Solve for x. 9(x - 2) = 18 x = 0 x = x = x = 4

Sauron [17]

$\dfrac{\csc^2\theta-3\csc\theta+2}{\csc^2\theta-1}$

Identity:

$\sin^2\theta+\cos^2\theta=1\implies1+\cot^2\theta=\csc^2\theta$

So we can rewrite the denominator to get

$\dfrac{\csc^2\theta-3\csc\theta+2}{\cot^2\theta}$

Multiply numerator and denominator by $\sin^2\theta$ . Several terms will cancel since $\sin\theta\csc\theta=1$ . Also, $\cot\theta=\dfrac{\cos\theta}{\sin\theta}$ . We get

$\dfrac{1-3\sin\theta+2\sin^2\theta}{\cos^2\theta}$

Factorize the numerator, and write $\cos$ in terms of $\sin$ in the denominator to factorize it further to get

$\dfrac{(1-\sin\theta)(1-2\sin\theta)}{\cos^2\theta}=\dfrac{(1-\sin\theta)(1-2\sin\theta)}{1-\sin^2\theta}=\dfrac{(1-\sin\theta)(1-2\sin\theta)}{(1-\sin\theta)(1+\sin\theta)}$

The $1-\sin\theta$ factors cancel, leaving you with

$\dfrac{1-2\sin\theta}{1+\sin\theta}$

which you could simplify a bit further by writing

$\dfrac{1+\sin\theta-3\sin\theta}{1+\sin\theta}=1-\dfrac{3\sin\theta}{1+\sin\theta}$

3 0

4 years ago

Question 5 (1 point)

Airida [17]

Answer:

y = 90

Step-by-step explanation:

If y varies jointly as x and z, then;

y = kxz

If y = 18 when x = 2 and z = 3

18 = k(2)(3)

18 = 6k

k = 18/6

k = 3

To get y when x = 5 and z = 6

y = kxz

y = 3(5)(6)

y = 15*6

y = 90

Hence the value of y is 90

3 0

3 years ago

Write a scenario that could be represented by this equation: 3/4x = 12

Aneli [31]

Answer:

x=1 or x=16

Step-by-step explanation:

3/4x = 12 or 0.75x = 12

3/4x/3/4 = 12/3/4 or 0.75x/0.75 = 12/0.75

x=12/1 / 3/4

x= 4/4

x = 1 or x = 16

8 0

3 years ago

X- 8 TRANTLATE ALGEBRAIC EXPRESSION

n200080 [17]

Answer:

x 8 Putting it all together: (x 2 )4 = (x 2 )( ... zwj;x‍x‍x‍x‍x = x 8 Note that (x 2 )4 = x 8 , and that 2 × 4 = 8. This demonstrates the second exponent

Step-by-step explanation:

5 0

3 years ago

For each of the following expressions, indicate the order in which the operators will be evaluated by writing a number beneath e

Anvisha [2.4K]

Answer:

The answers are as shown in the explanation

Step-by-step explanation:

it should be noted that multiplication and division has a higher precedence than addition and subtraction. however, if there is parenthesis, then it will be given a preference before multiplication and division as such the order is as follows;

Parenthesis ()

percentage %

division /

multiplication *

Addition + and Subtraction -

a) for a - b - c - d

evaluation begins from left to right in the order 1 2 3

b) a - b + c + d

evaluation begins from left to right in the order 1 2 3

c) a / b * c * d

evaluation start from the left side since / is given precedence before the multiplication * in the order 1 2 3

d) a % b / c * d

here evaluation start from the % operator as it is given precedence before / and multiplication in the order 1 2 3

e) a % b % c % d

here evaluation start from the left side for the operator % in the order 1 2 3

f) a - (b - c) - d

the evaluation start from the bracket as it is given precedence before the subtraction operator in the order 2 1 3

g) (a - (b - c)) - d

similarly, evaluation start from the bracket as the precedence is before subtraction in the order 2 1 3

h) a - ((b - c) - d)

here, evaluation process start from the bracket operator as it has a high precedence before subtraction in the order 3 1 2

i) a % (b % c) * d * e

here, evaluation start from the bracket, then the % operator before the multiplication, in the order 2 1 3 4

j) a (b - c) * d - e

evaluation start from the bracket, then the multiplication operator before the subtraction, in the order 3 1 2 4

k) (a+ b) * c +d * e

evaluation start from the bracket operator, then the multiplication and then addition in the order 1 2 4 3

l) (a+ b) * (c / d) % e

here, evaluation start from the bracket, then the % operator, then division and multiplication in the order 1 4 3 2

7 0

3 years ago