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PSYCHO15rus [73]
2 years ago
10

Which of the points is NOT one of the vertices (s,t) of the shaded region of the set of inequalities shown below?

Mathematics
1 answer:
lorasvet [3.4K]2 years ago
7 0

Answer:

Option D

Step-by-step explanation:

Given: set of inequalities

To find: Points which do not satisfy all the inequalities

Solution:

For point (15,0):

15\leq 30-3(0)=30\\15\geq 15-0=15\\15\leq 25-0=25\\15\geq 0\\0\geq 0

So, (15, 0) satisfies all the inequalities

For point (7.5,7.5):

7.5\leq 30-3(7.5)=30-22.5=7.5\\7.5\geq 15-7.5=7.5\\7.5\leq 25-7.5=17.5\\7.5\geq 0\\7.5\geq 0

So, (7.5, 7.5) satisfies all the inequalities

For point (22.5,2.5):

22.5\leq 30-3(2.5)=30-7.5=22.5\\22.5\geq 15-2.5=12.5\\22.5\leq 25-2.5=22.5\\22.5\geq 0\\2.5\geq 0\\

So, (22.5,2.5) satisfies all the inequalities

For point (7.5 ,0):

Put s = 7.5 and t = 0 in s\geq 15-t

7.5\geq 15-0=15 which is false

So, (s,t)\neq (7.5,0)

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Find the coordinates of point P that lies along the directed line segment AB in a 2:3 ratio given A (-2, 1), B (3, 4).
saul85 [17]

Answer:

P(x,y) = (0,\frac{11}{5})

Step-by-step explanation:

Given

A = (-2,1)

B = (3,4)

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Required

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The coordinate of a point when divided into ratio is:

P(x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})

Where

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P(x,y) = (\frac{6 - 6}{5},\frac{8 + 3}{5})

P(x,y) = (\frac{0}{5},\frac{11}{5})

P(x,y) = (0,\frac{11}{5})

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A parallelogram has symmetry with respect to the point of intersection of its diagonals. t/f?
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Which of the following is the point and slope of the equation y - 8 = 4(x + 3)? a. (8, -3), 4 b. (3, -8), 4 c. (-8, 3), 4 d. (-3
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d

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This is point-slope form, and these coordinates make both sides equal to 0.

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