Line m is parallel to line n. the measure of angle 4 is (5a + 10)°. the measure of angle 6 is (3a + 10)°. what is the measure of angle 4?
a. 110°
b. 70°
c. 20°
d. 60°

A. 110

Step-by-step explanation:

Angles 4 and 6 are supplementary so if we add them together they will equal 180.

(5a + 10)° + (3a + 10)° = 180°

Simplify a bit to get 8a + 20 = 180

and 8a = 160.

a = 20.  Now sub that value of a into the expression for angle 4:

5a + 10 --> 5(20) + 10 = 110°

Option A.

Step-by-step explanation:

Given information: m║n, and  .

If a transversal line intersect two parallel lines, then the interior angles on the same sides are supplementary angles. It means their sum is 180.

From the given figure it is clear that angle 4 angle 6 are interior angles on the same side. So, angle 4 and 6 are supplementary angles.

On combining like terms we get

Subtract 20 from both sides.

Divide both sides by 8.

The value of a is 20.

Therefore, the correct option is A.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

d. vertex

step-by-step explanation: