You can add/subtract a multiple of one equation to/from another. This will let you eliminate a variable.
(1) x + 4y = 8
(2) 5x + 6y = 12
For this problem, we can multiply the first equation by 5:
(1) 5*(x+4y) = 5 * 8
(1) 5x + 20y = 40
Now both equations...
Look at the atomic number of the element copper (Cu). That is the number of protons in the nucleus (as well as the number of electrons). Copper is 29.
The elementary charge per proton (or electron) is 1.602x10^-19 coulomb. This is a positive charge for protons and negative for electrons...
It looks like two brothers each have an account. One is adding money monthly and the other is making withdrawals. If that is the case, you left an "m" out of the equation. Also, is the starting value of one account really a negative number?
First I'll assume that my scenario is correct,...
To answer the question you asked, the equation is
If you want to know what x is:
5.5x = 57-32 =25
x = 25/5.5
x = 4.5454...
Yes, the function is linear. How can you tell? It's because the term with x in it is just x. If it had a term with x2 or x3, it would curve instead of being a straight line (linear).
The equation is actually already in slope intercept form!
Besides the unknown...
Average speed is just the total distance traveled divided by the total time.
You already have the total time. It's 100 + 100 = 200 seconds.
Calculate the two distances, add them together, then divide by 200:
D1 = 100 * 5 = 500 m
D2 = 100 * 1 = 100 m
Another way to get the answer is to put the equation in slope-intercept form: y = mx + b
2y = -3x + 9
y = (-3/2)x + 9/2
The slope (-3/2) tells you how much y changes for each unit change in x.
If x increases 2 units, y changes by mx = (-3/2)...
Don't let the minus sign confuse you.
Just multiply both sides of the equation by -9:
I'll include extra parentheses for more clarity.
a / (-9) = 2
(a) * (-9) / (-9) = 2 * (-9)
a * 1 = -18
a = -18
Mathematically, the answer is definitely "yes"!
A line with positive slope rises from left to right, negative slope falls from left to right.
When they intersect the x-axis and you measure the angle of the intercept from left to right, two lines with the same magnitude slope...
Simple interest uses the formula:
I = prt
where p = the initial principal,
r = the interest rate per unit time
t = time in the units used to express the interest rate.
Your time unit is "year", and the interest rate is annual interest (per year).
Expand the right side using the distributive rule:
12=4b - 4*2
12=4b - 8
Add 8 to both sides:
12+8 = 4b - 8 + 8
20 = 4b
Divide both sides by 4:
20/4 = 4b / 4
5 = b
All you need to know is the distributive rule of multiplication:
I can't be sure what form the answer is expected to have.
You could divide the numerator and denominator by -4x2:
-20x6 - 24x4 - 12x2 5x4 + 6x2 + 3
----------------------- = ---------------
Or you could do this:
This question is testing your understanding of what a natural logarithm is.
There is a special number called "e". There is some power that you could raise e to that will give you the result of 5. As a formula, that would look like this:
ex = 5.
That x is defined as the natural logarithm...
The difference between a scalar and a vector is that one is just a number, while the other represents a number pointed in some direction.
Speed is a scalar. It's just a magnitude and doesn't specify any direction.
Velocity is a vector. Its magnitude is the speed and its direction is northwest...
The trick with word problems is to pick them apart to see what you know, then build equations that you can solve. It takes some practice.
In this problem, we know that one train starts two hours before the other one and travels at a known rate. Let's calculate how far it goes in those two hours:
The formula as written has all of the correct symbols, but it's missing some important stuff.
M = Pr(1+r)^t / [(1+r)^t - 1] looks like the equation you are using.
First, are you sure that the MONTHLY interest rate is 0.05? That's 60% annual interest!
Try r = 0.05 / 12 to convert a 5%...
For your introduction to this type of problem you should solve it this way so you understand how it works:
Since you started with $650 and it went up by 17%, you can calculate what 17% of $650 is, then add that to the starting amount.
17% is the same as 0.17, so 17% of $650 is:
If you're still wondering how to come up with
11.76% = 0.1176
Divide it by 1. You don't need to write this step down. It just shows you how it works.
0.1176 = 0.1176
Multiply both the numerator and denominator by 10 until both numbers...
Equation of a line: y = mx + b
m = slope ("gradient")
b = y-intercept
You know a pair of values for x and y, so plug them and the slope into the equation and solve for b:
Point (x, y) = (-3, 3)
m = 3
y = mx + b
3 = (3)(-3) + b y=3, m=3, x=-3
3 = -9 + b
ax2 + bx + c
When the first coefficient is not 1, it's easiest to use what's called AC factoring.
1. Multiply a by c. ac = (6 * 2) = 12
2. Find two factors of ac that add up to b.
You'll have to pay attention to the signs. If ac is positive, both factors will have the same...