Two lines are perpendicular if and only if the product of their slopes is - 1.
So, you just need to find the slope of each line and find out the product of their slopes.
I will do one example for you.
L1: y = 3x + 5
L2: y = - 3x + 14
L3: y = -x/3 + 14
The slope of a line is the coefficient of the x.
So the slopes are:
L1: slope 3
L2: slope -3
L3: slope -1/3
So now multiply the slopes of each pair of lines:
L1 and L2: 3 * (-3) = - 9 => No, they are not perpendicular
L2 and L3: (-3) * (-1/3) = 1 => No, they are not perpendicular
L1 and L3: (3) * (-1/3) = -1 => Yes, they are penpendicular.
Okie dokie,
When converting a decimal, you use the place the decimal is in...
Let's review the places: tenths, hundredths, thousandths, etc.
You look at the last number to determine what place you're using!
-------------------
Now here's an example for the
tenths place:
.5
it's in the tenths place, right? so put it over that number (with no decimal) over a
10.
(mobile) 5/10 or

Now, decide if you can simplify. You can! 5/10 simplifies down to
1/2.

is your answer!
--------
Example for the
hundredths place:
.26
the last number is in the hundredths place, so put the number (without a decimal) over
100!26/100 or

You can simplify this!
13/50 is your answer!
Calculators can also come in handy!
Good luck!
Answer:
Step-by-step explanation:
2x⁴ + 4x³ - 30x² = 2x²*(x² + 2x - 15)
x² + 2x - 15
Sum = 2
Product = -15
Factors = 5 ; (-3)
x² + 2x - 15 = x² + 5x - 3x - 3 *5
= x(x + 5) - 3(x + 5)
= (x + 5)(x - 3)
2x⁴ + 4x³ - 30x² = (2x²) (x + 5)(x - 3)
Answer:
what are the answers?
Step-by-step explanation:
Hey there!
The answer is C.
First of all, let's assign variables. We can use t for tricycles and b for bicycles.
Next let's look at the first statement:
"There are at most 12 bicycles and tricycles in a school playground."
"At most" means the number 12 will be included in the inequality, so the sum of b and t is at most 12.
We can write this as b + t ≤ 12.
Now we can look at the second statement:
"There are at least 17 wheels altogether."
"At least" means the number 17 will be included in the inequality.
Since each bicycle has 2 wheels and each tricycle has 3 wheels, the sum of 2b and 3t is at least 17.
That can be written as 2b + 3t ≥ 17.
Our final system of inequalities:
b + t ≤ 12
2b + 3t ≥ 17
This matches option C.
Hope this helps!