multiply (3-6i)^2 write in standard form

Answer:

-(x-3)(x-2)

Step-by-step explanation:

-(x²-5x+6)

-(x²-3x-2x+6)

-{x(x-3)-2(x-3)}

-(x-3)(x-2)

Over the past forty years, there has been a sharp rise in the quantity and variety of interest groups. .

In general, federal courts handle cases involving federal law, while state courts hear cases involving state law. Because most crimes are violations of local or state law, state courts typically hear criminal cases.

The 94 District Courts (trial courts), 13 Courts of Appeals (intermediate appellate courts), and the United States Supreme Court are the three main categories of federal courts within the federal system (the court of final review).

The three main causes of this surge are the "New Politics" movement, the increase of the role of government, and grassroots conservative action. Federal jurisdiction over a wide variety of public policy problems was expanded throughout the 1960s and 1970s, and there was a matching rise in the number of interest organizations that could exert pressure on elected officials

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Answer: -6y-12 and 5.5h+14

Step-by-step explanation:

-2(3y+6) = -6y-12

5.1h-2.6h+3(h+4)= 2.5h + 3h+14 = 5.5h+14

Answer:

4.25

Step-by-step explanation:

she has a total of 20 dollars and she wats to buy ice cream each at 3.15 for a total of 5 people including her self.

so 3.15(5) is 15.75

then subtract 15.75 from 20

20 - 15.75 = 4.25

The correct answer is: III only. Variance investigation is typically based on a cost-benefit analysis.

Statement I is incorrect because the relative size of a variance, in comparison to other variances, can be important in understanding its significance.

Statement II is incorrect because variance investigation does not focus solely on unfavorable variances. Both favorable and unfavorable variances are considered during the investigation.

Statement III is true. Variance investigation is typically based on a cost-benefit analysis, where the potential benefits of investigating and addressing variances are weighed against the associated costs.

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The numeric value of ms within is = 19.

To find the numeric value of ms within:

Given: Swithin = 70, sample size = 17 and number of groups = 3.

So, 17 × 3 = 51

70 - 51 = 19

Therefore, the numeric value of ms within is = 19.

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Answer:

Numbers from greatest to least (greatest is further up and least is further down)

650.202

650.02

650.002

650

649.99

649.099

Step-by-step explanation:

I looked into the tens places and if they were the same i looked into the decimal points. then i compared from there

The equation of the quadratic function is: f(x) = 3x² - 18x - 48

To find the equation of a quadratic function in standard form, we need to use the zeros of the function and one additional point.

Given that the zeros are x = 8 and x = -2, we can write the equation in factored form as:

f(x) = a(x - 8)(x + 2)

To find the value of "a," we can use the fact that f(2) = -72.

Substituting x = 2 into the equation, we have:

-72 = a(2 - 8)(2 + 2)

Simplifying, we get:

-72 = a(-6)(4)

-72 = -24a

Dividing both sides by -24, we find:

3 = a

Now that we know the value of "a," we can rewrite the equation in standard form:

f(x) = 3(x - 8)(x + 2)

So, the equation of the quadratic function is:

f(x) = 3x² - 18x - 48

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===========================================================

Explanation:

Focus on the endpoints (0,15) and (10,0). They are the y and x intercepts in that order. This is the starting point and ending point of the ball.

The average rate of change is the slope of the line connecting these endpoints. This is when we consider the entire time the ball is in the air.

Let's use the slope formula to get the following:

\((x_1,y_1) = (0,15) \text{ and } (x_2,y_2) = (10,0)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{0 - 15}{10 - 0}\\\\m = \frac{-15}{10}\\\\m = -\frac{3}{2}\\\\\)

The slope is -3/2, which is the average rate of change.

It tells us that the height is decreasing by 3/2 = 1.5 meters per second, which is an average speed.

In other words, the ball is going downward at an average speed of 1.5 meters per second.

Keep in mind the instantaneous speed of the ball is changing all the time. The result of -3/2 = -1.5 only applies to the average speed.

------------

Note how the slope formula involves computing the change in y (which was us computing \(y_{2} - y_{1} = 0 - 15 = -15\). It indicates the ball had gone down 15 meters when going from the start point to the ending point. This is the change in distance. The change in time is the \(x_{2} - x_{1} = 10-0 = 10\) portion, meaning the duration is 10 seconds.

In short,

slope = rise/run

slope = (change in distance)/(change in time)

slope = (-15)/(10)

slope = -3/2

So this may be a better way to see what's going on rather than rely on a formula in the previous section.

Answer:

15x - 6

Step-by-step explanation:

To solve this, Given the expression 12 x + 3 ( x − 2 )

To simplify, expand

12 x + 3 * x −3 * 2

Knowing that

- * + = -

then the expression becomes

= 12 x + 3x - 6

= 15x - 6

The expression given is equivalent to 15x - 6

Euler's formula,\(e^{ix} = \cos(x) + i \sin(x)\), relates complex numbers, exponentiation, and trigonometric functions, highlighting the deep connection between exponential, trigonometric, and imaginary numbers.

Given that the length of the strut is 10m, cross-sectional values of 610 x 229 x 113 (mm x mm x kg/mm), it is treated as fixed on both ends when it buckles about its weaker axis and pinned on both ends when it buckles about its stronger axis. Elastic modulus E = 210 GPa and yield stress \(\sigma_y\) = 260 MPa.

The Rankine constant for a strut with both ends fixed is 1/6400. We need to calculate the least buckling load for the strut using the Euler and Rankine formulae. Euler's formula for the buckling load is given as

\(P = \frac{\pi^2 EI}{(KL)^2}\)

Where,P is the least buckling load.K is the effective length factor K = 1 for both ends pinne dK = 0.5 for one end fixed and one end freeK = 0.7 for both ends fixed L is the unsupported length of the strut.I is the moment of inertia E is the modulus of elasticity Substituting the given values, the buckling load is:

\(P = \frac{\pi^2 \cdot 210 \cdot 10^9 \cdot 610 \cdot 229^3 \cdot 10^{-12}}{(1 \cdot 10^4 \cdot 10^2)^2} = 228.48 \text{ kN}\)

Using Rankine formula for least buckling load for both ends fixed, the formula is given as

\(P = \frac{\pi^2 EI}{(\frac{L}{KL_r})^2 + (\frac{\pi EI}{\sigma_y})^2}\)

Where \(L_r\) is the Rankine effective length factor.

\(L_r\) = L for both ends fixed \(L_r\) = 0.707L

for both ends pinned Substituting the given values, we get:

\(P = \frac{\pi^2 \cdot 210 \cdot 10^9 \cdot 610 \cdot 229^3 \cdot 10^{-12}}{((10/1)^2 + (\pi^2 \cdot 210 \cdot 10^9 \cdot 610 \cdot 229^3 \cdot 10^{-12}/260^2))} \approx 187.18 \text{ kN}\)

Therefore, the least buckling load using Euler's formula is 228.48 kN while that using Rankine's formula is 187.18 kN. Since the given strut is fixed at both ends, it is better to use the Rankine formula.

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Answer:

C. 3 × 100 + 4 × 10 + 7 × 1 + 8 × (1/10) + 5 × (1/100)

Step-by-step explanation:

3: hundreds

4: tens

7: ones

8: tenths

5: hundreths

Therefore, to make the game fair, you should earn a profit of $3 when you win.

To determine the profit you should earn when you win in order for the game to be fair, we need to consider the overall expected value.

In this gambling game, you win 25% of the time and lose 75% of the time. Let's assume that when you win, you earn a profit of P dollars. When you lose, you lose $1.

The expected value can be calculated as follows:

Expected Value = (Probability of Winning * Profit) + (Probability of Losing * Loss)

Since the game should be fair, the expected value should equal zero. Thus, we can set up the equation:

0 = (0.25 * P) + (0.75 * (-1))

Simplifying the equation:

0 = 0.25P - 0.75

0.75 = 0.25P

P = 0.75 / 0.25

P = 3

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The value of the expression − || 6c − 16b || + 1 if a = −12, b = 34, and c = −23 is - 681.

We that the modulus always gives a positive quantity.

For example: || -5 || = 5, etc.

We are given;

a = −12, b = 34, and c = −23.

We need to find − || 6c − 16b || + 1.

The solution of an algebraic expression is obtained by substituting the given values in the expression.

Substitute the given value in the above expression, we will get;

− || 6c − 16b || + 1

= − || 6 * -23 − 16 * 34 || + 1

=  − || - 138 − 544 || + 1

= − || - 682 || + 1

= − 682 + 1

= - 681

So, the value of − || 6c − 16b || + 1 is - 681.

Thus, the value of the expression − || 6c − 16b || + 1 if a = −12, b = 34, and c = −23 is - 681.

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Answer:

Logan's swimming average is 2.25 kilometers per hour.

Mila's swimming average swimming speed is 34.44 m/min.

The distance swam by Logan = 750 m

The distance swam by Mila =  of Logan's distance = \(\frac{2}{3}\)  × 750 = 2 × 250 = 500.

This should help. :)

Logan's swimming Average 2.25 kilometers per hour

and Mila's swimming speed is 34.44 m/min.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

The distance swam by Logan = 750 m

Logan's swimming average is 2.25 kilometers per hour.

Mila swam 2/3 of logans distance in 1/4 of an hour

So,

The distance swam by Mila =  2/3 of Logan's distance

= 2/3  × 750

= 2 × 250

= 500.

So, Mila's swimming speed is 34.44 m/min.

Hence, Logan's swimming Average 2.25 kilometers per hour and Mila's swimming speed is 34.44 m/min.

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Answer:

add all the sides, 156

Step-by-step explanation:

50+50+28+28

In a convex pentagon, the measure of angle D is 132°.

If a planar polygon has all the line segments connecting any given pair of its points, it is said to be convex pentagon.

Properties of a Convex Polygon are-

Calculation for the measure of angle D.

The sum of the interior angles  = 540°

Let A, B , C  =   D - 40

And let  E  = D

So we have

A + B + C + D + E  = 540

(D - 40) + (D - 40)  + (D - 40)  + D + D  =  540

5D  - 120  = 540

5D = 660

D = 660 / 5  

D =  132°

Therefore, the measure of angle D is 132°.

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Answer:

P(A)=1/3    P(B)=5/12

P(C)=1/4    P(A or B)=3/4

P(B or C)=2/3    P(A,B, or C)= 1

Answer:

231.1 gm

Step-by-step explanation:

1040 J / .9 j/(gm-C)   / 5C = 231.1 gm

The mass of the metal is 231.111 gram.

The specific heat capacity of a substance is the heat capacity of a sample of the substance divided by its mass, also known as massic heat capacity.

The formula for heat is given by the formula,

Q = mC(ΔT)

Given the metal has a specific heat of 0.900 J/g °C requires 1,040 J of heat to raise the temperature (the change in temperature) by 5 °C. Therefore, we can write,

Q = mC(ΔT)

1,040 = m × 0.900 × 5

m = 1040/(0.900×5)

m = 231.111 g

Hence, the mass of the metal is 231.111 gram.

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Therefore, the volume of the solid generated by revolving the region bounded by y= x2, y = 0, and x = 2 about the x-axis is 16.

To find the volume of the solid generated by revolving the region bounded by y=x^2, y=0, and x=2 about the x-axis, we will use the method of cylindrical shells.
First, let'sgraph the region to better visualize it.
graph{y=x^2 [-10, 10, -5, 5]}

The region is bounded by the x-axis, the line x=2, and the curve y=x^2. When we revolve this region about the x-axis, we will generate a solid with a cylindrical shape. To find the volume of this solid, we will slice it into thin cylindrical shells and add up the volumes of each shell.
Let's consider a thin slice of the region at x. The height of this slice will be given by the curve y=x^2, and the thickness of the slice will be dx. When we revolve this slice about the x-axis, it will generate a cylindrical shell with radius x and height x^2. The volume of this shell can be calculated using the formula for the volume of a cylinder:

V = 2πrxh

where r is the radius of the cylinder, h is its height, and π is the constant pi. In this case, we have r = x and h = x^2, so
V = 2πx(x^2)
V = 2πx^3
To find the total volume of the solid, we need to add up the volumes of all these cylindrical shells from x=0 to x=2:
V = ∫(0 to 2) 2πx^3 dx
V = πx^4 |(0 to 2)
V = π(2^4 - 0^4)
V = 16π
Therefore, the volume of the solid generated by revolving the region bounded by y=x^2, y=0, and x=2 about the x-axis is 16π.

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Answer:

10

Step-by-step explanation:

The triangle in the pic is a right-angled triangle. And in right-angled triangles , Pythagorean Theorem. So , according to Pythagorean Theorem

\(Base^{2} +Perpendicular^{2} =Hypotenuse^{2}\) where 'c' is the hypotenuse and 'a' & 'b' are the other two sides.

Using Pythagorean Theorem ,

\(Hypotenuse^{2} = 8^{2} +6^{2} =64+36=100\\=>Hypotenuse = \sqrt{100} =10\)

a) f(4) ≈ 11,456.9

b) f^9(0) = 9!

c) k = 1

d) The first few terms of S: ao = 1/4, a₁ = 0, A₂ = -1/

Given the Taylor series of f(x) = x^5e^22 about x = 0 as 7.9 + 11x + 713x^2 + ..., we need to find various quantities related to this series.

a) To find f(4), we substitute x = 4 into the series:

f(4) = 7.9 + 11(4) + 713(4)^2 + ...

     = 7.9 + 44 + 713(16) + ...

     = 7.9 + 44 + 11,408 + ...

     = 11,456.9

b) To compute the 9th derivative of f(x) at x = 0, we use the Maclaurin series for f(x):

f(x) = arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...

Differentiating term by term, we find the 9th derivative:

f^9(x) = 9!

At x = 0, the 9th derivative of f(x) is:

f^9(0) = 9!

c) Evaluating the integral of 1/(x^2 + 4) using the power series representation involves finding the series expansion for 1/(x^2 + 4) and integrating it term by term. The power series representation for 1/(x^2 + 4) is:

1/(x^2 + 4) = 1/4 - x^2/16 + x^4/64 - x^6/256 + ...

Integrating term by term, we get:

S = ∫ (1/(x^2 + 4)) dx = (1/4)x - (1/48)x^3 + (1/256)x^5 - (1/1536)x^7 + ...

To find the value of k, we need to determine the coefficient of x in the power series expansion. In this case, the coefficient of x is 1/4, so k = 1.

d) The first few terms of S, the integral of 1/(x^2 + 4), are:

ao = 1/4

a₁ = 0

A₂ = -1/48

a₃ = 0

a₄ = 1/256

c) The answers to part (a) and (b) are equal because the integral of 1/(x^2 + 4) is directly related to the arctan function. Hence, dividing the infinite series from part (b) by k gives an estimate for the value of π/4 in terms of an infinite series.

To approximate the value of π/4, we can sum the first 5 terms of the series:

π/4 ≈ (1/4) - (1/48)x^3 + (1/256)x^5 - (1/1536)x^7 + (1/8192)x^9

d) To find the upper bound for the error in the estimate using the first 11 terms, we can use the alternating series estimation theorem. The error is given by the absolute value of the next term in the series, which is the 12th term in this case:

Error ≤ (1/8192)x^11

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Answer:

Step-by-step explanation:

-125/4

-124/4=-31

-31 1/4

The time to calculate her rate along the summit Rate = 1.5 mph

Rate = Distance / Time

To solve this problem, we will first need to calculate the time it took Jane to reach the peak. Since she rode 40 miles uphill, we can use the rate of 5 mph slower than when she reached the peak to calculate this time.

Time = Distance / Rate

Time = 40 miles / (Rate - 5 mph)

Time = 40 miles / (Rate - 5 mph)

Time = 40 miles / (Rate - 5)

Time = 8 hours

Since Jane spent 2 hours exploring the mountain, the total time it took her to reach the peak was 8 hours. We can now use this time to calculate her rate along the summit.

Rate = Distance / Time

Rate = 12 miles / 8 hours

Rate = 1.5 mph

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Answer:

Step-by-step explanation:

we have the diameter =60 cm, the radius is 60/2=30 cm

A circle is 3.14*r^2=2827 cm^2

Answer: C. 2827 cm2

Step-by-step explanation:

The area of a circle is calculated by pir^2; r = the radius

In the diagram, the diameter is provided. The radius is half of the diameter. 60/2 = 30, so the radius is 30 cm.

Plug these values into the formula

A = 3.14*30^2

A = 2827.43, which would round to 2827 cm2

Step-by-step explanation:

p : q

= 2⁷ : 2⁹

= 2⁰ : 2²

= 1 : 4.

Answer:

Step-by-step explanation:

\(\dfrac pq=\dfrac{ 2^7}{2^9} \\\\\dfrac pq=\dfrac{ 2^7}{2^7\cdot2^2} \\\\\dfrac pq=\dfrac{1}{2^2} \\\\\dfrac pq=\dfrac14\)

p/q= 2⁷/2⁹   ⇒   p:q = 1:4 = 0.25