what is the quotient when x^3-5x^2+2x+5 is divided by x-2

Answer:

The price per unit of chocolate bars is £0.3.

Step-by-step explanation:

The cost of 4 chocolates bars is  £1.20.

The cost of 1 chocolate bars is \(\frac{1.20}{4}\)

The cost of 1 chocolate bars is £0.3.

Answer: $4.80 (us dollars)

Step-by-step explanation:

The equilibrium E2 corresponds to a stationary point where p increases (p' > 0) and q does not change (q' = 0).

To construct the phase plane for the given system of differential equations, we first need to find the nullclines and identify the equilibria.

(a) Nullclines and Equilibria:

For the first equation, p' = p(1 - p - q), we set p' = 0 and solve for p:

p(1 - p - q) = 0

This equation has two solutions:

p = 0

1 - p - q = 0

For the second equation, q' = q(2 - 3p - q), we set q' = 0 and solve for q:

q(2 - 3p - q) = 0

This equation also has two solutions:

q = 0

2 - 3p - q = 0

Now we can plot the nullclines on the phase plane:

Nullcline for p' = 0: p = 0 (horizontal line)

Nullcline for 1 - p - q = 0: q = 1 - p (diagonal line)

Nullcline for q' = 0: q = 0 (vertical line)

Nullcline for 2 - 3p - q = 0: q = 2 - 3p (diagonal line)

Next, we identify the equilibria by solving the equations:

Equilibrium for p = 0 and q = 1 - p: p = 0, q = 1 (Equilibrium E1)

Equilibrium for q = 0 and 2 - 3p - q = 0: p = 2/3, q = 0 (Equilibrium E2)

Now we can plot the equilibria on the phase plane.

To indicate the direction of motion, we can choose a few points in different regions of the phase plane and evaluate p' and q' at those points. This will help us determine the direction of the vector field arrows.

(b) Expression for each equilibrium:

For Equilibrium E1: p = 0, q = 1

Substituting these values into the given system of differential equations:

p' = 0(1 - 0 - 1) = 0

q' = 1(2 - 3(0) - 1) = 1

The equilibrium E1 corresponds to a stationary point where p does not change (p' = 0) and q increases (q' > 0).

For Equilibrium E2: p = 2/3, q = 0

Substituting these values into the given system of differential equations:

p' = (2/3)(1 - 2/3 - 0) = 2/9

q' = 0(2 - 3(2/3) - 0) = 0

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please refer to the attached image. i'm sorry i can't help you with the proofs. try looking up "how to prove things in geometry." that might help.

Answer:

Step-by-step explanation:

Answer:

y=3x+15

Step-by-step explanation:

bbbbbbbbbbbbbbb bbbbbbbbbbbbbb

Answer:

See proof below

Step-by-step explanation:

Two triangles are said to be congruent if one of the 4 following rules is valid

Let's consider the two triangles ΔABC and ΔAED.

ΔABC sides are AB, BC and AC

ΔAED sides are AD, AE and ED

We have AE = AC and EB = CD

So AE + EB = AC + CD

But AE + EB = AB and AC+CD = AD

We have

AB of ΔABC  = AD of ΔAED

AC of ΔABC =  AE of ΔAED

Thus two sides the these two triangles. In order to prove that the triangles are congruent by rule 4, we have to prove that the angle between the sides is also equal. We see that the common angle is ∡BAC = ∡EAC

So  triangles ΔABC and ΔAED are congruent

That means all 3 sides of these triangles are equal as well as all the angles

Since BC is the third side of ΔABC and ED the third side of ΔAED, it follows that

BC = ED  Proved

A plane in r3 is defined parametrically as the set of points is n · u * b + n · v * c = n · (P - a).

To give an implicit description of a plane in R3, we need to find a single equation that describes all the points in the plane.

Let's assume that the plane is defined parametrically as the set of points:

P(u,v) = a + u * b + v * c

where a, b, and c are vectors in R3 and u and v are parameters.

To find the implicit equation, we can start by taking the cross product of the vectors b and c, which gives us a normal vector to the plane. Let's call this vector n.

n = b x c

Next, we can take the dot product of the normal vector n with the vector (P - a), where P is any point on the plane. This will give us an equation that describes all the points in the plane:

n · (P - a) = 0

Expanding this equation, we get:

n · (u * b + v * c) = n · (P - a)

Simplifying further, we get:

n · u * b + n · v * c = n · (P - a)

This is the implicit equation of the plane in R3.

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Answer:

\(root = 3\)

Step-by-step explanation:

A zero or a root is determined at the point where the curve cuts or meets the x-axis or horizontal axis.

Answer:

156 divided by 13

Step-by-step explanation:

  156/12 =  13

13 bags

Answer:

Market price = Rs. 15,000

Step-by-step explanation:

Let Market price = x

discount = 20% of x

              = 0.20 *x = 0.2x

Selling price after discount = x - 0.2x = 0.8x

Value added tax = 15% of 0.8x

                            = 0.15 * 0.8x

                           = 0.12x

Selling price with VAT = 0.8x + 0.12x = 0.92x

Differences between SP with vat and SP after discount = rs.1800

0.92x - 0.8x = 1800

0.12 x = 1800

x = 1800/0.12

x = Rs. 15,000

Answer:

1) Add 4

2) Add 6

Step-by-step explanation:

In Q1, you add 4 to the input to get the output.

13+4=17

20+4=24

In Q2, you add 6 to the input to get the output.

14+6=20

28+6=34

Hope this helps :)

a. The present value of the winnings is $23.88 million.
b. The present value of the winnings, if the first payment comes immediately, is $24.04 million.

To calculate the present value of the winnings, we can use the formula for the present value of an annuity:
PV = C * (1 - (1 + r)^(-n)) / r
where PV is the present value, C is the annual payment, r is the discount rate, and n is the number of years.
a. In this case, the annual payment is $1.6 million, the discount rate is 11.80%, and the number of years is 27. Plugging these values into the formula:
PV = 1.6 * (1 - (1 + 0.118)^(-27)) / 0.118
PV = 1.6 * (1 - 0.2694) / 0.118
PV = 1.6 * 0.7306 / 0.118
PV = 23.88 million

b. If the first payment comes immediately, the number of years is reduced by 1. Plugging the values into the formula:
PV = 1.6 * (1 - (1 + 0.118)^(-26)) / 0.118
PV = 1.6 * (1 - 0.2634) / 0.118
PV = 1.6 * 0.7366 / 0.118
PV = 24.04 million
So, the present value of the winnings is $23.88 million if the first payment comes in 1 year, and $24.04 million if the first payment comes immediately.

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The probability is equal to the ratio of the area of the region where the area of triangle XYD is at most 12 to the total area of triangle XYZ. The probability that the area of triangle XYD is at most 12 is 2/3 or 0.67.

Triangle XYZ has legs of length XY = 12 and YZ = 6. The area of triangle XYZ can be calculated using the formula A = (1/2) * base * height, where the base is XY and the height is YZ. Substituting the given values, we find that the area of triangle XYZ is 36 square units.

To determine the probability that the area of triangle XYD is at most 12, we need to consider the range of possible positions for point D within triangle XYZ.

The area of triangle XYD can also be calculated using the formula A = (1/2) * base * height, where the base is XY and the height is the perpendicular distance from point D to line XY. Since point D is chosen randomly within triangle XYZ, we can consider the ratio of the areas to determine the probability.

If the area of triangle XYD is at most 12, it means that the height of triangle XYD is at most (2 * 12) / XY = 2 units. Therefore, point D must lie within a region of height 2 units above line XY within triangle XYZ.

To calculate the probability, we compare the area of this region (a trapezoid shape) to the total area of triangle XYZ. The area of the trapezoid can be calculated using the formula A_trap = (1/2) * (base1 + base2) * height, where base1 and base2 are the lengths of the parallel sides of the trapezoid and height is the height of the trapezoid.

In this case, base1 = base2 = XY = 12, and the height of the trapezoid is 2. Plugging these values into the formula, we find that the area of the trapezoid is 24 square units.

Therefore, the probability that the area of triangle XYD is at most 12 is given by the ratio of the area of the trapezoid (24 square units) to the total area of triangle XYZ (36 square units), which simplifies to 24/36 = 2/3, or approximately 0.67.

In conclusion, the probability that the area of triangle XYD is at most 12 is 2/3 or approximately 0.67.

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Answer:

–3{6+2π} +7 =4

–3+8π+7=4

5π+7=4

12π =4

π =12/4

π=3

it help you

The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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7.82 % is probability that all reservation holders who show will be accommodated.

What is probability in math?

If 236 are booked.

and there is only room of 213.

if 214 or 215 or 216 ............  etc

all the way to 236

there won't be enough seats.

P( X = 214 ) = ²³⁶C₂₁₄ * ( 0.9005 ) ²¹⁴   * ( 0.995 )²²

P( X = 214 ) = 0.08439109

                   = 8.44 %

P( X = 215 ) =  ²³⁶C₂₁₅ *  ( 0.9005 ) ²¹⁵   * ( 0.995 )²¹

                    = 0.0781522

                     = 7.82 %

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Answer: The number 12 represents admission charge in Mariana's equation.

Step-by-step explanation:

As per given ,

Total cost = ( Charge per ticket) (Number of tickets) +  (Admission fees)  (i)

For x = Number of tickets, the total cost (c) for a day at the amusement park is given as

\(c = 1.50x + 12\)                                       (ii)

Here, 12 = Admission fees                 [Comparing (i) and (ii)]

Hence, the number 12 represents admission charge in Mariana's equation.

Answer:

1/6

Step-by-step explanation:

1/6

Answer:

Step-by-step explanation:

Eddie deposits $1090 in an account that earns 6% interest compounded annually for 3 years. What is the total interest earned after 3 years? Round to the nearest cent.

A: 196.20

B: 208.20

C: 1286.20

D: 1298.20

{4, 5, 6, 7} has 4 elements, so there should be 2⁴ = 16 subsets.

• empty set: { }

• each set containing only 1 element: {4}, {5}, {6}, {7}

• each set containing 2 elements: {4, 5}, {4, 6}, {4, 7}, {5, 6}, {5, 7}, {6, 7}

• each set containing 3 elements: {4, 5, 6}, {4, 5, 7}, {4, 6, 7}, {5, 6, 7}

• the set itself: {4, 5, 6, 7}

Count them up to make sure we have them all:

1 + 4 + 6 + 4 + 1 = 16

Answer:

Its A

Step-by-step explanation:

The length of the curve for t∈[0,1] is 4/9. To find the length of the curve defined by x(t)=\(2t^3\) and y(t)=\(4t^2\)+2, we need to use the arc length formula:

L = ∫√\((dx/dt)^2 + (dy/dt)^2\) dt from t=0 to t=1.
First, let's find dx/dt and dy/dt:
dx/dt = \(6t^2\)
dy/dt = 8t
Now we can plug these into the arc length formula:
L = ∫√\((6t^2)^2\)+ \((8t)^2\) dt from t=0 to t=1
L = ∫√(\(36t^4 + 64t^2\)) dt from t=0 to t=1
L = ∫√(\(4t^2(9t^2 + 16)\)) dt from t=0 to t=1
L = 2∫√(\(9t^2\) + 16) dt from t=0 to t=1
To integrate this expression, we can use a trig substitution. Let u = (3/4)\(t^2\) and du = (3/2)t dt. Then:
L = 2∫√(9(4/3)u + 16) (2/3) du from u=0 to u=3/4
L = (4/3)∫√(12u + 48) du from u=0 to u=3/4
L = (4/3)∫√(12(u + 4)) du from u=0 to u=3/4
L = (4/3)∫2√(u + 4) du from u=0 to u=3/4
L = (8/3)[(2/3)\((u + 4)^{(3/2)}\)] from u=0 to u=3/4
L = (8/3)[(2/3)\((3/4 + 4)^{(3/2)}\) - \((2/3)(4)^{(3/2)}\)]
L = (8/3)[(2/3)\((25/4)^{(3/2)}\) - (2/3)(8)]
L = (8/3)[(25√25)/6 - 16/3]
L = (8/3)(25/6 - 16/3)
L = (8/3)(1/6)
L = 4/9

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Answer:

x=125

Step-by-step explanation:

all angles of a triangle add up to 180 degrees.

30+25=55

180-55=125

The solution x = 2 is valid for the original equation.

To solve the rational equation (4/x) = (3x + 2)/x², we can start by multiplying both sides of the equation by x² to eliminate the denominators:

x² * (4/x) = x² * [(3x + 2)/x²]

Simplifying:

4x = 3x + 2

Next, we can isolate the x term by subtracting 3x from both sides:

4x - 3x = 3x + 2 - 3x

x = 2

So, the solution to the rational equation is x = 2.

Now, let's check for extraneous solutions by substituting x = 2 back into the original equation:

(4/2) = (3(2) + 2)/(2²)

2 = (6 + 2)/4

2 = 8/4

2 = 2

Since the equation is true when x = 2, there are no extraneous solutions.

Therefore, for the initial equation, x = 2 is a viable answer.

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Answer:

no it's a rational number

3 over 2 is equal to 1.5  if a number can be clearly defined as a fraction, then it is a rational number, not irrational

Answer:

24 13/34

Step-by-step explanation:

The distance covered by Dennis will be 9.23 miles.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. Speed is a scalar quantity and does not require any direction to represent it.

Given that Dennis can walk about 2(5/6) miles each hour. The distance covered by Dennis in 3 hours 15 minutes will be calculated as:-

Distance = 2 ( 5 /  6)  x  3 hour 15 minute

Distance = 2.84 x 3 ( 1 / 4)

Distance = 2.84 x 3.25

Distance = 9.23 miles.

Therefore, the distance covered by Dennis will be 9.23 miles.

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According to the information in the nutritional table, it can be inferred that the amount of milligrams of sodium that we should consume during the rest of the day must be less than 2,175mg,

To calculate the amount of sodium that we can consume during the rest of the day after breakfast, we must subtract the value of sodium consumed to the amount of total sodium that we want to ingest as shown below:

According to the above, it can be inferred that after consuming the cereal bar at breakfast, we should consume an amount less than or equal to 2,175mg of sodium in the other meals of the day (lunch, dinner and snacks).

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