What is the slope of a line which passes through the points (-6, 4) and (4, 6)?
A) 5
B)1/5
C)2
D)1/2

Answer:

C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The equation of the function is g(x) = √(x + 5) - 2

From the question, we have the following parameters that can be used in our computation:

f(x)=√(x + 2) - 3

The transformation is given as:

3 units left and 1 unit up

This is represented as

(x + 3, y + 1)

Substitute the known values in the above equation, so, we have the following representation

g(x) = √(x + 2 + 3) - 3 + 1

Evaluate

g(x) = √(x + 5) - 2

Hence, the equation is g(x) = √(x + 5) - 2

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The coterminal angle is 330°, which lies in Quadrant fourth, with a reference angle of 258 degrees.

We have 588 ° between 0° ≤θ<360

Coterminal angle in [0, 360°) range is 330°, located in the fourth quadrant.

Then for the reference angle will be

588 -330= 258

Thus, the reference angle is 258°

Therefore, we can conclude that  coterminal angle is 330°, which lies in Quadrant fourth, with a reference angle of 258 degrees.

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Answer:

3

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

X,Y,Z

During the 24-hour period between 4pm on 12/26/2015 and 4pm on 12/27/2015, the dew point temperature changed substantially. The water vapor content and relative humidity were also affected by this change.

Based on the information provided, it is indicated that the dew point temperature changed substantially during the 24-hour period. The dew point temperature is the temperature at which air becomes saturated, causing water vapor to condense into dew or fog. A substantial change in the dew point temperature suggests a significant shift in the moisture content of the air.

As a result, the water vapor content and relative humidity are also affected. Water vapor content refers to the amount of water vapor present in the air, while relative humidity measures the percentage of moisture in the air compared to its maximum capacity at a given temperature. When the dew point temperature changes substantially, it implies that the air's capacity to hold water vapor has also changed, thus influencing the relative humidity.

Therefore, the main conclusion is that the change in the dew point temperature had a substantial impact on both the water vapor content and the relative humidity during the entire 24-hour period.

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Answer:

To get a function of degree 5, either functions of degree 1 and 4 or functions of degree 2 and 3 should be multiplied.

This function will have a total of 5 zeros, same as its degree.

The function of degree 5 will have at least one and up to five real zeros

The rest of the zero's are imaginary.

So if has 2 real zeros, then the remaining 3 will be imaginary.

Maximum number of imaginary zero's is 4.

The actual distance between City C and City D is 466.67 miles.Therefore, the actual distance between City C and City D is 466.67 miles.

To find the actual distance between City C and City D, we can use the scale on the map. We know that 1.5 feet represents 200 miles, so we can set up a proportion:

1.5 feet : 200 miles = 3.5 feet : x miles

Cross-multiplying, we get:

1.5 feet * x miles = 3.5 feet * 200 miles

Simplifying, we get:

x miles = (3.5 feet * 200 miles) / 1.5 feet

x miles = 466.67 miles

Therefore, the actual distance between City C and City D is 466.67 miles.

Using the given information, we can set up a proportion to find the actual distance between City C and City D.

On the map:
1.5 feet represents 200 miles (between City A and City B)

Let x be the actual distance between City C and City D:
3.5 feet represents x miles

Now we can set up a proportion:

1.5 feet / 200 miles = 3.5 feet / x miles

Cross-multiply and solve for x:

1.5 * x = 3.5 * 200
1.5x = 700

Now divide by 1.5:

x = 700 / 1.5
x = 466.67 miles (approximately)

The actual distance between City C and City D is approximately 466.67 miles.

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Answer:

B and then A

Step-by-step explanation:

volume is × so the . means times

so it's the only option

and then the second area is

6×3×4= 72cm³

Answer:

one

Step-by-step explanation:

Answer:

Mabey B) if someone else says other wise follow them.

The probability that she will go to softball practice in a striped jersey and green shorts is 1/6.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Given:

Meredith has a green, white, or striped jersey.

So, probability that she will go to softball practice in a striped jersey and green shorts

= 1/3 x 1/3

= 1/6

Hence, probability that she will go to softball practice in a striped jersey and green shorts is 1/6.

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The equation that can be used is the exponential growth equation p = p0 * e^(kt), where p0 is the initial population, e is Euler's number, k is the growth rate constant, and t is the number of years after.

In this case, we need to solve for t when p = 3p0. The given formula for modeling population growth, p = p0 * e^(kt), is an exponential growth equation. In this equation, p0 represents the initial population, e is Euler's number (approximately 2.71828), k is the growth rate constant, and t is the number of years after.

To find the number of years after which the population triples, we need to solve for t when p = 3p0. Substituting 3p0 for p in the equation, we get 3p0 = p0 * e^(kt). By canceling out p0 on both sides, we have 3 = e^(kt). To solve for t, we take the natural logarithm of both sides to eliminate the exponential term. Applying the natural logarithm to both sides gives us ln(3) = ln(e^(kt)). Since the natural logarithm and exponential functions are inverse operations, the exponential term simplifies to kt. Therefore, t = ln(3) / k.

By substituting the specific growth rate constant value, we can determine the exact number of years after which the population will triple.

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An exponential function has the form

Therefore, to find an exponential function that satisfies our condition, we need to find a and b.

From f(-2) = 1, we have

and from f(7) = 63, we have

Solving for a in equation (1) gives

substituting this value of a into equation (2) gives

With the value of b in hand, we now find the value of a:

Hence, the exponential function is

Evaluating the above function at x = 1 gives

which is our answer!

Answer:

365°, (65 +20t)°

Step-by-step explanation:

Temperature of oven

= initial temperature + 20°(number of minutes passed after it was turned on)

Temperature of oven after 15 minutes

= 65 +20(15)

= 65 +300

= 365°

Temperature after t minutes

= (65 +20t)°

Answer:

Step-by-step explanation:

When the signs of the two numbers are the same, the answer will be positive.

When the signs of the two numbers are different, the answer will be negative.

1) General solution for second order differential equation, y" – 2y' + y = 0, is y = (c₁x + c₂)eˣ .

2) General solution for differential equation, 9y" + 6y' + y = 0, is y =(c₁x + c₂)e⁻³ˣ.

3) General solution for differential equation, 4y"- 4y'- 3y = 0, is y = c₁ e⁶ˣ+ c₂e⁻⁴ˣ.

4) General solution for differential equation, 4y" + 12y' +9y = 0, is y = (c₁x + c₂)e⁻⁶ˣ.

5) General solution for differential equation, y" – 2y' + 10y = 0, is y = eˣ (c₁cos(6x) + c₂sin(6x)).

6) General solution for differential equation, y" – 6y' +9y = 0 is y = (c₁x + c₂)e³ˣ.

7) General solution for differential equation, 4y" + 17y' + 4y = 0, is y = c₁e⁻ˣ + c₂e⁻¹⁶ˣ.

8) General solution for differential equation, 16y" + 24y' +9y = 0, is y = (c₁x + c₂)e⁻¹²ˣ.

9) General solution for differential equation, 25y" – 20y' + 4y = 0, is y = (c₁x + c₂)e¹⁰ˣ.

10) General solution for differential equation, 2y" + 2y' + y = 0, is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)).

General solution is also called complete solution and complete solution = complemantory function + particular Solution

Here right hand side is zero so particular solution is equals to zero. Therefore, evaluating the complementary function will be sufficient to determine the general solution to the differential equation.

1) y"-2y' + y = 0, --(1)

put D = d/dx, so (D² - 2D + 1)y =0

Auxiliary equation for (1) can be written as, m² - 2m + 1 = 0 , a quadratic equation solving it by using quadratic formula,

\(m =\frac{-(- 2) ± \sqrt { 4 - 4}}{2}\)

=> m = 1 , 1

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)eˣ .

2) 9y" + 6y' + y = 0 or (9D² + 6D + 1)y =0 Auxiliary equation can be written as, 9m² + 6m + 1 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (6) ± \sqrt {36 - 4×4}}{2}\)

=> m = - 6/2

=> m = -3 , -3

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻³ˣ.

3) 4y"- 4y'- 3y = 0

put D = d/dx, so (4D² - 4D - 3)y = 0

Auxiliary equation can be written as, 4m² - 4m - 3 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{-(-4) ± \sqrt {16 - 4×4×(-3)}}{2}\)

=> m = (4 ± 8)/2

=> m = -4 , 6

The roots of equation are real and equal. So, general solution is y = c₁ e⁶ˣ + c₂e⁻⁴ˣ.

4) 4y" + 12y' +9y = 0 or (4D² + 12D + 9)y= 0

Auxiliary equation can be written as, 4m² + 12m + 9= 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{-(12) ± \sqrt{144 - 4×4×9}}{2}\)

=> m = -12/2

=> m = -6 , -6

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻⁶ˣ.

5) y" – 2y' + 10y = 0 or (D² - 2D + 10)y = 0 Auxiliary equation can be written as, m² - 2m + 10 = 0 , a quadratic equation

solving it by using quadratic formula,

\(m =\frac{ - (-2) ± \sqrt {4 - 4×1×10}}{2}\)

=> m = (2 ± 6i)/2 ( since, √-1 = i)

=> m = 1 + 6i , 1-6i

The roots of equation are imaginary and unequal. So, general solution is y =eˣ (c₁cos(6x) + c₂sin(6x)).

6) y" – 6y' +9y = 0 or (D²- 6D + 9)y =0

Auxiliary equation can be written as, m² - 6m + 9 = 0 , a quadratic equation

solving it by using quadratic formula,

\(m =\frac{ - (-6) ± \sqrt {36 - 4×1×9}}{2}\)

=> m = 6/2 = 3,3

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e³ˣ.

7) 4y" + 17y' + 4y = 0 or (4D²+ 17D + 4)y=0

Auxiliary equation can be written as, 4m² + 17m + 4 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{- (-17) ± \sqrt {16 - 4×4×17}}{2}\)

=> m = ( -17 ± 15)/2

=> m = (-17 + 15)/2, (- 17 - 15)/2= -1, -16

The roots of equation are real and unequal. So, general solution is y = c₁e⁻ˣ + c₂e⁻¹⁶ˣ.

8) 16y"+24y'+9y =0 or (16D²+ 24D + 9)y= 0

Auxiliary equation can be written as, 16m² + 24m + 9 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (24) ± \sqrt {576 - 4×9×16}}{2}\)

=> m = (-24 ± 0)/2

=> m = -12,-12

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻¹²ˣ.

9) 25y"- 20y' +4y =0 or (25D²-20D + 4)y = 0

Auxiliary equation can be written as, 25m²- 20m + 4 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (-20) ± \sqrt {400 - 4×4×25}}{2}\)

=> m = 20/2

=> m = 10 , 10

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e¹⁰ˣ.

10) 2y" + 2y' + y = 0 or (2D²+ 2D + 1)y =0

Auxiliary equation can be written as, 2m² + 2m + 1 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (2) ± \sqrt {4 - 4×1×2}}{2}\)

=> m = (- 2 ± 4i)/2 ( since, √-1 = i)

=> m = -1 + 2i , -1 - 2i

The roots of equation are imaginary and unequal. So, general solution is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)). Hence, required solution of differential equation is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)).

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Answer:

3.15 ft

Step-by-step explanation:      

                                                                                              V

Volume of a cylinder:  πr²h.  Solving for r², we get r² = ---------

                                                                                             πh

Here, we get r² = (117.1 ft³) / (3.14·15 ft) = 2.48 ft² and r = √(2.48 ft²), or

1.58 ft, so that the diameter is 2r, or 3.15 ft

The diameter of the base of the cylinder is 3.15 ft.

Answer:

j=|x|

Step-by-step explanation:

Answer:

2pi

Step-by-step explanation:

3 + 7x - (2 + 9x )

3 + 7x - 2 -9x

1-2x

Answer:

1-2x

Step-by-step explanation:

3+7x-(2-9x)

(if there's a minus in front of parenthesis then you have to change the sign in the parenthesis)

3+7x-2-9x(take out from parenthesis)

1-2x(combine/simplify like terms)

Answer:

-60

Step-by-step explanation:

     First do the operation in the inner most brackets.

{4 - [-2 - (1 + 3)] }*(-6) ={ 4 - [-2 - 4] } * (-6)

                          = { 4- [ -2 - 4] } * (-6)

                         = {4 - [-6] } * (-6)

                         = { 4 + 6} * (-6)

                           = 10 * (-6)

                            = -60

Answer:

C

Step-by-step explanation:

An obtuse triangle has ONLY one greater-than-180 angle measure, so this fact rules out B. An equilateral triangle has 3 exact same sides and an isosceles triangle has 2 equal side lengths. Since the "tally marks" is all different, this mean it's neither equilateral nor isosceles, so this fact also rules out A and D. Since a scalene triangle has no equal side length, and the only option available is C. SO THE FINAL ANSWER IS C

The given triangle is obtuse and scalene. Therefore, the correct answer is option C.

Isosceles triangles are those triangles that have at least two sides of equal measure and two base angles are equal.

In the triangle, all the sides are unequal and one of the angle measure greater than 90 degree.

The definition of an obtuse angle in geometry states that 'an angle whose measure is greater than 90° and less than 180° is called an obtuse angle.

So, it is obtuse angled triangle

If all the sides of triangle are unequal, then it is scalene triangle.

Therefore, the correct answer is option C.

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Answer:

The answer is 17

Step-by-step explanation:

Now, Evaluate

a² – 4b + 2c

(1)² – 4(-3) + 2(2)

1 + 12 + 4 = 17

Thus, The value is 17

-TheUnknownScientist 72

The value of x from the figure is 30 degrees

Parallel lines are lines that have the same slope and have 0 degrees as the angle between them.

The sum of angle 5 and angle 6 are supplementary. Hence;

m<5 + m<6 = 180

3x - 33 + 123 = 180

3x + 90 = 180

3x = 180 - 90

3x = 90

Divide both sides by 3

3x/3 = 90/3

x = 30

Hence the value of x from the figure is 30 degrees

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Algorithm 1: Worst case - M questions, linear time complexity. Algorithm 2: Worst case - M questions, linear time complexity. Both algorithms have the same worst-case behavior and time complexity, as they require the same number of questions to be asked.

Algorithm 1: In the worst case, Algorithm 1 will ask a total of M questions, where M is the number of people in the room. This is because for each person, you ask them if they have attended the same number of classes as you. So, if there are M people in the room, you will need to ask M questions in the worst case. In terms of complexity, Algorithm 1 has a linear time complexity since the number of questions asked is directly proportional to the number of people in the room.

Algorithm 2: In the worst case, Algorithm 2 will also ask a total of M questions, where M is the number of people in the room. This is because you only ask the number of classes attended to person 1, who then asks person 2, and so on until person M. Each person asks only one question to the next person in line. So, if there are M people in the room, you will need to ask M questions in the worst case. In terms of complexity, Algorithm 2 also has a linear time complexity since the number of questions asked is directly proportional to the number of people in the room.

To summarize:

- Algorithm 1: Worst case - M questions, linear time complexity.

- Algorithm 2: Worst case - M questions, linear time complexity.

Both algorithms have the same worst-case behavior and time complexity, as they require the same number of questions to be asked.

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Answer:

392 square units

Step-by-step explanation:

We can make 2 right trapezoids out of this shape.

The area of a trapezoid would be 1/2×(b1+b2)×h or (b1+b2)×h ÷ 2.

If we do 1 half it would be 1/2×(14+14)×14 = 196

Now if we multiply by 2 (because we have 2 trapezoids) it would be 392.

if radius is 45

V≈1.78×10^5

if radius is 28

V≈1.11×10^5

volume = pi times radius squared times height

if radius is 45

volume = pi times 45 squared times 28

Answer:

m(WXY) = 224°

Step-by-step explanation:

<C is an inscribed angle.

Arc(WXY) is an intercepted arc whose end points are on <C.

Thus:

m(WXY) = 2(m<C)

Substitute

m(WXY) = 2(112°)

m(WXY) = 224°