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olga_2 [115]
3 years ago
12

What is the least value of x which the inequality is true? 16 is greater than or equal to -2x

Mathematics
1 answer:
tia_tia [17]3 years ago
6 0

Answer:Then the system of inequalities that represents the graph is second option:

2x +y is less than or equal to 3, and y-x is greater than or equal to 2

Step-by-step explanation: The area shaded is below the blue line and above the red line.

1.) The blue line goes through the points:

P1=(0,3)=(x1,y1)→x1=0, y1=3

P2=(1,1)=(x2,y2)→x2=1, y2=1

Slope: m=(y2-y1)/(x2-x1)

m=(1-3)/(1-0)→m=(-2)/(1)→m=-2

Point-slope form:

y-y1=m(x-x1)

y-3=-2(x-0)→y-3=-2(x)→y-3=-2x→y-3+3=-2x+3→y=-2x+3

The area below the blue line is:

y<=-2x+3→y+2x<=-2x+3→2x+y<=3

2x +y is less than or equal to 3

2.) The red line goes through the points:

P1=(0,2)=(x1,y1)→x1=0, y1=2

P2=(-2,0)=(x2,y2)→x2=-2, y2=0

Slope: m=(y2-y1)/(x2-x1)

m=(0-2)/(-2-0)→m=(-2)/(-2)→m=1

Point-slope form:

y-y1=m(x-x1)

y-2=1(x-0)→y-2=1(x)→y-2=x→y-2+2=x+2→y=x+2

The area above the red line is:

y>=x+2→y-x>=x+2-x→y-x>=2

y-x is greater than or equal to 2

Then the system of inequalities that represents the graph is:

2x +y is less than or equal to 3, and y-x is greater than or equal to 2

Read more on Brainly.com - brainly.com/question/11890005#readmore

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How many positive integers $n$ from 1 to 5000 satisfy the congruence $n \equiv 5 \pmod{12}$?
irga5000 [103]
The equivalence n \equiv 5 \pmod{12}

means that n-5 is a multiple of 12.

that is

n-5=12k, for some integer k

and so

n=12k+5


for k=-1, n=-12+5=-7

for k= 0, n=0+5=5 (the first positive integer n, is for k=0)


we solve 5000=12k+5 to find the last k

12k=5000-5=4995

k=4995/12=416.25

so check k = 415, 416, 417 to be sure we have the right k:

n=12k+5=12*415+5=4985

n=12k+5=12*416+5=4997

n=12k+5=12*417+5=5009


The last k which produces n<5000 is 416


For all k∈{0, 1, 2, 3, ....416}, n is a positive integer from 1 to 5000,

thus there are 417 integers n satisfying the congruence.


Answer: 417

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Factor completely. 5x2 - 45 A. 5(x + 3)(x - 3) B. 5(x2 - 45) C. 5(x - 9)(x + 9) D. (5x + 9)(x - 5)
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Answer:

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Step-by-step explanation:

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