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Mathematics

1 answer:

VARVARA [1.3K]2 years ago

3 0

Aa Bb Cc Dd Ee Ff Gg Hh Ii Jj Kk Ll Mm Nn Oo Pp Qq Rr Ss Tt Uu Vv Ww Xx Yy and Zz

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The spoke of a wheel reaches from the center of the wheel to its rim. If the circumference of the rim of the wheel is 27 inches,

ipn [44]

Circumference = 2 x pi x radius
27 in = 2 x 3.14 x radius

Solve for the radius

5 0

3 years ago

JIMMMMMM

Vitek1552 [10]

>= means greater than or equal to
<= means less than or equal to

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Part A

The graph of y >= -3x+3 will have a solid boundary line and the shading will be above the boundary line.

The boundary line y = -3x+3 has a negative slope so it moves down as you read it from left to right. It goes through the points (0,3) and (1,0)

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The graph of y < (3/2)x - 6 will have a dashed or dotted boundary line. The shading is below the boundary.

The graph y = (3/2)x-6 goes through the two points (0,-6) and (2,-3)

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If you graph both y >= -3x+3 and y < (3/2)x - 6 together, you get what you see in the attached image. This solution shaded region is the result of the overlapping prior shaded regions.

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Part B

Plug (x,y) = (-6,3) into each inequality to see if we get a true inequality or not

For the first inequality we have
y >= -3x+3
3 >= -3*(-6)+3
3 >= 18+3
3 >= 21
which is false. The value 3 is not larger or equal to 21. So right off the bat we know that (-6,3) is NOT a solution. It is NOT in the solution region.

Let's check the other inequality just for the sake of completeness
y < (3/2)x - 6
3 < (3/2)*(-6) - 6
3 < -9 - 6
3 < -15
this is also false. The value -15 is smaller than 3, since it is to the left of 3

We're given more evidence that (-6,3) is NOT in the solution area. It is outside of both shaded areas.