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1 answer:
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If the first 10 bricks come out at $ 4.5, I would be spending $ 45. The other 10 bricks come out at $ 3.5 so he would be spending $ 35. Therefore, he has $ 20 available to buy bricks at $ 2.5, which would be buying 8 additional bricks. Thus, in total, with $ 100, 28 bricks were purchased.
Answer:
We conclude the equation is linear because it can be rewritten in the form .
Hence, option D is correct.
Step-by-step explanation:
The slope-intercept form of the line or linear equation
where
is the slope
is the y-intercept
<u>Important Tip:</u>
The graph of a linear equation is always a straight line.
Convert the given equation in the slope-intercept form
subtract 18x from both sides
simplify
divide both sides by 9
Now, comparing the equation with a slop-intercept form of linear equation
- The slope m = -2
- The y-intercept b = -416/9
Therefore, we conclude the equation is linear because it can be rewritten in the form .
From the attached graph, is also clear that the graph of the equation is a straight line.
Hence, option D is correct.
A geometry program can show you the total displacement is about 10.14 miles.
_____
You can use a vector calculator to find the solution, too. Using bearing angles, the sum is
4∠90° + 3∠135° + 3∠180° + 4∠225° + 3∠90° ≈ 10.1390∠141.6354°
_____
If you want to do it by hand, you can recognize the sum will be
7 miles east + 3 miles south + 3 miles southeast + 4 miles southwest
Distances that are not in the direction of one of the coordinate axes can be translated to rectangular coordinates by
displacement*(cos(angle), sin(angle))
Angles can be measured in the conventional way—from the positive x-axis. A direction of southeast will be +315° or -45°. A direction of southwest will be +225° or -135°.
Then the sum of the displacements in rectangular coordinates is ...
= (7, -3) + 3*(cos(-45°), sin(-45°)) + 4*(cos(-135°), sin(-135°))
= (7, -3) + ((√2)/2)*((3, -3) + (-4, -4))
= (7, -3) + 0.707107*(-1, -7)
= (6.2929, -7.9497)
Then the Pythagorean theorem is used to find the direct distance from home to this displaced location.
d = √(6.2929² +(-7.9497)²) ≈ √102.7990
d ≈ 10.1390 . . . . miles
_____
You can use a vector calculator to find the solution, too. Using bearing angles, the sum is
4∠90° + 3∠135° + 3∠180° + 4∠225° + 3∠90° ≈ 10.1390∠141.6354°
_____
If you want to do it by hand, you can recognize the sum will be
7 miles east + 3 miles south + 3 miles southeast + 4 miles southwest
Distances that are not in the direction of one of the coordinate axes can be translated to rectangular coordinates by
displacement*(cos(angle), sin(angle))
Angles can be measured in the conventional way—from the positive x-axis. A direction of southeast will be +315° or -45°. A direction of southwest will be +225° or -135°.
Then the sum of the displacements in rectangular coordinates is ...
= (7, -3) + 3*(cos(-45°), sin(-45°)) + 4*(cos(-135°), sin(-135°))
= (7, -3) + ((√2)/2)*((3, -3) + (-4, -4))
= (7, -3) + 0.707107*(-1, -7)
= (6.2929, -7.9497)
Then the Pythagorean theorem is used to find the direct distance from home to this displaced location.
d = √(6.2929² +(-7.9497)²) ≈ √102.7990
d ≈ 10.1390 . . . . miles