You can put this solution on YOUR website!
I need help to solve these problem I am having problems figuring it out.
Identify the axis summetry, greate a suitable table of value, then sketck the graph(include the axis of summetry).
The first one is y=x^2-4x
Y=(X-2)^2-4
HENCE X=2 IS THE LINE OF SYMMETRY
X...........-2......0...........2.........4.........6....ETC
Y=X^2-4X....12......0..........-4.........0.........12...ETC


and the other one is y= -x^2+3x-3 = 1.5^2-3-[X^2-2*X*1.5+1.5^2]
Y=-0.75-(X-1.5)^2
X=1.5 IS LINE OF SYMMETRY
X...............-3.........-1.........0.........1.........3...ETC.
Y=-X^2+3X-3.....-21........-7........-3........-1........-3...ETC

You can put this solution on YOUR website!
I need help to solve this problem I am having problems figuring it out
Find the x - intercepts y=x^2-2x+4
thanks a million
THAT IS WE HAVE TO FIND X WHEN Y=0
X^2-2X+4=0
DISCRIMINANT = (-2)^2-4*1*4=4-16=-12<0
HENCE X IS IMAGINARY.
HENCE THERE ARE NO REAL X INTERCEPTS

You can put this solution on YOUR website!
1)Given the binary operation * defined over the set of real numbers R by a*b=a+b+ab. What are the invertible elements of R with respect to *.
LET I BE THE IDENTITY ELEMENT WRT * OPERATION.SO
A*I=A=A+I+AI
I(A+1)=0
I=0
HENCE IF X IS INVERSE OF A THEN
A*X=I=0=A+X+AX
X(A+1)= -A
X=-A/(A+1)
HENCE A SHOULD NOT BE -1
SO ALL ELEMENTS IN R EXCEPT A=-1 ARE INVERTIBLE

You can put this solution on YOUR website!
How do i evaluate the following:
log3 81
WRITE THE NUMBER AS A POWER OF BASE.THAT POWER IS THE LOG OF THE NUMBER TO THE BASE.
HERE NUMBER = N =81
BASE = B =3
WE KNOW THAT
3*3*3*3=3^4=81........P=4
HENCE
LOG(81) TO BASE 3 = 4
[LOGARITHM] = P=4
log4 256
N=256.......B=4............4^4=256.....P=5
LOGARITHM =4

log2 (1/32)
N=1/32.B=2...........[2*2*2*2*2]^(-1) =2^(-5)=1/32........P=-5
LOGARITHM =-5



log5 1
N=1........B=5...........5^0=1.........P=0
LOGARITHM =0

log3 (-1)
N=-1....B=3.........WE HAVE NO POWER P WHICH MAKES 3^P=-1
SO IT DOES NOT EXIST...
INFACT LOG OF 0 OR NEGATIVE NUMBER DO NOT EXIST
WE CAN HAVE LOGS FOR POSITIVE NUMBERS ONLY.
Please help
thanks
Lucy

You can put this solution on YOUR website!
Find an exponential function of the form f(x)=ba^x+c with y-intercept 2, horizontal asymptote y=-2, that passes through the point P(1,4).
Y=B(A^X)+C
Y INTERCEPT =2...THAT IS AT X=0...Y=2
2=B*(A^0)+C = B+C..................1
PASSES THROUGH (1,4).........Y=4 AT X=1
4=BA+C...................2
HORIZONTAL ASYMPTOTE IS Y=-2......THAT IS AS X TENDS TO + OR - INFINITY,Y TENDS TO -2...HERE WE TAKE X TENDING TO -INFINITY AS OTHERWISE , A^X WILL BE INFINITE.HENCE
-2=B*0+C............3
C=-2
FROM EQN.1,WE GET
B-2=2
B=4
NOW FROM EQN.2
4=4A-2
A=6/4=1.5
HENCE EQN. IS
Y=4*(1.5)^X -2

You can put this solution on YOUR website!
Write an equation for the linear function f satisfying the given conditions.
f(3) = 4 and f(0) = 9
I know that these would be looked at as (3,4) and (0,9), but I don't know what type of "equation" they're looking for. Thanks so much!!
CORRECT...CONTINUE...USE EQN. OF A STRAIGHT LINE(LINEAR) JOINING 2 POINTS (X1,Y1)
AND (X2,Y2) IS
Y-Y1=[(Y2-Y1)/(X2-X1)][X-X1]
Y-4=[(9-4)/(0-3)][X-3]
Y-4=-5(X-3)/3
3Y-12=-5X+15
5X+3Y=27...........OR................
Y=(27-5X)/3
IS THE FUNCTION

You can put this solution on YOUR website!
Solve the equation 4^2x+1=2^3x+6.
(4)^(2X+1)= (2^2)^(2X+1)=(2)^{2(2X+1)}=(2)^(4X+2)
(2)^(4X+2) = (2)^(3X+6)
HENCE
4X+2=3X+6
4X-3X=6-2=4
X=4

You can put this solution on YOUR website!
YOU MAY TRY THESE SITES.
THEY WILL NOT TEACH YOU.
BUT YOU CAN DO SELF STUDY
http://www.sosmath.com/algebra/algebra.html
http://academic.sun.ac.za/mathed/MALATI/

You can put this solution on YOUR website!
A list of numbers consists of p positive and n negative numbers. If a number is picked at random from this list, the probability that the number is positive is 3/5. What is the value of n/p?
PROBABILITY OF PICKING A POSITIVE NUMBER = P/(N+P)=3/5
HENCE
P/{(N+P)-P}= P/N =3/(5-3)=3/2
N/P = 2/3

You can put this solution on YOUR website!
I am not good at these and I am having some problems
Find the x- intercepts
y=x^2-5x-10
X INTERCEPT MEANS WHERE THE LINE MEETS X AXIS...AT THAT POINT Y COORDINATE=0
HENC
X^2-5X-10=0



HENCE X INTERCEPTS ARE

AND

and y=x^2-4x+4 =0
X^2-2*2X+(2)^2=(X-2)^2=0
HENCE X INTERCEPT IS X=2

Thanks you

You can put this solution on YOUR website!
In triangle ABC, C is the right angle, B = 30 degrees, and side b = 3. Find the exact value of the missing sides. Thank you for your help.
WE HAVE SIN(B)=SIN(30)=0.5=AC/AB=b/c=3/c
AB = c =3/0.5=6
TAN(B)=TAN(30)=SQRT(3)=1.7321=AC/BC=b/a=3/a
BC = a = 3/1.7321=1.7321

You can put this solution on YOUR website!
Eight times the first of three consecutive odd integers is ten more than twice the second.
ANY INTEGER IS N
EVEN NUMBER IS 2N
ODD INTEGER IS 2N+1
NEXT ODD INTEGER IS 2N+1+2=2N+3
THE NEXT ODD INTEGER IS 2N+3+2=2N+5
8 TIMES THE I = 8(2N+1)=16N+8
TWICE THE SECOND = 2(2N+3)=4N+6
TEN MORE =4N+6+10=4N+16.............HENCE
16N+8=4N+16
16N-4N=16-8
12N=8
N=8/12=......THERE IS NO SOLUTION.......PLEASE CHECK THE DATA IN THE PROBLEM
FOR ANY MISTAKES IN TYPING.

You can put this solution on YOUR website!
Solve each system by substitution method. Indicate whether each system is independent, inconsistent or dependent.
3y=y+5...............IS THIS 3X=Y+5?CHECKUP..ASSUMING SO.PUTTING THIS IN THE EQN.
3x-9y= -10
Y+5-9Y=-10
-8Y=-10-5=-15
Y=15/8
3X=15/8 + 5 = (15+40)/8 =55/8
X=55/24
SYSTEM IS INDEPENDENT

You can put this solution on YOUR website!
Here'e the question that I can't fiqure out. I might be using the wrong equation or system of equations?
A Semielliptical window has a height of 28 in and a length of 64 inches. Find the height of the window 25 inches from one end.
Thanks
EQN.OF ELLIPSE WITH CENTER AS O(0,0), MAJOR AXIS=POQ =2A AND MINOR AXIS=ROS=2B IS
[X^2/A^2] + [Y^2/B^2]=1
WE HAVE POQ = 2A=64....PO=OQ=A=32
AND RO=OS=B=28
HENCE EQN. IS
(X^2/32^2) + (Y^2/28^2) = 1
POINT P' IS 28" FROM ONE END MEANS PP'=28
OP'=32-28=4"=X FROM CENTER.
HENCE WE GET
4^2/32^2 + (Y^2/28^2)=1
Y^2/28^2 = 1-16/32^2=1-(1/64)= 63/64
Y^2=28^2(63/64)
Y=28*SQRT(63/64) IS ALMOST EQUAL TO 28"

You can put this solution on YOUR website!
In this question, to find the answer I know I need to find a vertex, but can't seem to get a quadratic type equation to figure the points:
A wholesaler of appliances finds that she can sell (1200-p) televisions when the price is p dollars. What price will maximize revenue? What is the maximum revenue?
REVENUE = R = ITEMS SOLD * PRICE/ITEM=P(1200-P)=1200P-P^2
R=-[P^2-1200P]=-[P^2-2P*600+600^2-600^2]
R= 600^2 - [P-600]^2
AT P=600, WE GET MAXIMUM REVENUE
R MAX = 600^2=360000 $
HENCE VERTEX IS AT (600,360000)
PRICE OF 600 $ WILL MAXIMISE THE REVENUE.

You can put this solution on YOUR website!
Can I please get some help with this word problem?
The price of an item is given by p = 2x^2 - 100. Find the polynomial that represents the rvenue generated from the sale of x items.
Thanks.
REVENUE=R= NO.OF ITEMS SOLD*PRICE/ITEM = X[2X^2-100]=2X^3-100X
R = 2X^3 - 100X

You can put this solution on YOUR website!
Ruffy is 3/4 as old as Orlie.Four years ago,Ruffy was 1year more than 1/2 old as Orlie...........ORLIE NOW ? OR ORLIE 4 YEARS AGO?...TAKING IT AS 4 YEARS AGO. .How old is each
LET ORLIE BE O YEARS
RUFFY IS R YEARS = 3*O/4 YEAR
4 YERS AGO ORLIE WAS = O-4 YEARS
4 YEARS AGO RUFFIE WAS =3*O/4 -4=(3*O-16)/4 YEARS
HALF AS OLD AS ORLIE = (O-4)2 YEARS
MORE BY 1 YEAR = (O-4)/2 +1=(O-2)/2
HENCE
(O-2)/2 = (3*O-16)/4
4*O-4*2=2*3*O-2*16
32-8=6*O-4*O
2*O=24
O=12
R=3*12/4=9 YEARS

You can put this solution on YOUR website!
Sketch the graph of the hyperbola y^2/25- x^2/4= 1. Draw the fundamental rectangle. Find the equations of the asymptotes and label the asymptotes on your graph
STD. EQN IS
(Y-K)^2/B^2 - (X-H)^2/A^2 =1
COMPARING H=K=0....A=2......B=5
CENTER IS (H,K)=(0,0)
TRANSVERSE AXIS IS X=H=0
LENGTH OF TRANSVERSE AXIS = 2B=10
CONJUGATE AXIS IS Y=K=0
LENGTH OF CONJUGATE AXIS = 2A =4
VERTICES ARE [H,K+-B]=(0,5) AND (0,5)
USE THIS DATA TO SKETCH.IF NECESSARY GIVE SOME VALUES TO X AND FIND Y AND PLOT
CURVES ARE SYMMETRIC ABOUT AXES
ASYMPTOTES ARE GIVEN BY
Y^2/25 - X^/4 = 0
[(Y/5)+(X/4)][(Y/5)-(X/4)]=0
Y/5 = X/4
AND Y/5 = -X/4
GRAPH IS SHOWN BELOW

You can put this solution on YOUR website!
two boys who live 14 miles apart start at noon to walk toward each other at rates of 3 mph and 4 mph respectively . in how many hours will they meet?
RELATIVE VELOCITY WHILE TRAVELING IN OPPOSITE DIRECTIONS =V1+V2=3+4=7 MPH
DISTANCE OF SEPARATION=14
TIME NEEDED TO MEET =14/7 = 2 HRS

You can put this solution on YOUR website!
I need help with this: find a polynomial with integer coefficients that has the given zeros -4, -1+i, -1-i
CONJUGATE ROOTS ARE -1+I AND -1-I
SO EQN. FOR THESE 2 ROOTS IS
[X-(-1+I)][X-(-1-I)]=0=(X+1)^2-I^2=X^2+2X+1+1=0=X^2+2X+2=0
NOW THIRD ROOT IS REAL -4
SO MULTIPLY THE ABOVE WITH X+4 TO GET THE POLYNOMIAL
(X+4)(X^2+2X+2)=0
X^3+2X^2+2X+4X^2+8X+8=0
X^3+6X^2+10X+8=0

You can put this solution on YOUR website!
I have a question that states: find the vertical and horizontal asymptotes for the rational function f(x)= Y =(2x^2-5x-3)/(x^2-4)
FIND LIMIT Y AS X TEND TO INFINITY
LIMIT Y = 2/1=2
HENCE Y=2 IS THE HORIZONTAL ASYMPTOTE.
FIND WHEN Y TENDS TO INFINITY
THIS HAPPENS WHEN D.R=X^2-4=0
X=+2 AND X=-2
THESE ARE THE 2 VERTICAL ASYMPTOTES

You can put this solution on YOUR website!
A common mistake when solving equations is the following:
The equation: 2(x – 2) = x + 3
First step in solving: 2x – 2 = x + 3
THE ERROR IS IN LHS IN NOT MULTIPLYING WITH 2 EACH AND EVERY TERM IN THE BRACKET.
IT SHOULD BE
2*X-2*2 =2X-4 AND NOT 2X-2 ON LHS
THIS IS DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER ADDITION & SUBTRACTION.
ONE SHOULD PAY ATTENTION TO THIS PROPERTY TO AVOID SUCH MISTAKES
Write a clear explanation of what error has been made. What could be done to avoid this error?

You can put this solution on YOUR website!
Business and finance. If the total bill at a restaurant, including a 15% tip, is $65.32, what was the cost of the meal alone?
LET ACTUAL BILL $ = 100
TIP=15 $ = 15
TOTAL BILL = 115
HENCE IF TOTAL IS 115..........ORGL....IS 100
IF TOTAL IS 65.32...........ORGL.IS = 65.32*100/115 = 56.80

You can put this solution on YOUR website!
Business and finance. The electricity costs of a business decreased from $12,000 one year to $10,920 the next. What is the rate of decrease?
ORGL=12000
AFTER 1 YEAR =10920
DECREASE = 12000-10920=1080
RATE OF DECREASE =1080/10920 = 0.0989...OR....9.89%

You can put this solution on YOUR website!
) Business and finance. The electricity costs of a business decreased from $12,000 one year to $10,920 the next. What is the rate of decrease?
ORGL=12000
AFTER 1 YEAR =10920
DECREASE = 12000-10920=1080
RATE OF DECREASE =1080/10920 = 0.0989...OR....9.89%

You can put this solution on YOUR website!
If you are rolling a fair die, what is the probability of rolling an even number and then, on a second roll, rolling the very same number that you rolled on the first roll.
(even# and same #)=
TOTAL THERE ARE 6 FACES
THEY HAVE 1 TO 6 NUMBERS
EVEN NUMBERS ARE 3
SO PROBABILITY OF GETTING AN EVEN NUMBER ON I THROW = 3/6
TO GET SAME NUMBER IN II THROW PROBABILITY=1/6
HENCE COMBINATION PROBABILITY = (3/6)(1/6)=1/12

You can put this solution on YOUR website!
I am so lost doing inequalities. Could someone explain how you would write this?
You have at least $30 in change in your drawer, consisting of dimes and quarters. Write an inequality that shows the different number of coins in your drawer.
LET NUMBER OF DIMES BE = D..........ITS VALUE =10D CENTS
LET NUMBER OF QUARTERS = Q............ITS VALUE =25D CENTS
TOTAL VALUE =10D+25Q CENTS
THIS IS AT LEAST 30$=3000 CENTS
10D+25Q>=3000
2D+5Q>=600

You can put this solution on YOUR website!
1. Find two consecutive integers such that the sum of there square is 85.
N^2+(N+1)^2=85
N^2+N^2+2N+1=85
2N^2+2N-84=0
N^2+N-42=0
N^2+7N-6N-42=0
N(N+7)-6(N+7)=0
(N-6)(N+7)=0
HENCE N=6 OR -7
THE 2 INTEGERS ARE 6&7
OR -7 AND -6
2. A garden area is 30ft long and 20ft wide. A path of uniform width is set around the edge. If the remaining garden area id 400ft ^2, what is the width of the path?
GARDEN AREA =400 SQ.FT.
IF THE WIDTH OF PATH IS X FEET , THEN
LENGTH OF GARDEN = 30-X-X=30-2X
WIDTH OF GARDEN =20-X-X=20-2X
AREA OF GARDEN =(30-2X)(20-2X)=400
600-60X-40X+4X^2=400
4X^2-100X+200=0
X^2-25X+50=0


=2.2 FT

You can put this solution on YOUR website!
find the determinate of the matrix. Book shows below is 1 set or ()
(8+4a 4)
(5+3a 3)
D=(8+4A)*3-4(5+3A)=24+12A-20-12A=4

You can put this solution on YOUR website!
A swing starts at the angle of 53 degrees to the horizontal swing. Every time the swing stops to turn in the opposite direction, the angle between the chain and the vertical is 1 degree less. How many times did the swing pass the vertical position before it stopped? What amount of degrees did it move through from beginning until it stopped?
ORIGINAL ANGLE =53
ANGLE IN THE I PASS BEYOND THE VERTICAL =53
II PASS =52
III PASS =51
........
NTH PASS =53-N+1 =0 WHEN IT COMES TO STOP
N=54..PASSES
TOTAL DEGREES MOVED =53+52+51+.............3+2+1=53(53+1)/2=1431

You can put this solution on YOUR website!
I am really confused with this question, please help
Use a coordinate geometry to prove that the quadrilateral OPQR with vertices O(0,0), P(9,3),Q(9,8), and R(-3,4) is an isosceles trapezoid
SLOPE OF OP=(3-0)/(9-0)=3/9=1/3
SLOPE OF QR=(4-8)/(-3-9)=-4/-12=1/3
HENCE OP||QR
HENCE OPQR IS A TAPEZIUM
OR^2=(-3-0)^2+(4-0)^2=9+16=25
PQ^2=(9-9)^2+(3-8)^2=0+25=25
HENCE
OR=PQ
HENCE IT IS AN ISOSCELES TRAPEZIUM