111 = 14a This part is for the extra characters
1 answer:
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<u><em>Answer:</em></u>
A box of 50 stickers would cost $13
<u><em>Explanation:</em></u>
<u>1- getting the equation representing the price:</u>
We have two variables; the number of stickers and the price of the box
We can note that the price is the dependent variable (y) while the number of stickers is the independent one (x)
<u>We are given that:</u>
A box of 15 stickers cost $6..........> first point is (15,6)
A box of 25 stickers cost $8 ........> second point is (25,8)
The general equation of the linear line is:
y = mx + c
where m is the slope and c is the y-intercept
<u>i. getting the slope:</u>
The equation now became: y = 0.2x + c
<u>ii. getting the y-intercept:</u>
To get the y-intercept, use any of the given points and substitute in the equation we got in part i. I will use the point (15,6)
y = 0.2x + c
6 = 0.2(15) + c
c = 6 - 0.2(15) = 3
<u>The final equation is:</u>
y = 0.2x + 3
where y is the price of the box and x is the number of stickers it contains
<u>2- getting the price of a box with 50 stickers:</u>
To get the price of a box of 50 stickers, simply substitute with x = 50 in the equation we got from part 1
<u>This is done as follows:</u>
y = 0.2(50) + 3 = 13
Therefore, a box of 50 stickers will cost $13
Hope this helps :)
<h3>Answer: roughly 12.6274 meters</h3>
The more accurate value is 12.6274169979696, though it's not fully exact.
Round this however you need to.
The exact distance 32*sin(45) - 10 meters.
===========================================================
Explanation:
Refer to the diagram below.
I'll use point A in place of point O since the letter 'oh' is very similar looking to the number zero.
Plot point A at the origin (0,0). While at point A, look directly north. Then turn 30 degrees eastward to look at the bearing 030°. Next, move 20 meters along that bearing direction to arrive at point R. Segment AR is 20 meters long.
In the diagram, note how angle RAB is 30 degrees. The side opposite this is BR = m.
We can use the sine ratio to say that
sin(angle) = opposite/hypotenuse
sin(A) = BR/AR
sin(30) = m/20
m = 20*sin(30)
m = 10
-----------------------------------
While still at point A, look directly north and turn 135 degrees clockwise (ie toward the east) and move 32 meters along that bearing. You'll arrive at point S as the diagram shows.
Notice how
angle RAB + angle RAC + angle CAS = 30+60+45 = 135
The remaining angle DAS is 180-135 = 45 degrees.
When focusing on triangle DAS, we can say
sin(A) = DS/AS
sin(45) = n/32
n = 32*sin(45)
n = 22.6274169979696
This value is approximate.
----------------------------------
Subtract the values of m and n
n - m = 32*sin(45) - 10 = exact distance
n - m = 22.6274169979696 - 10
n - m = 12.6274169979696
n - m = 12.6274 = approximate distance
Round it however you need to. I'm choosing to round to four decimal places.
So we see that point S is roughly 12.6274 meters east of point R.
If your teacher wants the exact distance, then stick with 32*sin(45)-10.