1) ACT Prep: Linear Pair angles have measures (6x -9)°and (9x-6)° 1.

Mathematics

1 answer:

iris [78.8K]3 years ago

5 0

The measure of angles are 69 degree and 111 degree

Solution:

Given is linear pair angles

The measure of angles are: (6x - 9) degrees and (9x - 6) degrees

A linear pair of angles is formed when two lines intersect.

The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

Therefore,

$(6x - 9) + (9x - 6) = 180\\\\\text{Remove the parenthesis and solve}\\\\6x - 9 + 9x - 6 = 180\\\\\text{Combine the like terms}\\\\6x + 9x - 15 = 180\\\\15x - 15 = 180\\\\\text{Move the constants to right side}\\\\15x = 180 + 15\\\\15x = 195\\\\x = 13$

Thus the measure of angles are:

$(6x - 9) \text{ degrees } = 6(13) - 9 = 78-9 = 69 \text{ degrees }\\\\(9x - 6) \text{ degrees } = 9(13) - 6 = 117 - 6 = 111 \text{ degrees }$

Thus measure of angles are 69 degree and 111 degree

You might be interested in

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!! Graph g(x) = 3x^2 - 12x - 3

Paul [167]

Answer: Vertex = (2, -15) 2nd point = (0, -3)

Step-by-step explanation:

g(x) = 3x² - 12x - 3

= 3(x² - 4x - 1)

a=1 b=-4 c=-1

Find the x-value of the vertex by using the formula for the axis of symmetry: $x = \dfrac{-b}{2a}$

$x = \dfrac{-(-4)}{2(1)}$

$= \dfrac{4}{2}$

= 2

Find the y-value of the vertex by plugging the x-value (above) into the given equation: g(x) = 3x² - 12x - 3

g(2) = 3(2)² - 12(2) - 3

= 12 - 24 - 3

= -15

So, the vertex is (2, -15) ← PLOT THIS COORDINATE

Now, choose a different x-value. Plug it into the equation and solve for y. I chose x = 0

g(0) = 3(0)² - 12(0) - 3

= 0 - 0 - 3

= -3

So, an additional point is (0, -3) ← PLOT THIS COORDINATE

5 0

3 years ago

Rochelle works part-time at the college museum, which pays her at a rate of $10 per hour. She also makes small bracelets that sh

katrin [286]

We know for our problem that Rachel makes $10 per hour. Since $x$ represent the number of hours that she works, $10x$ will be the total amount that she will make for working $x$ hours. We also know that she sells bracelets for $5 each. Since $y$ represents the number of of bracelets that she sells, $5y$ will be her total revenue for selling $y$ bracelets. We also know that she needs to earn at least $200 a week to cover her expenses, so the sum of $10x$ and $5y$ must be equal or greater than 200:

$10x+5 \geq 200$

We can conclude that the graphs that shows the inequality that represents this situation, with its solution region shaded is: