You can put this solution on YOUR website!

Set B for the number of boys on the first day. Set G for the number of girls.
so (A for all), where (sixty percent).

Six girls move

and six boys come

And now the boys make up 75% of the class

Using and , plug in .6A for B:

Subtract .6A from both sides:

Now divide both sides by .15

So there were 40 kids in all on the first day. 60% of them were boys, so:

40-24=G

So on the first day of school, there were 24 boys and 16 girls.

You can put this solution on YOUR website!
If it's a square, all the sides are the same length. So the area of a square is the length times the height (or the length squared).

Area= 196 centimeters squared

You can put this solution on YOUR website!
-4, 14, 10, 24,....
Find the pattern.
-4+14=10
14+10=24
10+24=34
So the next number in the pattern is 34.

You can put this solution on YOUR website!

y-intercept is where x=0.



Y-intercept:

x-intercept is where y=0.




X-intercept:

You can put this solution on YOUR website!

M=my age
Y=your age

My age is now four times yours:

But five years ago it was five times yours:

Plug in 4Y for M:

Simplify both sides

So "your age" is 20. "My age" is 80.

If you check it, that works. Five years ago "you" would have been 15 and "my age" would have been 75. 15*5=75

You can put this solution on YOUR website!
area of a circle = pi*r^2=841
841/pi=r^2
267.6986=r^2
16.36=r
circumference of a circle=pi*2r
pi*32.72=102.79 cm

You can put this solution on YOUR website!
9000=total money
Money at 9%=x
Money at 8%=9000-x (because it's the rest)

increase interest=770. so 9000+770= 9770.
So set up the equation:
Because x+ 9% of x and (9000-x) + 8% of that equals 9770.
Simplify

Simplify again

Subtract 9720 from both sides.

Divide each side by .01

Therefore:
$5000 was invested at 9%, and $4000 was invested at 8%.

You can put this solution on YOUR website!
1 dime 3 nickels
1 dime 15 pennies
1 dime 1 nickel 10 pennies
1 dime 2 nickels 5 pennies
2 dimes 5 pennies
2 dimes 1 nickel
1 nickel 20 pennies
2 nickels 15 pennies
3 nickels 10 pennies
4 nickels 5 pennies
5 nickels
25 pennies

You can put this solution on YOUR website!

Set C as the total number of cows. Set G as the grazing cows, S as the sleeping cows, and D as the drinking cows. Set up the equation like so;

Total numbers of cows=all grazing, sleeping, and drinking cows.

Half the total cows are grazing:

Three fourths of the REMAINING cows are sleeping

9 cows are drinking from the pond


Plug all these answers into the original equation and get

Now simplify:

Combine all the C's on both sides:

Now multiply both sides by 8:

Answer: 72 cows
To check, plug in 72 for C.
There are 72 cows, if half of them are grazing, then 36 are grazing. If three-fourths of the rest (36 more) are sleeping, then 27 are sleeping, which leaves 9 drinking.

You can put this solution on YOUR website!

Think of it this way. Take it one at a time. For every one sandwich, there are two different soups you can have (disregard the drinks for now). That's two combinations, for three sandwiches, so three times two, which gives you six.

Now, for every one sandwich and one drink (six), there are four different drinks you can choose from. Six times four is 24.

In other words, multiply all the numbers together.

You can put this solution on YOUR website!
You got to okay. Then you would have to solve for y.
Take the cube root of both sides:

And now add 7 to both sides:

Flip it for sanity's sake:

Now change y to f(x) and voila!!
Answer:

You can put this solution on YOUR website!
Louis makes 30 dollars per yard mowed, so his profit from that is 30 times the number of yards or . Louis makes 20 dollars per lawn weeded, so his profit from that is 20 times the number of lawns or . Added all together he wants at least 150 dollars.
Solution:

You can put this solution on YOUR website!
14 legs. 2 per girl.

You can put this solution on YOUR website!
x---money invested at 3%
y---money invested at 6%

1x+1y=6000----------b/c she has 6000 to invest
1.03x+1.06y=6315-------------b/c of the percent of investment and the final amount of money

solve eq. 1 for x
x=6000-y

plug that in to the second eq.
1.03(6000-y)+1.06y=6315

Distribute
6180-1.03y+1.06y=6315

Combine like terms
.03y=135

Solve for y
y=4500

x=6000-y
x=6000-4500
x=1500

Check answers:
x+y=6000
1500+4500=6000-------true
1.03(1500)+1.06(4500)=6315-----true
-------------------------------------------
Answers:
money invested at 3%----$1500
money invested at 6%----$4500

You can put this solution on YOUR website!
y=mx+b

First find the slope (m) using the difference of the y's over the difference of the x's.




so the slope is 1
y=x+b

Plug in one of the points, it doesn't matter which one.
0=4+b

Solve for b
b=-4

Answer:
y=x-4

You can put this solution on YOUR website!
(a)age=14
(h)hieght=67"
Solve the formula for age(a). Estimate how old you will be when your air volume is 90% of its current volume.

(use current height)

solve the formula for a:
V=0.104h-0.018a-2.69
V+2.69=0.104h-0.018a
V+2.69-0.104h=-0.018a

----------------------------------------------
Solve for V so you can plug 90% of it in later...

V at a=14 and h=67:
V=0.104h-0.018a-2.69
V=0.104(67)-0.018(14)-2.69
V=4.026
----------------------------------------------

a for h=67 and .9V when V=4.026--------->90% of V
V=0.104h-0.018a-2.69
.9V=(0.104h-0.018a-2.69)
.9(4.026)=(0.104(67)-0.018a-2.69)
3.6234=6.968-.018a-2.69)
3.6234=4.278-.018a
-.6546=-.018a
36.4=a

You can put this solution on YOUR website!
.
(h,1)------------>this is in point form (x,y)

plug h in for x and 1 in for y:



Now simplify



Now subtract 4 from each side

You can put this solution on YOUR website!
Two-thirds of a number is less than eight. Find the largest integer that will satisfy the inequality.
A. 12
B. 11
C. 10
D. 13

First find: two-thirds of x is eight. Once you do that, the solution to: "Two-thirds of a number is less than eight" would be any number less than x.





"Two-thirds of a number is less than eight"---the number is less than x, which is 12, so it would anything 11 and under.

So the largest integer to satisfy that would be 11.

You can put this solution on YOUR website!
Can you tell me what the perimeter of a rectangular backyard is that is
6x + 6 yards. If the width is x yards, can you please find a bionomial that
represents the length. Thanks!

The perimeter is 2 times the width plus 2 times the length. If the width is x and the perimeter is 6x+6, than the expression that equals the length would be:



The expression above is derived from the following:





Now simplify the expression :

You can put this solution on YOUR website!
"Marlena is making her own bracelets. Each bracelet will have 10 beads. Write a function rule to describe the number of beads she will use. Find a reasonable domain and range for the fuction if Marlena makes up to 7 bracelets."

We'll have "x" be the number of bracelets and "y" be the number of beads.

"Marlena makes up to 7 bracelets": because of this statement, we know that x, the number of bracelets, may not go over 7.



Logically, Marlena cannot make a negative number of bracelets, so we also know that x has to be more than (or equal to) 0.



So our logical domain would be:

----------------------------------------------------
We know that each bracelet has ten beads, so the amount of beads used would be ten times the amount of bracelets, or ---in f(x) form, this is the function----> .

To get the logical range, all we have to do is use the logical domain, which we already have, and use the same inequality signs.

Plug in 7 and 0, our logical domain, for x to get the logical range, y.







So the logical range would be

--------------------------------------------
Domain:
Range:

You can put this solution on YOUR website!
200 more adult admission tickets...than children admission tickets:

a=c+200

adults=$11 each
children=$8 each
total receipts=at least $5000





System:
a=c+200


Use substitution


Distribute


Combine like terms


Subtract 2200 from both sides


Divide both sides by 19
--------this is rounded up from 147.3, since you can't sell .3 of a ticket.

a=c+200
a=148+200
a=348

----since c might be more than 148.

Answer:
148 childrens tickets
348 adults tickets

You can put this solution on YOUR website!
h=amount of hours
mph(h)=distance

the passenger train travels the same distance (set equal to each other) in 1.5 h less time than the freight train.



Simplify each side by multiplying


Eliminate the denominators, since they are the same thing


Subtract 60h from both sides


Divide both sides by -20


Passenger train: (h-1.5)
Freight train: (h)

Plug in 4.5 for h

4.5-1.5=3.0
---------------------------------------------------------
Answer:

Passenger train= 3 hours
Freight train= 4.5 hours

You can put this solution on YOUR website!
Admission to a park is x dollars per person for the first 3 people in a group and y dollars per person for each additional person.
write a formula for the total cost c when the number of people in a group p
is more than 3
------------------------------------------------------------------------------
3x would be the cost for the first three people.

ny would be the cost of the rest, for which n would be the number of people in the group minus three, because three people are already paid for.

There are p people in the group, so ny becomes (p-3)y.

Add those prices together to get the total price for one group.

You can put this solution on YOUR website!
Here is the simple conversion from inches to centimeters:
1 inch=2.54cm

Therefore,
1(x) inches=2.54(x) cm

Plug in your numbers
1(10) inches= 2.54(10) cm

Simplify
10 inches=25.4 cm

You can put this solution on YOUR website!
a=2 b=3 c=?

Pythagorean Theorem:







Functions:
sin=b/c
cos=a/c
tan=b/a

cse=c/b
sec=c/a
cot=a/b
-----------------------------------------------
I hope this helped!
-Alani

You can put this solution on YOUR website!
GE = y, EH = y-1, GH = 11

If this is a triangle: any two sides added together must exceed the measure of the third side (that's a property of triangles).

So:






If this is a line segment: the parts add up to the whole.

So:






I hope this helped!
-Alani

You can put this solution on YOUR website!


Common denominator=(x-1)(x+1)---because x^2-1 = (x-1)(x+1)



Add the numerators on the left side


If this is true, than 2x+1=x-1



Subtract x from both sides


Subtract 1 from both sides

----------------------------------------------
I hope this helped!
-Alani

You can put this solution on YOUR website!
f(x)=1/x^2-9

To find the domain, you would have to find [what x can be without making the denominator zero]. So set the denominator, x^2-9, equal to zero:

x^2-9=0

Now factor out the left side.

(x-3)(x+3)=0

Now take each expression separately and set them equal to zero and solve.

x-3=0
x=3

x+3=0
x=-3

So to make the denominator zero, x would have to be 3 or -3. So to get the domain, "what x can be without making the denominator zero", you would say anything but these two values. In other words:

x is not 3 or -3.

Do you follow?
I hope this helped!

-Alani

You can put this solution on YOUR website!
How many liters of a 70% acid solution are needed to be mixed with 18 liters of a 10% acid solution to get a mixture which is 25% alcohol?

Alcohol? Yes, he probably meant to say "acid". Let's work it out for acid.

How many liters of a 70% acid solution are needed to be mixed with 18 liters of a 10% acid solution to get a mixture which is 25% ACID?

(amount of liters)
coefficient=percent

70(x)+10(18)=25(x+18)

Distribute everything.
70x+180=25x+450

Subtract 25x from both sides
45x+180=450

Subtract 180 from both sides
45x=270

Divide both sides by 45
x=6

Answer: 6 liters
---------------------------------------------------
Now let's assume he actually meant alcohol. 25% alcohol means 75% acid. So:

(amount of liters)
coefficient=percent

70(x)+10(18)=75(x+18)

Do you follow?
25 is changed to 75 because it is 75% acid now.

Distribute, like before
70x+180=75x+1350

Subtract 75x from both sides
-5x+180=1350

Subtract 180 from both sides
-5x=1170

Divide by -5
x=-234

Negative means you would have to subtract, and logically speaking, you wouldn't take away acid to increase the percentage of acid. Therefore, the logical answer is:

6 liters
-------------------------------------------------------
I hope this helped!
-Alani

You can put this solution on YOUR website!
You would have to know the height of the building and the proximity of the fire to the building. Then to find the angle, you would have to do the inverse tangent function. You do that by taking your calculator and pushing the "2nd" button, then the "TAN" button. Then enter in the value or fraction for [(how far the fire is from the building)/(the height of the building)], in other words, the opposite over the adjacent of this angle. Close the parentheses and press "ENTER". The value you get is the measure of the angle.

I hope this helped!
-Alani

You can put this solution on YOUR website!
(z+3)/2 + 7/2

Add the numerators.
(z+3+7)/2

Combine like terms.
(z+10)/2