Mathematics, 08.07.2019 06:00 yoyo6710

1)which system of linear inequalities is graphed? a){x< −2y≤−x−1 b){x< −3y≤−x+1 c){x≤−3y≤−x−3 d){x< −3y≤−x−1 2)which system of linear inequalities is graphed? a) {y≤2x+1x+y≥−2 b) {y≥2x+1x+y≤−2 c) {y< 2x+1x+y> −2 d) {y> 2x+1x+y< −2

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Answer from: twistedhyperboles

1 ) D

2 ) D

Step-by-step explanation:

The general form of the straight line is given by y=mx+c, where m is the slope and c is y-intercept.

1 ) According to the graph, we get the co-ordinates (0,-1) and (-1,0).

Using these so-ordinates, we will find the equation of the line.

i.e. Slope $m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

i.e. $m = \frac{0-(-1)}{-1-0}$

i.e. m = -1

Now, substituting m and (0,-1) in general form, we get c = -1.

So, the equation of this straight line is y = -x-1.

We will now use 'Zero Test' i.e. substitute (0,0) in the required equation and since the given regions are away from the origin, this pair of points will not satisfy the equation.

So, we get y < -x-1 and as the region is given to less than x= -3.

Hence, option D is correct.

2) Now, according to the second graph, we get the points (0,-2), (-2,0) and (0,1), (-1,-1) for two lines respectively.

Solving as in 1) we get that the equations of the lines are given by x+y = -2 and y = 2x+1 respectively.

Again using 'Zero Test', we see that these pair of points does not satisfy the equations.

So, we get x+y < -2 and y > 2x+1.

Hence, option D is correct.

Answer from: Quest

x= -3 and $x=\frac{-3+/-3i\sqrt{3} }{2}$

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

$(x^3-a^3)=$ $(x-a)(x^2+ax+a^2)$

where a is the cube root of $a^3$ .

here this is 27 and the cube root of 27 is 3. so we write using the form:

$(x-3)(x^2+(3)x+3^2)\\(x-3)(x^2+3x+9)$ .

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

where a = 1, b=3, and c=9

$x=\frac{-3+/-\sqrt{3^2-4(1)(9)} }{2(1)} \\x=\frac{-3+/-\sqrt{9-36)} }{2} \\x=\frac{-3+/-\sqrt{-27)} }{2}\\x=\frac{-3+/-3i\sqrt{3} }{2}$

this cubic has two complex roots.

Answer from: Quest

1. isolate the variable, in this case, d. subtract 35.5 on both sides of the equation.2. 52 subtracted by 35.5 is 16.53. therefore your answer would be d= 16.5this is the basics of pre algebra, isolating variable through adding, subtracting, multiplying, and dividing, if you have any other questions to ask just comment!

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1)which system of linear inequalities is graphed? a){x< −2y≤−x−1 b){x< −3y≤−x+1 c){x≤−3y≤−x−3...

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