Answer:
(Choice C) C Replace one equation with a multiple of itself
Step-by-step explanation:
Since system A has the equations
-3x + 12y = 15 and 7x - 10y = -2 and,
system B has the equations
-x + 4y = 5 and 7x - 10 y = -2.
To get system B from system A, we notice that equation -x + 4y = 5 is a multiple of -3x + 12y = 15 ⇒ 3(-x + 4y = 5) = (-3x + 12y = 15).
So, (-x + 4y = 5) = (1/3) × (-3x + 12y = 15)
So, we replace the first equation in system B by 1/3 the first equation in system A to obtain the first equation in system B.
So, choice C is the answer.
We replace one equation with a multiple of itself.
Answer:
The answer is 25.67and then you multiply by8 and get you 205.36
Step-by-step explanation:
Answer:
$9 for 36
Step-by-step explanation:
Divide the price by the quantity to receive the unit price. Here are the unit prices for each option:
1. $0.54
2. $0.43
3. $0.31
4. $0.28
5. $0.25
Basically, you want the lowest price. So, $9 for 36 is the best value because it costs $0.25 per pen.
We are going to make simultaneous equations.
x will be our $3 ice cream and y will be our $5 ice cream
Equation1 ---- x + y = 50 (the sum of all the ice creams they sell)
Equation 2 ---- 3x + 5y = 180 Sum of all the $3 and $5 ice creams is $180
Since we can't solve for both variables we will put one of the variables in terms of the other.
Take x+y=50 and subtract y from both sides. (I could have done subtracted x - it did not matter). Now we have x= ₋ y +50 (negative y +50)
Now I am going to take equation 2 and replace the x with -y +50
3 (-y +50) + 5y = 180
Now I will use the distributive law on the 3 and what's in the parentheses:
-3y + 150 + 5y = 180
Now I will combine like terms (the -3y and the 5y)
2y + 150 = 180
Now subtract 150 from both sides of the equation
2y = 30
Divide both sides by 2
and get y= 15 They sold 15 ice creams that cost $5 each
Since equation 1 is x+y=50 we can replace y with 15
x + 15 = 50 Now subtract 15 from both sides x = 35
Since x represents the $3 ice creams, they sold 35 of those.
Check:
35 X 3 = $105
15 x 5 = + <u>75
</u> $180
Answer:
Step-by-step explanation:
The formula for <u>exponential growth</u> is y = ab^x.
To write this equation, we know it has to start with 48 (which is the variable a). We need to add the rate of growth. This is 11/6 (which is variable b). But we also need to account for the "every 3.5 years" part, so divide the x as an exponent by 3.5.
N(t) = 48 * 11/6^(t/3.5)
This equation is easy to test, and it's a good idea to test it after you write it. For example, after 3.5 years we know that it should have 48*11/6 branches. Does our equation work? Yes.
