Which expression could be modeled by decimal grid?

Please Help ASAP! Will name Brainliest! Question: Minimize the objective function P = 5x + 8y for the given constraints. x ≥ 0 y

maksim [4K]

Answer:

Option D.

Step-by-step explanation:

Minimize the objective function P = 5x + 8y for the given constraints.

$x\geq 0,y\geq 0$

$2x+3y\geq 15$

$3x+2y\geq 15$

The related equations of above inequalities are

$2x+3y=15$

$3x+2y=15$

For $2x+3y=15$ ,

x y

0 5

7.5 0

Plot (0,5) and (7.5,0) and join them by straight line.

For $3x+2y=15$ ,

x y

0 7.5

5 0

Plot (0,7.5) and (5,0) and join them by straight line.

Check the inequalities for (0,0).

$2(0)+3(0)\geq 15\Rightarrow 0\geq 15$ False

$3(0)+2(0)\geq 15\Rightarrow 0\geq 15$ False

It means both lines are solid lines and shaded region for each lies opposite side of (0,0).

From the below graph it is clear that the vertices of feasible region are (0,7.5), (3,3), (7.5,0).

Point P = 5x + 8y

(0,7.5) P=5(0)+8(7.5)=60

(3,3) P=5(3)+8(3)=15+24=39

(7.5,0) P=5(7.5)+8(0)=37.5 (Minimum)

So, minimum value is 37.5.

Therefore, the correct option is D.

3 0

2 years ago

In a bucket, there are 5 red marbles, 3 blue marbles, and 2 green marbles. A marble is chosen randomly and then put back into th

nadezda [96]

Answer:

The required probability is $\frac{1}{10}$ .

Step-by-step explanation:

Probability:

The ratio of the favorable outcomes to the all possible outcomes.

Given that, in a bucket, there are 5 marbles red in color, 3 marbles blue in color and 2 marbles green in color.

Total number of marbles are = 5+3+2= 10

The probability that first marble was red

$=\frac{\textrm{Number of red marbles}}{\textrm{Total number of marbles}}$

$=\frac{5}{10}$

$=\frac12$

The probability that second marble was green is

$=\frac{\textrm{Number of green marbles}}{\textrm{Total number of marbles}}$

$=\frac{2}{10}$

$=\frac15$

The required probability is

$=\frac12 \times \frac15$

$=\frac1{10}$

8 0

2 years ago

Places A and B are 100km apart from each other on a highway. A car starts from A and another from B at the same time. If they mo

Mashutka [201]

Answer:

Speed of the first car = x = 35km/hr

Speed of the second car = 25km /hr

Step-by-step explanation:

The calculation of speeds of the cars is given below:-

Assume that the speed of the 1st car which is opening from A = x km/hr

and assume the Speed of the 2nd car which is starting from B

= y km/hr

As we know that

Time = Distance ÷ Speed

So, the distance lies between two places i.e. A and B are

80km d = 80 km

1. now when the car moves in the similar direction

So, the corresponding speed of them = (x + y)km/hr

Time = 8hr

d = 80km

$8 = \frac{80}{(x + y)}\\\\x + y = \frac{80}{8}\\\\x + y = 10 ..... (i)$

2. when two cars moving in the inverse direction,

So, the corressponding speed = (x - y) km / hr

Time = 1 hr 20 minutes

That means

= (1 + 20 ÷ 60) hr

= (80 ÷ 60)

= 4/3 hr

d = 80km

Now

4 ÷ 3 = 80 ÷ (x -y)

x -y = (80 × 3) ÷ 4

x - y = 60 ..... (ii)

Now, we will sum equation 1 and equation 2 we will get

2x = 70

x = 35

now, Put x = 35 in (i) we will get

y = 25

Speed of the first car = x = 35km/hr

Speed of the second car = 25km /hr

8 0

3 years ago

1. Graph the set of integers (-2, -5, 1} on a number<br> line.

ivanzaharov [21]

Answer: Its below

Step-by-step explanation:

4 0

2 years ago

Find the coordinates of the fourth vertex that completes the construction of the rectangle on the coordinate plane.

Feliz [49]

Answer:

There is no given picture or enough information to reply with a detailed answer. My apologies

Step-by-step explanation:

Perhaps a image upload failure?

7 0

3 years ago

Read 2 more answers