Answer:
Step-by-step explanation:
Hi there!
<u>What we need to know:</u>
- Linear equations are typically organized in slope-intercept form:
where m is the slope and b is the y-intercept (the value of y when x is equal to 0)
<u>1) Determine the slope (m)</u>
where two points that the line passes through are 
and 
We're given the point (2,10) and the y-intercept of 4. Recall that the y-intercept occurs when x is equal to 0. This means that the y-intercept occurs at (0,4), giving us our second point.
Plug these points into the equation
Therefore, the slope of the line is 3. Plug this into
<u>2) Determine the y-intercept (b)</u>
The y-intercept is given; it is 4. Plug this back into
I hope this helps!
Answer is 53911
Step-by-step explanation:
Just multiply to get the answer
Answer:
Step-by-step explanation:
Notice that all three sides of the given triangle has one tick mark.
This means that all three sides are congruent, meaning that we have an equilateral triangle.
And for equilateral triangles, all three angles are also congruent.
So:
Also, recall that the interior angles of a triangle is always 180. Thus:
Substitute:
Combine like terms:
Substitute:
Multiply:
Thus:
And we are done!
Answer:
x(15) = 21 lb
Step-by-step explanation:
Rate of change in volume of salt water solution = rate of volume incoming - rate of volume outgoing
dV/dt = 4 - 2 =2gal/min
So, the equation for volume at cetain time t at given conditions and values becomes,
V(t) = 2t + V
V(t) = 2t + 20 gal-------------------euqation (1)
Rate of change in amount of salt = rate of salt in - rate of salt out
dx/dt = {0.5*4} - {[x(t)/V(t)]*2}
dx/dt = 2-2[(x(t))/(2t+20)]
dx/dt = 2-[(x(t))/(v(t))] lb/min
Now, with integrating factor, we get
exp[∫(1/(1+10))dt)] = t+10
the equation becomes
(t + 10)*x' + x = 2*(t+10)
((t+10)*x') = 2*(t+10)
(t+10)*x = t² + 20t + C
As x(0) = 0,
x(t) = (t²+20t)/(t+10)
x(15) = (15²+20*15)/(15+10)
x(15) = 21 lb
Answer:
29°
Step-by-step explanation:
Angles 1 and 8 are alternate exterior angles where a transversal crosses parallel lines, so are congruent.
m∠1 = m∠8
3x+25 = 4x-17
42 = m . . . . . . . . add 17-3x
Then the measure of ∠1 is 3·42 +25 = 151 (degrees), and the measure of its supplement, ∠2 is ...
m∠2 = 180° -151° = 29°
