Please help thank you..

I need the answers and explanation to a b c and d

snow_lady [41]

Answer:

a) 4x -3y ≥ -24

b) 2x +3y ≥ -12

c) 4x -3y ≤ 12

d) 2x +3y ≤ 24

Step-by-step explanation:

All of the given points are on the axes, so it is useful to know the intercept form of the equation for a line is ...

x/a +y/b = 1 . . . . . . where a is the x-intercept and b is the y-intercept.

The boundary line for the first side is ...

x/-6 +y/8 = 1

4x -3y = -24 . . . . . . multiply by -24 to put in standard form

The graph shows the quadrilateral is to the right of this line, so its inequality is ...

4x -3y ≥ -24

__

The boundary line for side 2 has equation ...

x/-6 +y/-4 = 1

2x +3y = -12 . . . . . multiply by -12

The quadrilateral is to the right of this line, as well, so its inequality is ...

2x +3y ≥ -12

__

We can see from the graph that the x-intercept of the boundary line for side 3 is x=3. The equation for that boundary line is ...

x/3 +y/-4 = 1

4x -3y = 12

The quadrilateral is to the left of this line, so its inequality is ...

4x -3y ≤ 12

__

Apparently, side 4 is intended to use points already given. We assume it passes through (6, 4) and (0, 8). This boundary is parallel to side 2, so will have the same equation, but with a different constant.

2x +3y = 2(0) +3(8) = 24

The quadrilateral is to the left of this line, so its inequality is ...

2x +3y ≤ 24

__

The second attachment shows a graph of the four inequalities with their shading.

_____

<em>Additional comment</em>

All of the inequalities are written in standard form, so the x-coefficient is positive for all of them. The direction of the inequality symbol can be chosen to select values of x that are greater than or less than those on the boundary line. If the shading is to be to the right, then larger x-values are required, and the inequality will have the form ax + by ≥ c (a > 0). If shading is to the left, then smaller x-values are required, and the inequality symbol points in the other direction.

The figure is a parallelogram, not a rectangle.

7 0

2 years ago

A bacteria culture contains 100 cells and grows at a rate proportional to its size. After one hour the population has increased

xenn [34]

We know it begins at 100. If we use a*b^t, then 100 is our a. 100*b^t. We can now divide 480 by 100. This is 4.8. 4.8 is b. f(t) = 100(4.8)^t

7 0

2 years ago

Part A

alexgriva [62]

Answer:

6=2 , 12=4, 15=5, 24=8

Step-by-step explanation:

6 0

3 years ago

Daniel left a $9 tip for the waiter at a restaurant. If the tip was 15 percent of the bill, how much was the bill?

Pie

Without the tip it was $60. If you are being asked to add the tip it will be $69

5 0

3 years ago

Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calcul

umka21 [38]

Answer:

The number of calculators is 4871

Step-by-step explanation:

If we integrate dx/dt we get x, which is the number of calculators. To find the number of calculators between the beginning of third week to the end of fourth week (the beginning of fifth week), this integration must be evaluated at t between 3 and 5.

$x=\int\limits^5_3 {\frac{dx}{dt}} \, dt =\int\limits^5_3 {5000(1-\frac{100}{(t+10)^2})} \, dt$

the result of the integration is:

$x=5000(t+\frac{100}{t+10})$ to be evaluated between 3 and 5, which is:

$x=5000(5+\frac{100}{5+10})-5000(3+\frac{100}{3+10})=\frac{190000}{39}=4871.8$

6 0

3 years ago