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Quadratic_Equations/714624: How would you find the roots and vertex of y=8x(squared)+16x?
1 solutions
Answer 438924 by Gogonati(809) About Me  on 2013-02-14 19:17:04 (Show Source):
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y=8x%5E2%2B16x To find the roots solve y=0
8x%28x%2B2%29=0 the roots are x=0 or x=-2
The vertex is the point (x,y) where x=-b%2F2a
x=-16%2F16
x=-1,and
y=8%28-1%29%5E2%2B16%28-1%29
y=-8.


Inequalities/714635: Express the set -4 x+18 < 2 x+12 using interval notation.
1 solutions
Answer 438921 by Gogonati(809) About Me  on 2013-02-14 18:59:55 (Show Source):
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-4x-2x<12-18
-6x<-6 Divide both sides by -6 and reverse the inequation.
x>1
solution: (1,infinity)

Probability-and-statistics/714645: 4to9=10tox
1 solutions
Answer 438919 by Gogonati(809) About Me  on 2013-02-14 18:53:37 (Show Source):
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4%2F9=10%2Fx Cross-multiply
4x=90 Divide by 4 both sides
x=45%2F2

Graphs/713382: If the graph of the equation ax-4y=12 is parallel to the graph of the equation 2x-y=3, find the value of a.

1 solutions
Answer 438406 by Gogonati(809) About Me  on 2013-02-11 19:43:47 (Show Source):
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The slope of the line 2x-y=3 or y=2x+3 is m=2.
since lines are parallel the slopes are equal:4y=ax-12 or y=%28a%2F4%29-3
Thus a%2F4=2 or a=8.

Linear-equations/713365: write an equation describing the line that is parallel to the y-axis and that is 6 units to the right of the y-axis
1 solutions
Answer 438404 by Gogonati(809) About Me  on 2013-02-11 19:33:12 (Show Source):
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The equation of y-axis is x=0
The equation of requested line will be:x=6.

Sequences-and-series/713371: how do i figure out the sequence of 7, 3, -1, -5
thank you amy
1 solutions
Answer 438400 by Gogonati(809) About Me  on 2013-02-11 19:24:25 (Show Source):
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We see the difference between two successive terms:
3-7=-4, -1-3=-4, -5-(-1)=-4. The difference of this sequence is -4
the sequence will be:7, 3, -1, -5, -9, -13, -17, ...

test/710982: -10<3x-4<5
1 solutions
Answer 437262 by Gogonati(809) About Me  on 2013-02-05 22:37:35 (Show Source):
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Adding 4 we get:
-10%2B4%3C3x%3C5%2B4 Simplify
-6%3C3x%3C9 Divide by 3
-2%3Cx%3C3 The solution is the interval (-2,3)or
the solution set [x from R such that:+-2%3Cx%3C3]

Trigonometry-basics/711009: Verify the Identity. (Use of Pythagorean Identities)
csc x - sin x = cos x cot x
1 solutions
Answer 437259 by Gogonati(809) About Me  on 2013-02-05 22:26:37 (Show Source):
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%281%2Fsinx%29-sinx=cosx%28cosx%2Fsinx%29 multiply both sides by sinx
1-%28sinx%29%5E2=%28cosx%29%5E2
%28sinx%29%5E2%2B%28cosx%29%5E2=1

Functions/710470: suppose that for some function g, g(x+5)=3x+2. find g(-2)
1 solutions
Answer 437014 by Gogonati(809) About Me  on 2013-02-04 22:45:48 (Show Source):
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g(x+5)=g(-2) if x+5=-2 or x=-7 Since g(-7)=3x+2 we get 3(-7)+2=-19
As a conclusion g(-2)=-19.

absolute-value/710487: What is the answer to |5x+9|+6=1-> abs%285x%2B9%29=-5 The last equation has no solution because the absolute value is always positive.
1 solutions
Answer 437010 by Gogonati(809) About Me  on 2013-02-04 22:32:31 (Show Source):
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By the abs. value definition we have to equations:
1. abs%285x%2B9%29=5x%2B9 if 5x%2B9%3E0
The solution is 5x%2B9%2B6=1 and the root is x=-14%2F5
2. abs%285x%2B9%29=-5x-9 if 5x%2B9%3C0
The solution is -5x-9%2B6=1 and the root is x=-4%2F5

Linear-equations/710483: Write the equation of the line containing the given point and parallel to the given line
(8, -4) 5x-9y=4

1 solutions
Answer 437006 by Gogonati(809) About Me  on 2013-02-04 22:09:32 (Show Source):
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write the equation in the slope-intercept form.
9y=5x-4 -> y=%285%2F9%29x-4%2F9
the slope of the line is 5%2F9 Parallel lines have the same slope.
The equation of the line through the point (8,-4)is:
y-%28-4%29=%285%2F9%29%28x-8%29 Simplify and get:
y%2B4=%285%2F9%29x-40%2F9Multiply both sides by 9:
9y%2B36=5x-40 Write the equation in standard form.
5x-9y-76=0

Polynomials-and-rational-expressions/709936: How do you solve x^3+10x^2+25x=0?
1 solutions
Answer 436820 by Gogonati(809) About Me  on 2013-02-03 21:46:02 (Show Source):
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Factor x
x%28x%5E2%2B10x%2B25%29=0 x=0 is one solution. Factor:
x%28x%2B5%29%5E2=0 x=-5 is the other solution.

Functions/709433: Given f(x) = 2x - 1 and g(x) = 2/x+1 for x>-1, find fg(5)
1 solutions
Answer 436588 by Gogonati(809) About Me  on 2013-02-02 12:08:17 (Show Source):

Geometry_Word_Problems/709460: Find the area of a square whose side length is one fourth the value of its area.
1 solutions
Answer 436587 by Gogonati(809) About Me  on 2013-02-02 12:00:44 (Show Source):
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Solution: Let the side of square be x then its area is x%5E2
x=%281%2F4%29x%5E2
%281%2F4%29x%5E2-x=0
x%28%281%2F4%29x-1%29=0 The sln. x=0 is not allowed. Thus
%281%2F4%29x=1
x=4
Answer: The side of square is 4.

logarithm/709448: 5x^(2/3)-4=16
1 solutions
Answer 436586 by Gogonati(809) About Me  on 2013-02-02 11:51:06 (Show Source):
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5x%5E%282%2F3%29=20
x%5E%282%2F3%29=4 Cubed both sides and get:
%28x%5E%282%2F3%29%29%5E3=4%5E3 Simplify
x%5E2=4.4%5E2 Take the square root for both sides
x=8 Check: 5.8%5E%282%2F3%29-4=16 -> 5.4-4=16 -> 20-4=16

Equations/709457: how would i solve?
4x=3(x-2)+30
1 solutions
Answer 436585 by Gogonati(809) About Me  on 2013-02-02 11:38:59 (Show Source):
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Solution:
4x=3x-6+30
4x-3x=24
x=24

Geometric_formulas/708885: Find the slope of the line containing points (-6, 4) and (3, 2).
1 solutions
Answer 436306 by Gogonati(809) About Me  on 2013-01-31 16:30:19 (Show Source):
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The equation is:

+y-2=%28%282-4%29%2F%283%2B6%29%29%28x-3%29
After simplifying we get:
2x%2B9y-24=0

Graphs/708889: what does y=x^2+2 look like
1 solutions
Answer 436303 by Gogonati(809) About Me  on 2013-01-31 16:21:16 (Show Source):

test/707550: The opposite angle of a parallelogram are (3x-2)and (50-x)find the measure of each angle of parallelogram
1 solutions
Answer 435734 by Gogonati(809) About Me  on 2013-01-28 23:09:09 (Show Source):
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Since the opposite sides of parallelogram are equal.
3x-2=50-x
3x%2Bx=50%2B2
4x=52
x=13
50-13=37
Each angle is equal to 37 degree.

Linear-equations/707541: find the slope of a line parallel to the graph of each equation
3x+4y=12
1 solutions
Answer 435731 by Gogonati(809) About Me  on 2013-01-28 22:54:25 (Show Source):
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Write the equation in the slope-intercept form: y=mx+b
4y=12-3x Divide both sides by 4: y=3-%283%2F4%29x
The parallel lines have the same slop: m=-3%2F4

Linear_Equations_And_Systems_Word_Problems/706874: A square has side length s, while an equilateral triangle has length s+1. Write and solve a system of linear equalities to determine the length of the side at which the perimeters of the triangle and the rectangle would be equal.
1 solutions
Answer 435416 by Gogonati(809) About Me  on 2013-01-27 17:04:11 (Show Source):
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Let's the perimeter of square or triangle is p. the system will be:
system+%28p=4s%2C+p=3%28s%2B1%29%29
s=p%2F4, substitute and get:
+p=3%28p%2F4%29%2B3 => 4p-3p=12 => p=12
The perimeter of square or equilateral triangle is 12cm and the side of square is 3 cm while the side of equilateral triangle is 4cm.

Quadratic-relations-and-conic-sections/706357: Can I get a step by step of this?
A conic section has the equation x2 + y2 + 12x + 8y = 48. Determine the following: type of conic, domain and range, axes of symmetry, and center.
1 solutions
Answer 435115 by Gogonati(809) About Me  on 2013-01-25 22:48:36 (Show Source):
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%28x%5E2%2B12x%2B6%5E2%29%2B%28y%5E2%2B8y%2B4%5E2%29=48%2B6%5E2%2B4%5E2
As you see I add to both sides of equation the same sum 6%5E2%2B4%5E2
%28x%2B6%29%5E2%2B%28y%2B4%29%5E2=10%5E2 Which is a circle.

Square-cubic-other-roots/706359: square root of -5 times square root of -5.
1 solutions
Answer 435113 by Gogonati(809) About Me  on 2013-01-25 22:20:50 (Show Source):
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sqrt%28-5%29 is not defined in the set of real numbers.
For complex numbers we can argue the following:Since i=sqrt%28-1%29 we write:
,
because i%5E2=-1

Polynomials-and-rational-expressions/660496: Please help me solve for C: 27(C − 57) = 25,650
1 solutions
Answer 411210 by Gogonati(809) About Me  on 2012-10-02 12:23:52 (Show Source):
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Using distributive property we get:27C-1539=25650 => 27C=25650+1539 => 27C=27189
Divide both sides by 27 and get the result: C=1007.

Linear_Algebra/660484: What is the standard form of y=7x+15
1 solutions
Answer 411209 by Gogonati(809) About Me  on 2012-10-02 12:18:21 (Show Source):
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The standard form of linear equation is: ax+by=c. In our case the standard equation will be:7x-y=-15.

Exponential-and-logarithmic-functions/660485: What are the two values of x?
3^(x-x^2)=1/81x
1 solutions
Answer 411208 by Gogonati(809) About Me  on 2012-10-02 12:15:10 (Show Source):
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3%5E%28x-x%5E2%29=3%5E%28-4x%29 because 1%2F81=3%5E%28-4%29
x-x%5E2=-4x Solving this quadratic equation we get:
x%5E2-5x=0
x%28x-5%29=0. The two values of x are: {0, 5}

Linear-equations/660490: Find slope for the given equation of line:
5x + 2y = 10
1 solutions
Answer 411207 by Gogonati(809) About Me  on 2012-10-02 12:06:17 (Show Source):
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We transform the equation in the slope intercept form:
5x%2B2y=10
2y=-5x%2B10
y=%28-5%2F2%29x%2B5. From the final equation we get the slope m=-2.5

logarithm/660455: Log(6x-1)+ log x= 1/2 log 4
1 solutions
Answer 411203 by Gogonati(809) About Me  on 2012-10-02 11:40:12 (Show Source):
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Using log properties we get:
log%28x%286x-1%29%29=log4%5E%281%2F2%29
x%286x-1%29=2
6x%5E2-x-2=0 Solving the final quadratic equation we get the solution set: {-1/2, 2/3}

Exponents/660476: Hi I have a question on fractions, it is "evaluate 1/4 to the fifth power."
1 solutions
Answer 411202 by Gogonati(809) About Me  on 2012-10-02 11:30:12 (Show Source):

Linear-equations/660472: Please tell me the standard equation for the line -2x + y = 7.
Is it 2x - y = -7? Thank you.
1 solutions
Answer 411200 by Gogonati(809) About Me  on 2012-10-02 11:26:41 (Show Source):
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The standard form of the line equation is: y=ax+b. In our case we have y=2x+7.

Travel_Word_Problems/660466: Suppose a car purchased for $22,225 is expected to depreciate according to the formula y = −1,270x + 22,225, where y is the value of the car after x years. When will the car be worthless?
1 solutions
Answer 411198 by Gogonati(809) About Me  on 2012-10-02 11:13:01 (Show Source):
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The car will be worthless where y=o or -1,270x+22,225=0 => x=17.5 year.