- Solve for x and y
2^(x - 1) * 3(y + 1) = 72 * 6^(y - x + 2)
3^(x - 1) * 2^(y + 1) = 3 * 6^(x - y - 2)
2. Find the error in this proof. Prove: 5 = 7
Let a = b
Multiply both sides by a and add a^2 - 2ab to both sides:
2a^2 - 2ab = a^2 - ab
Take 2 as a common factor:
2(a^2 - ab) = a^2 - ab
Divide by a^2 - ab:
2 = 1
Multiply by 2:
4 = 2
Add 3 to both sides:
7 = 5
3. A rectangle with sides of lengths x and y has perimeter P. Prove that the largest area of this rectangle is given when the rectangle is a square.
4. Two pipes fill a swimming pool in 11 1/9 hours (eleven hours and one ninth of an hour) together. One pipe can fill the pool in 5 hours less than the other pipe. Find out how much times it takes each pipe to fill up the swimming pool separately.
5. A pharmacist has two iodine solutions: one with a concentration of 30% and one with a concentration of 80%. How much of each solution the pharmacist needs to create 8 liters of a 50% solution?
6. Mary needs to refuel her car with 60 liters of gasoline and get back home. She has two choices: drive to a gas station 20 km away from her house which charges $1.16/liter or drive to a gas station adjacent to her house which charges $1.24/liter. Mary's car's mileage is 10 km/liter. Which is cheaper for Mary?
7. A brother and a sister are mowing the lawn on their backyard. It takes the brother 15 minutes longer to mow the lawn than it takes his sister. Together they mow the lawn in 56 minutes. How long does it take each of them to mow the lawn?
ok for question two...
ReplyDeletewhere did the 'b' in the '2ab' on the left hand side of the equation come from?and ab + a^2 - 2a = ab + a^2 - 2a.
and it is not possible to take '2' as the common factor, as there is only one term on the right hand side of the equation that has a 2 in it.
Thank you
ReplyDeleteI made a mistake IT was suppose to be
multiply by a on both sides
then
add a^2 - 2ab on both sides
But your comment on the common factor is not too clear
a common factor is something that is common with all the terms
for question two the is an error when multiplying the r.h.s
ReplyDeleteb*a=ab.....but it has a^2
sp the r.h.s should be.. ab+ a^2-2ab
which simplifies as a^2-ab
Rhs is b
ReplyDeletemultiply by a gives
ba
add a^2 gives
ab + a^2
-2ab gives
ab + a^2 -2ab is simplified as
a^2 -ab which is what I posted
7)x+x+15=56
ReplyDelete2x+15=56
2x=56-15
2x=41
x=41/2
x=20.5
it takes the sister 20 minutes and 30 seconds
and it takes the brother 20.5+15=35.5
35 minutes and 30 seconds.
6) Mary needs 60 litres of gas.
ReplyDeleteIf she were to purchase the gas adjacent to her home, she would spend 60X1.24= $74.40,
but if she were to go to the gas station 20km away, with a car of fuel efficiency 10km/litre:
she would spend: 60x1.16=$69.60, but in the process she burns 4 litres of gas to and from the gas station, so if we're takin into consideration she must have 60 litres of gas in her tank afterwards...it would cost her 64x1.16 = $74.24. It would be cheaper by 16cents to fill the car at the further gas staion....i wish gas was really that cheap right now though
4. let X represent the faster pipe
ReplyDeletelet Y represent the slower pipe
X+Y = 11 1/9
(Y = X+5)
X + (X+5) = 11 1/9
2X +5 = 11 1/9
2X = 6 1/9
X= 3 1/18
therefore one pipe can fill the in 3 1/18 hours whereas the other fills the pool in 8 1/18 hours?
2. a = b
ReplyDelete(x a): a^2 = ab
(+ a^2 - 2ab): 2a^2 - 2ab = a^2 - ab
pull out Common Factor of 2.....ERROR
Both sides of the equation have no common factor, there what was done is wrong.
This comment has been removed by the author.
ReplyDeletefor ques 7
ReplyDeletex+15+x=56
2x+15=56
2x=56-15
2x=41
x=41/2
x=20.5
time taken for the bro to mow the lawn is
15+20.5=35.5
i.e 35mins and 30 secs
time taken for the sis to mow the lawn is
20.5
i.e 20 mins and 30 secs
3.
ReplyDeleteA square could be a rectangle but a rectangle could never be a square.
OH LORDY WHERE DO I START...so many questions...*deep breath* here goes...
ReplyDeleteI totally agree with "cheez" for question 2.
ReplyDeleteSTEP1. Let a=b
STEP2. (*a then + a^2-2ab)
a*a + a^2 - 2ab = a*b + a^2 - 2ab
a^2 + a^2 -2ab = ab + a^2 - 2ab
2a^2- 2ab = a^2 - ab
STEP3. take out 2 as a common factor.
That is the error!!!
EXPLAINATION FOR QUESTION 2.
ReplyDeleteWhat you do to one side of the equation you must also do to the other. The number 2 in common only on the left side of the equation,but it is not common on the right side.
THEREFORE you cannot take out 2 as a common factor because it is not common with all the terms in the equation.
For question 3.
ReplyDeletePerimeter of a rectangle = x+x+y+y
therefore, P=2x+2y----(1)
When Perimeter of a square= x+x+x+x
P= 4x-----(2)
sub equation(1) into equation(2)
4x=2x+2y
4x-2x=2y
2x=2y
x=y
Therefore when x=y,the sides of the rectangle is a square.
Maybe i interpreted this question wronge, feel free to correct it...
For question 7.
ReplyDeleteLet the sister=x minutes
If the brother takes 15 minutes more, than the sister then the brother is x+15
Together they take 56 minutes
so togther they take
x+x+15=56
2x=56-15
2x=41
x=41/2
x=20.5 minutes
So the sister takes 20 mintes 30 seconds to mow the lawn while the brother takes-
sub x=20.5 into x+15
20.5+15=35.5
brother takes 35 minutes and 30 seconds to mow the lawn
for question 3
ReplyDeleteP= 2x + 2y -----(1)
A= 4x -----(2)
solve two sim.
2x + 2y+ 4x
2y= 2x
y=x
therefore when the two sides are equal the square will have the largest area.
2. Find the error in this proof. Prove: 5 = 7
ReplyDeleteLet a = b
Multiply both sides by a and add a^2 - 2ab to both sides:
2a^2 - 2ab = a^2 - ab
Take 2 as a common factor:
2(a^2 - ab) = a^2 - ab
Divide by a^2 - ab:
2 = 1
Multiply by 2:
4 = 2
Add 3 to both sides:
7 = 5
SINCE a=b
Dividing by a^2 - ab is like dividing by
a^2-a^2=0
it is not a valid since Division by zero is an operation for which you cannot find an answer
3. A rectangle with sides of lengths x and y has perimeter P. Prove that the largest area of this rectangle is given when the rectangle is a square.
ReplyDeleteP=2x+2y
for square 1 side = (2x+2y)/4
largest area = [(2x+2y)/4]*[(2x+2y)/4]
=(4x^2+4xy+4xy+4y^2)/16
=(2x^2+2xy+y^2)/4
7. A brother and a sister are mowing the lawn on their backyard. It takes the brother 15 minutes longer to mow the lawn than it takes his sister. Together they mow the lawn in 56 minutes. How long does it take each of them to mow the lawn?
ReplyDeletex+x+15=56
2x+15=56
2x=56-15
2x=41
x=41/2
it takes the sister 21mins 30sec
it takes the brother 36mins 30sec
7.
ReplyDeleteLOL
2x + 15 = 56
2x=56-15 = 41
x - 41/2 = 20.5
So the sister takes 20 mintes 30 seconds to mow the lawn while the brother takes-
sub x=20.5 into x+15
20.5+15=35.5
brother takes 35 minutes and 30 seconds to mow the lawn
8. and say that is equal to
ReplyDeletei dont understand ?
Question 3
ReplyDeleteP= 2x + 2y -----(1)
A= 4x -----(2)
solve two sim.
2x + 2y+ 4x
2y= 2x
y=x
therefore when the two sides are equal the square will have the largest area.
3.
ReplyDeleteA rectangle is a parallelogram with four right angles.
While the definition states "parallelogram", it is sufficient to say: "A quadrilateral is a rectangle if and only if it has four right angles.", since any quadrilateral with four right angles is a parallelogram.
question 7
ReplyDeletesister takes - x minutes
brother takes - x + 15 minutes
x + x + 15 = 56
2x + 15 - 15 = 56-15
2x = 41
2x/2 = 41/2
x = 20.5 minutes
sister takes - x minutes
= 20.5 minutes
brother takes - x + 15 minutes
= 20.5 + 15
= 35.5 minutes
it takes the sister 20.5 minutes and it takes the brother 35.5 minutes
P=2x+2y
ReplyDelete1 side = (2x+2y)/4
largest area = [(2x+2y)/4]*[(2x+2y)/4]
=(2x^2+2xy+y^2)/4
4. let X represent the faster pipe
ReplyDeletelet Y represent the slower pipe
X+Y = 11 1/9
(Y = X+5)
X + (X+5) = 11 1/9
2X +5 = 11 1/9
2X = 6 1/9
X= 3 1/18
therefore one pipe can fill the in 3 1/18 hours whereas the other fills the pool in 8 1/18 hours?
7.
ReplyDeleteLet the sister=x minutes
If the brother takes 15 minutes more, than the sister then the brother is x+15
Together they take 56 minutes
so togther they take
x+x+15=56
2x=56-15
2x=41
x=41/2
x=20.5 minutes
So the sister takes 20 mintes 30 seconds to mow the lawn while the brother takes-
sub x=20.5 into x+15
20.5+15=35.5
brother takes 35 minutes and 30 seconds to mow the lawn