M∠klp+m∠plm =



2. +m∠plm = substitution

3. m∠plm = algebra

4. m∠pmn=m∠p+m∠

5. = +180°−3x substitution

6. x= algebra

1.

2.

3.

4.

5.

6.

Step-by-step explanation:

Please find the attached diagram for the complete question.

We are supposed to complete the given blanks.

1.

We can see from our given diagram that angle KLP and angle PLM are linear angles, so their measure will be equal to 180 degrees. Therefore, the correct expression for blank in 1st step would be .

2.

Now, we will substitute the measure of angle angle KLP in our equation. We can see that measure of angle angle KLP is . Therefore, the correct expression for blank in 2nd step would be .

3.

Our next step is to find the measure of angle PLM in terms of x by subtracting from both sides as:

Therefore, our 3rd step would be .

4.

We can see that angle PMN is an exterior angle of our given triangle, so its measure will be equal to the sum of the opposite interior angles.

We can see that angle P and angle PLM are opposite interior angle of angle PMN, so we can set an equation as:

Therefore, the correct expression for blank in 4th step would be .

5.

Our next step is to substitute the values of angle PMN and angle P as given in the diagram.

Therefore, our 5th step would be .

6.

Now, we need to solve for x using algebra as:

Therefore, the value of x is 27 degrees.

1: m<KLP+m<PLM=180 Definition of Supplementary

2: 3x+m<PLM=180 Substitution

3: m<PLM=180-3x Algebra

4: m<PLM=m<P+m<PLM Exterior Theorem

5: 2x+72=x+180-3x Substitution

6: x=27 Algebra

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3

b

step-by-step explanation: