L1: 2x+4y-3=0 ..........(1)
P: (2,0)
The point on the line L1 closest to the given point P is at the intersection of L1 with L2, which is the perpendicular passing through P.
Slope of L1=-2/4=-1/2
Slope of L2=-1/(-1/2)=2
Since it passes throug P(2,0), we can use the point-slope formula:
(y-0)=2(x-2) =>
L2: 2x-y-4=0.............(2)
Solve for x & y using (1) and (2) to get intersection point required:
(1)-(2)
2x-2x + 4y-(-y) -3 -(-4) =0
5y=-1, y=-1/5
Substitute y=1/5 in equation (1)
2x+4(-1/5)-3=0 =>
2x-19/5=0
x=19/10
=> the point on L1 closest to (2,0) is (19/10, -1/5)
Answer:
$51.12
Step-by-step explanation:
Hello there!
In number 19, we want to find the total price of a sweatshirt that costs $48 dollars but has 6.5% sales tax
Sales tax is a small percentage of the cost of an item that is added to items when they are being sold.
In this problem, 6.5% of the cost of the sweatshirt will be added to the cost of the sweatshirt in the form of sales tax. The price of the sweatshirt plus the amount in sales tax will be the total cost of the sweatshirt.
Translating that as an equation,
48 + 48*6.5%=total cost
You can calculate 48*6.5% as
, which is equal to 3.12
So that means that $3.12 will be added to the cost of the sweatshirt.
Therefore,
48 + 3.12=<u>$51.12</u>, which will be the total cost of the sweatshirt, including sales tax
Hope this helps!
Step-by-step explanation:
23. area of rect,r = 11 x 3.5 = 38.5cmsq
area of tri, t = 6 x3.5/2 = 10.5 cmsq
area of shaded region, sr = r-t
=> sr = 38.5- 10.5 = 28.5cmsq
24. area of square, s = 10x10 = 100mmsq
area of circle, c = pi x 5^2 = 78.5mmsq
area of shaded region, sr = s - c
=> sr = 100- 78.5 = 22.5mmsq
25. area of circle, c = pi x 6^2 = 113.04insq
area of tri, t = 6x12/2 = 36insq
area of shaded region, sr = c - t
=> sr = 113.04 - 36 = 77.04insq
Answer:
720 ways to arrange
Step-by-step explanation:
Use the factorial of 6 to find this solution. Namely, 6!
This means 6*5*4*3*2*1 which equals 720
It seems like a huge number, right? But think of it like this: For the first option, you have 6 collars. After you fill the first spot with one of the 6, you have 5 left that will fill the second spot. After the first 2 spots are filled and you used 2 of the 6 collars, there are 4 possibilities that can fill the next spot, etc.
So first, find out the total amount of money you make in 3 months.
If you make 1200 dollars a month, then in 3 months, you can make 3600 dollars. This is because 1 month salary + 1 month salary + 1 month salary = 3 month salary, and 1 month salary = 1200. So 1200 + 1200 + 1200 = 3600.
Since you're saving 2/5 of that, the simplest method to do this is to divide by 5, to find 1/5 of 3600, then multiply by 2 to find 2/5.
3600/5 = 720
720 * 2 = 1440
So you can save $1440 in three months.