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3 years ago

What is the minimum value of 2x + 2y in the feasible region?

1 answer:

6 0

Find and graph the feasible region for the following constraints: x + y < 5. 2x + y > 4 ... y = 10/3. x = 30/3 - 10/3 = 20/3. Intersects at (20/3, 10/3). -x + 2y = 0. x - 2y = 0.

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John has decided to prepare an old field for his son's new horse. the length of the field is 10 meters less than 4 times its wid

tatuchka [14]

Answer: The total money invested in the field will be $1,623.80

Step-by-step explanation:

step 1

Find the dimensions of the field

Let

x -----> the length of the field

y -----> the width of the field

p=2(x+y)

p(4.80)=1,584

p=330m

we know that

The perimeter of the field is equal to

330=2(x+y)----> equation A

x=4y-10 ------> equation B

substitute equation B in equation A and solve for y

330=2(4y-10+y)

165=(5y-10)

5y=165+10

y+35

Find the value of x

x=4(35)-10+130

therefore

The length of the field is 130 meters and the width of the field is 35 meters

step 2

Find the area of the field

The area of the field is

A=xy

substitute

A=(130)(35)=4,550m2

step 3

Find the number of bags of seed

Divide the area by 460

4,550/460=9.89 bags

Round up to the nearest whole number

9.89 bags=10 bags

step 4

Find the cost of the seed

(10 )(3.98)=$19.8

step 5

Find the total money invested in the field

1,584+$39.8=$1,623.80

7 0

2 years ago

Read 2 more answers

The difference between the two roots of the equation 3x^2+10x+c=0 is 4 2/3 . Find the solutions for the equation.

andrezito [222]

Answer:

Given the equation: $3x^2+10x+c =0$

A quadratic equation is in the form: $ax^2+bx+c = 0$ where a, b ,c are the coefficient and a≠0 then the solution is given by :

$x_{1,2} = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$ ......[1]

On comparing with given equation we get;

a =3 , b = 10

then, substitute these in equation [1] to solve for c;

$x_{1,2} = \frac{-10\pm \sqrt{10^2-4\cdot 3 \cdot c}}{2 \cdot 3}$

Simplify:

$x_{1,2} = \frac{-10\pm \sqrt{100- 12c}}{6}$

Also, it is given that the difference of two roots of the given equation is $4\frac{2}{3} = \frac{14}{3}$

i.e,

$x_1 -x_2 = \frac{14}{3}$

Here,

$x_1 = \frac{-10 + \sqrt{100- 12c}}{6}$ , ......[2]

$x_2= \frac{-10 - \sqrt{100- 12c}}{6}$ .....[3]

then;

$\frac{-10 + \sqrt{100- 12c}}{6} - (\frac{-10 + \sqrt{100- 12c}}{6}) = \frac{14}{3}$

simplify:

$\frac{2 \sqrt{100- 12c} }{6} = \frac{14}{3}$

$\sqrt{100- 12c} = 14$

Squaring both sides we get;

$100-12c = 196$

Subtract 100 from both sides, we get

$100-12c -100= 196-100$

Simplify:

-12c = -96

Divide both sides by -12 we get;

c = 8

Substitute the value of c in equation [2] and [3]; to solve $x_1 , x_2$

$x_1 = \frac{-10 + \sqrt{100- 12\cdot 8}}{6}$

$x_1 = \frac{-10 + \sqrt{100- 96}}{6}$ or

$x_1 = \frac{-10 + \sqrt{4}}{6}$

Simplify:

$x_1 = \frac{-4}{3}$

Now, to solve for $x_2$ ;

$x_2 = \frac{-10 - \sqrt{100- 12\cdot 8}}{6}$

$x_2 = \frac{-10 - \sqrt{100- 96}}{6}$ or

$x_2 = \frac{-10 - \sqrt{4}}{6}$

Simplify:

$x_2 = -2$

therefore, the solution for the given equation is: $-\frac{4}{3}$ and -2.

3 0

3 years ago

Which is a better deal 12.4 ounces for $4.99 or 21 ounces for $6.49?

ella [17]

Answer:

Getting 21 ounces for $6.49 is a better deal!

Step-by-step explanation:

4.99 / 12.4 = 0.402419...

6.49 / 21 = 0.30904...

0.4 is larger than 0.30 therefore 0.30 is less and a better deal.

Have an amazing day! ^-^

4 0

3 years ago

. What is the solution set for this inequality? -3r+5<-7 please answer quickly!

irinina [24]

Answer:

r>4

Step-by-step explanation:

-3r+5<-7

-3r+5-5 <-7-5

-3r<-12

-3r/3

12/3

r>4

4 0

3 years ago

What are the coordinates of the midpoint between the points (-1,4) and (2,-5)

Minchanka [31]

Answer:

(1/2, -1/2)

Step-by-step explanation:

To find a midpoint add the two x's and divide by 2 so -1+2 / 2 = 1/2

add the two y's and divide by 2 so 4-5 / 2 = -1/2

Put the two numbers together as a coordinate (1/2, -1/2)

5 0

3 years ago