Answer:
z = -ln│5eᵗ + C│
Step-by-step explanation:
dz/dt + 5eᵗ⁺ᶻ = 0
dz/dt = -5eᵗ⁺ᶻ
dz/dt = -5eᵗeᶻ
-e⁻ᶻ dz = 5eᵗ dt
e⁻ᶻ = 5eᵗ + C
-z = ln│5eᵗ + C│
z = -ln│5eᵗ + C│
To find angle Y, take 180 degrees (linear pair) minus 35 degrees (angle X).
180-35=145 degrees
Angle Y=145 degrees
Angle W is also 145 degrees since it’s a vertical angle to Angle Y.
To find angle N, take 90 degrees (complementary angle) minus 55 degrees (angle M).
90-55=35 degrees
Angle N=35 degrees
Hope this helped!
Answer:

Step-by-step explanation:
From inspection of the graph, we can see that the curve intercepts the x-axis at (-4, 0), (-1, 0) and (3, 0)
Therefore,
x = -4 ⇒ x + 4 = 0
x = -1 ⇒ x + 1 = 0
x = 3 ⇒ x - 3 = 0
Because (-4, 0) touches the x-axis, then (x + 4)² will be a factor
So (x + 4)², (x + 1) and (x - 3) are all factors of the polynomial

If we multiply the constants, this will give us the y-intercept:
⇒ 4² x 1 x -3 = -48
From inspection of the graph, the y-intercept is -6
So to get from -48 to -6 we need to multiply -48 by 1/8
Therefore, n = 1/8

Answer:
The number of boys in the school is;

Explanation:
Given that the ratio of boys to girls in a school is 5:4;

And there are 500 girls in the school.
The number of boys in the school will be;

Therefore, the number of boys in the school is;
Answer:
The domain is (2,5,-3,0)
Step-by-step explanation:
we know that
For a set of ordered pairs, the first elements of each ordered pair represents the domain of the function and second elements of each ordered pair represents the range of the function.
The domain of a function is the set of all possible values of x
In this problem we have
![A= \ [(2,3), (5,1).(-3,-2), (0, 3)\ ]](https://tex.z-dn.net/?f=A%3D%20%5C%20%5B%282%2C3%29%2C%20%285%2C1%29.%28-3%2C-2%29%2C%20%280%2C%203%29%5C%20%5D)
therefore
The domain is (2,5,-3,0)