This is a Fractions as division word problems. NEED HELP!!​

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

==========================================

We have the points (-1, 2) and (4, -3).

Calculate the slope:

[tex]m=\dfrac{-3-2}{4-(-1)}=\dfrac{-5}{5}=-1[/tex]

Put the value of the slope an the coordinates of the point 9-1, 2) to the equation of a line:

[tex]2=(-1)(-1)+b[/tex]

[tex]2=1+b[/tex]              subtract 1 from both sides

[tex]1=b\to b=1[/tex]

Finally:

[tex]y=-x+1[/tex]

Answer:

A line in form of y = ax + b passes (0, 2)

=> 2 = 0x + b => b = 2

This line also passes (4, 6)

=> 6 = 4x + 2 => x = 1

=> Equation of this line: y = x + 2

=> Option C is correct

Hope this helps!

:)

Step-by-step explanation:

Answer:

C.) 4

Step-by-step explanation:

You can solve this a couple ways but I solved it by looking at the graph. g(x) is 4 units above f(x). Adding four to f(x) would shift it up 4 units. Hope that helped.

Answer:

The correct option is C.

Step-by-step explanation:

The translation is defined as

[tex]g(x)=f(x)+k[/tex]

Where, a is horizontal shift and b is vertical shift.

If k>0, then the graph shifts b units up and if k<0, then the graph shifts b units down.

In the given graph red line represents the the function g(x) and blue line represents the function f(x).

y-intercept of g(x) = 1

y-intercept of f(x) = -3

[tex]k=1-(-3)=1+3=4[/tex]

It means the graph of f(x) shifts 4 unit up to get the graph of g(x). So, the value of k is 4.

Therefore the correct option is C.

Answer:

Top to Bottom:

Step-by-step explanation:

Subtract 1 from the number in parentheses (the base of the exponential factor). Multiply the result by 100%. This gives you the percentage growth (positive) or decay (negative).

  (1.12 -1)×100% = +12% (growth)

  (0.88 -1)×100% = -12% (decay)

  (0.80 -1)×100% = -20% (decay)

  (1.22 -1)×100% = +22% (growth)

_____

The sign of the change (+ or -) and the description (growth or decay) convey the same information. It can be confusing to say -12% decay. Rather, the decay is 12%, or the growth is -12%. Above, we tried to indicate that positive is growth and negative is decay. We're not trying to say that the decay is -12%.

Answer:

a) 4 calories per minute

b) 0.25

Step-by-step explanation:

a) If you look at the line it intercepts the x and y axis at the origin (0,0). therefore if you take any point on the line you will see that the calories per minute are constant:

Look at point (40,10)

Calories per minute = x/y = 40/10 = 4

Look at point (80,20)

Calories per minute = x/y = 80/20 = 4

b) you can use any two points on the line. Lets use point 1 as (20,5) and point 2 as (60,15).

The slope of a straight line is defined as:

slope = (y2-y1)/(x2-x1) = (15-5)/(60-20) = 0.25

Answer:

1. If an individual from Swaziland has tested positive, what is the probability that he carries HIV ?

P=0.8249 or 82.49%

2. If an individual from Swaziland has tested negative, what is the probability that he is HIV free ?

P=0.9988 or 99.88%

Step-by-step explanation:

Make the conditional probability table:

  Individual

              Infected       Not infected

ELISA

Positive              

Negative  

Totals      

The probability of an infected individual with a positive result from the ELISA is obtained from multiplying the probability of being infected (25.9%) with the probability of getting a positive result in the test if is infected (99.7%), the value goes in the first row and column:

P=0.259*0.997=0.2582 or 25.82%

              Individual

              Infected       Not infected Totals

ELISA

Positive    25.82%        

Negative    

Totals      

The probability of a not infected individual with a negative result from the ELISA is obtained from multiplying the probability of not being infected (100%-25.9%=74.1%) with the probability of getting a negative result in the test if isn't infected (92.6%), the value goes in the second row and column:

P=0.741*0.926=0.6862 or 68.62%

              Individual

              Infected       Not infected Totals

ELISA

Positive    25.82%        

Negative                     68.62%

Totals      

In the third row goes the total of the population that is infected (25.9%) and the total of the population free of the HIV (74.1%)

Individual:

              Infected       Not infected Totals

ELISA

Positive    25.82%        

Negative                        68.62%          

Totals       25.9%             74.1%          

Each column must add up to its total, so the probability missing in the first column is 25.9%-25.82%=0.08%, and the ones for the second column is 74.1%-68.62%=5.48%.

             Individual

              Infected       Not infected Totals

ELISA

Positive    25.82%          5.48%            

Negative    0.08             68.62%          

Totals       25.9%             74.1%            

             Individual

The third column is filled with the totals of each row:

              Infected       Not infected Totals

ELISA

Positive    25.82%          5.48%            31.3%

Negative    0.08             68.62%          68.7%

Totals       25.9%             74.1%            100%

The probability A of tested positive is 31.3% and the probability B for tested positive and having the virus is 25.82%, this last has to be divided by the possibility of positive.

P(B/A)=0.2582/0.313=0.8249 or 82.49%

The probability C of tested negative is 68.7% and the probability D for tested negative and not having the virus is 68.62%, this last has to be divided by the possibility of negative.

P(D/C)=0.6862/0.687=0.9988 or 99.88%

Answer:

18 antelopes/km^2

Step-by-step explanation: Took the test ;)

Final answer:

The population density of antelopes near the watering hole is approximately 9 antelopes per km² when rounded to the nearest whole number.

Explanation:

The concept of population density is fundamental in ecology and refers to the number of individuals of a species per unit of area.

To calculate population density for the population of antelopes the biologist is studying, we first need to determine the area covered, which is a circle with a radius of 34 km.

Using the given value of pi (3.14), the area (A) is calculated with the formula A = πr², where r is the radius.

The area is therefore 3.14 × (34 km)² = 3.14 × 1,156 km² = 3,629.44 km².

Next, the population density (D) is determined by dividing the number of individuals (N) by the area (A), which in this case is D = N / A = 32 antelopes / 3,629.44 km² ≈ 0.00 88 antelopes per km².

Rounding the final value to the nearest whole number gives us a population density of 9 antelopes per km².

Answer:

The second, third and fourth are parallel to the given equation

Step-by-step explanation:

In order to determine if the slopes are the same, put all of the equations in slope-intercept form:  y = mx + b.  In order for lines in this form to be parallel, the m values of each have to be the exact same number, in our case, 4.  Equation 2 has a 4 in the m position, just like the given, so that one is easy.  Equation 2 is parallel.

Let's solve the third equation for y:

12x - 3y = 6 so

-3y = -12x + 6 and

y = 4x - 2.  Equation 3 is parallel since there is a 4 in the m position.

Let's solve the fourth equation for y:

-20x + 5y = 45 so

5y = 20x + 45 and

y = 4x + 9.  Equation 4 is also parallel since there is a 4 in the m position.

Answer:

  x = 10^10

Step-by-step explanation:

You are right to question the question. As posed, it makes no sense.

The idea of an x-intercept is applicable to a relation involving two variables that can be graphed on a coordinate plane.

If you graph this equation on an x-y plane, it will be a vertical line at x = 10^10, so that would be the x-intercept.

_____

I suggest you ask for an explanation from your teacher.

_____

The graph of y=log(x) is something else entirely, as you know. The x-intercept of that graph is x=1.

Answer:

3 < x OR 5 > x

Step-by-step explanation:

Divide 3 on both sides; move 9 to the other side of the inequality symbol to get 6x < 30. Then divide both sides by 6.

**NOTE: The ONLY time you reverse the inequality sign is when you are dividing\multiplying by a negative [this does not apply so no need to worry].

I am joyous to assist you anytime.

The solution to both the inequalities will lie in (3 , 5) region, this is represented by line C.

An Inequality is the statement formed when two algebraic expressions are equated using an Inequality operator.

The inequalities are

7x>21 and  6x-9<21

    Dividing 7 on the both sides

     x >3

      Adding 9 on both sides

       6x < 30

     Dividing 6 on both sides

      x < 5

Therefore, the solution to both the inequalities will lie in (3 , 5) region, this is represented by line C.

The complete question is attached with the answer.

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Answer:

median: 10.1

mean: 10.333

SD: 0.632

The median of the data set is 10.1 mph. The mean of the data set is 10.26 mph. The population standard deviation of the data set is approximately 0.5339 mph.

The median of a data set is the middle value when the data is arranged in ascending or descending order. To find the median of the given data set, we need to arrange the wind speeds in ascending order:

Since we have 12 values in the data set, the median will be the average of the 6th and 7th values, which are both 10.1. Therefore, the median of the data set is 10.1 mph.

The mean or average of a data set is found by summing all the values and dividing by the number of values. For the given data set, the sum of the wind speeds is 123.1 mph (9.6 + 9.7 + 9.9 + 9.9 + 10.0 + 10.1 + 10.1 + 10.3 + 10.7 + 10.8 + 11.0 + 11.9) and there are 12 values. Dividing the sum by 12, the mean of the data set is 10.26 mph.

The population standard deviation is a measure of the spread or dispersion of the data. To calculate it, we need to subtract the mean from each value, square the result, sum them all, divide by the number of values, and take the square root. Using the given wind speeds:

Summing these values gives us 3.4368. Dividing by 12, we get 0.2864. Finally, taking the square root, the population standard deviation of the data set is approximately 0.5339 mph.

Answer:

The length of rectangular plot of land is 160 ft.

Step-by-step explanation:

L = 2 W (the length is twice the width)

P = 480 ft. (perimeter of rectangular plot of land)

L = ?

2. 2W + 2W= 480 ft  >>> (2 times twice width=L) + 2W=480 ft.

4W + 2W= 480 ft >>>> 6W= 480 ft.

W= 80 ft.

L = 2. 80 = 160 ft. (Length is twice the width)

P= 2L + 2W (formula for the perimeter)

2. 160 + 2. 80 = 480 ft.

Answer:  

Outcome     :  A(Country)    B(Rock & roll)    C(blues)

Probability  :     [tex]\dfrac{11}{36}[/tex]                     [tex]\dfrac{17}{36}[/tex]                     [tex]\dfrac{1}{9}[/tex]

Step-by-step explanation:

A probability model is a mathematical display of a random situation S contain various sets .

Let A be the event that they play a country music, B be the event that they play rock & roll and C be the event that they play blues.

Then , n (A) = 11, n(B)=17 and n(C)=8

Let S be the combined set of number of times music played in local restaurant.

Then ,  [tex]n(S)=11+17+8=36[/tex]

Then , [tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{11}{36}[/tex]

[tex]P(B)=\dfrac{n(B)}{n(S)}=\dfrac{17}{36}[/tex]

[tex]P(C)=\dfrac{n(C)}{n(S)}=\dfrac{8}{36}=\dfrac{1}{9}[/tex]

Now, the required probability model:-

Outcome     : A(Country)    B(Rock & roll)    C(blues)

Probability  :     [tex]\dfrac{11}{36}[/tex]                     [tex]\dfrac{17}{36}[/tex]                     [tex]\dfrac{1}{9}[/tex]

Answer:

country = 0.31

rock and roll =0.47

Blues = 0.22

Step-by-step explanation: Here we go :O

Let's put the count of each type of music from the sample into a table.

country = 11

Rock and roll= 17

blues = 8

Total = 36

We get the probabilities by dividing the frequencies by the total. (Remember to round to the nearest hundredth.)

11/36 = country

17/36 = rock and roll

8/36 = blues

Divide these

country = 0.31

rock and roll =0.47

Blues = 0.22

Answer:

Ostrich can run in 5 second = 105 meter .

Step-by-step explanation:

Given  : The double number line shows that in 3 seconds an ostrich can run 63 meters .

To find : Based on the ratio shown in the double number line how far can the ostrich run in 5 seconds.

Solution : We have given

ostrich can run in 3 second = 63 meter .

Let ostrich can run in 5 second = x meter .

By the Ratio : 63 : 3 :: x : 5

[tex]\frac{63}{3} =\frac{x}{5}[/tex]

On cross multiplication

63 * 5 = 3 * x

315 = 3 x

On dividing both sides by 3

x = 105 meter .

Therefore, ostrich can run in 5 second = 105 meter .

Check the picture below.

For this case we have to define trigonometric relationships in rectangular triangles that the sine of an angle is given by the leg opposite the angle, on the hypotenuse of the triangle.

If we have to:

[tex]Sin A = \frac {3} {5}[/tex]

So:

Leg opposite angle A is: 3

The hypotenuse is: 5

If we apply the Pythagorean theorem, we find the value of the other leg:

[tex]x = \sqrt {5 ^ 2-3 ^ 2}\\x = \sqrt {25-9}\\x = \sqrt {16}\\x = 4[/tex]

So, the Sine of B is given by:

[tex]Sin B = \frac {4} {5}[/tex]

Answer:

[tex]SinB = \frac {4} {5}[/tex]

[tex]\bf \begin{array}{ccll} term&value\\ \cline{1-2} s_5&10\\ s_6&10r\\ s_7&10rr\\ s_8&10rrr\\ &10r^3 \end{array}\qquad \qquad \stackrel{s_8}{80}=10r^3\implies \cfrac{80}{10}=r^3\implies 8=r^3 \\\\\\ \sqrt[3]{8}=r\implies \boxed{2=r} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ s_n=s_1\cdot r^{n-1}\qquad \begin{cases} s_n=n^{th}\ term\\ n=\textit{term position}\\ s_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=8\\ s_8=80\\ r=2 \end{cases}\implies 80=s_1(2)^{8-1} \\\\\\ 80=s_1(2)^7\implies \cfrac{80}{2^7}=s_1\implies \cfrac{80}{128}=s_1\implies \boxed{\cfrac{5}{8}=s_1}[/tex]

Answer:

A. X = 15 is the correct answer.

Step-by-step explanation:

It's the only one that really makes sense.

Hope this helped :)

The value of the variable x will be 15. Then the correct option is A.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoid, one pair of opposite sides are parallel.

The trapezoid is an isosceles trapezoid.

An isosceles trapezoid is the form of trapezoid on which the non-parallel sides are of equal length.

In the isosceles trapezoid, the sum of the opposite angles is 180 degrees.

Then the sum of the angle B and angle D will be 180°.

∠B + ∠D = 180°

 9x + 3x = 180

        12x = 180°

            x = 180°

            x = 15°

Thus, the value of the variable x will be 15.

Then the correct option is A.

The question was incomplete, but the complete question is attached below.

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Answer:

12

Step-by-step explanation:

Alright so we are asked to find the intersection of y=(x-8)^2 and y=36.

So plug second equation into first giving:  36=(x-8)^2.

36=(x-8)^2

Take square root of both sides:

[tex]\pm 6=x-8[/tex]

Add 8 on both sides:

[tex]8 \pm 6=x[/tex]

x=8+6=14 or x=8-6=2

So we have the two intersections (14,36) and (2,36).

We are asked to compute this length.

The distance formula is:

[tex]\sqrt{(14-2)^2+(36-36)^2}[/tex]

[tex]\sqrt{14-2)^2+(0)^2[/tex]

[tex]\sqrt{14-2)^2[/tex]

[tex]\sqrt{12^2}[/tex]

[tex]12[/tex].

I could have just found the distance from 14 and 2 because the y-coordinates were the same. Oh well. 14-2=12.

Answer:

See explanation

Step-by-step explanation:

We can express

[tex] \tan( \theta) = \frac{ \sin \theta}{ \cos \theta } [/tex]

in so many ways using trigonometric identities.

Let us rewrite to obtain:

[tex]\tan( \theta) = \frac{1}{ \cos \theta } \times \sin \theta[/tex]

This implies that

[tex]\tan( \theta) = \sec \theta \sin \theta[/tex]

When we multiply the right side by

[tex] \frac{ \cos \theta}{ \cos \theta} [/tex]

we get:

[tex]\tan( \theta) = \frac{ \sin \theta \cos \theta }{ \cos ^{2} \theta } [/tex]

[tex]\tan( \theta) = \frac{ \sin 2\theta }{ 2 - 2\sin^{2} \theta } [/tex]

Etc

Answer:

Perpendicular intersecting lines.

Step-by-step explanation:

A '+' has intersecting perpendicular lines.

Answer:

∠ZYX = 58°

Step-by-step explanation:

The measure of an inscribed angle or a tangent- chord angle is one half the measure of the intercepted arc.

arc XY is the intercepted arc, hence

∠ZYX = 0.5 × 116° = 58°

Answer: [tex]ZYX=58\°[/tex]

Step-by-step explanation:

It is important to remember that, by definition:

[tex]Tangent\ chord\ Angle=\frac{1}{2}Intercepted\ Arc[/tex]

 In this case you know that for the circle shown in the figure, the arc XY measures 120 degrees, therefore you can find the measure of the angle ZYX. Then you get that the measure of the this angle is the following:

[tex]ZYX=\frac{1}{2}XY\\\\ZYX=\frac{1}{2}(116\°)\\\\ZYX=58\°[/tex]

Answer:

Step-by-step explanation:

The base of the exponential factor in a growth formula is the growth factor. Here, that is 1.30. It represents the multiplier of the number of spores each week.

Putting 4 into the formula, we find ...

  f(4) = 345×1.30^4 ≈ 985 . . . . mold spores after 4 weeks

Answer:

george floyd

Step-by-step explanation:

cmon start bouncing

Answer:

46.80 m

Step-by-step explanation:

Given:

Magnetic field, B = 2.6 kG = 2600 G = 0.26T

Diameter of the plastic tube = 12 cm = 0.12m

Length of the plastic tube = 60 cm

Current, I = 2 A

The formula for the magnetic field (B) at the center of a solenoid is calculated as:

[tex]B=\frac{\mu_oNI}{L}[/tex]

where,

I = current

N = Turns

L = Length

[tex]\mu_o[/tex]= permeability of the free space

on substituting the values in the above equation, we get

[tex]0.26=\frac{4\pi \times10^{-7}\times N\times 2}{0.6}[/tex]

or

N = 62070.42 Turns

also, each turn is a circumference of the plastic tube.

The circumference of the plastic tube, C = 2π×0.12 =  0.7539 m

Thus,

The total length of the wire required, L = (62070.42) × 0.7539 m = 46799.99 ≈ 46800 m  = 46.80 km

Sample size--

It is the collections of all the possible outcomes of an event.

(A)

It is given that:

Shona spins a spinner with three equal-sized spaces—red, green, and yellow and then rolls a six-sided die numbered from 1 to 6.

This means that the possible outcomes are given as follows:

(Red,1)          (Green,1)           (Yellow,1)

(Red,2)         (Green,2)          (Yellow,2)

(Red,3)         (Green,3)           (Yellow,3)

(Red,4)         (Green,4)           (Yellow,4)

(Red,5)         (Green,5)           (Yellow,5)

(Red,6)         (Green,6)           (Yellow,6)

This means that the total number of outcomes are: 18

Hence, the sample size for this compound event is:  18

(B)

If the spinner has four colored spaces.

Let the fourth color be: Blue

Then the possible outcomes are given by:

(Red,1)          (Green,1)           (Yellow,1)           (Blue,1)

(Red,2)         (Green,2)          (Yellow,2)          (Blue,2)

(Red,3)         (Green,3)           (Yellow,3)          (Blue,3)

(Red,4)         (Green,4)           (Yellow,4)          (Blue,4)  

(Red,5)         (Green,5)           (Yellow,5)          (Blue,5)

(Red,6)         (Green,6)           (Yellow,6)          (Blue,6)

Hence, the total number of outcomes are:  24

The sample size of this compound event would be 24.

Answer:

a- 18

b- 24

Step-by-step explanation:

Answer:

  about 32,000

Step-by-step explanation:

You are being asked to evaluate the quartic for x=7.

f(7) = (((-0.022·7 +0.457)7 -2.492)7 -5279)7 +87.419

  = ((.303·7 -2.492)7 -5.279)7 +87.419

  = (-0.371·7 -5.279)7 +87.419

  = -7.876·7 +87.419

  = 32.287

The number of dolls sold in 2000 was approximately 32,000.

Answer:

B: between 1 and 2

Step-by-step explanation:

Since you share 5 kg amongst 4 you need to divide it by 4.

5 / 4 = 1.25 kg

This is between 1 and 2 kg

Answer: B. Between 1 and 2 kilograms.

Step-by-step explanation: Divide the amount of coffee by the number of people.

5/4=1.25.

Each person will get 1.25 kilograms of coffee, which is between 1 and 2 kilograms.

The question is vague and lacks crucial contextual information required to provide a reliable mathematical proof.

Unfortunately, the question is ambiguous and it lacks the sufficient details to be able to provide a reliable proof. Based on the information provided it appears to be algebraic or geometric. If it's an algebraic equation, such as m+5 = m+6, the proof m+3 = m+4 would not hold since this would imply that 3 = 4 which is not true.

If it's related to geometric figures like angles or sides of a triangle where m represents the measure of an angle or length of a side, we need concrete contextual information to proceed. With more specific details, the required steps to solving your problem could be accurately outlined.

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To prove m3 = m4, we use the given information that m5 = m6 and apply the transitive property of equality.

Given: m5 = m6

We need to prove: m3 = m4

Using the given information, we can see that m5 = m6. This means that the measures of angles 5 and 6 are equal.

By the transitive property of equality, if m5 = m6 and m6 = m3, then m5 = m3.

Similarly, if m5 = m6 and m6 = m4, then m5 = m4.

Therefore, we have proven that m3 = m4.

Answer: [tex]ZYX=60\°[/tex]

Step-by-step explanation:

It is important to remember that, by definition:

[tex]Tangent\ chord\ Angle=\frac{1}{2}Intercepted\ Arc[/tex]

 In this case you know that for the circle shown in the figure, the arc XY measures 120 degrees, therefore you can find the measure of the angle ZYX. Then you get that the measure of the this angle is the following:

[tex]ZYX=\frac{1}{2}XY\\\\ZYX=\frac{1}{2}(120\°)\\\\ZYX=60\°[/tex]

Answer:

∠ZYX = 60°

Step-by-step explanation:

The measure of an inscribed angle or tangent- chord angle is one half the measure of its intercepted arc, hence

∠ZYX = 0.5 × 120° = 60°

Answer:

The area is equal to [tex]8\ units^{2}[/tex]

Step-by-step explanation:

we have

A(0, 0), B(2, -2), C(0, -4), D(-2, -2)

Plot the figure

The figure is a square (remember that a regular polygon has equal sides and equal internal angles)

see the attached figure

The area of the square is

[tex]A=AB^{2}[/tex]

Find the distance AB

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

substitute the values

[tex]AB=\sqrt{(-2-0)^{2}+(2-0)^{2}}[/tex]

[tex]AB=\sqrt{(-2)^{2}+(2)^{2}}[/tex]

[tex]AB=\sqrt{8}[/tex]

[tex]AB=2\sqrt{2}\ units[/tex]

Find the area of the square

[tex]A=(2\sqrt{2})^{2}[/tex]

[tex]A=8\ units^{2}[/tex]

Answer:

  The ball bounces to 70% of its previous height with each bounce.

Step-by-step explanation:

In physics terminology, the number 0.7 is the coefficient of restitution. It is the ratio of the height of bounce (n+1) to the height of bounce (n).

The meaning of the number is that the ball bounces to 70% of the height of the previous bounce.

Answer:

The ball bounces to 70% of its previous height with each bounce.

Step-by-step explanation:

A ball is dropped from a certain height. The function below represents the height f(n), in feet, to which the ball bounces at the nth bounce:

f(n) = 9(0.7)n

The number 0.7 represents that the ball bounces to 70% of its previous height with each bounce.

Answer:

  A.  -12

Step-by-step explanation:

A graph shows the vertices of the feasible region to be (0, 6), (3, 0) and (0, -3). Of these, the one that minimizes f(x, y) is (0, -3). The minimum value is ...

  f(0, -3) = 3·0 + 4(-3) = -12

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Comment on the graph

Here, three regions overlap to form the region where solutions are feasible. By reversing the inequality in each of the constraints, the feasible region shows up on the graph as a white space, making it easier to identify. The corner of the feasible region that minimizes the objective function is the one at the bottom, at (0, -3).

The minimum value of the function f(x,y) = 3x+4y in the feasible region defined by the given system of inequalities is -19, which unfortunately does not match any of the given options. The steps involve graphing the inequalities, finding the vertices of the feasible region, and substituting those points into the function to find the minimum value.

This problem includes finding the minimum value of the given function in a defined region dictated by the system of inequalities. I will guide you step by step on how to reach the solution. This is basically an optimization problem dealing with linear programming. The system of inequalities yields a feasible region, and the function you want to minimize is the given f(x, y) = 3x + 4y.

Your first step is to graph the inequalities and find the feasible region, this will give you the points (vertices) that we need. The inequalities are: y ≥ x ­- 3,  y ≤ 6 ­- 2x and 2x + y ≥ - ­3. By graphing these inequalities, the intersection points are: (3,0), (1,-2), and (-1,-4).

The minimal value for the function, f(x,y), must be at one of these vertices. Substitute each of these points into the function f(x,y) = 3x+4y to see which gives the smallest result:

Therefore, the minimum value of f(x,y) in this region is -19, however, this option is not listed among your choices. It may be that there's a mistake. Ensure you've copied the questions and options accurately.

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