This problem can be readily solved if we are familiar with the point-slope form of straight lines:
y-y0=m(x-x0) ...................................(1)
where
m=slope of line
(x0,y0) is a point through which the line passes.
We know that the line passes through A(3,-6), B(1,2)
All options have a slope of -4, so that should not be a problem. In fact, if we check the slope=(yb-ya)/(xb-xa), we do find that the slope m=-4.
So we can check which line passes through which point:
a. y+6=-4(x-3)
Rearrange to the form of equation (1) above,
y-(-6)=-4(x-3) means that line passes through A(3,-6) => ok
b. y-1=-4(x-2) means line passes through (2,1), which is neither A nor B
****** this equation is not the line passing through A & B *****
c. y=-4x+6 subtract 2 from both sides (to make the y-coordinate 2)
y-2 = -4x+4, rearrange
y-2 = -4(x-1)
which means that it passes through B(1,2), so ok
d. y-2=-4(x-1)
this is the same as the previous equation, so it passes through B(1,2),
this equation is ok.
Answer: the equation y-1=-4(x-2) does NOT pass through both A and B.
Answer:
x = 25
Step-by-step explanation:
Since it is an equilateral triangle it means that all the sides are 50. Each side is equal so, if you divide 150 by 3 you get 50. (and since perimeter is the adding of each side)
Now you want to try to figure out what the altitude is of the triangle so you divide it in half. Making the bottom side length now 25 because half of 50 is 25. You now have to use Pythagoreans theorem to figure out the altitude:
c^2 - a^2 = b^2
50^2 - 25^2 = b^2
2500 - 625 = b^2
1875 = b^2
√1875 = b
43.30127019
now you put that into the expression: x√3:
x√3 = 43.30127019
x = (43.30127019) ÷ (√3)
x = 25
Hope this helped!
The equation representing the given statement is ~
The least number of lawns that he can cut and buy the computer is 10 lawns ~
Total savings should be greater or equal to $ 820 in order to buy the computer,
And his total savinga is equal to ~
Money he saved + money got from cutting lawns.
let's assume the lawns cut by Tyrod be x,
Money earned by cutting lawns is equal to
- total number of lawns cut × $50
total savings is equal to ~
hence,
by solving for " x (number of lawns cut) " we get ~
Hence, the least number of lawns he has to cut is the number that is greater than 9.8, which is
Present Value of an annuity is given by the formular
PV = P(1 - (1 + r)^-n)/r; where PV = $28,000, r = 0.081/12 = 0.00675, n = 35 and P is the periodic (monthly) payment.
P = PVr/(1 - (1 + r)^-n) = (28,000 x 0.00675)/(1 - (1 + 0.00675)^-35) = 189/0.2098 = 900.90
Therefore, the monthly payment is $900.90
