A student flips a coin four times. what is the probability the coin lands tails up exactly one time?
1 answer:
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Answer:
Step-by-step explanation:
The equation of a line is y = mx + b
Where:
- m is the slope
- b is the y-intercept
First, let's find what m is, the slope of the line.
Let's call the first point you gave, (-3,1), point #1, so the x and y numbers given will be called x1 and y1.
Also, let's call the second point you gave, (2,-1), point #2, so the x and y numbers here will be called x2 and y2.
Now, just plug the numbers into the formula for m above, like this:
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
- (-3,1). When x of the line is -3, y of the line must be 1.
- (2,-1). When x of the line is 2, y of the line must be -1.
Now, look at our line's equation so far: .
is what we want, the -
is already set and x and y are just two 'free variables' sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-3,1) and (2,-1).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!
You can use either (x,y) point you want. The answer will be the same:
- (-3,1). y = mx + b or
, or solving for b:
.
.
- (2,-1). y = mx + b or
, or solving for b:
.
See! In both cases, we got the same value for b. And this completes our problem.
The equation of the line that passes through the points (-3,1) and (2,-1) is
We have been given that Morgan is throwing a pizza party. She has 1 7/8 pounds of cheese available and she needs 1/5 pound of cheese to make each pizza. We are asked to find the number of full pizzas that Morgan can make with the amount of cheese she has.
To solve our given problem, we will divide total amount of cheese by amount of cheese used to make each pizza.
Now we will convert our division problem into multiplication problem by flipping the 2nd fraction.
We are asked to find the number of full pizzas and we can see that Morgan can make 9 full and pizzas.
Since there are 9 full pizzas, therefore, Morgan can make 9 full pizzas with the amount of cheese she has.