find the cosine ratio of angle θ. hint: use the slash symbol ( / ) to represent the fraction bar, and enter the fraction with no spaces.

triangle abc is shown. ab measures 4. bc measures 5. ca measures 3. the angle formed at point c is marked theta and angle a is the right angle.

answer for blank 1:

The cosine of the angle theta is given as:

cos θ=3/5

Step-by-step explanation:

We know that cosine of any angle theta is defined as:

Where theta is the angle formed with whose respect we apply the trignometric identity. ( As we are given an right angled triangle so we can easily apply our trignometric identity)

Now here we have base=CA=3

and hypotenuse=BC=5.

Hence, cos θ=3/5

Also the figure of the question is attached to the answer.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.