of a=-7, and smallest possible value of b=11.

Polynomials-and-rational-expressions/467576: Hello, Could you please help me solve this? It looks so complicated. Thanks!!
(30b^3+13b^2+32b+41)divided by (6b+5). Huge final exam due soon. Appreciate your help!
1 solutions

Answer 320843 by Gogonati(809) on 2011-07-06 11:18:06 (Show Source):

You can put this solution on YOUR website!
%2830b%5E3%2B13b%5E2%2B32b%2B41%29%2F%286b%2B5%29=%285b%5E2-2b%2B7%29%2B6%2F%286b%2B5%29

Linear-equations/467587: Please help me find the slope intercept form of the line that passes through the given points: (3, -3) (-2, 5)

1 solutions

Answer 320841 by Gogonati(809) on 2011-07-06 11:09:32 (Show Source):

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The slope of the line is m=%285%2B3%29%2F%28-2-3%29=-%288%2F5%29

, and its equation will be:
y-5=-%288%2F5%29%28x%2B2%29

, converting it in the standard form we get:
5y-25=-8x-16

<=>

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