Write in Interval form/notation

The maximum value of the objective C = 5x -4y over given constraints is

In any optimization problem, when we need to either maximize or minimize some objective function for that we are given some limitations or logical conditions which the objective function  needs to satisfy in order to maximize or minimize.

These constraints are in the form of equalities or inequalities, where a feasible region satisfying all these equalities or inequalities is first found and then we maximize/minimize our objective on the boundary points of this feasible region.

Given problem is:

Maximize Objective function C = 5x-4y

When system of constraints are (i) x≥0 , (ii) y≥0 , (iii) 4 ≤y+ x

(iv) y ≤ (1/5)x +1

We will graph this system of constraints to find the feasible area.

x≥0,y≥0 represents that feasible area is in the 1st quadrant

For 4 ≤ x + y, we will use corresponding x+ y = 4 equality

When x= 0 then y=4 and when y=0 then x=4 , then y+ x = 4 is a line passing through (0,4) and (4,0)

When be substitute (0,0) in 4 ≤ x + y we get 4 ≤0 which is a false statement .

Therefore,4 ≤y + x is the region starting with line x+ y = 4 and area above this line in opposite direction of origin.

For y ≤ (1/5)x +1, we will use y = (1/5)x +1, put x= 0 we get y=1 and put y=0 then x= -5 , then y= (1/5)x +1 is a line passing through (0,1) and (-5,0)

And on substituting (0,0) in y ≤ (1/3)x +1 we get 0 ≤ 1 which is a true statement .

Therefore, y ≤ (1/5)x +1 is region including the line y = (1/5)x +1 and area on the side of this line that is towards origin

The feasible region is shown in the attached picture with the boundary points of the shaded area.

ABC is the shaded area is feasible area,  where A= (0,4)   ,B= (2.5, 1.5 ), C= (0,1)

Z at A : 5(0) -4 (4) =-16

Z at B : 5(2.5) -4(1.5) =6.5

Z at C : 5(0) -4(1) = -4

Clearly, maximum value of z in feasible area is Z= 6.5 at point (2.5, 1.5)

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Answer:

Each shirt costs $35.00

Step-by-step explanation:

1 jeans = $40

4 shirts =$180 - $40 = $140.00

1 shirt = $140 ÷ 4 = $35.00

Answer:

33

Step-by-step explanation:

43 - 10 = 33

Answer:33

Step-by-step explanation:hope it helps, brainliest? i could really use it

The value of the expression -1/2 * (10x - 4) - (4x - 2) is -9x + 4

The expression is given as

-1/2 (10x-4) -( 4x-2)

Rewrite properly as

-1/2 * (10x - 4) - (4x - 2)

Open the brackets

So, we have

-1/2 * (10x - 4) - (4x - 2) = -5x + 2 - 4x + 2

Collect the like terms in the above expression

So, we have

-1/2 * (10x - 4) - (4x - 2) = -5x  - 4x + 2 + 2

Evaluate the like terms in the above expression

So, we have

-1/2 * (10x - 4) - (4x - 2) = -9x + 4

Hence, the value of the expression -1/2 * (10x - 4) - (4x - 2) is -9x + 4

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Answer:

12

Step-by-step explanation:

___ * ___ * ___

At the first one you have 3 choices so

_3_ * ___ * ___

then you have two choices for the second and third code

so 3 * 2 * 2 = 12

Answer:

15 Gigabites

Step-by-step explanation:

The closest you can can get to is $70, so by adding five in the times tables it gets you up to 15 x 5 which is 70.

Answer:

If 100%=1200 what about 100%-18%.

You get 984$

Answer:

a=4+3b-c

a=5+6b-9c/ 3

a=9+9b-10c /4

Answer:

1) -2a + 2

2) x + 1

3) -5x + 5

Step-by-step explanation(1):

[tex]\left(7a+4\right)-\left(9a+2\right)\\=7a+4-\left(9a+2\right)\\=7a+4-9a-2\\=7a-9a+4-2\\=-2a+4-2\\=-2a+2[/tex]

Step-by-step explanation(2):

[tex]\left(2x+5\right)-\left(x+4\right)\\=2x+5-\left(x+4\right)\\=2x+5-x-4\\=2x-x+5-4\\=x+5-4\\=x+1[/tex]

Step-by-step explanation(3):

[tex]\left(2x+4\right)-\left(7x-1\right)\\=2x+4-\left(7x-1\right)\\=2x+4-7x+1\\=2x-7x+4+1\\=-5x+4+1\\=-5x+5[/tex]

Hope this helps. Notify me of any concerns.

The value of the expression, 8 + (18 ÷6) x (2 x 9 - 4) is 50.

The order of operations gives a guideline with which mathematical operations are solved. The order of operations are provided using the BODMAS rule.

According to BODMAS, the order of operations are brackets, of, division, multiplication, addition and subtraction.

The expression is:

8 + (18 ÷6) x (2 x 9 - 4)

The terms in the bracket would be solved first :

(18 ÷6) = 3

(2 x 9 - 4)

The multiplication would be solved first, then 4 would be subtracted from the result of the multiplication : 18 - 4 = 14

The expression becomes: 8 + 3 x 14

The multiplication would be solved first and then 8 would be added to the result: 8 + 42 = 50

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According to the solving it is proved that DE is parallel to BC.

Coordinates are numerical lengths or angles that uniquely identify points on two-dimensional (2D) or three-dimensional (3D) surfaces ( 3D ). Mathematicians, physicists, and engineers employ a variety of coordinate systems.

In-parallel refers to something that is the same distance as well as the direction away from something else. Two lines of individuals standing straight across from each other is an example of in-parallel. noun. 1. In-parallel means traveling the same direction and distance as something else.

To obtain the coordinates of each midpoint, use the midpoint formula.

(x, y) = (½ (x₁ + x₂), ½(y₁ + y₂))

Coordinates of D:

(x, y) = (½ (4 + 2), ½(6 + -2))

(x, y) = (3, 2)

Coordinates of E:

(x, y) = (½ (4 + -2), ½(6 + -4))

(x, y) = (1, 1)

Slope of DE:

m = Δy / Δx

m = (2 − 1) / (3 − 1)

m = 1/2

Slope of BC:

m = Δy / Δx

m = (-2 − -4) / (2 − -2)

m = 1/2

Therefore, DE is parallel to BC.

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to get the y-intercept, we can simply set x = 0 and solve for "y".

[tex]2x-4y=4\implies 2(\stackrel{x}{0})-4y=4\implies -4y=4\implies y=\cfrac{4}{-4}\implies y=-1 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (0~~,~~-1)~\hfill[/tex]

The probability of randomly drawing the chip number 564 is 1 / 713 or 0.0014

Probability is used to determine the odds that a random event would happen. The odds that the event would happen is a distribution that lies between 0 and 1.

If it is certain that the event would occur, the probability value would be 1. If  it is certain that the event would not occur, the probability value would be 0. If it is equally likely that the event would happen or not happen, the probability value would be 0.5.

The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability of randomly drawing the chip number 564 = number of chips numbered 564 / total number of chips

1 / 713 = 0.0014

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Answer:

x=4

Step-by-step explanation:

22x-3+35+60=180

add like numbers.

22x+92=180

180-92=88

22x=88

88 divided by 22

x=4

check work=

22(4)-3+35+60=180

Step-by-step explanation:

I will assume that DC is 16,

16 x 2= 32

Answer:

the cost per book is 3$. you can buy 7 books for 21$.

Step-by-step explanation:

15 divided by 5 is 3, so they cost 3 each. 21 divided by 3 is 7.

The sum of -9 + 6 on the number line will be calculated by starting from -9 and counting 6 times to the right. This will be -3.

It should be noted that a number line simply means the straight line which has numbers that are arranged at equal segments or intervals that are along its length in Mathematics. It should be noted that the number line is usually shown horizontally and that it can be extended in any direction.

It should further be noted that the number line simply gives a representation of the graduated straight line which can be used to represent real numbers visually. In this case, every point on the number line simply corresponds to the real number, and every real number simply corresponds to a point.

It should further be noted that counting the numbers to the right indicates addition while to the left indicates subtraction.

In conclusion, the sum of -9 + 6 on the number line will be calculated by starting from -9 and counting 6 times to the right and this gives -3.

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The whole number that represents the value of the underlined digit in each case is as follows:

The value of a digit is the worth of the digit within its number place.

The number place determines the value of an underlined digit.

For instance, the number place values of 5 in the first and second situations are in the thousands and ten thousand place values.

The number place value of 9 in the third situation is in the hundred thousand place values, while the place value of 5 in the last example is in the ten place value.

Thus, the value of an underlined digit depends on its place value, and the place value is a digit's value based on its position.

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For each number, give the whole number that represents the value of the underlined digit.

155,349

651,907

947,502

317,055

Answer:

-13

Step-by-step explanation:

Plug in -2 to x:

5(-2) - 3

Multiply 5x-2:

-10 - 3

Because two negatives make a positive, add -10 and -3:

-13

Answer: [tex]j=1, k=2[/tex]

Step-by-step explanation:

[tex]4(x+j)+k(3x-5)=10x-6\\\\4x+4j+3kx-5k=10x-6\\\\x(4+3k)+(4j-5k)=10x-6\\\\\implies 4+3k=10 \implies k=2\\\\\implies 4j-5k=4j-10=-6 \implies j=1[/tex]

Answer:167

Step-by-step explanation: 360 - 90-35-68=167

The magnitude of an earthquake is related to the relative intensity by

magnitude = log(relative intensity).

Magnitude is a measure of earthquake size and remains unchanged with distance from the earthquake. Intensity, however, describes the degree of shaking caused by an earthquake at a given place and decreases with distance from the earthquake epicentre.

A better measure of the size of an earthquake is the amount of energy released by the earthquake, which is related to the Richter Scale by the following equation:

Log E = 11.8 + 1.5 M

(where Log refers to the logarithm to the base 10, E is the energy released in ergs and M the Richter magnitude).

Magnitude is determined from measurements on seismographs. Intensity measures the strength of shaking produced by the earthquake at a certain location. Intensity is determined from effects on people, human structures, and the natural environment.

An earthquake's magnitude is inversely proportional to its relative intensity (magnitude = log) (relative intensity)

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Answer:

$63

Step-by-step explanation:

Penny = $0,01

Nickel = $0.05

Dime = $0.1

Quarter= $0.25

Number of pennies = 6*50 = 300

Number of nickels = 5*40= 200

Number of dimes = 4*50= 200

Number of quarters = 3*40 = 120

The total amount of money:

300*0.01+ 200*0.05 + 200*0.1 + 120*0.25 = $63

The expression can use mental math to simplify the expression

9.15. 2 most easily is (15×2)×9.

Expression:

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression.

Possible expressions for the given question:

1) (15×9)×2

2)(15×2)×9

3)(2×9)×15

1⇒ Becomes complicated because of multiplication of 15 and 9

2⇒ Becomes easy because of (15×2) and then multiplication with  9

3⇒ Becomes complicated because of multiplication of 15 and (2×9)

Therefore,The expression can use mental math to simplify the expression 9.15. 2 most easily is (15×2)×9.

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Answer:

[tex]\sf {3x}^{2} [/tex]

Step-by-step explanation:

[tex] \rightarrow \sf 3x(\frac{1}{{x}^{-4}}) {x}^{-3} [/tex]

[tex] \rightarrow \sf \frac{ {3x}^{5} }{ {x}^{3} } [/tex]

[tex] \rightarrow \sf {3x}^{2} [/tex]

The slope of the equation of the line described is equal to 1/3.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + c

Where:

y + 2 = 1/3(x-8)

y + 2 = 1/3x - 8/3

y = 1/3x - 8/3 - 2

y = 1/3x - 2/3

Therefore, the slope of the equation of the line described is equal to 1/3.

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Answer: 9/2

Step-by-step explanation:

Mary's expected payback based on the information illustrated is 0.865. This isn't a fair game.

Based on the information, the chances of Donna winning will be 1/2.

It was also stated that each day Donna and Mary toss a coin to see who buys the other person coffee ($1.73 a cup).

Therefore, Mary's expected payback will be:

= (0 × 1/2) + (1.73 × 1/2)

= 0 + 0.865

= 0.865.

Therefore, Mary's expected payback based on the information illustrated is 0.865. This isn't a fair game.

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Plan B is less expensive than Plan A when you use at least 25

Inequalities can simply be defined as mathematical expressions in which both or two sides of the expression are not equal.

From the information given, we have that;

Now, let's write the inequality that represents Plan B < Plan A

If Plan B < Plan A

Then,

0. 19m + 6. 00 <  0. 25m

Let's simply the inequality

6. 00 < 0. 25m - 0. 19m

0. 06m < 6. 00

Make 'm' the subject

m < 6. 00/ 0. 06

m < 100

Thus, Plan B is less expensive than Plan A when you use at least 25

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