<h2>Question :</h2>
<em>Write the equation of a line that is perpendicular to the given line and that passes through the given point. y=2/3x+9 m (–6, 5)</em>
<h2>Answer :</h2>
<em>y = -3/2x - 4 </em>
<h2>Explanation :</h2>
y = mx + c
*m = gradien
•>looking for gradients
y=2/3x+9
m1 = 2/3
m2 = -3/2
•>line equation (-6,5)
y - y1 = m(x - x1)
y - 5 = -3/2(x - (-6))
y - 5 = -3/2(x + 6)
y - 5 = -3/2 - 9
y = -3/2x - 9 + 5
y = -3/2x - 4
Answer:
B
Step-by-step explanation:
Just got it on apex
Answer:
Bobby around 131 minutes and Billy around 111 minutes
Step-by-step explanation:
To solve the problem it is important to raise equations regarding what happens.
They tell us that Billy (Bi) and Bobby (Bo) can mow the lawn in 60 minutes. That is to say that what they prune in a minute is giving as follows:
1 / Bo + 1 / Bi = 1/60 (1)
They say Billy could mow the lawn only in 20 minutes less than it would take Bobby, therefore
1 / Bi = 1 / (Bo-20) (2)
Replacing (2) in (1) we have:
1 / Bo + 1 / (Bo-20) = 1/60
Resolving
(Bo - 20 + B0) / (Bo * (Bo-20) = 1/60
120 * Bo - 1200 = Bo ^ 2 - 20Bo
Rearranging:
Bo ^ 2 - 140Bo -1200 = 0
Now applying the general equation
Bo = 130.82 or Bo = 9.17, <em>this last value cannot be because Billy took 20 minutes less and neither can he prune faster than the two together</em>, therefore Bobby only takes around 131 minutes and Billy around 111 minutes
Checking with equation 1:
1/131 +1/111 = ~ 1/60
Ok. because those two angles are sumplimentary, (they equal 180 degrees) we can set up an equations.
3n+n+14=180
then isolate the variable
4n+14=180
-14 -14
4n=166
then divide to undo the multiplication
4n=166
--- ----
4 4
n=41.5
Answer:
The linear function that discribes the size of the population in function of the t in years is p = 700t - 1,397,300
Step-by-step explanation:
A linear function is defined by a line, so in order to determine the linear function we can use the two points that were given to us to create a line equation and use that as our linear function. The points given to us were (2009; 9000) and (2014; 12500), in this case the year is our value of "x" and the size of the population is our value of "y". The first step is to find the slope of the line which is given by:
m = (y2 - y1)/(x2 - x1)
m = (12500 -9000)/(2014 - 2009) = 3500/5 = 700
Then we can use the slope and the first point to build the equation:
p - 9000 = 700*(t - 2009)
p = 700t - 1406300 + 9000
p = 700t - 1397300