How much is 28 + 56 + 93

The dual problem of the primal problem "Maximize Z = 7X1 + 5X2, Subject to X1 + 2X2 ≤ 6, 4X1 + 3X2 ≤ 12, X1, X2 ≥ 0" is:

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Greater than (or greater than or equal to), less than (or less than or equal to), or not equal to signs are used in place of the equal sign.

Minimize Z = 6Y1 + 12Y2

Here

Y1 + 4Y2 ≥ 7

2Y1 + 3Y2 ≥ 5

Y1, Y2 ≥ 0

(b) The dual problem of the primal problem "Maximize Z = 3X1 + 4X2, Subject to 5X1 + 4X2 ≤ 200, 3X1 + 5X2 ≤ 150, 8X1 + 4X2 ≥ 80, X1, X2 ≥ 0" is:

Minimize Z = 200Y1 + 150Y2

Subject to:

4Y1 + 5Y2 ≥ 3

5Y1 + 3Y2 ≥ 4

4Y1 + 8Y2 ≤ -80

Y1, Y2 ≥ 0

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"Your question is incomplete, probably the complete question/missing part is:"

Write the dual of following problems:

(a) Maximize Z = 7X1 + 5X2

Subject to:

X1 + 2X2 ≤ 6

4X1 + 3X2 ≤ 12

X1, X2 ≥ 0

(b) Maximize Z= 3X1 + 4X2

Subject to:

5X1 + 4X2 ≤ 200

3X1 + 5X2 ≤ 150

8X1 + 4X2 ≥ 80

X1, X2 ≥ 0

Answer:

Needs to specify. But here, this may help

Step-by-step explanation:

Depending on if the x and/or y are positive or negative will depend on were the dots will be placed on the graph.

Places the points are simple.

X is across, Y is up and down.

Example,

If you need to plot (4, 3)

You will need to start at the center point (0,0)

You must go over to the right 4 places, and go up 3 places. That is the easiest way to graph.

Labeling,

It will kind of be the same way. Find out how many places the point is from the (0,0) on the x axis, and y axis.  

Answer:

directrix: x=-1

focus: (1,0)

Step-by-step explanation:

Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

Using the circles:

A circle with a radius of 8 inches has an area and circumference given by:

A = πr² = π(8²) ≈ 201.06 square inches

C = 2πr = 2π(8) ≈ 50.27 inches

Rounding to the nearest hundredth:

A ≈ 201.06 square inches

C ≈ 50.27 inches

Therefore, the area is approximately 201.06 square inches and the circumference is approximately 50.27 inches.

A circle with a diameter of 20 meters has a radius of 10 meters. The area and circumference are given by:

A = πr² = π(10²) ≈ 314.16 square meters

C = 2πr = 2π(10) ≈ 62.83 meters

Rounding to the nearest hundredth:

A ≈ 314.16 square meters

C ≈ 62.83 meters

Therefore, the area is approximately 314.16 square meters and the circumference is approximately 62.83 meters.

Using these relationships, find the measures of some of the angles:

a) mJKP = mJKN (by vertical angles) and mJKP + mPKL = 90° (by complementary angles), so mJKN + mPKL = 90°.

b) mJKN = mJKP (by vertical angles) and mJKN + mKNM = 90° (by complementary angles), so mJKP + mKNM = 90°.

c) mJLK = mMPL (by alternate interior angles) and mMPL = 63°, so mJLK = 63°.

d) mKNM = 90° - mJKN (by complementary angles). We cannot determine the measure of mJKN.

e) mJLK = mMPL (by alternate interior angles) and mJLR = mJLP (by vertical angles), so:

mJLK + mKLP + mPLJ + mJLP = 360° (by the sum of angles in a quadrilateral)

63° + 90° + mPLJ + mJLP = 360°

mPLJ + mJLP = 207°

f) mJLR = mJLP (by vertical angles) and mKPL = 90°, so:

mJLR + mJLP + mKPL = 180° (by the angles in a triangle)

mJLR + mJLP + 90° = 180°

mJLR + mJLP = 90°

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Image transcribed:

Use the circle below for questions 1-7.

1. Name a radius.

2. Name a diameter.

1.

2.

3.

R

3. Name a chord that is not a diameter.

P

4. Name a central angle.

4.

S

5. Name a minor arc.

5.

6. Name a major arc.

7.

7. Name a semicircle.

For questions 8 and 9, find the area and circumference. Round to the nearest hundredth.

8.

A =

C=

9.

A =

20 m

8 in

C=

10. If m∠MPL = 63°, find each measure.

K

a) mR= =

= m KNM d) 이이

=

b) - =

c) L

=

f) mJLR =

N

M

Gina Wilson (All Things Algebra, LLC), 201

Step-by-step explanation:

tan0=opp/adj

where opposite =3,adjacent =x,=70

tan 70=3/x

2.7474=3/x

2.7474x=3

divide both sides by 2.7474

x=3/2.7474

x=1.0919

x=1.10 to 1 d.p

Answer:

Step-by-step explanation:

Statement                     Reason

PR ≅ TR                        Given

<PQR≅<TSR                 Given

<PRQ≅<TRS                Vertical Angles Theorem

PQR=TSR                      SAS  Theorem   (Side-Angle-Side)

The situation Veronica receives $21 for babysitting, and then spends the same amount, $21, on a new shirt quantities combine to make 0.The correct answer is option C.

When we add +21 (the money she receives) and subtract -21 (the money she spends), the result is 0. This means that the net change in Veronica's money is zero, indicating that the quantities combine to make 0.

In situations A, B, and D, the quantities do not combine to make 0. In situation A, the player earns 4 points for getting an answer right and then earns an additional 4 points for making it around the board.

The total points earned in this situation would be 8, which is not equal to 0.

In situation B, the car is initially filled with 10 gallons of gas, but then half of that, which is 5 gallons, is used on a day's drive. The remaining fuel in the car would be 5 gallons, which is also not equal to 0.

In situation D, the bird flies 25 feet up in the air and then 25 feet across to its nest. The total distance traveled by the bird would be 50 feet, which is not equal to 0.

Therefore, only in situation C, where Veronica receives and spends the same amount of money, do the quantities combine to make 0.

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The probable question may be:

In which of these situations do the quantities combine to make 0?

A. A player a game earns 4 points for getting an answer right. She then earns 4 points for making it around the board.

B. A car is filled with 10 gallons of gas. Half of the 10 gallons are then used on a day's drive.

C. Veronica receives $21 for babysitting. She then spends $21 on a new shirt.

D. A bird flies 25 feet up in the air. It then flies 25 feet across to its nest.

Answer:

see photo

Step-by-step explanation:

Answer: Convert the mixed numbers to improper fractions, then find the LCD and combine them.

Exact Form:

188

5

Decimal Form:

37.6

Mixed Number Form:

37

3

5

hope this helped have a nice day! :)

Answer:

Step-by-step explanation:

(124+64) /5

= 188/5

Answer is = 37.5

Answer:

a. VY, WX, ST

b. RU, UT, VY, YX

c. (RSWV, UTXY), (STXW, RUYV)

d. TX, SW

HOPE THIS HELPS YOU

Follw me = 10 thanks

Mark as brainliest = 10 thanks

1 thanks to me = 2 thanks

The mixture must be heated an amount of 23 °F to reach a temperature of 132 °F.

Temperature is the measure of how "hot" a system is. Physically speaking, temperature is closely related to atomic and molecular motion within a system. In this problem we find a mixture that must be at a certain temperature, higher than its real one.

Therefore, the amount required to increase the temperature of the mixture is defined by following subtraction:

ΔT = R - r

Where:

If we know that r = 109 °F and R = 132 °F, then the temperature difference is:

ΔT = 132 °F - 109 °F

ΔT = 23 °F

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Answer: 21.5

Step-by-step explanation:

Subtract it all

Answer:

yes

Step-by-step explanation:

Yes this triangle is right angled and can be justified using the Pythagorean theorem. The theorem states that: \(a^{2} +b^{2} = c^{2}\). Substitute using the given values:

(9^2)+(12^2)=15^2

81 + 144 = 255

255 = 255.

It satisfies the theorem therefore it is a right angle triangle.

Answer: 39

Step-by-step explanation:

156/4

4 payments

Total 156

So divide that and you will get 39

The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

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Answer:

16

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors. Hope this helps! <3

Answer:g(x)=-4^2+4x-5

Step-by-step explanation:

The valid equations are written below. Then the correct options are C, D, and E.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The sum of the two interior angles is equal to the exterior angle of the third angle.

The sum of the supplementary angle will be 180°.

From the diagram, the equations are written as,

m∠5 + m∠6 = 180°               (Supplementary angle)

m∠2 + m∠3 = m∠6              (Exterior angle)

m∠2 + m∠3 + m∠5 = 180°   (Angle sum of triangle)

Then the correct options are C, D, and E.

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The complete question is attached below.

Answer:

Step-by-step explanation:

Answer:

The answer is "Option A".

Step-by-step explanation:

\(\to Base= 2 \ cm\\\\\to height=3.1 \ cm\\\\\)  

Formula:

\(\bold{Area= base \times height}\\\\\)

         \(=2 \times 3.1 \\\\= 6.2 \ cm^2\)

if the height value is 3 then area is =6

Using the given profit function, it is found that 1,250 is the break-even point, that is, the amount of garments cleaned for which her profit is 0.

Elena's monthly profit, P(g), for g garments cleaned, is given by:

\(P(g) = 3.20(g - 1250)\)

Hence, 1,250 is the break-even point, that is, the amount of garments cleaned for which her profit is 0.

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Answer:

Sonu is 15years and Monu is 21 years

Step-by-step explanation:

7! = 5040 ways

We know that

• Sarah holds 400 shares.

• The firm has 40,000 shares.

• The recent earnings are $80,000.

• The stock has been selling for $22.

• The firm intends to pay 10% of the dividend.

To find the proportion, we just have to divide the number of shares Sarah holds and the total number of shares the firm has. Take into account it is after the stock dividend. Observe that 10% of 400 is 40, so we have to divide 440 by 40,000.

Then, we multiply by 100 to express in percentage.

Answer:

3053.63 yd^3

Step-by-step explanation:

There is a formula to this, the formula goes,V=4/3πr^3, you subsitute, 9 in for r, cube "r", and do 9*3.14 or whatever you use for PI, and then you times that by 4/3.

Answer:

20 1/4

Step-by-step explanation:

Substitute for the variables, the solve