You can put this solution on YOUR website!
>>If Alex beat Chris by 14 votes, then the number of votes that colin got was
Probably you meant the number of votes Chris got and not Colin...
Assumption : everyone voted.
Assume Chris got x votes,
Since Alex beat Chris by 14 votes, which means he got 14 votes more
ie x+14

Total votes= total number of people
x+x+14=38
=>2x+14=38
=>2x=24
=>x=12
Chris got 12 votes and alex got 26 votes (12+14)

You can put this solution on YOUR website!
To make 8 flags it requires 6 meters of cloth
=> to make 1 flag it requires 6/8 meters of cloth
=> to make 20 flags it would require of cloth
=120/8
=15 meters of cloth

You can put this solution on YOUR website!
Let the smaller number be x
Now the larger number = 5 less thann 2 times the smaller number
= 2x -5
Difference of the sqaures of the 2 numbers is 88
=88
=>=88
=>=0 Grouping the common terms together
=>
=>
=>
=>and
=>and
=>
Therefore the smaller number is 9 and the bigger number is 2*9-5= 13
Ignoring the negative -7/3 as 2 times this number - 5 that is (-14/3 -5 =-29/5),gives a smaller number and not a larger number as in the problem statement

You can put this solution on YOUR website!
Sum of the complementary angles is 90 degress.
If one of the angles is 2x , the other angle is 13x
(from the given condition that their ratios are 2:13)
=> 2x + 13x = 90
=> 15x = 90
=> x=6
Measure of the smaller angle is 2x = 2* 6 =12 degrees

You can put this solution on YOUR website!

In 4 Hours , Prof Ortiz would have travelled 4* 6 = 24 miles west
In 4 Hours ,Wilson would have travelled 4* 2.5 = 10 miles south
B
|
|
|
0--------A

The distance between them is the distance AB as depicted in the figure.
Note that they form 2 sides of a right angled triangle.
Using the Pyathogrean theorem,

You can put this solution on YOUR website!
Let the height be x
So the base is x/3 (One third of the height )
Area of a triangle
=1/2 * base * height
According to the given condition
1/2 * x/3 * x = 24
x^2/6 = 24
Multiplying both sides by 6
x^2 = 24*6
x^2=144
x=sqrt(144)
therefore x=12
and x/3 = 4
Base is 4 and height is 12

You can put this solution on YOUR website!
Prove that tan x (cot x + tan x) = sec^2x
LHS (Left hand side)
tan x (cot x + tan x)
=tan x * cot x + (tan x)(tan x)
=1+ tan^2 x
=1 + sin^2 x/cos ^ x
=(cos ^ 2 x + sin ^ x)/cos ^2 x
=1/cos^2 x
=sec ^2 x = RHS (right hand side)

You can put this solution on YOUR website!
Simplify "(5 + 3i)(5 - 3i)." Is the result real, complex, or both?
Note the expression is of the form (A+B)(A-B)= A^2 - B^2
therefore we can write
5 + 3i)(5 - 3i)
as 5^2 - (3i)^2
=25 - 9i^2
=25 -9(-1) as i^2 = -1
=25+9
=34 which is real number.

You can put this solution on YOUR website!
(x+3)^2-10(x+3)+24
Let's replace x+3 by A
So, the given expression would transform to
A^2 -10A + 24
Rewriting it as
A^2 - 6A -4A + 24
A(A-6) -4(A-6)
Taking A-6 as the common factor,
(A-6)(A-4)
Substituting A=x+3 back into the expression we get
(x+3-6)(x+3-4)
(x-3)(x-1) is the required factor.
==========================================================================
write a quadratic equation and answer the following: the shortest leg of a right triangle is two less than the hypotenuse. the hypotenuse is one longer than the longest leg.
Let the longest leg be x
So the hypotenuse is (x+1) {the hypotenuse is one longer than the longest leg}
And the shortest leg is (x+1)-2=x-1 {the shortest leg of a right triangle is two
less than the hypotenuse}
Using Pythagoras's theorem,
hypotenuse^2 = shorter leg^2 + longer leg^2
we get
(x+1)^2 = (x-1)^2 + x^2
Expanding the LHS and the RHS
x^2 + 2x+ 1 = x^2 -2x+1 + x^2
Moving the Right hand side expression to Left hand side we get
x^2 + 2x+ 1 - (x^2 -2x+1 + x^2)= 0
grouping the like terms,
(x^2 - x^2 -x^2) + (2x + 2x ) + (1 -1)=0
-x^2 + 4x =0
-x(x-4)=0
which gives x=0 and x=4 as two possible solutions. But we cannot have a triangle with side of length 0. So discarding x=0 we get the other solution as x=4
Hence, the sides of the triangle are
The longest side=4
The shorter side=4-1=3
hypotenuse=4+1=5

You can put this solution on YOUR website!
What is "consecutive" anyways?
By consecutive we mean appearing one after the other. So for example 1,3,5 are consecutive odd integers.Again 7,9,11 are similarly 3 consecutive odd integers.
Now to the solution of the actual problem.
Let the three integers
be x,x+2,(x+2)+2 Notice in the example above how they differ by 2.
i.e. x,x+2 and x+ 4 are the 3 consecutive odd integers.
Given
=
=
=
Group the like terms
=
x=21
therefore the other 2 numbers are 23 and 25
Numbers are 21,23,25

Verify

You can put this solution on YOUR website!
Let the total spinach cans in the case be x
On Monday he ate of the spinach cans.
So amount left after Monday =
=
=2x/3
On Tuesday he ate 75% of the remaining
i.e.
Given that on Tuesday he at 12 cans. Therefore,
=
= simplifying 75/100 as 3/4
=


The amount he ate on Monday = x/3
= 24/3
= 8 cans

You can put this solution on YOUR website!
The total different outcomes of the two spinners are
4* 4= 16
The outcomes are (10,1),(10,2),(10,3),(10,4),(12,1),(12,2),(12,3),(12,4),(14,1),
(14,2),(14,2),(14,3),(18,1),(18,2),(18,3),(18,4)

Out of these pairs, the ones for which the difference is multiple of 3 are:
(10,1), difference 9
(10,4) difference 6
(12,3) difference 9
(14,2) difference 12
(18,3) difference 15
So the required probability = favorable outcomes/ total outcome
= 5/16

You can put this solution on YOUR website!
Before giving out the solution to the problem here is something you should
know
[x] means the greatest integer value less than or equal to x
so for e.g [1.2] = 1
[-5.6] = -6
[4]=4
now to the questions
1. [2x] < 8
2[x] < 8 (Note [2x] is not = 2[x] but [2x] <= 2[x] so without loss of inequality we can write [2x] as 2[x]) in the above inequality
[x]< 4

for all x < 4, [x] <4
hence solution set for the above is x< 4
2. [ p + 2] <6
for all p+2 < 6 , [p+2] will be less than 6
p < 4
3 [z +3 ] >2
since [z+3] is an integer value [z+3] should be >=3 ( integer greater than 2)
which gives z>=0
4.y-3<2x? (0,0)or(1,5)or(-2,0).
substitue x=0, y=0
0-3< 2*0
-3 <0 hence it satisfies the equation
Substituting x=1 , y=5
5-3 < 2*1
2< 2
It does not satisfy the equation
Substituting x= -2 , y=0
0 - 3 < 2* -2
-3 < -4
it does not satisfy the equation
The only point satisfying the equation is (0,0)

You can put this solution on YOUR website!

(1 * 2 * ( 3 + 4 ) * 5 ) + 6 + 7 + 8 + 9 =100

verification:
(2 * 7 * 5 ) + 6+7+8 +9
70 + 30 =100

You can put this solution on YOUR website!
total weight of the rings = 18 * 5 = 90g
total amount of silver = 10/100 *90 = 9g
Total amount of gold in all the 5 rings = 90 -9 =81g
Let the amount of silver added be x grams
total weight of the mixture now = 90 + x
percentage of gold = 81/(90+x) *100
since the percentage of gold now is to be 75
81/(90+x) *100 = 75
81 * 100 = 75 (90+x)
27 * (3 * 25) * 4= 75(90+x)
canceling out 75 on both sided
27* 4 = 90 +x
x = 108 -90
=18g

You can put this solution on YOUR website!
3(x+2)(x-4)+6(x+2)(x+1)
=3(x+2)[((x-4 + 2(x+1)]
=3(x+2)( x-4 + 2x +2)
=3(x+2)(3x -2)

You can put this solution on YOUR website!
Slope =
=
= infinity
which means that the line is perpendicular to the x-axis
equation of the line is x=3

You can put this solution on YOUR website!
3*8+6squared-8/2=26




which is true ..does it make sense now
((3*8) + (6^2 - 8 ))/2 =26

You can put this solution on YOUR website!
Since there are 2 variables in the equation x-y=4 , you need at least 2 equations to find the values of x and y

You can put this solution on YOUR website!
Use the distance formula
D =
10 =
square on both sides



x-4 = +-8
x=12 and x=-4
So your answer of 12 is also correct

You can put this solution on YOUR website!
Given equation
6n^2= -8n-1
add 8n +1 on both sides
6n^2 + 8n + 1 =0 ( looks more familiar now ?)
use the quadratic formula





n= -1.193 and n= -0.1396

You can put this solution on YOUR website!
number of bags required = 27,500/5,000
= 5.5 bags

You can put this solution on YOUR website!
Let the second number be x
from the problem statement "the third is 11 less than ten times the second"
third number = 10x -11
again from the problem statement "first is 7 more than three times the second"
first number = 3x + 7
Sum of the numbers =105
3x+7 + x + 10x-11 =105
14x = 109
x= 109/14
second number is 109/14
first number = 10* 109/14 -11
=936/14
third number = 3* 109/14 + 7
=425/14

You can put this solution on YOUR website!
3. MEASURE OF ANGLE K +MEASURE OF ANGLE J=MEASURE OF ANGLE P + MEASURE OF ANGLE 1.
4. MEASURE OF ANGLE A = MEASURE OF ANGLE K + MEASURE OF ANGLE J
5. MEASURE OF ANGLE F = MEASURE OF ANGLE P + MEASURE OF ANGLE 1.
6. MEASURE OF ANGLE A = MEASURE OF ANGLE F.
THE QUESTION ASKS WHAT THE REASON IS FOR STEP 6?
A. SYMMETRIC PROPERTY OF EQUALITY
B. SUBSTITUTION PROPERTY OF EQUALITY
C. ANGLE ADDITION POSTULATE
D. REFLEXIVE PROPERTY OF EQUALITY
the answer is B. Substitution property of equality
Reason
from the statements
3. MEASURE OF ANGLE K +MEASURE OF ANGLE J=MEASURE OF ANGLE P + MEASURE OF ANGLE 1.
4. MEASURE OF ANGLE A = MEASURE OF ANGLE K + MEASURE OF ANGLE J
we have by substituting MEASURE OF ANGLE K + MEASURE OF ANGLE J=MEASURE OF A IN
in 3
MEASURE OF ANGLE A = MEASURE OF ANGLE P + MEASURE OF ANGLE 1.
Now statement 5
5. MEASURE OF ANGLE F = MEASURE OF ANGLE P + MEASURE OF ANGLE 1.
Substituting MEASURE OF ANGLE P + MEASURE OF ANGLE 1 as MEASURE OF ANGLE F in the statement above
MEASURE OF ANGLE A = MEASURE OF ANGLE F which is statement 6

You can put this solution on YOUR website!
the number which is one-third between 3 and 5 is
= (3+5)/3
=11/3 or 3 2/3

You can put this solution on YOUR website!
Increase in members = 40,000 - 16,000
=24,000
percentage increase = (increase in members/ initial members )*100
= (24,000/40,000)*100
=60%
Answer : the members grew by 60%

You can put this solution on YOUR website!
after taking 25% what you are left with is 75% of 3181 dollars
Amount left =75/100 * $3181
=$2385.75

You can put this solution on YOUR website!
Any number which cannot be expressed in the form a/b where b not equal to zero is a irrational number
the given numbers are
17/3 since its in the form of a/b with b!=0 hence rational
-1.82 = -182/100 again can be expressed in the form of a/b where b!=0
cannot be expressed in the form of a/b and is IRRATIONAL
5.3/3 = 53/10 can be expressed as a/b and is rational

You can put this solution on YOUR website!
The given equation is :
5x + 8 + 3x - x + 5 = 6x - 3
the way to solve such equations is first to group all the variable terms (here x) at one side and the constants on the other.
So we have :
5x + 3x - x - 6x = -8 - 5 - 3
x = -16

You can put this solution on YOUR website!
let the total credit C after M minutes of call be given by
C = $(a*M + b) where a and b are some constants.
So we have:
21.78 = a * 23 + b (1) and
17.02 = a * 57 + b (2)
Subtracting equation (2) from (1):
4.76 = -34a
a = -4.76/34
= -.14
Putting this value of a in equation (1):
21.78 = -.14 * 23 + b
therefore, b = 21.78 + 3.22
= 25
So the linear equation for the credit remaining after M minutes of call is
C = $(-.14 * M + 25)
So, the remaining credit after 87 minutes
C = -.14 * 87 + 25
= $12.82

You can put this solution on YOUR website!