What’s the conjugate of 2x+3

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

andriy [413]

Answer:

The point that maximizes the objective function is (3,0)

Step-by-step explanation:

we have

Constraints:

$x\geq 0\\y\geq 0\\-x + 3\geq y\\y\leq \frac{1}{3}x+1$

Using a graphing tool

The feasible region is the shaded area

see the attached figure

The vertices of the feasible region are

(0,0),(0,1),(1.5,1.5) and (3,0)

we know that

To find the point in the feasible region that maximizes the objective function, replace each ordered pair of vertices in the objective function and then compare the results.

The objective function is

$C=5x-4y$

For (0,0) -----> $C=5(0)-4(0)=0$

For (0,1) -----> $C=5(0)-4(1)=-4$

For (1.5,1.5) -----> $C=5(1.5)-4(1.5)=1.5$

For (3,0) -----> $C=5(3)-4(0)=15$

therefore

The point that maximizes the objective function is (3,0)

8 0

3 years ago

A combined total of $53,000 is invested in two bonds that pay 5% and 6.5% simple interest. The annual interest is $3,085.00. How

m_a_m_a [10]

Answer:

Step-by-step explanation:

the amount of money invested at the rate of 5% is $24000

the amount of money invested at the rate of 6.5%. Is $29000

Step-by-step explanation:

Let x represent the amount of money invested at the rate of 5%.

Let y represent the amount of money invested at the rate of 6.5%.

The combined total of $53,000 is invested in two bonds that pay 5% and 6.5% simple interest.. This means that

x + y = 53000

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time

Considering the investment at the rate of 5%,

P = x

R = 5

T = 1

I = (x × 5 × 1)/100 = 0.05x

Considering the investment at the rate of 6.5%,

P = y

R = 6.5

T = 1

I = (y × 6.5 × 1)/100 = 0.06.5y

The annual interest is $3,085.00.

it means that

0.05x + 0.065y = 3085 - - - - - -1

Substituting x = 53000 - y into equation 1, it becomes

0.05(53000 - y) + 0.065y = 3085

2650 - 0.05y + 0.065y = 3085

- 0.05y + 0.065y = 3085 - 2650

0.015y = 435

y = 435/ 0.015 = 29000

Substituting y = 29000 into

x = 53000 - y

x = 53000 - 29000

x = $24000

6 0

3 years ago

If MN=14, NO=11, and QR=27, find the length of PQ. Round your answer to the nearest tenth if necessary. Figures are not necessar

allsm [11]

Answer:

PQ = 34.4

Step-by-step explanation:

First, we know that the angles in a triangle add up to 180 degrees. Therefore, angle M = 48 and angle R = 74

Next, because there is a corresponding angle in each triangle, they are similar. This means that the ratios between corresponding sides are the same. For example, the side opposite angle O (MN) over the side opposite angle R (PQ) is equal to the side opposite angle N (OM) over the side opposite angle Q (RP)

This can be written as MN/PQ = OM/RP. Note that both the numerators are on the same triangle, and MN and PQ correspond, as well as OM and RP.

We are given MN, NO, and QR. Because NO is opposite a 48 degree angle (angle M) as well as QR (angle P), we can say that NO/QR = another ratio of a pair of corresponding sides. Because we want to find PQ, and both PQ and MN are opposite 74 degree angles, we can say that

NO/QR = MN/PQ

Thus,

11/27 = 14/PQ

multiply both sides by PQ to remove a denominator

PQ * 11/27 = 14

multiply both sides by 27 to remove the other denominator

PQ * 11 = 14 * 27

divide both sides by 11 to isolate the PQ

PQ = 14 * 27 /11

PQ = 34.4

4 0

3 years ago

Find the slope of the line that contains (−9, 1) and (3, 6).

Neko [114]

Answer:

5/12

Step-by-step explanation:

slope is $\frac{1y-2y}{1x-2x}$

so $\frac{6 - 1}{3 - (-9)}$ and that is 5/12

Please mark brainliest!!! Thanks.

6 0

3 years ago

Which of the numbers below is the next number in the following pattern?<br> 2,-3,4,-5,

GarryVolchara [31]

Answer:

df

Step-by-step explanation:

8 0

3 years ago