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what is 15y3+6y2+3y divided 3y when you simplify

Because the bottom is a monomial we can separate the terms like this:

Divide and you get:

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What is 14% as a ratio?
We can write %'s as fractions by putting 100 under them.

Reduce the top and bottom by 2

Sometimes, they prefer to to write them this way: 7:50
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Combine like terms


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solve this problem (+7)-(-3)+(+16)-(+8)
To me...all the extra parentheses confuse things...but some people like them...I remove them. + keeps the sign in the parenthesis the same - makes it opposite.





I took more steps than necessary to show you...I just combined the 2 numbers on the left as I went down.
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Find the LCD and then find equivalent fractions to the fractions.
,
First find the factors of the denominators:


They have a 7 and an a in common so don't count them twice.
LCD=
Notice that we took the highest power of the things they had in common.
What ever you have to multiply the denominators by to get the LCD, you have to multiply by the numerators as well.
,
,
Happy Calculating!!!

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-6x+y=-4 find the slope and y-intercept
The slope intercept form of a line is:
y=mx+b where m = slope and (0,b) = y-intercept
So...solve the equations for y:

add 6x to both sides of the equation.


The 6 is in the m spot...it is the slope.
The -4 is in the b spot...it is the y coordinate of the y-intercept. (0,-4)
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Find slope : (1,-4) , (6, -2)
When you have two points (x1,y1), (x2,y2)
The formula for slope (We call it m) is:




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Draw a right triangle. One of the legs measures 8cm. The other leg measures 6cm. What is the length of the hypotenuse?
I can't really draw a right triangle for you here, but the Pythagorean Theorem helps us to find the hypotenuse: (leg)^2+(other leg)^2=(hypotenuse)^2
Usually, we use a and b for the legs and c for the hypotenuse.






The hypotenuse is 10 cm.
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Find a positive value of C so that the following trinomial is factorable.
x^2-7x+c
In order to be able to factor this...we need to split the -7 into two numbers that will add back together and get -7. Because c has to be positive, and we need to be able to multiply those same two numbers back together to get it, both numbers have to be negative. There are several possibilities:
(-1)(-6)=
(-2)(-5)=
(-3)(-4)=
Any of them will work:



I hope that cleared things up.

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verify that the equations are identitites:
sinx + tanx = tanx (1+cosx)
There is a trig identity you have to know to prove this.

The rule of thumb is to try to use identities and properties in math to make the more complicated side look like the less complicated side....so attack the right side of the equation.
use the identity to replace tan(x)

Distribute

The cos(x) cancels

Then use the identity again only we are replacing sin(x)/cos(x).

Addition is commutative, so...

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Graph line with given point and slope.the line through (2,1)with slope 5/3.
please let me know to graph this?

You need two points to graph a line. The first point is (2,1)


We can get the second point if we know that slope = rise/run. It is helpful to let your rise be either positive or negative...and always run to the right.


Our y's are up and down...our rise...so if you add 5 to 1, you get 6.


Our x's are left and right...our run...so if you add 3 to 2, you get 5.


so our second point is (5,6)


connect the points but keep going to the end of the graph.


Hope that was clear. Happy calculating!!!

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Yes.
Integers are like whole numbers, but they also include negative numbers ... but still no fractions allowed!
So, integers can be negative {-1, -2,-3, -4, -5, … }, positive {1, 2, 3, 4, 5, … }, or zero {0}
We can put that all together like this:
Integers = { ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }

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The larger of two numbers is 9 more than the smaller. Their sum is 95.

If we called the smaller number n, then the larger would be n+9


larger + smaller = 95







The smaller number is n=
The larger number is n+9 or 43+9=
****************************************************
Sanity check...do the two numbers really add to 95?
43+52 does equal 95, so we are not completely crazy :)

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Solve for x by completing the square

First get the x's together and the constant on the other side.

Then divide the whole equation by any coefficient in front of the x^2...in this case, 2.


At this point, if we call the coefficient of x, b....then we would add (b/2)^2 to both sides.
->

Factor the left and simplify the right. Perfect squares always factor to be the sqrt or the front and back with the sign that is in front of the x term between them...like this.

Take the square root of both sides...don't forget it is always + or -.
=+ or -
If you are only allowed to use "real" solutions...you are done...there is no "real" solution. However, if you are using imaginary or complex numbers...keep going as follows:
x-1= + or -3i
x=1 + or -3i
This is two answers:
or
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log to the base "x" (64) = 3
logb(a)=m can be rewritten as

At this point you can either take the cubed root of both sides of the equation, or raise both sides of the equation to the 1/3 power...it's easiest to type this way...but either is valid.



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f(x)= ; g(x)=
solve:
(f+g)(x)=
(f+g)(x)=
(f+g)(x)=
(f+g)(x)=
***********************************
Explanation....first you simplify the radicals. You can only add and subtract like terms. Radicals are only like terms when the indexes and roots are exactly the same.
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How do i do |3x-1|+10=12 ?
First isolate the absolute value.
|3x-1|+10-10=12-10
|3x-1|=2
Then because the stuff inside of the absolute value can be + or - 2 to get 2, you set the inside equal to them both and solve 2 equations.
or
or
or
or
or
*****************************************************
It seems not to make sense to do that...but let's check to see that both answers are correct:
for x=-1/3
|3(-1/3)-1|+10=12
|-1-1|+10=12
|-2|+10=12
12=12 True....so x=-1/3 for sure.
for x=1
|3(1)-1|+10=12
|3-1|+10=12
|2|+10=12
2+10=12
12=12 True....so x also can = 1
Often teaches want set notation of x={-1/3,1}
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Simplest form of radical expression. Please explain
3 square root 24 - 2 square root 54 + 2 square root 18

You can either look for perfect squares, and take the square root of that part...or use any prime factors that you two of.





The only ones you can add and subtract are the like terms. They have to have the same indexes and roots in order to add them.



Hope that was clear...wish I could point and talk to explain. lol

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"what is the square root of z to the 20th?"
Squares and square roots cancel each other.



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Can you solve these two questions?

log10 (1/100) and
log5 5/5
I am not sure I am reading this the way you intend...but if I am....
so...




***************************************************************




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what value should be added to each side to complete the square of:
x^2+20x=-8
When you have a binomial in this form:

There is a formula that tells you what will complete the square:
For us...b=20



************************************************************************


Some find it easier to visualize the end...guessing what it has to be to make a perfect square...that falls apart for most when fractions and decimals are introduced.
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Find the product of (4+5i) and (4-5i) What are pairs of complex numbers like these called?
These are called "conjugates" of each other because they are the same binomials with opposite signs in the middle.
You need to know that then you can foil as always...but conjugates always multiply to be the difference of squares...so it is not necessary...but it works every time.




The above is the difference of squares that you can skip to for conjugates.



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qual é o resultado da
-5x-2(-3x-4)=-5x-2
First simplify both sides of the equation using the orders of operation.
En primer lugar simplificar ambos lados de la ecuación utilizando las órdenes de operación.


Then move the variables to one side and the constants to the other by adding their inverses to both sides of the equation.
Luego mover las variables a un lado y las constantes a la otra mediante la adición de sus inversos a ambos lados de la ecuación.




Last divide by the number being multiplied by the variable.
Última divide por el número que se multiplica por la variable.


¡Buena suerte!

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The numerator of a fraction is 4 less than its denominator. If you add 1 to both the numerator and the denominator, the resulting fraction is equal to 2/3. What is the original fraction?

Let the denominator = x


Then the numerator is 4 less than that: x-4


If you add 1 to the denominator you have: x+1


If you add one to the numerator you have: x-4+1 or x-3

So your algebraic equation is:

Cross Multiply:






Your denominator is x=11
Your numerator is: x-4=11-4=7
The original fraction is:

Do a sanity check...if you add 1 to the numerator and denominator, does it indeed reduce to 2/3's?

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Vertical angles are equal to each other....so the angle opposite of the 36 degree angle is also 36 degrees.
Adjacent angles form a straight line of 180 degree...so the angle next to the 36 degree angle is 180-36 = 144 degrees
The angle opposite of the 144 degree angle is also 144 degrees.
So the four angles are: 36, 144, 36, 144 degrees.
Happy Calculating. :)

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-7v+5_>-79
-7v+5-5_>-79-5
-7v_>-84
Reverse the inequality symbol when you multiply or divide both sides of an inequality by a negative number.
_<
v_<12
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Alexander and Judy are 31 miles apart on a calm lake paddling toward each other.
Alexander paddles at 5 miles per hour, while Judy paddles at 8 miles per hour. How long will it take them to meet?
Assuming that they left at the same time: Distance = rate*time
Let t = time in hours
Alexander's distance: 5t
Judy's distance: 8t
total distance: 31



t= 2.3846 hours
or
t= 2hrs+60(.3846)mins
t=2hrs and 23 mins
Barring any fatal careless errors, that should be it.
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You can cross multiply when you have a fraction equal to another, however multiplying both sides by the LCD works every time for rational equations.
The LCD is (x+5)(x+2)

The denominators cancel:

Foil and solve:









*Note* Always check and make sure that your answer does not make any denominator 0...that makes fractions undefined. If you had gotten -5 or -2, then there would be no solution.
Happy Calculating.

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Two ants are at a common point at time t=0, the first ant starts crawling along a straight line at the rate of 4 ft/min. Two minutes later, the second ant starts crawling in a direction perpendicular to that of the first, at a rate of 5 ft/min. How fast is the distance between them changing when the first insect has traveled 12 feet?

Let r be the distance between them, x be the distance of the first and y be the distance of the second. Then according to the Pythagorean theorem:


Taking the derivative of the equation with respect to time yields:

Everything is divisible by 2 so divide the whole thing by 2 to make things easier.

Now use a little algebra to find the missing components.
Given:
the rate of the first ant
the rate of the second ant
the distance the first ant traveled.

distance = rate*time

We get t from the first ant.



Therefore the second ant traveled.




We use the Pythagorean Theorem to find r







Take all the parts and put them into the equation you took the derivative of.





ft/min
That should be it barring any careless mistakes. Happy Calculating!

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Use your unit circle or 45,45,90 and 30,60,90 triangles to evaluate:

Simplify:

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Find the squares within the square roots:

Square roots cancel squares: