The total number of such groupings of 12 people into groups of 3, 4, and 5, regardless of Henry's placement, is
where
is the binomial coefficient. This is because we initially pick 3 people from the total 12, leaving 9 available; then 4 people from these 9, leaving 5 more; then the remaining 5 are all selected.
If Henry claims a spot in the group of 4, then we effectively can only pick 3 people from the 8 non-Henrys to get
such groupings.
Answer:
2 bags of topsoil.
Step-by-step explanation:
The attached figure shows a flower bed.
One bag of topsoil covers 15 square meters.
We need to find how many bags of topsoil does Tom need to cover his flower bed.
The area of the flower bed is :
Let he has to cover x bags of topsoil. So,
x = Area of flower bed/Area of 1 bag of top soil
x = 30/15
x = 2
Hence, he will need 2 bags of topsoil to cover his flower bed.
Answer:
Proven
Step-by-step explanation:
We prove the polynomial with factorization. We must first simplify the expression before we can factorize:
4 is the common number and we can take it out of the expression:
We can factorize further with the x term being zero. For this to be true we must have -2x and 2x to cancel out and therefore the expression is proven:
Since the slope-intercept form of a line is given by the expression:
Where, m is the slope and b is the y-intercept.
Then, for the function:
The slope is -2 and the y-intercept is (0, 3)
2 Answers:
Parallel lines always have equal slope, but different y intercepts.
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Explanation:
Let's solve the second equation for y
3y - x = -7
3y = -7+x
3y = x-7
y = (x-7)/3
y = x/3 - 7/3
y = (1/3)x - 7/3
The equation is in y = mx+b form with m = 1/3 as the slope and b = -7/3 as the y intercept. We see that the first equation, where y was already isolated, also has a slope of m = 1/3. The two equations of this system have the same slope. Choice C is one of the answers.
However, they don't have the same y intercept. The first equation has y intercept b = -4, while the second has b = -7/3. This means that they do not represent the same line. They need to have identical slopes, and identical y intercepts (though the slope can be different from the y intercept of course) in order to have identical lines. So we can rule out choice D and E because of this.
Because the two equations have the same slope, but different y intercepts, this means the lines are parallel. Choice B is the other answer.
Parallel lines never touch or intersect, which in turn means there is no solution point. A solution point is where the lines cross. We can rule out choice A.
I recommend using your graphing calculator, Desmos, GeoGebra, or any graphing tool (on your computer or online) to graph each equation given. You should see two parallel lines forming. I used GeoGebra to make the graph shown below.
