to find the point, find the location
realize that the shortest line that crosses through the origin and y=9x+8 is perpendicular to y=9x+8
perpendicular lines have slopes that multiply to get -1
y=9x+8 has a slope of 9
9*m=-1, m=-1/9
the slope of the mystery line is -1/9
since it passes through the origin, the y intercept is 0
y=(-1/9)x is the equation of the line from the point to the origin
find the intersection of this line and the original line
set them equal to each other
(-1/9)x=9x+8
multily both sides by 9
-x=81x+72
minus 81 both sides
-82x=72
divide both sides by -82
x=-36/41
find y
y=(-1/9)x
y=(-1/9)(-36/41)
y=4/41
the point is 
Answer:
1 : 2
Step-by-step explanation:
Express the ratio as the number of oranges in each box, that is
box A : box B
= 18 : 36
Simplify the ratio by dividing both parts by 18, thus
ratio = 1 : 2 ← in simplest form
Answer:
<em> The distance from your eyes to the stage is 8.85 ft</em>
Step-by-step explanation:
Your distance to the stage is 6 feet
Your eyes are 6.5 feet tall
You need to find the distance of your eyes towards the stage.
This situation can be modeled using a rectangle triangle, where the adjacent side x is the horizontal distance to the stage and the opposite side h is the vertical distance of your eyes to the stage.
<u>Observe the attached image.</u>
Then, we look for the distance z from your eyes to the stage. This distance is the hypotenuse of the right triangle.
So, using the Pythagorean theorem we have:
Where
therefore:
Answer: $3 per pound
Step-by-step explanation:
Since Carson buys 4 pounds of peaches for $12, you can find the value of one pound by dividing 4 by 4. You must also divide the 12 by 4. In conclusion, you pay $3 per pound.
Answer:
145
Step-by-step explanation:
Adjacent interior angle = x
Sum of exterior angle and adjacent interior angle = 180
35 + x = 180
x = 180 - 35
x = 145
