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Two angles are complementary if the sum of their angles equals 90 degrees
So, one angle is 40 degrees if it is 50 degrees more than its complement.
Hope this helps.
:-)

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If a car is travelling at 60km for 4 hrs
Speed = Distance/ Time
It is travelling at an average speed of 15km/hr
Hope this helps.
:-)

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Add all the ratios
3+4+5 = 12
180 degrees in a triangle.
3/12 x 180 = 45
4/12 x 180 = 60
5/12 x 180 = 75
Total = 180
So, smallest angle = 45 degrees.
Hope this helps.
:-)

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If you meant 2 -(3j/5)... J=15
If you meant (2-3j)/5... J=3/2

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Let m be marks current age
Let s be his sisters current age
m=5s #1
(m-3) + (s-3) = 27 #2
From 1
5s-3+s-3=27
6s=33
s=11/2
m=55/2

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This equation is untrue :)

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First off please don't use caps to gain attention it's unnecessary...
using formulas
Mx=(x1+x2)/2
My=(y1+y2)/2
-1=(5+x2)/2
2=(y1-9)/2
Point A is at (5,-5)
Point B is at (-7,-9)

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Defince unknowns
Let M = Man's current age
Let S = Son's current age
Dissect the question to get your equations
(M-2) = 7(S-2) #1
(M+3) = 4(S+3) #2
From #1 M = 7S-12
Sub above into #2
7S-9=4S+12
3S=21
S=7
Sub S into #1
M-2=7(7-2)
M=37
So the man's current age is 37 years old and his son's age is 7 years old

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s.s {-3,-1}

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Q:
Not really sure where to start on this problem. Any help you can give me would be greatly appreciated.
Determine whether the distribution is a discrete probability distribution?
x,P(x)
0,0.21
1,0.28
2,0.02
3,0.28
4,0.21
-------------------------------------------------------------
A:
, the distribution is a discrete probability distribution
because = 0.21 + 0.28 + 0.02 + 0.28 + 0.21 = .

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2logx-2=log (x-25)
2logx-log (x-25)=2


x^2=100x-2500
x^2-100x+2500=0
(x-50)^2=0
x=50

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Refer to the graph of y = tan x to find the exact values of x in the interval (−π/2, 3π/2) that satisfy the equation. (Enter your answers as a comma-separated list.)
tan x = 1/square root of 3
***
x=π/6, 7π/6 in Q1 and Q3 where tan>0

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find csc(theta), given that cos(theta)=(-(√2/2)) and cot(theta)=1
Given data shows angle theta is in quadrant III where cos and sin<0, and cot>0
cot(theta)=1
theta=225º
reference angle=45º
sin(theta)=sin225º=-√2/2
csc(theta)=1/sin(theta)=-2/√2=-√2

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why is it necessary to check the solutions of a logarithmic equation.
Because arguments of logarithms>0, that is, if the solution makes any of the arguments≤0, the solution is rejected. Example: log(x-5), x>5

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Determine the equation of the hyperbola whose asymptotes are x±2y=0 and which passes through (4,3)
***
Hyperbola has a vertical transverse axis since it passes thru (4,3)
Its standard form of equation: (y-k)^2/a^2-(x-h)^2/b^2=1, (h,k)=(x,y) coordinates of center
Asymptotes are two straight line equations that intersect at center, y=mx+b, m=slope, b=y-intercept
Equation of asymptote with positive slope:
x-2y=0
2y=x
y=x/2
m=1/2, b=0
..
Equation of asymptote with negative slope:
x+2y=0
2y=-x
y=-x/2
m=-1/2, b=0
This means center is at (0,0)
..
slopes of asymptotes with vertical transverse axis
=±a/b=±1/2
b=±2a
b^2=4a^2
..
solving for a^2 and b^2 using coordinates of given point(4,3)
(y-k)^2/a^2-(x-h)^2/b^2=1
y^2/a^2-x^2/4a^2=1
9/a^2-16/4a^2=1
9/a^2-4/a^2=1
5/a^2=1
a^2=5
b^2=4a^2=20
Equation:

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4 people have p number of provisions requiring 30 days to consume.
1 person could use p provisions over a period of 4*30 days to consume.

The analysis is to understand the pattern affecting the use of p number of provisions. Changing from 4 people to 1 person requires multiplying time by 4. Now to change from 4 people to 6 people should require multiplying by .

The short analyzed pattern should indicate 6 people need days to consume the provisions.

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QUESTION: A. What was the population in California in 2005?

You just substitute the values and compute A.


QUESTION: B. When will the population of California reach 40 million?

Solve for t before doing anything else.





Substitute the desired value for A and compute t.

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Your question is incomplete. Please repost.

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Factor:

Answer:
(2m + 3)(3m - 2)

Check:
2m * 3m = 6m^2
2m * -2 = -4m
3 * 3m = 9m
3 * -2 = -6
6m^2 - 4m + 9m - 6
Combine like terms:
-4m + 9m = 5m
6m^2 + 5m - 6

Answer:
(2m + 3)(3m - 2)










Lennox Obuong
Algebra Tutor
Nairobi, Kenya
Email: lennoxobuong@yahoo.com

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Substitution method:

1. Solve one equation for one of the variables.

2. Substitute that value for the variable in the second equation.

3. Solve the second equation for the remaining variable.

4. Substitute that value into the first equation to find the value of the first variable.

1. 6x - 5y = 3

6x = 5y + 3

x = (5/6)y + 1/2

2. 4x + 3y = 21 (sub (5/6)y + 1/2 for x)

4((5/6)y + 1/2) + 3y = 21

(20/6)y + 2 + 3y = 21

(10/3) y + (9/3)y = 19

19y = 57

y = 3

x = (5/6)y + 1/2

x = (5/6)* 3 + 1/2 = 5/2 + 1/2 = 6/2 = 3

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One might imagine i is the imaginary unit, that i*i=-1.

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Very plainly, 60% of 20 gallons. Finding the answer requires nothing more than just that. 60% is the same as 6/10 or 3/5.

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given:
the point A(,)
the point B(,)

Plot A(,) and B(,)in a rectangular coordinate system.
Draw the tangent line, , which cuts the x-axis at (,) .
By looking at the position of the points , , and at the path of the tangent
line, think that the point where the tangent touches the circle could be (,)
or close to.
Plan: The center of the circle is at the intersection point of the perpendicular line to tangent at the point of tangency, and the perpendicular bisector of the segment (reason: a tangent to a circle is perpendicular to its radius; the perpendicular bisector of a chord passes through the center).
Solution:
Let's suppose that (,) is the point of tangency.
Find the midpoint of :
= (, ) = (,)
Find the of the line that passes though and :

Find the of the bisector of (whose slope must be and passes through (,)):
; ....let (,)= (,)


so, the of the bisector of is

Find the equation of the perpendicular line to the tangent (whose slope is since the perpendicular lines have negative reciprocal slopes) and passes through (,)):
;...... let (,)= (,)



Find the intersection point of and



implies
So the point (,)... ..=> could be the of the circle.
If we compute the distances between (,) and (, ), (, ), (,), we see that they have the same length, , then we say the center of the circle is (,) and the radius has a length of .
Thus, the equation of the circle that passes through (, ) and (, ) is the equation of a circle with center (, ) and a radius of .

Let's solve the problem without risking extra work (we clearly see that our guess for the point of tangency was right).
After we draw the given information on the rectangular system, we would like to draw a parallel line to the tangent line that passes through the point B (, ).
For this we need the equation of the line to use its slope to draw it and to find the point of intersection with the perpendicular bisector of segment (since the center of the circle lies there; see above); (the slope is , since parallel line have the same slope).
; .......let (, ) = (, )



Let's find the intersection point of and


implies , say the center is at (, )
Let's find the length of the congruent ( lies on the bisector) segments and , maybe they are radii.
.
Since the point lies in the same time on the perpendicular bisector of and on the parallel line to the tangent, let's find the equation of the perpendicular line to the tangent that passes through (the slope is since the perpendicular lines have negative reciprocal slopes):
;.... let (, ) = (, )



Let's find the intersection point of and (maybe this would be the point of tangency):


implies ; say T(, )
Let's find the length of :
.
Since , , and have the same length, they are radii of the circle with center O(, ). So our guess was right!

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a rectangle has an area of 27 square inches.The length is one third as long as the width. Find the length and width of the recrtangle
-----------
3 by 9

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Determine the value of 0 to the nearest degree.
a) cot0= 3.2404
cot = 1/tan
------------
c) sec0= 1.4526
sec = 1/cos
---------------
Just use a calculator.

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A right triangle having a 32.5 degree angle is inscribed in a circle with radius 42.5 cm. How long are the legs of the triangle?
------------
Hint: The hypotenuse is the diameter = 85 cm

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-6i + i = 5i
------------
If i is used as a variable, then
-6i + i = 5i
-5i = 5i
-10i = 0
i = 0

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a=76
c=155
what is b?
-----------
No way to know.
Is b related to a & c somehow?

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company makes two types of water skis, a trick ski and a slalom ski.
The trick ski requires 6 labor hours for fabricating and 1 labor
hour for finishing.
The slalom ski requires 4 labor hours for fabricating and 1 labor
hour for finishing.
The maximum labor hours available per day for fabricating and
finishing are 108 and 24, respectively.
If X is the number of trick skis and Y is the number of slalom skis
produced per day, write a system of linear inequalities that
indicates appropriate restraints on X and Y.
Find the set of feasible solutions graphically for the number of each type of ski that can be produced.
:
Fabricating equation
6x + 4y <= 108
:
Finishing equation
1x + 1y <= 24
:
since you can make negatives skis
x => 0
y => 0
:
Find the set of feasible solutions graphically for the number of each
type of ski that can be produced.
We have to put the equations into the slope/intercept to graph
6x + 4y = 108
4y = -6x + 108
divide by 4
y = -1.5x + 27; Red
and
x + y = 24
y = -x + 24; Green
Graph these two equations

The feasibility region is at or below the area bounded by the points
x=0, y=24; x=6, y=18; x=18; y=0
:
you can prove this to yourself using the fabricating equation
6x + 4y <= 108
x=6 trick skies, y=18 salom skies
6(6) + 4(18) =
36 + 72 = 108 total hrs

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x³ + 7x² - x - 7

Factor x² out of the first two terms and -1 out of the last two terms:

x²(x + 7) - 1(x + 7)

Factor (x + 7) of of the two terms:

(x + 7)(x² - 1)

Factor the second parentheses as the difference of two squares:

(x + 7)(x - 1)(x + 1)

Edwin