If 0 < z ≤ 90 and sin(9z − 1) = cos(6z + 1), what is the value of z?

z = 3
z = 4
z = 5
z = 6

z=6.  quick maths

Step-by-step explanation:

z = 6

Step-by-step explanation:

we know that

if  sin(A)=cos(B)

then

angle A and angle B are complementary angles

therefore

In this problem

sin(9z − 1) = cos(6z + 1)

then

(9z − 1)+(6z + 1)=90° > by complementary angles

Solve for z

15z=90

z=90/15=6

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175