(2*10^4)x(4*10^5) is the exact same as
(2*4)*(10^4*10^5) due to the associative property
Obviously 2*4 = 8
When multiplying exponents you add them so...
10^4*10^5 = 10^(5+4) = 10^9
Your answer is then simply 8*10^9 and in the form your question is asking for
it will be 8 with 9...
Since the statement, "the length is twice its width" puts one dimension in terms of the other it's easiest to use "w" as the variable.
w = width
2w = length
The perimeter is the sum off all the sides of the rectangle
P = w + w + l + l = 2w...
Your question doesn't really explain which direction your are drawing the line through the ellipse. But, in general you know that the equation of an ellipse
centered at the origin is given by:
(x2/a2) + (y2/b2) = 1
a = radius on the x axis
b = radius on the y axis
x2 + 3x + 5
For equations of the form:
ax2 + bx + c
where a = 1 it will factor to
(x + c1)(x + c2)
If you multiply that out you'll end up with
x2 + c1x + c2x + c1*c2 = x2 + (c1 + c2)x + c1*c2
This means that
b = c1+c2...
Using properties of exponents remember that
(xn)m = x(m*n) and x-n = 1/xn
So using your equation we have:
(3x-3y-2)-2 = 3-2x(-3*-2)y(-2*-2) = (1/9)x6y4
Since everything is a singular product (it's all multiplied together) you can write it out like this:
x(y2/2)*(6x/x2) = x*y2*(1/2)*6*x*(1/x2)
Now group your like terms
6*1/2 = 3
x2/x2 = 1
y2 has no other terms so it simplifies to
From the subject headings you know that this is going to have to be converted into a quadratic equation of the form
ax2 + bx + c = 0
So, using the equation you provided, distribute x on the right side
x*(x+3) = x2 + 3x
and then collect all of your terms on one side...
Since both sides of the equation are three raised to some power, you can omit the base from the equation entirely.
3(2x-1) = 3(x+2)
2x - 1 = x + 2
This is because in order for the two sides to be equal, the exponents on both sides have to be equal as well...
(4*102)*(2*103) = (4*2)*(102*103)
When you multiply exponents they are added together so the problem becomes
8*10(2+3) = 8*105 = 800000
In fact, if you notice the other two numbers are powers of the base 2 so the problem can actually be thought of like this:
3x2 + 2x - 16 = 0
a = 3
b = 2
c = -16
x = [-b ± √(b2 - 4ac)]/2a
b2 - 4ac = 4 - (4*3*-16) = 196
x = (-2 ± √196)/6
x = (-2 + 14)/6 = 12/6 = 2
x = (-2 - 14)/6 = -16/6 = -8/3
Check your solutions by plugging them back in to the original...
Substitution means that you take one equation and put the variables in terms of each other, then you substitute that value in for the other variable in the remaining equation.
Since there are two equations in two variables you can substitute 4 total ways.
Using your equations:
3x - y...
For 4 perfect exam scores Sergio would have had 400 total points, as it was he ended up with 70% of those points or
0.7*400 = 280 points
By dropping a test grade Sergio reduced the number of possible points to 300 and his grade improved to 80%
0.8*300 = 240 points
This type of motion is described as projectile motion, ideally in one dimension meaning that the rocket is going straight up and straight down.
The equation for motion in one direction is given by
d = vit + (1/2)at2
where d is the displacement
vi = initial velocity
a = acceleration
3(x-2) + 5x = 10
The first step is to recognize that 3(x-2) = 3*x - 3*2 = 3x - 6
So putting that back in to the equation it's
3x - 6 + 5x = 10
Now add like "x" terms on the left side and add 6 to both sides
8x - 6 + 6 = 10 + 6
8x = 16
let n = the numerator
n+4 = the denominator
So your fraction is
The second step says that if they are both increased by 8 the result is 8/9, so you just add eight to both
n+8/(n+4+8) = 8/9
Now cross multiply both sides to get
Let x = number of dimes
y = number of quarters
Equation 1 is then x + y = 100, that one is easy.
Now you have to worry about values of each, and since a dime is $0.10 and a quarter is $0.25, that means that the number of each times their respective dollar amounts has to add...
If you notice the ratio 9:3:11 is the same as saying 9 out of every 23 (or 9/23) pieces of fruit are grapes, 3 out of every 23 (or 3/23) pieces of fruit are walnuts, and 11 out of every 23 (or 11/23) pieces of fruit are oranges,
because 9 grapes + 3 walnuts + 11 oranges =...
3r2 + 8r -3
a = 3
b = 8
c = -3
You use the product of a*c = -9
Now ask yourself what factors of -9 could add up to 8?
it's gonna be 9 and -1 so you write that out in place of 8r
3r2 + 9r - 1r -3
Now separate your common terms
3r(r + 3) -...
In essence, it accounts for the number of particles that can occur in "ideal" solutions. The typical definition is that it is the ratio of the actual concentration of particles in solution to the concentration of the solute as calculated by its mass.
So for non-ionic compounds in solution,...
Place the decimal after the first non-zero digit and then count the number of spaces to determine how much to raise ten by an exponent.
In your example:
You have 7 decimal places after the first number and you have to include up to the last non zero number after that.