Hi there!
You can use distributive property to solve this equation.
These are the list of terms you have to multiply :
a × a² = a³
a × -ab = -a²b
a × b² = ab²
b × a² = a²b
b × -ab = -ab²
b × b² = b³
add all of those terms...
a³ - a²b + ab² +a²b -ab² + b³
simplify by adding like terms... (- a²b + a²b , ab² - ab²)
a³ + b³
Hope this helped!! :)
Answer:
B (5, 13)
Step-by-step explanation:
9x + 4y = 97
9x + 6y = 123
To solve by elimination, we want to <em>eliminate</em> a variable. To do this, we must make one variable cancel out.
First, we can see that both equations have 9x. To cancel out x, we must make <em>one</em> of the 9x's <em>negative</em>. To do this, multiply <em>each term</em> in the equation by -1.
-1(9x + 6y = 123)
-9x - 6y = -123
This is one of your equations. Set it up with your other given equation.
9x + 4y = 97
-9x - 6y = -123
Imagine this is one equation. Since every term is negative, you will be subtracting each term.
9x + 4y = 97
-9x - 6y = -123
___________
0x -2y = -26
-2y = -26
To isolate y further, divide both sides by -2.
y = 13
Now, to find x, plug y back into one of the original equations.
9x + 4(13) = 97
Multiply.
9x + 52 = 97
Subtract.
9x = 45
Divide.
x = 5
Check your answer by plugging both variables into the equation you have not used yet.
-9(5) - 6(13) = -123
-45 - 78 = -123
-123 = -123
Your answer is correct!
(5, 13)
Hope this helps!
Answer:
Step-by-step explanation:
Mrs. Siebenaller bought a bus for 25,000 with a 7% interest rate and she gets a loan payoff of 60 months,
We know that,
![\text{PV of annuity}=P\left[\dfrac{1-(1+r)^{-n}}{r}\right]](https://tex.z-dn.net/?f=%5Ctext%7BPV%20of%20annuity%7D%3DP%5Cleft%5B%5Cdfrac%7B1-%281%2Br%29%5E%7B-n%7D%7D%7Br%7D%5Cright%5D)
Where,
PV = Present value of annuity = 25000,
r = rate of interest of each period = 
% monthly
n = number of periods = 60 months,
Putting the values,
![\Rightarrow 25000=P\left[\dfrac{1-(1+\frac{0.07}{12})^{-60}}{\frac{0.07}{12}}\right]](https://tex.z-dn.net/?f=%5CRightarrow%2025000%3DP%5Cleft%5B%5Cdfrac%7B1-%281%2B%5Cfrac%7B0.07%7D%7B12%7D%29%5E%7B-60%7D%7D%7B%5Cfrac%7B0.07%7D%7B12%7D%7D%5Cright%5D)
![\Rightarrow P=\dfrac{25000}{\left[\dfrac{1-(1+\frac{0.07}{12})^{-60}}{\frac{0.07}{12}}\right]}](https://tex.z-dn.net/?f=%5CRightarrow%20P%3D%5Cdfrac%7B25000%7D%7B%5Cleft%5B%5Cdfrac%7B1-%281%2B%5Cfrac%7B0.07%7D%7B12%7D%29%5E%7B-60%7D%7D%7B%5Cfrac%7B0.07%7D%7B12%7D%7D%5Cright%5D%7D)
Hence total amount paid is,
Therefore interest amount is,
Answer:
A
Step-by-step explanation:
Its A the other ones don't make sense
The first thing we must do for this case is to define variables.
We have then:
x: number of cats
y: number of dogs
We write the system of equations:
x / y = 2/3
(1/4) x + (1/2) y = 48
Solving the system we have:
x = 48
y = 72
The total number of animals is:
x + y = 48 + 72 = 120
Answer:
The total number of animals in the pet store is:
120
