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First, we want to get rid of the fractions in the equation.

We can do this by multiplying by the least common denominator, which is 45.
(x/9)*45+(2x/5)*45=3
5x+18x=3*45
Then, we can combine our x's and multiply the two numbers in the second half of the equation.
23x=135
Finally, we can divide both sides by 23 to isolate the variable.
x=5.869565217...
We can round this number to 5.87.
So, x is about 5.87.

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We have two equations and two variables, which means that we can probably solve this problem.
First, we will find y in terms of x. We will use the first equation to determine this.
4x+2y=2
We can subtract 4x from both sides:
2y=2-4x
And then divide both sides of the equation by two:
y=1-2x
Since we now have y in terms of x, we can substitute this into our second equation.
-3x-y=-3
-3x-(1-2x)=-3
Then, we can distribute the minus sign
-3x-1+2x=-3
-x-1=-3
Next, we can add 1 to both sides of the equation.
-x=-2
Finally, we divide both sides by negative one to isolate x.
x=2
Now that we have x's value, we can find y's value.
The first thing that we determined is:
y=1-2x
We can substitute in the value of x to this equation.
y=1-2x

y=1-4
y=-3
Therefore, we now have the values of both variables.
x=2
y=-3

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I'll assume aces are NOT considered face cards. There are Kings, Queens, and Jacks in each of the 4 suits, for a total of 3*4 = 12 face cards.
When trying to determine the probability that there will be at least one in some number of picks, it's easier to determine the probability of the opposite outcome, then subtract it from 1. In this case, let's determine the probability that we get 0 face cards after picking 5 cards, then subtract that probability from 1.
This is a problem of the sort called "sampling without replacement". There is a formula, but it's easier just to walk through the example.
So, what is P(choose no face card on first pick)? It's the number of available non-face cards divided by the number of available cards, or:

When it comes time to choose the second card, what is P(choose no face card on second pick)? It's still the number of available non-face cards divided by the number of available cards. But we know that the first pick must have been a non-face card, so that reduces both the number of remaining non-face cards and the total number of cards by one. So it's:

When it comes time to pick the third card, it's the same story, except the number of available non-face cards and total cards have been reduced by 2:

And so on for each pick until we reach a total of 5 picks. What do we do with each of these individual probabilities? They must ALL be true in order to have the right outcome. In other words you must pick no face card the first time AND no face card the second time AND no face card the third time, etc. That means we can simply multiply those probabilities together.
So, the probability is:

Or,
or

So, this answer is the probability that you will get 0 face cards in five picks. Remember, we need to subtract the probability of this outcome from 1 to get the desired answer (at least one face card in a total of five picks):
or

This is the answer as a non-reduced fraction. If an exact answer is desired, you can reduce this fraction. Otherwise, we'll convert it to decimal by doing the division and we come up with 0.7468...
So, in decimal, the probability is 74.68...% (or about 75%) that at least one card out of five picks will be a face card.

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x = -3 is a vertical line, because x has the same value regardless of the value of y.
The perpendicular of a vertical line is a horizontal line, one which has the same value of y regardless of the value of x. We can choose any constant for the value. So, choosing one at random to provide an answer:
y = 2

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Let's put both line equations into slope-intercept form:
y = mx + b, where m is the slope of the line.

The first equation is already in the right form:
y = 3x + 7, so it has a slope of 3.
The second equation is:
x + 2y = -10, subtracting x from both sides:
x + 2y - x = -10 - x
2y = -10 - x or
2y = -x - 10
And dividing each side by 2 to isolate y:
, distributing the division:
, or
y = - (1/2)*x - 5
so the slope of the second line is -1/2
So the answer to the first question is that the lines are not parallel, since the slopes are not identical.
Lines are perpendicular if the slopes are negative reciprocals of each other. The negative reciprocal of the first slope (3) is , but the slope of the second line is , so the answer to the second question is that the lines are not perpendicular.
The last question is whether the lines intersect. Since the lines are not parallel (see question 1), they must intersect somewhere (the question doesn't ask us to find where).

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The sum of Weng's age and Yayo's age is 20 yrs. In one year, Weng's age will be nine times Yayo's age one yr. ago. Find their present ages.
First, we'll assign variables to both ages.
let W=Weng's age
let Y=Yato's age

Then, we'll come up with two equations to solve our two variables.
The sum of Weng's age and Yayo's age is 20 yrs. So, we have our first equation:
W + Y = 20
Solving this equation for W (it could be Y but we chose one at random):
W = 20 - Y
We have two variables, so we need another equation. We also know that in one year,
Weng's age will be nine times Yayo's age one yr. ago. In one year, Weng's age will be
W + 1. One year ago, Yato's age was Y - 1. We also know that the the first expression
is nine times the second, so:
W + 1 = 9(Y - 1) or
W + 1 = 9Y - 9
Substituting our value of W in from the first equation:
(20 - Y) + 1 = 9Y - 9
20 - Y + 1 = 9Y - 9
21 - Y = 9Y - 9

Adding 9 to both sides:
21 + 9 - Y = 9Y - 9 + 9
30 - Y = 9Y
Now adding Y to both sides:
30 - Y + Y = 9Y + Y
30 = 10Y
3 = Y
And substituting the value of Y into our first equation,
W = 20 - Y
W = 20 - 3
W = 17

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Let
f = amount of 50% solution used
t = amount of 20% solution used.
The problem states that we want a total of 12 liters of solution, so:
f + t = 12
We solve for f (we could solve for t, but we picked one at random):
f = 12 - t

We can also form an equation based on the anount of acid in each term.
The amount of acid contributed by f and the amount of acid contributed
by t added together need to add up to the amount of acid in the final solution.
To do this, we convert each percentage to the equivalent decimal factor
(50% = .5; 20% = .2; 30% = .3)
So, in equation form:
.5f + .2t = (.3)*12
.5f + .2t = 3.6
Let's multiply the entire equation by 10 just so we can use whole numbers:
5f + 2t = 36
Now we substitute the value of f from the first equation into the second equation:
5(12 - t) + 2t = 36
60 - 5t + 2t = 36
60 - 3t = 36
Subtract 60 from both sides to isolate the term with a variable:
60 - 3t - 60 = 36 - 60
-3t = -24
Divide both sides by -3 to solve for t:

t = 8
And since f = 12 - t, we can solve for f:
f = 12 - 8
f = 4

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is the same as :

since subtracting a negative number is the same as adding the positive.
So, the answer is 8.

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First, we'll plug the value of y into the first equation.
8x-2y=-100
8x-2(3x+36)=-100
8x-6x-72=-100
Then, we'll combine both x's
2x-72=-100
Next, we subtract 72 from both sides of the equation.
2x=-28
x=-14
Then, we can find the value of y, by substituting x into the second equation.
3x+36=y
3(-14)+36=y
Then, we just do the math.
-42+36=y
-6=y
Finally, we can check the answer.
8x-2y=-100
I'll plug in the values for x and y.
=-100
-112-(-12)=-100
-112+12=-100
-100=-100
Since negative 100 is equal to negative 100, the values of x and y are true.

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A percentage can be written as a decimal. 73.5% is the same as 0.735. The percentage of a number is found by multiplying the number and its percentage. We will assign a variable to the number we are looking for which is being multiplied by 0.735.
let n equal the number that 22 is 73.5% of.
To find 'n,' just make an equation for it.
0.735n=22
Simply divide both sides by 0.735 to isolate the variable.
0.735n=22
n=29.93197279...
n is around 29.93

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This is already simplified as far as it can be. x cannot be solved for because there is no inequality or equals sign in the equation.

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First of all, w divided by w has to be 1, because any number divided by itself is one.

Now, we have two terms which say 1 and negative 1.
These, obviously, cancel each other out.

This is as far as it can be simplified.

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First, we have to put this into an inequality equation.
"Five more than" means "5+"
"Twice an number" means "2n," because we will use n as our variable.
"Is at least 60" means
When you combine these fragments, you get:

To solve this, first subtract 5 from both sides.

Then, isolate the variable by dividing by two.

This, as a decimal, is 27.5.

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You cannot solve for y, because there is no equation. However, you can simplify the statement you have given.
All that needs to be done is to distribute the 2 over the parentheses.
2(5y-3)

10y-6
This is as far as it can be simplified.

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Realize that y is a variable, meaning that any number can take its place. A good way to check if an answer is correct is by plugging in a random number to see if you get the same result. In 4y-4y, if you plug in 1, you get:



It is the same with any number. 4y and 4y are the same number no matter what you substitute in for y. Any number minus itself is always zero. Therefore, 4y-4y has to be 0.

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The equation for circumference is:

The equation for area is:

First, we'll find the circumference.
The 'r' in the equation stands for radius. The radius of a circle is half of its diameter, so the circle's radius is half of 6--3 inches.
So, we can substitute 3 in for 'r' and 3.14 in for


Then, we can simply multiply.


Therefore, the circumference of the circle is 18.84
Next, we'll find the circle's area.
Again, we can substitute 3 in for 'r' and 3.14 in for


The, we'll square three and multiply.



Therefore, the circumference is 18.84 and the area is 28.26.

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The equation for slope-intercept form is:
y=mx+b
First, we need to find the slope for the original line.
We'll put the line into y=mx+b form:
-2x-7y=-14
-7y=2x-14
y=x+2
Now, we have the slope of the original line. To find the perpendicular slope, we just find the negative reciprocal--
The new line has a slope, but no y intercept.
We'll plug in the values of x and y that have been supplied to find our 'b'.
y=mx+b


17=b
Therefore, b is 17
Finally, we know the perpendicular line's slope and y intercept. Therefore, we can make a slope intercept equation for the perpendicular line.
y=mx+b
y=x+17

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First, we can substitute the value of y into the first equation.
2x+2y=10
2x+2(x+1)=10
Then, we distribute the two in the equation's first half.
2x+2(x+1)=10
2x+2x+2=10
Then, we combine the two "2x"s
4x+2=10
Next, we subtract 2 from both sides.
4x+2=10
4x+2-2=10-2
4x=8
Finally, we divide both sides by four to isolate the variable.
4x=8

x=2
To check:
y=x+1
y=4+1
y=5
2x+2y=10
=10
4+6=10
10=10
This is correct, so x is equal to 2.

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To make this simpler, I'll just multiply all the terms by 12. 12 is the least common denominator between the two fractions, and making all numbers whole makes solving equations far easier.
12a-8=24a+20
Then, we can add 8 to both sides of the equation to combine it with the 20.
12a-8+8=24a+20+8
12a=24a+28
Next, we can subtract 24a from both sides of the equation.
12a-24a=24a+28-24a
-12a=28
Finally, we can divide both sides by negative 12 to isolate the variable.

a=-2 1/3
If we plug this solution into the equation, we get:
36=36
This is true, therefore our answer is right.
'a' equals negative 2 and one third.

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Solved by pluggable solver: SOLVE linear system by SUBSTITUTION

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Money_Word_Problems/386953: 6 % OF WHAT NUMBER IS 36? 1 solutions Answer 273487 by gwendolyn(128)   on 2010-12-16 05:36:28 (Show Source): You can put this solution on YOUR website! First, remember that a percent can be written as a decimal. 6% is equal to 0.06. The number we are trying to find needs a variable. We'll assign it the variable 'n': Let n= the number that 36 is 6% of. We are looking for 6 percent of n, which equals 36. This can be put into an equation: 0.06n=36 Now, we can divide both sides by 0.06. n=600 So, 6% of 600 is 36.

Inequalities/386159: hi, i need help understanding solving inequalities, like i literaly have no clue what i am doing like 5(x-10)>6(x-1) i am homeschooled and these book are just not helping me get the point on how to do it. i have gotten down to 5x-10>6x-1, now i am stumped. 1 solutions Answer 273486 by gwendolyn(128)   on 2010-12-16 05:25:28 (Show Source): You can put this solution on YOUR website! Your first step was close, but not quite right. You did the first half of the equation correctly, but you didn't distribute the 6 to the x AND the 1. When you distributed, you should have gotten: 5x-10>6x-6 The next step is to add ten to both sides. 5x-10+10>6x-6+10 5x>6x+4 Now, we want to get our variable on one side of the equation. -1x>4 The final step is to divide both sides by negative one to isolate the variable. However, since the number being divided is negative, you have to flip the inequality. (Whenever dividing or multiplying by a negative number, we flip the inequality.) x<-4 Therefore, x is less than negative four.

Triangles/386032: What type of triangle is one with 80 degrees, 73 degrees, and 27 degrees? Obtuse, accute, or oblique? 1 solutions Answer 273370 by gwendolyn(128)   on 2010-12-15 19:33:18 (Show Source): You can put this solution on YOUR website! The triangle is both acute and oblique. Obtuse triangles have an angle that is greater than 90 degrees, which the triangle described does not. Acute triangles have all their angles under 90 degrees, which our triangle does. Oblique triangles are all triangles that do not have a 90 degree angle. Since our triangle does not have a 90 degree angle, it is oblique.

test/386035: Write the formula for simple interest, explaining what the variables represent. 1 solutions Answer 273365 by gwendolyn(128)   on 2010-12-15 19:28:16 (Show Source): You can put this solution on YOUR website! I=PRT I is the simple interest P is the principle, or starting amount invested R is the rate, or the percentage of the original money gotten per unit of time (eg. .05% per year) T is the amount of time that money is invested

Age_Word_Problems/386758: Mona's age is 4 times Bailey's age. The sum of their ages is 15. Find the age of each. 1 solutions Answer 273359 by gwendolyn(128)   on 2010-12-15 19:21:03 (Show Source): You can put this solution on YOUR website! First, we'll assign variables to both ages. let M=Mona's age let B=Bailey's age Then, we'll come up with two equations to solve our two variables. Mona's age is 4 times Bailey's age. This can be shown algebraically as below: M=4B We also know that Mona's age plus Bailey's age is 15. This, in an algebraic statement, can be written as below: M+B=15 We can substitute the value of M in terms of B from the first equation into the second equation: 4B+B=15 5B=15 Then, we can divide both sides of the w equation by 5: B=3 Therefore, Bailey is 3 years old. We also want to know Mona's age, so we can simply plug in Bailey's age to either equation and find it. M+B=15 M+3=15 M=12 Therefore, Mona is 12 and Bailey is 3.

Signed-numbers/386749: need help in solving order of operations problem. I'm just not getting this! s x 4 + 300 ÷ (10 - 20) = 14 Solution (s = 11) 1 solutions Answer 273350 by gwendolyn(128)   on 2010-12-15 19:10:15 (Show Source): You can put this solution on YOUR website! The way to solve Order of Operations is by using PEMDAS: Parenthesis Exponents Multiplication Division Addition Subtraction . First, we'll solve the parentheses: 4s+300÷(10-20)=14 4s+300÷(-10)=14 There are no exponents, and no multiplication that can done right now. So, we'll divide 300 and negative 10. 4s+300÷(-10)=14 4s+(-30)=14 4s-30=14 Then, we can add 30 to both sides. 4s-30=14 4s=44 Now that the equation is simplified, we can divide both sides by 4. 4s=44 s=11 Since you stated that s was equal to 11, we know that this answer is correct.

Age_Word_Problems/386638: If Jen's current age is 32 and Devin's current age is 6. Write an equation which models how old, in years, Jen will be when she is 3 times as old as Devin. 1 solutions Answer 273308 by gwendolyn(128)   on 2010-12-15 15:33:13 (Show Source): You can put this solution on YOUR website! First, we'll assign Jen and Devin's ages variables. let J=Jen's age let D=Devin's age Next, we'll write the equations for Jen's and Devin's ages. J=32 D=6 We need to know how many years it will be until Jen's age is three times Devin's. We'll assign a variable to this amount of time. let x=the number of years until Jen's age is 3 times Devin's Then, we can write the equation that will satisfy the question. Jen's age will be 3 times that of Devin's in x years, so: (J+x)=3(D+x) After that, we can substitute in the values of J and D: 32+x=3(6+x) Following this, we distribute the 3 over the parentheses 32+x=18+3x We could use this as the equation, but I will solve it just in case you need me to. To solve the equation, we subtract 18 from both sides: 14+x=3x And then we subtract x from both sides: 14=2x Finally, we divide both sides by two to isolate the variable. 7=x x=7 Therefore, in seven years, Jen's age will be triple Devin's.

Length-and-distance/386624: how many square yards of fabric are needed to make a triangle team banner base is 6ft and whose height is 6ft 1 solutions Answer 273305 by gwendolyn(128)   on 2010-12-15 15:16:35 (Show Source): You can put this solution on YOUR website! This question is very simple if you know what formula to use. Because you are making a banner and need a certain amount of fabric, you are trying to find the area of the triangle that will act as the banner. The formula to find the area of a triangle is below: let A=the area of the triangle let h=the hight of the triangle let b=the base of the triangle A= This formula works because a triangle is always half of a rectangle, and the formula for a rectangle is: Now, we can easily plug in the length of the height and base to find the triangle's area. A= A= A= A= The area is , but we need to know the area in square yards. There are 3 feet per yard, so there are 9 square feet per square yard. Therefore, if you divide our answer in square feet by 9, you will get our answer in square yards. 18 divided by 9 is 2. There are 2 square yards of fabric needed.

Age_Word_Problems/386382: julio is 4 times as old as maria his sister. in 6 years he will only be twice as old. how old is julio and maria now 1 solutions Answer 273199 by gwendolyn(128)   on 2010-12-15 07:09:19 (Show Source): You can put this solution on YOUR website! We want to determine the ages of Julio and Maria, so we will assign them both variables: let j= Julio's age let m= Maria's age Now, we can use these variables in equations. The problem states that Julio is four 4 times as old as Maria. This means that Julio's age is four multiplied by Maria's age. This can be set up as the equation below: j=4m We have two variables, so we need another equation. We also know that in six years, Julio's age will be twice (two times) Maria's age. The way to write this is a little bit more complicated. First, we have to remember that this equation is from "in 6 years." Because of this, we need to add 6 to each age. [(j+6); (m+6)] Since Julio's age six years from now will be twice Maria's age 6 years from now, we can write the equation as below: j+6=(m+6)*2 Since we already know j's value in terms of m (from above, j = 4m), we can substitute 4m for the j in our second equation: 4m + 6 = (m + 6)*2 Both halves of the equation can be simplified. First, we'll distribute the two in the second half of the equation: 4m + 6 = 2m + 2*6 Then we can multiply the 6 and 2 in the second half: 4m + 6 = 2m + 12 After that, we can subtract 6 from each side: 4m + 6 -6 = 2m + 12 - 6 4m = 2m + 6 Now, we can subtract 2m from both sides. 4m - 2m = 2m + 6 -2m 2m = 6 And divide each side by 2: m =3 Therefore, Maria is 3 years old. We also need to determine Julio's age. We know Julio is 4 times Maria's age so we can plug Maria's age into that equation: j=4m j = 4*3 j = 12 So, Julio is 12 years old and Maria is 3 years old.

Angles/386358: how can i tell what type of angles i am looking at? 1 solutions Answer 273198 by gwendolyn(128)   on 2010-12-15 06:09:13 (Show Source): You can put this solution on YOUR website! I'll take it that you mean acute, right, obtuse, or strait by "type." If an angle is acute, it is less than 90 degrees. If an angle is right, it is exactly 90 degrees. Often times, a right angle will have a small square in the corner to show that it is right. If an angle is obtuse, it is greater than 90 degrees. If an angle is straight, it is 180 degrees and is therefore a straight line.

Triangles/386410: How can you find the other 2 side lengths if you only have 1? 1 solutions Answer 273197 by gwendolyn(128)   on 2010-12-15 06:01:41 (Show Source): You can put this solution on YOUR website! If you only know the length of one side of a triangle, you need to know two of the angles to determine the length of the other sides.