We have two unknowns: x and y. Now, we have to formulate 2 equations. The first would come from the use of the given ratio:
We use the distance formula to find the distance between coordinates:
3/4 = √[(x-4)²+(y-1)²] / √[(4-12)²+(1-5)²]
√[(x-4)²+(y-1)²] = 3√5
(x-4)²+(y-1)² = 45
x² - 8x + 16 + y² - 2y + 1 = 45
x² - 8x + y² - 2y = 28 --> eqn 1
The second equation must come from the equation of a line:
y = mx +b
m = (5-1)/(12-4) = 1/2
Substitute y=5 and x=12 for point (12,5)
5 = (1/2)(12) + b
b = -1
So, the second equation is
y = 1/2x -1 or x = 2 + 2y --> eqn 2
Solving the equations simultaneously:
(2 + 2y)² - 8(2 + 2y) + y² - 2y = 28
Solving for y,
y = -2
x = 2+2(-2) = -2
Therefore, the coordinates of point A is (-2,-2).
5x + 60y = 35
x +y = 1.5 : rewrite as x = 1.5-y and substitute this formula for x in the first one:
5(1.5-y) + 60y = 35
distribute:
7.5 - 5y + 60y = 35
combine like terms:
7.5 + 55y = 35
subtract 7.5 from both sides:
55y = 27.5
divide both sides by 55 to solve for y
y = 27.5 / 55 = 0.5
now substiute 0.5 for y in the 2nd equation:
x + 0.5 = 1.5
x = 1.5 - 0.5 = 1
he walked for 1 hour
Answer:
Not right.
Step-by-step explanation:
m <HGJ + m <KGJ =180°
So, m <HGJ = 180° - m <KGJ = 180° - 86° =94°
The salesman earns $850 per automobile he sells.
Since x represents the amount of automobiles the salesman sells, we can apply the commission as a coefficient to this variable. Therefore, the total commission that the salesman earns can be represented by $850x.
The bonus cheque is only received if the salesman's commission income is <em>at least </em>$6,800. 'at least' means that the salesman can still receive the cheque if his commission is exactly $6,800. The sign that we can use for this situation is the greater than or equal to sign, ≥.
The inequality that shows the commission income needed for the cheque is $850x ≥ $6,800. However, this question asks for the number of automobiles the salesman must sell to get the cheque.
Divide both sides by $850, as that represents his sales from one commission:
x ≥ 8
The inequality x ≥ 8 represents the amount of automobiles the salesman will need to sell to get the bonus cheque.
The answer is b
i think , im not sure
