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earnstyle [38]
3 years ago
5

Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than

or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions?

Mathematics
1 answer:
Fittoniya [83]3 years ago
4 0
Inequation 1: 

\frac{2}{3}x-3 \geq y

to plot the pairs (x, y) for which the inequation holds, draw the line y=\frac{2}{3}x-3

then pick a point in either side of the line. If that point is a solution of the inequation, than color that region of the line, if that point is not a solution, then color the other part of the line.

we do the same for the second inequation. Then the solution, is the region of the x-y axes colored in both cases.

inequation 2: 

y+ \frac{2}{3}x\ \textless \ 4

y\ \textless \ - \frac{2}{3} x+ 4



draw the lines 

i)  y=\frac{2}{3}x-3          use points (0, -3),  (3, -1)

ii)y=- \frac{2}{3} x+ 4       use points ( 0, 4),   (3, 2)


let's use the point P(3, 3) to see what region of the lines need to be coloured:

\frac{2}{3}x-3 \geq y  ; 
\frac{2}{3}(3)-3 \geq 3
2-3 \geq 3, not true so we color the region not containing this point


y+ \frac{2}{3}x\ \textless \ 4
(3)+ \frac{2}{3}(3)\ \textless \ 4
3+ 5\ \textless \ 4 not true, so we color the region not containing the point (3, 3)

The graph representing the system of inequalities is the region colored both red and blue, with the blue line not dashed, and the red line dashed.



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\left \{ {{x+3y=9~(3)} \atop {3x-y=7(-1)}} \right. \\
\\ \left \{ {{3x+9y=27} \atop {-3x+y=-7}} \right. \\ \\10y=20\\
\\y= \frac{20}{10} \\y=2

x+3y=9\\x=9-3y\\x=9-3.2\\x=3

S=\{3,2\}

One solution.
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3 years ago
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These People! I can’t do this!!! I need YOU!
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Let’s solve for “a” and “s”.

a = 927 - 45s
a = 792 - 36s

927 - 45s = 792 - 36s
927 - 792 = 45s - 36s
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5 0
2 years ago
A patio blueprint has a key that shows 1 inch is equal to 12 feet. If the owner wants the length to be 30 feet, how many inches
harkovskaia [24]

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5 0
3 years ago
Yolanda buys
Stells [14]

Answer:

The unit price is 4.15 dollars per gallon

Step-by-step explanation:

- Yolanda buys 5.8 gallons of gas for $24.07

- We need to find the unit price in dollars per gallon

- Unit price means the price of each gallon

∵ The number of gallons = 5.8 gallons

∵ The price of the gallons = $24.07

∵ The unit price = the amount of money ÷ number of gallons

∴ The unit price = 24.07 ÷ 5.8

∴ The unit price = 4.15 dollars per gallon

* <em>The unit price is 4.15 dollars per gallon</em>

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3 years ago
If one zero of the polynomial (a^2+9)x^2+13x+6a is the reciprocal of the other, find the value of a.​
mihalych1998 [28]

Answer: a^2x^2+9x^2+13x+6a

Step-by-step explanation:

(a^2+9) x^2+ 13x +6a

x^2(a^2+9)+13x+6a

Expand:x^2(a^2+9): a^2 x^2+9^2

x^2 a^2 +x^2*9

a^2 x^2+9x^2

  a^2 x^2+9x^2+13x+6a

5 0
3 years ago
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