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4 years ago

Which of the following would be a possible solution to the system of inequalities given below?

Mathematics

1 answer:

Nataly [62]4 years ago

5 0

Answer:

(0,5)

Step-by-step explanation:

we have

$2x+3y > 12$ ----> inequality A

$x-y\leq 1$ ----> inequality B

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities of the system (makes true both inequalities)

Verify each ordered pair

Substitute the value of x and the value of y of each ordered pair in the inequality A and in the inequality B and then compare the results

case 1) (0,5)

For x=0,y=5

Inequality A

$2(0)+3(5) > 12$

$15 > 12$ ----> is true

The ordered pair satisfy inequality A

Inequality B

$0-5\leq 1$

$-5\leq 1$ ---> is true

The ordered pair satisfy inequality B

therefore

The ordered pair would be a solution of the system

case 2) (5,2)

For x=5,y=2

Inequality A

$2(5)+3(2) > 12$

$16 > 12$ ----> is true

The ordered pair satisfy inequality A

Inequality B

$5-2\leq 1$

$3\leq 1$ ---> is not true

The ordered pair not satisfy inequality B

therefore

The ordered pair is not a solution of the system

case 3) (0,4)

For x=0,y=4

Inequality A

$2(0)+3(4) > 12$

$12 > 12$ ----> is not true

The ordered pair not satisfy inequality A

therefore

The ordered pair is not a solution of the system

case 4) (6,0)

For x=6,y=0

Inequality A

$2(6)+3(0) > 12$

$12 > 12$ ----> is not true

The ordered pair not satisfy inequality A

therefore

The ordered pair is not a solution of the system

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Don’t know how to graph certain formulas asked by my teacher (geometry

goldfiish [28.3K]

The given vertices of the quadrilateral are

L(- 5, 1), M(- 2, - 2), N(- 1, - 3), O(2, - 2)

We would find the slope of the lines connecting the pairs of vertices. Recall, the opposite sides of a parallelogram are parallel. This means that they would have the same slope. The formula for calculating slope is expressed as

slope = (y2 - y1)/(x2 - x1)

Considering L(- 5, 1) and M(- 2, 2),

x1 = - 5, y1 = 1

x2 = - 2, y2 = 2

slope = (2 - 1)/(- 2 - - 5) = 1/(- 2 + 5) = 1/3

Slope of LM = 1/3

Considering N(- 1, - 3) and O(2, - 2)

x1 = - 1, y1 = - 3

x2 = 2, y2 = - 2

slope = (- 2 - - 3)/(2 - - 1) = (- 2 + 3)/(2 + 1) = 1/3

Slope of NO = 1/3

Since the slopes of the opposite sides are equal, it is a parallelogram

We would plot the coordinates of the vertices on a graph as shown below.

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2 years ago

A deposit of 4,000 at 6.5% for 270 days

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Some institutions use 360 days a year (because then they charge more interest than 365 days).

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4 years ago

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Oksana_A [137]

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4 years ago

In one day, there are two high tides and two low tides in equally spaced intervals. The high tide is observed to be 6 feet above

creativ13 [48]

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The "dependent variable" is the measurement (in feet) above or below the sea level, and this is plotted on the "y-axis". These values cannot be "manipulated" in the sense that one cannot "choose" what value or measurement the tide level would be at any particular time.

Hope these answers—and explanations—are of help to you.
Best wishes!

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4 years ago

point O lies in the interior of angle MNP. if the measure of MNO is x^2 + 10x, the measure of ONP is x^2 - 2x , and the measure

Triss [41]

Answer:

x = 6; ∠ONP = 24°

Step-by-step explanation:

1. Find the value of x

$\begin{array}{rcl}\angle MNP & = & \angle MNO + \angle ONP\\3x^{2} + 12 & = & x^{2} + 10x + x^{2} - 2x\\3x^{2} + 12 & = & 2x^{2} + 8x\\x^{2} + 12 & = & 8x\\x^{2} -8x + 12 & = & 0\\(x - 2)(x - 6) & = & 0\\\end{array}$

$x = 2 \text{ or }x = 6$

2. Find the measures of the angles

(a) x = 2

∠ ONP = x² - 2x = 2² - 2(2) = 4 - 4 = 0

This answer does not make sense because O lies in the interior of ∠MNP.

We disregard x = 2.

(b) x = 6

∠ ONP = x² - 2x = 6² - 2(6) = 36 - 12 = 24

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4 years ago