At heart we're being asked for a line through two points,

In general the line through (a,b) and (c,d) is

Check that you understand why both (a,b) and (c,d) are on this line.
Here our indepedent variable, instead of x, is T, temperature. Our dependent variable is v, velocity. Substituting,





That's our answer; let's check it.
When T=40, v = (5/9)40 + (2995/9) = 355 good
When T=49, v= (5/9)49 + (2995/9) = 360 good
Answer:
The solution for f(x) = g(x) are;
x = 1 and x = -1
Step-by-step explanation:
The given equations for the functions, g(x) are;

g(x) = 2 + x
The solution for f(x) = g(x), is given by equating the equations of the two functions as follows;
When f(x) = g(x), we have;

By cross multiplication, we have;
1 + 2·x = x × (2 + x) = 2·x + x²
∴ x² + 2·x - 2·x - 1 = 0
x² - 1 = 0
(x - 1)·(x + 1) = 0
x = 1, or x = -1
f(x) = g(x) = 2 + 1 = 3, or 2 - 1 = 1
Therefore, the solution for f(x) = g(x) are;
f(x) = g(x) = 3 or 1 where x = 1 and x = -1.
<span>There are 4 long rows and 5 short rows in the theater. x represents the number of chairs in each long row and y represents the number of chairs in each short row.
So, total number of chairs in 4 long rows= 4x
Total number of chairs in 5 short rows = 5y
Total number of chairs in the theater on a normal day = 4x + 5y
When 2 chairs are added to each long row, the number of chairs will change to (x+2).
So, total number of chairs in 4 long rows will be = 4(x+2)
When 3 chairs are added to each short row, the number of chairs will change to (y+3)
So, total number of chairs in 5 short rows will be = 5(y+3)
Thus, total number of chairs in the theater in rush day = 4(x+2) + 5(y+3)
= 4x + 8 + 5y + 15
= 4x + 5y + 23
Thus we can say the number of chairs increase by 23 as compared to a normal day.
</span>
Answer:
- 0.100
Step-by-step explanation:
Length of the ladder, H = 6 m
Distance at the bottom from the wall, B = 1.3 m
Let the distance of top of the ladder from the bottom at the wall is P
Thus,
from Pythagoras theorem,
B² + P² = H² .
or
B² + P² = 6² ..............(1) [Since length of the ladder remains constant]
at B = 1.3 m
1.3² + P² = 6²
or
P² = 36 - 1.69
or
P² = 34.31
or
P = 5.857
Now,
differentiating (1)

at t = 2 seconds
change in B = 0.3 × 2= 0.6 ft
Thus,
at 2 seconds
B = 1.3 + 0.6 = 1.9 m
therefore,
1.9² + P² = 6²
or
P = 5.69 m
on substituting the given values,
2(1.9)(0.3) + 2(5.69) ×
= 0
or
1.14 + 11.38 ×
= 0
or
11.38 ×
= - 1.14
or
= - 0.100
here, negative sign means that the velocity is in downward direction as upward is positive
Answer:
3.75
Step-by-step explanation:
5 1/4÷1/3
so,
= 5 1/4×3/1
= 5 × 0.75
= 3.75