Answer:
sweatshirts cost $42
t-shirts cost $18
Step-by-step explanation:
9x+3y=288
x+6y=270
substitute 270-6y for x in the first problem
9(270-6y) +3y=288
2430-54y+3y=288
2430-51y=288
51y=-2142
y=42
then plug y=42 into the second equation
x+6(42)=270
x+252=270
x=18
17 * 0 + -2.
Now we rewrite the equation and make it 17 * 0 - 2 and u get -2.
By evaluating the quadratic function, we will see that the differential quotient is:
<h3>
How to get (f(2 + h) - f(2))/h?</h3>
Here we have the quadratic function:
Evaluating the quadratic equation we get:
So we need to replace the x-variable by "2 + h" and "2" respectively.
Replacing the function in the differential quotient:
If we simplify that last fraction, we get:
The third option is the correct one, the differential quotient is equal to 8 + 4.
If you want to learn more about quadratic functions:
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The term "closed" in math means that if you take two items from a set, do some operation, then you'll always get another value in the same set (sometimes you may get the same value as used before). For example, adding two whole numbers leads to another whole number. We therefore say "the set of whole numbers is closed under addition". This applies to integers as well because integers are positive and negative whole numbers. So we can say that integers are closed under addition.
Integers are not closed under division. Take two integers like 2 an 5 and divide: 2/5 = 0.4 which is not an integer. Integers don't have decimal parts.
The set of whole numbers is {0,1,2,3,...} and we can subtract the two values 1 and 2 to get 1-2 = -1. The order matters here. Subtracting a larger value from a smaller leads to a negative. The value -1 is not in the set of whole numbers. So we can say that whole numbers is not closed under subtraction
Finally, the set of irrational numbers is closed under addition. Adding any two irrational numbers leads to another irrational number. For instance, pi+sqrt(2) = 3.142 + 1.414 = 4.556; I'm using rounded decimals as approximate values. An irrational number is one where we cannot write it as a fraction of integers. Contrast that with a rational number in which we can write it as a fraction of integers. Example: 10 = 10/1 is a rational number.
Answers:
- C) Factored form
- C) Standard form
- D) The y intercept is -8
- B) Two solutions: x = -5 or x = 5
- B) Apply square root to both sides
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Explanations:
- For problems 1 and 2, there's not much to say other than you'll just have to memorize those terms. Standard form is ax^2+bx+c in general. The exponents count down 2,1,0. Factored form is where we have two or more factors multiplying with each other. Think of something like 21 = 7*3 showing that 7 and 3 are factors of 21.
- For problem 3, the y intercept is the last value. It's the constant value. Plug in x = 0 and you'll get y = -8 as a result. The y intercept always occurs when x = 0.
- In problem 4, we apply the square root to both sides to get x = -5 or x = 5. The plus or minus is needed. This is because (-5)^2 = 25.
- In problem 5, we apply the square root to both sides to undo the squaring operation.
