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

You can put this solution on YOUR website!
At 40 feet from the base of a light house, the angle of elevalation from the ground to the top of a light house is 40 degrees. Find the height of the light house.
TAN(40)=HEIGHT/GROUND DISTANCE = H/40
H=40*TAN(40)=33.54 FEET

You can put this solution on YOUR website!
My Problem Is To Figure Out What:
Ten Plus 6 times a number is equal to 5 less than the number.
Any help with this problem would be greatly appreciated;}
Kia Jayy,Thank YOu
LET THE REQUIRED NUMBER BE X
6 TIMES THE NUMBER=6X
TEN PLUS TO IT =6X+10
THIS=5 LESS THAN THE NUMBER=X-5
6X+10=X-5
6X-X=-5-10
5X=-15
X=-3

You can put this solution on YOUR website!
Write slope intercept form of the equation of the line passing through the point (3,0) and parellel to the line y=-2x-5.
LINE PARALLEL IS
Y=-2X+K
IT PASSES THROUGH (3,0).HENCE
0=-2*3+K
K=6
HENCE EQN. IS
Y=-2X+6

You can put this solution on YOUR website!
Hello,
I am having diffuclty on solving the following problem.
Rewrite each expression in the form
quotient + remainder/divisor
Use synthetic divsion
x^2+3x+2 / x+3
Thank you
.X+3]X^2+3X+2[X=QUOTIENT
.....X^2+3X
-----------------
...........+2=REMAINDER
X+[(2)/(X+3)]=X^2+3X+2

You can put this solution on YOUR website!
How would I write these two expressions in simplest form?
4x-28/5x-35
=[4(X-7)]/[5(X-7)]=4/5
4r^2-25s^2/2r^2+3rs-20s^2
=[(2R)^2-(5S)^2]/[2R^2+8RS-5RS-20S^2]
=[(2R+5S)(2R-5S)]/[2R(R+4S)-5S(R+4S)]
=[(2R+5S)(2R-5S)]/[(2R-5S)(R+4S)]
=(2R+5S)/(R+4S)

You can put this solution on YOUR website!
Can someone review this problem for me? I was supposed to factor
4x^2-7xy+16x-28y completely.
=X(4X-7Y)+4(4X-7Y)
=(4X-7Y)(X+4)IS THE ANSWER
My result is 16x^2-7xy+16x-28y. Is this problem factored completely? Thanks
NO....SEE ABOVE

You can put this solution on YOUR website!
I had to factor 14x^2+24x+10 completely. My answer is 2(x+1)(7x+5) Did I factor the problem completely?
PERFECT GOOD JOB KEEP IT UP!!

You can put this solution on YOUR website!
Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by $5. How many students attended the get-together?
LET N BE NUMBER OF STUDENTS ATTENDED.
TOTAL NUMBER OF STUDENTS = N+5
FOOD BUDGET = 500 $
BUDGETED COST PER HEAD = 500/(N+5)
ACTUAL COST INCURRED PER HEAD ATTENDED = [500/(N+5)]+5 = (500+5N+25)/(N+5)
TOTAL ACTUAL COST =N*(5N+525)/(N+5)
HENCE
(5N^2+525N)/(N+5)=500
5N^2+525N=500(N+5)=500N+2500
5N^2+25N-2500=0
N^2+5N-500=0
N^2+25N-20N-500=0
N(N+25)-20(N+25)=0
(N-20)(N+25)=0
N=20
HENCE 20 ATTENDED THE FUNCTION

You can put this solution on YOUR website!
Okay, if the profit on a watch is given by P=x^2-13x-80, where x is the number of watches sold per day. How many watches were sold on a day when there was a $50 loss?
P=-50....SINCE IT IS LOSS
-50=X^2-13X-80
X^2-13X-30=0
X^2-15X+2X-30=0
X(X-15)+2(X-15)=0
(X-15)(X+2)=0
I tried and I keep getting 15. Am I right?
SURE YOU ARE 1000000% CORRECT!GOOD JOB!!KEEP IT UP!!HAVE SELF BELIEF!!YOU WILL GO UP!
I do NOT have a clue. Please Help!!!
Thank You

You can put this solution on YOUR website!
I need som serious help with this word problem: A triangle has sides 2x-5, 3x+1, and 4x+2. Find the polynomial that represents it's perimeter.
(a) 9x-2
(b)(2x-5)(3x+1)(4x+2)
(c)10x-8
(d)24x-10
My answer is D...Am I right?
PERIMETER IS SUM OF ALL SIDES
=2X-5+3X+1+4X+2=9X-2.................A IS THE ANSWER

You can put this solution on YOUR website!
the following matrix is a reduced augmented matrix obtained from a system of equations. The system has ____ solutions?

1 0 3 -5 |7
0 1 -2 0 |4
0 0 0 0 |0
0 0 0 0 |0
THE RANK OF COEFFICIENT MATRIX=2 < 4 THE ORDER....SO IT HAS EITHER ZERO
OR INFINITE SOLUTIONS.
RANK OF AUGMENTED MATRIX = 2 = RANK OF COEFFICIENT MATRIX
HENCE THE SYSTEM IS CONSISTENT.
HENCE IT HAS INFINITE SOLUTIONS
A. One
B. Two
C. Infinite
D. No

You can put this solution on YOUR website!
SEE THE FOLLOWING EXAMPLE AND TRY.
IF IN DIFFICULTY PLEASE COME BACK
find the inverse, if it exists,in the matrix. I am not sure and don't understand how to do the inverse. I used the underscore to separate the numbers within the matrix.
2_ 0_ 4
3_ 1_ 5
-1_1_-2
SEE THE FOLLOWING WORK
1.FRAME AUGMENTED MATRIX ADDING UNIT MATRIX OF ORDER(3,3)
2.BY SERIES OF OPERATIONS INDICATED ,MAKE A AS UNIT MATRIX..
THEN RHS MATRIX BECOMES INVERSE.
NR1=NEW ROW1…….R1=OLD ROW 1 ETC..
2 0 4 1 0 0
3 1 5 0 1 0
-1 1 -2 0 0 1
NR1=R1/2……..NR2=R2-3R1/2……NR3=R3+R1/2………
1 0 2 0.5 0 0
0 1 -1 -1.5 1 0
0 1 0 0.5 0 1
NR3=R3-R2
1 0 2 0.5 0 0
0 1 -1 -1.5 1 0
0 0 1 2 -1 1
NR2=R2+R3………….NR1=R1-2R3
1 0 0 -3.5 2 -2
0 1 0 0.5 0 1
0 0 1 2 -1 1
INVERSE IS
-3.5 2 -2
0.5 0 1
2 -1 1
IF IN DOUBT PLEASE COME BACK

You can put this solution on YOUR website!
Find all the discontinuities for the function below. Label each as a vertical asymptote or removable discontinuity.
y = 4x + 28/ x^2 + 6x - 7 = (4X+28)/(X+7)(X-1)
DR VANISHES AT X=-7 AND X=1
HENCE THESE ARE THE 2 POINTS OF DISCONTINUITY

You can put this solution on YOUR website!
Find all the discontinuities for the function below. Label each as a vertical asymptote or removable discontinuity.
y = x - 6/ x^2 - 6x = (X-6)/[X(X-6)]
AT X=0 AND X=6 THE DENOMINATOR VANISHES AND HENCE THE FUNCTION IS DISCONTINUOUS AT THESE 2 POINTS

You can put this solution on YOUR website!
I am trying to find the inverse of each function and express it in the form y=f inverse -1(x). And I need to verify each result by showing that (f composed of f)(x)=f inverse -1 composed pf f)(x)=I(x). The problem to be solved is:
x = 4y + 1
GENERALLY WE ARE GIVEN Y=F(X)=SOME FUNCTION OF X SAY Y=F(X)=4X+1...OR..SOME THING LIKE THAT THEN PROCEDURE IS
PUT
1.Y=4X+1
2.SOLVE FOR X
4X=Y-1
X=(Y-1)/4
3.NOW PUT X IN PLACE OF Y ON THE RIGHT SIDE AND THEN WE GET
F INVERSE X =(X-1)/4
TO CHECK
F OF [F INVERSE X] = X
TO SIMPLIFY UNDERSTANDING AND FOR EASE OF WORK
PUT F INVERSE X =Z= (X-1)/4
F[F INVERSE X]=F[Z]= 4Z+1 =[4(X-1)/4]+1 = (4X-4+4)/4 = 4X/4=X
TO CHECK
F INVERSE OF [F(X)]=X
F INVERSE OF[4X+1] .....
TO SIMPLIFY UNDERSTANDING AND FOR EASE OF WORK....
PUT Z=4X+1
F INVERSE OF[Z]=(Z-1)/4 =[4X+1-1]/4=4X/4=X
HOPE YOU UNDERSTOOD
BUT YOU GAVE
X=4Y+1..........LET US FIND F INVERSE Y IN THE SAME MANNER
4Y=X-1
Y=(X-1)/4
HENCE
F INVERSE Y = (Y-1)/4

You can put this solution on YOUR website!
For what Values of p will the expression p+8x-3x^2 always be positive?
FOR NO VALUE OF P WILL IT BE ALWAYS POSITIVE.
QUADRATIC WILL ALWAYS HAVE ONE SIGN POSITIVE OR NEGATIVE IF ITS
DISCRIMINANT IS NEGATIVE.
THEN IT WILL ALWAYS BE +VE IF COEFFICIENT OF X^2 IS POSITIVE
OR IT WILL ALWAYS BE - VE. IF COEFFICIENT OF X^2 IS NEGATIVE,AS
IS THE CASE HERE.HENCE IF
D=8^2-4P(-3)<0...THAT IS 64-12P<0...THAT IS....P>64/12=16/3,THE FUNCTION WILL BE ALWAYS NEGATIVE.

You can put this solution on YOUR website!
I do not fully understand what domain is and I am having trouble with the following problem:
y= square root of(9-x^2) + square root of(1-x^2)
The answer on my key is domain=[1,3] but I do not understand why. Can you please explain?
HERE X IS CALLED INDEPENDENT VARIABLE AND Y DEPENDENT VARIABLE.
OUR UNIVERSE IS REAL NUMBERS FOR THIS PURPOSE.
NOW , THIS DOES NOT MEAN THAT X CAN TAKE ANY VALUE IN REAL NUMBERS.
IT CAN TAKE ONLY SUCH VALUES WHICH MAKE THE GIVEN FUNCTION F(X) OR Y IN SHORT MEANINGFUL.THAT IS A MATHEMATICALLY ALLOWED OPERATION.
CERTAIN OPERATIONS LIKE DIVISION BY ZERO , SQUARE ROOT OF A NEGATIVE NUMBER,LOG OF ZERO OR NEGATIVE NUMBER ARE NOT DEFINED.EITHER THEY ARE CALLED INFINITY(PLUS OR MINUS)OR IMAGINARY.
SO WE SAY X CAN NOT TAKE SUCH VALUES WHICH REQUIRES US TO PERFORM SUCH OPERATIONS.
X CAN TAKE VALUES OF ALL OTHER REAL NUMBERS.THE SET OF THESE REAL NUMBERS IS CALLED DOMAIN OF THE FUNCTION.
IF YOU HAVE
Y=1/(X-3)...DOMAIN IS ALL REAL VALUES EXCEPT 3 AS IT WILL LEAD TO DIVISION BY ZERO .
IN YOUR EXAMPLE THE FIRST TERM BECOMES MEANING LESS IF
9-X^2<0.HENCE
9-X^2>=0
9>=X^2
X^2<=9
|X|<=3......THAT IS X SHOULD BE BETWEEN -3 AND +3
WE SHOW IT AS X = [-3,3]......[..]..BRACKETS INDICATE X CAN EQUAL THE BORDER VALUES
THAT IS X=3 AND X=-3 ARE ALLOWED.
NOW THERE IS A SECOND TERM.SQRT.(1-X^2)
SIMILAR ARGUMENT LEADS US TO CONCLUDE X = [-1,1]
THE COMBINATION OF THE I AND II CONDITIONS MAKE US TO CONCLUDE THAT X = [-1,1]
YOUR ANSWER IS [1,3]WHICH IS NOT CORRECT.
ON THE OTHER HAND,IF SECOND TERM IS SQ.RT(X^2-1)....THEN |X| >=|
X<=-1......OR............X>=1...COMBINING THIS WITH I CONDITION , WE GET
X=[1,3] AND [-3,-1]

You can put this solution on YOUR website!
find the inverse, if it exists,in the matrix. I am not sure and don't understand how to do the inverse. I used the underscore to separate the numbers within the matrix.
2_ 0_ 4
3_ 1_ 5
-1_1_-2
SEE THE FOLLOWING WORK
1.FRAME AUGMENTED MATRIX ADDING UNIT MATRIX OF ORDER(3,3)
2.BY SERIES OF OPERATIONS INDICATED ,MAKE A AS UNIT MATRIX..
THEN RHS MATRIX BECOMES INVERSE.
NR1=NEW ROW1…….R1=OLD ROW 1 ETC..
2 0 4 1 0 0
3 1 5 0 1 0
-1 1 -2 0 0 1
NR1=R1/2……..NR2=R2-3R1/2……NR3=R3+R1/2………
1 0 2 0.5 0 0
0 1 -1 -1.5 1 0
0 1 0 0.5 0 1
NR3=R3-R2
1 0 2 0.5 0 0
0 1 -1 -1.5 1 0
0 0 1 2 -1 1
NR2=R2+R3………….NR1=R1-2R3
1 0 0 -3.5 2 -2
0 1 0 0.5 0 1
0 0 1 2 -1 1
INVERSE IS
-3.5 2 -2
0.5 0 1
2 -1 1
IF IN DOUBT PLEASE COME BACK

You can put this solution on YOUR website!
State the inverse of the function.
h(x) = (6x - 5)/2=Y SAY
6X-5=2Y
6X=2Y+5
X=(2Y+5)/6
HENCE INVERSE OF H(X) IS
(2X+5)/6
I came up with an answer of y=(2x+5)/6.
PERFECT!!GOOD!!KEEP IT UP!!HAVE CONFIDENCE IN YOUR ABILITY!YOU WILL GO UP!
I just wanted to know if this is correct and if not what I did wrong and what the correct answer is. Thank you!

You can put this solution on YOUR website!
i need to know:
when the problem is log base2 X + log base2 (X + 7) = 3
doesnt that need to be rewritten and then solved?
LOG[X(X+7)] TO BASE 2 =3
X(X+7)=2^3=8
X^2+7X-8=0
X^2+8X-X-8=0
X(X+8)-1(X+8)=0
(X-1)(X+8)=0
X=1..OR.......-8.........
SING LOG OF NEGATIVE NUMBER DOES NOT EXIST
X=1 IS THE ANSWER

You can put this solution on YOUR website!
SEE THE FOLLOWING EXAMPLE AND TRY.SEE SOURCE CODE FOR CORRECT FORMAT
COME BACK IF IN DIFFICULTY
TABULATE AND DO AS FOLLOWS.HOPE IT IS CLEAR.PLEASE COME BACK IF IN DOUBT
x X=x-M X^2
1 4 -2.4 5.76
2 5 -1.4 1.96
3 8 1.6 2.56
4 7 0.6 0.36
5 9 2.6 6.76
6 8 1.6 2.56
7 7 0.6 0.36
8 3 -3.4 11.56
9 6 -0.4 0.16
10 7 0.6 0.36

SUM=S= 64 S.S.D. = 32.4 S.S.D=SUM OF SQUARES OF DEVIATIONS
N0.=N = 10 N0. = N = 10
MEAN=M= 6.4 VARIANCE=V= 3.24 =MEAN OF SUM OF SQUARES OF DEVIATIONS
S.D = SQRT.(V) 1.8 =ROOT OF MEAN OF SUM OF SQUARES OF DEVIATIONS

You can put this solution on YOUR website!
I have a graph with numbers 10,30,60,100,150,210,280,360 and so on. I am having trouble finding the correct fomular for this problem.
thank you for your help
WHAT DO YOU WANT?
FORMULA FOR N TH. TERM???ASSUMING SO ......NOTE THE FOLLOWING
A2-A1=30-10=20
A3-A2=60-30=30
A4-A3=100-60=40
A5-A4=150-100=50
A6-A5=210-150=60
A7-A6=280-210=70
A8-A7=360-280=80
..............
WE ARE HAVING A.P. ON RHS 20,30,40,50...ETC..WITH D=10...TN=20+(N-1)*10=10N+10=10(N+1)...HENCE...TN-1=10(N-1+1)=10N
AN-A(N-1)=10N.........CHECK ABOVE PUTTING N=2,3,4 ETC....
------------------------ADDING ALL
AN-A1=20+30+................10N
AN-10=(N-1)[20+10N]/2=5(N-1)(N+2)
AN=10+5(N-1)(N+2)
CHECK
N=1.......A1=10
N=2.......A2=10+5*4=30
N=3.......A3=10+5*2*5=60
N=4.......A4=10+5*3*6=100.....
......ETC....OK

You can put this solution on YOUR website!
I have a graph with numbers 10,30,60,100,150,210,280,360 and so on. I am having trouble finding the correct fomular for this problem.
thank you for your help
WHAT DO YOU WANT?
FORMULA FOR N TH. TERM???ASSUMING SO ......NOTE THE FOLLOWING
A2-A1=30-10=20
A3-A2=60-30=30
A4-A3=100-60=40
A5-A4=150-100=50
A6-A5=210-150=60
A7-A6=280-210=70
A8-A7=360-280=80
..............
WE ARE HAVING A.P. ON RHS 20,30,40,50...ETC..WITH D=10...TN=20+(N-1)*10=10N+10=10(N+1)...HENCE...TN-1=10(N-1+1)=10N
AN-A(N-1)=10N.........CHECK ABOVE PUTTING N=2,3,4 ETC....
------------------------ADDING ALL
AN-A1=20+30+................10N
AN-10=(N-1)[20+10N]/2=5(N-1)(N+2)
AN=10+5(N-1)(N+2)
CHECK
N=1.......A1=10
N=2.......A2=10+5*4=30
N=3.......A3=10+5*2*5=60
N=4.......A4=10+5*3*6=100.....
......ETC....OK

You can put this solution on YOUR website!
If a lily pad doubles in size everyday and on the 60th day it covers a lake...
On what day did it cover just half of the lake?
FULL ON 60 TH DAY
ONE DAY BEFORE ...59 TH DAY
IT IS HALF FULL.
59 TH DAY .SINCE IT DOUBLES EVERY DAY AND FILLS THE LAKE ON 60 TH.DAY

You can put this solution on YOUR website!
can you please tell me--after putting 2x+3y=12 into slope form what or how do you get three values for x and substitue the values to find three values for y thank you
put in std. form
Y=MX+C WHERE M = SLOPE ........AND.......C=Y INTERCEPT OR SIMPLY CALLED INTERCEPT.
2X+3Y=12
3Y=-2X+12
Y=-2X/3+12/3=(-2/3)X+4
HENCE SLOPE =-2/3
PUT VALUES FOR X AND FIND Y AS FOLLOWS
X=....................0...................1.........................2
Y=-2X/3 + 4........=-2*0/3 +4 =4........=-2*1+4=2................=-2*2+4=0

You can put this solution on YOUR website!
1)Use the arithmetic sequence of numbers 2, 4, 6, 8,
10� to find the following:
a)What is d, the difference between any 2 terms?
Answer:
Show work in this space.
D= COMMON DIFFERENCE BETWEEN 2 CONSECUTIVE TERMS
4-2=6-4=8-6=10-8=2....CONSTANT...THIS IS THE PROPERTY
OF ARITHMATIC PROGRESSION
b)Using the formula for the nth term of an arithmetic
sequence, what is 101st term? Answer:
Show work in this space.
TN=A+(N-1)D=2+(N-1)2=2N
T101=2*101=202
c)Using the formula for the sum of an arithmetic
series, what is the sum of the first 20 terms?
Answer:
Show work in this space.
SN=(N/2){2A+(N-1)D}=(N/2){2*2+(N-1)2}=(N/2)(2N+2)=N^2+N
S20=20^2+20=420
d)Using the formula for the sum of an arithmetic
series, what is the sum of the first 30 terms?
Answer:
Show work in this space.
S30=30^2+30=930
e)What observation can you make about these sums of
this series (HINT: It would be beneficial to find a
few more sums like the sum of the first 2, then the
first 3, etc.)?
Answer: 1.THE SUM IS A QUDRATATIC IN N.
2.IT IS EQUAL TO THE SUM OF NUMBER OF TERMS AND ITS
SQUARE

You can put this solution on YOUR website!
express as trignometric function of 1 angle sin44degreescos22degrees-cos44degreessin22degre
SIN(A-B)=SIN(A)COS(B)-COS(A)SIN(B)
A=44.......B=22
SIN(44-22)=SIN(22)

You can put this solution on YOUR website!
A 500g slab of cheese is completely eaten by two mice. If Minnie had eaten twice as much as she did, and Mickey had eaten half as much as he did, there would have been 100g left. If Minnie = x and Mickey = y, use the information to get the 2 equations relating to x and y.
TOTAL EATEN BY MINNIE AND MICKEY =
X+Y = 500.........................1
MINNIE ATE =X
IF SHE HAD EATEN TWICE IT WOULD BE =2X
MICKEY ATE =Y
IF HE HAD EATEN HALF OF IT ONLY IT WOULD BE = Y/2
TOTAL =
2X+(Y/2)=500-100=400
4X+Y=800...............................2
SOLVING
EQN.2-EQN.1
3X=300
X=100
Y=400

You can put this solution on YOUR website!
What's the number? If I multuply it by 3 and add 11, I get the same answer when I add 3 to it.
LET THE NUMBER BE X
MULTIPLY WITH 3 AND ADD 11.....3X+11
THIS IS SAME AS X+3
3X+11=X+3
2X=-8
X=-4

You can put this solution on YOUR website!

SEE THE FOLLOWING EXAMPLE AND TRY.
COME BACK IF IN DIFFICULTY
TABULATE AND DO AS FOLLOWS.HOPE IT IS CLEAR.PLEASE COME BACK IF IN DOUBT
x X=x-M X^2
1 4 -2.4 5.76
2 5 -1.4 1.96
3 8 1.6 2.56
4 7 0.6 0.36
5 9 2.6 6.76
6 8 1.6 2.56
7 7 0.6 0.36
8 3 -3.4 11.56
9 6 -0.4 0.16
10 7 0.6 0.36

SUM=S= 64 S.S.D. = 32.4 S.S.D=SUM OF SQUARES OF DEVIATIONS
N0.=N = 10 N0. = N = 10
MEAN=M= 6.4 VARIANCE=V= 3.24 =MEAN OF SUM OF SQUARES OF DEVIATIONS
S.D = SQRT.(V) 1.8 =ROOT OF MEAN OF SUM OF SQUARES OF DEVIATIONS