A, B & C lie on a straight line.
D, B & E lie on a different straight line.
∠
CBE = 40°.
Work out the angle marked
x

Given a point and a normal vector, the line is said to be perpendicular to the normal vector if it passes through the point and its direction is normal to the normal vector.

To solve this problem, we will first obtain the normal vector and then use it to derive the parametric equations. The normal vector must be perpendicular to both i j and j k. We obtain the normal vector as the cross product of these vectors:n = i j × j k= i kThe normal vector is a vector normal to both i j and j k and has a direction of i k. We can now use the normal vector to derive the parametric equations of the line.

The general equation of a line is given by:r = a + where a is the point on the line and n is the normal vector. In this case, we can use the point (3, 3, 0) and the normal vector (1, 0, 0) to obtain the parametric equation s:r = (3, 3, 0) + t(1, 0, 0)Expanding this equation gives:r = (3 + t, 3, 0)The parametric equations of the line are:r = (3 + t, 3, 0)Explanation:We obtained the normal vector n by taking the cross product of i j and j k, n = i j × j k = i k. Since the line is perpendicular to this vector, we used it as the normal vector to derive the parametric equations of the line. We used the general equation of a line, r = a + tn, where a is a point on the line and n is the normal vector. We then substituted the values of the point and the normal vector to obtain the specific parametric equations of the line, r = (3 + t, 3, 0).

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Answer:

y=-4x+4x-32

Step-by-step explanation:

Answer:

y=x-8

Step-by-step explanation:

4y-4x=-32

4y=4x+(-32)

4y=4x-32

y=4/4x-32/4

y=x-8

Answer:

5t+3

Step-by-step explanation:

1 Collect like terms.

(7t-2t)+3

2 Simplify.

5t+3

Answer:

(7t - 2t) + 3

Combine the like terms that include t.

\(7t - 2t = 5t\)

Turn into equation.

\(5t + 3\)

__________________________________________________________

Answer:

2.857m/s^2

Step-by-step explanation:

Acceleration (a) is the change in velocity (v) over the change in time (t), represented by the equation a = v/t.

Answer:

Unit rate= 20

words per minute/ 0.3

words per second

Step-by-step explanation:

We could work out the unit rate in 2 ways:

Per Minute or Per second.

First we will start of with per minute:

Rate=Word/minute=100/5=20

Answer:

100 words to 5 minutes

Step-by-step explanation:

We can see that there is at least one row where all premises are true (row 7), but the conclusion is false. Therefore, the argument is invalid.

To construct a symbolic model of the argument, let's define the following symbols:

P: Jayco qualifies as a small business.

Q: Jayco has sales that are not large enough to influence its environment.

R: Jayco is privately owned by a small group of individuals.

Now we can represent the statements in symbolic form:

Premise 1: P ≡ (Q • R)

Premise 2: ~P

Conclusion: ~R

To determine if the argument is valid or invalid, we can construct a truth table:

| P | Q | R | P ≡ (Q • R) | ~P | ~R |

|---|---|---|-------------|----|----|

| T | T | T |      T      |  F |  F |

| T | T | F |      F      |  F |  T |

| T | F | T |      T      |  F |  F |

| T | F | F |      F      |  F |  T |

| F | T | T |      F      |  T |  F |

| F | T | F |      T      |  T |  T |

| F | F | T |      F      |  T |  F |

| F | F | F |      T      |  T |  T |

From the truth table, we can see that there is at least one row where all premises are true (row 7), but the conclusion is false. Therefore, the argument is invalid.

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A sequence of transformation that would move ΔABC onto ΔDEF is: D. a dilation by a scale factor of 1/2, centered at the origin, followed by a 90° clockwise rotation about the origin.

In Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 1/2 that is centered at the origin as follows:

Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).

In Mathematics and Geometry, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction;

(x, y)                               →            (y, -x)

Ordered pair B' (-2, 1)   →          E (1, 2)

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After solving, the height of the cylinder is 6 meters.

The surface area of a cylinder is 24π m².

The distance around the base of the cylinder is 3π meter.

The diameter of a base of the cylinder is 4 meter.

Now the radius of the cylinder = diameter/2

The radius of the cylinder = 4/2

The radius of the cylinder = 2 meter.

The formula of surface area of cylinder:

S = 2πrh

From the question:

2πrh = 24π

Now putting the value of r

2π × 2 × h = 24π

4πh = 24π

Divide by 4π on both side, we get

h = 6

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The complete question is:

The surface area of a cylinder is 24π m². The distance around the base of the cylinder is 3π meter and the diameter of a base of the cylinder is 4 meter. What is the height of the cylinder? Enter your answer, in a simplified fraction, in the box.

The tension in the cable balances the weight in the vertical direction, the tension in the cable is also equal to 27,164.8 N.

Assuming that the wrecking ball is stationary and in equilibrium, the tension in each cable must be equal and opposite to the weight of the wrecking ball. We can use the force diagram to solve for the tension in the cable.

The force diagram for the wrecking ball is shown below:

     T

      |

      |

<-----|----->

      |

      | Fg

     \/

      m

where T is the tension in the cable, Fg is the weight of the wrecking ball, and the angle between the cable and the vertical is 40 degrees.

The weight of the wrecking ball is given by Fg = m * g, where g is the acceleration due to gravity, which is approximately \(9.81 m/s^2\).

Therefore,\(Fg = 3620 kg * 9.81 m/s^2 = 35,499.2 N\)

Since the tension in the cable is equal and opposite to the weight of the wrecking ball, the tension in the cable is also 35,499.2 N.

To find the tension in the cable that makes an angle of 40 degrees with the vertical, we need to resolve the weight vector into its horizontal and vertical components. The weight vector makes an angle of 50 degrees with the horizontal, which is equal to 90 degrees (vertical) minus the cable angle of 40 degrees.

The vertical component of the weight is \(Fg * sin(50 degrees) = 35,499.2\)N * sin(50 degrees) = 27,164.8 N.

Since the tension in the cable balances the weight in the vertical direction, the tension in the cable is also equal to 27,164.8 N.

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After four hours, the height of the candles will be the same.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A red candle has an 8-inch height and burns at a 7/10-inch per hour rate. A 6-inch tall blue candle burns at a rate of 1/5 inch per hour.

Let x be the number of hours and y be the height.

y = -0.70x + 8           ...1

y = -0.20x + 6             ...2

From equations 1 and 2, then we have

- 0.20x + 6 = - 0.70x + 8

(0.70 - 0.20)x = 8 - 6

0.50x = 2

x = 4 hours

After four hours, the height of the candles will be the same.

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Answer:

  -2/3

Step-by-step explanation:

  \(\ln{\dfrac{1}{\sqrt[3]{e^2}}}=\ln{e^{-\frac{2}{3}}}=-\dfrac{2}{3}\)

Answer:

-2/10

Step-by-step explanation:

First step

2          ( 3)           6

_    x    -(_)  =   -  __  

6          ( 5)          30

Simplified

 6         1

-__ =  - _

30        5

True. NPV (Net Present Value) can be used as an input variable in a sensitivity analysis. In conclusion, NPV is indeed utilized as an input variable in sensitivity analysis.

True. NPV (Net Present Value) can be used as an input variable in a sensitivity analysis. Sensitivity analysis is a technique used to determine how changes in certain variables, such as NPV, affect the outcome of a project or investment. By altering the value of NPV and observing the corresponding changes in the results, one can gain insights into the sensitivity or vulnerability of the project to different scenarios. This analysis helps in understanding the potential impact of changes in NPV on the overall feasibility and profitability of the project. In conclusion, NPV is indeed utilized as an input variable in sensitivity analysis.

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Answer:

48s plus 12p - 18

Step-by-step explanation:

Answer:

Add 48 + 12 and Subtract the sum from 18 (14+12-18)

Step-by-step explanation:

Sorry if I'm confusing you ;(

Answer:

314.882

Step-by-step explanation:

789.81 − 474.928 = 314.882

Mark as Brainliest

After the value at index 2 is tested, the binary search looking for 57 is complete. The array given is [7,1,23,2,41,3,46,4,55,57,64,70] and the value at index 2 is 57.

In the given array, we are looking for the value 57. The steps of the binary search are as follows:

1. Start with the left index at 0 and the right index at 7.
2. Calculate the middle index by adding the left and right indices and dividing by 2. The middle index is (0 + 7)/2 = 3.5, which we round down to 3.
3. Check the value at the middle index. The value at index 3 is 46.
4. Since 46 is less than 57, we know that 57 must be in the right half of the array. So, we update the left index to be one more than the middle index, which is 4.
5. Repeat steps 2-4 with the new left and right indices. The new middle index is (4 + 7)/2 = 5.5, which we round down to 5.
6. Check the value at the new middle index. The value at index 5 is 57, which is what we are looking for. So, we stop the search.

In total, we tested 2 values in the array (46 and 57) before finding the value we were looking for. Therefore, the answer to the question is 2.

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X = 23

Y = 129

Hope this is helpful!

Answer:

i think x = 23, y = 129

Step-by-step explanation:

5x+14+3x-18 = 180

8x-4 = 180

8x = 184

x = 23

3x-18+y = 180

3(23)-18+y = 180

69-18+y = 180

51+y = 180

y = 129

Answer

Explanation

The system of the equation:

From (i)

Substitute x as (13 -3y)/2 into (ii)

Since y = 1, then we shall substitute for y as 1 in (iii) to get x

Therefore the solution to the system is:

A vertically opposite angle is a pair of angles formed due to the intersection of two lines, and are said to be equal. Thus the angle that is the same as <BPD is <APC.

ii. The value of x is \(47^{o}\).

The intersection of two or more lines at a point will always produce a set of angles. Some of these angles when compared may have similar measures or properties.

Two angles can be equal with respect to their measure if they are vertically opposite. Vertically opposite angles are angles formed when two lines intersect, such that a pair of opposite angles about the point of intersection are equal.

Thus from the given question, the angle that is the same as <PBD is <APC.

i.e <BPD ≅ <APC (vertically opposite property)

Also,

x + 133 = 180 (sum of angles on a straight line)

x = 180 - 133

  = 47

x = \(47^{o}\)

Therefore the value of x is \(47^{o}\).

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Answer: D

Step-by-step explanation:

term is subtracted by 3 as the position changes

if we do B f(1) = 31 - 3(1) = 28 which does not equal 31

D is f(1) = 31 - 3(1-1) <- 3(0)

            = 31

Answer:

1: d. 3054^3

2: d. 20x

Step-by-step explanation:

1)

Well to find the volume of a sphere we use the following formula,

\(\frac{4}{3}\pi r^3\)

So the radius is 9.

9*9*9 = 729

729*pi = 2290.22104447

So it is 2290 rounded to the nearest whole number.

2290 * 4/3 = 3053.3333333

Thus,

the answer is d. \(3054^3\)

____________________________________________________________

So we have to factor 25x^2 - 9,

which is \(\left(5x+3\right)\left(5x-3\right)\).

So if the l and w are 5x + 3 and 5x - 3,

= 10x

10x + 10x = 20x,

Thus,

the answer is d. 20x

Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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Answer:

Step-by-step explanation:

I am not sure if this is the equation you ask about?

x²-4x-3√2 =0

... or is it ?

x²-4x-3 =0

9514 1404 393

Answer:

  fill in the coefficients and evaluate the formula

  x ≈ 2±√(4+3√2) ≈ {-0.871, 4.871}

Step-by-step explanation:

The quadratic formula for the solution of ...

  ax² +bx +c = 0

is ...

  \(x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

The use of this formula requires that you know the values of a, b, c. You can find these by comparing the given quadratic with the standard form, above.

When you are asked for "roots" or "zeros", you are being asked for the values of x that make the polynomial have a value of zero:

  x² -4x -3√2 = 0

In this form, you can see the coefficients are ...

  a = 1, b = -4, c = -3√2

Using these values in the quadratic formula, you have ...

  \(x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(-3\sqrt{2})}}{2(1)}=\dfrac{4\pm\sqrt{16+12\sqrt{2}}}{2}\\\\\boxed{x=2\pm\sqrt{4+3\sqrt{2}}\approx\{-0.871000, 4.871000\}}\)

To graph the solution, we draw a number line and plot a closed circle at -6 (since n is not equal to -6), and shade the area to the right of -6, since n is greater than -6.

How to do?

To solve the inequality:

-8n + 2 < 50

First, we need to isolate n on one side of the inequality. We can do this by subtracting 2 from both sides:

-8n < 48

Next, we need to get n by itself, so we divide both sides by -8. Remember, when we divide by a negative number, we need to flip the inequality sign:

n > -6

So the solution to the inequality is n > -6.

The open end indicates that the graph continues indefinitely to the right.

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Answer:

33, 35, 37

Step-by-step explanation:

Let the tree consecutive odd integers be x, x +2 and x + 4

According to the given information:

Sum of the first and the third is 70

\( \therefore x + x + 4 = 70\\\\

\therefore 2x = 70 - 4\\\\

\therefore 2x = 66\\\\

\therefore x = \frac{66}{2}\\\\

\therefore x = 33\\\\

\implies x + 2 = 33 + 2 = 35\\\\

\& \hspace{25 pt}x + 4 = 33 + 4 = 37\\\\\)

Thus, the three consecutive odd integers are 33, 35 and 37.

Verification: 33 + 37 = 70

An ogive is used to plot cumulative frequency or cumulative relative frequency of each class against the upper limit of the corresponding class when displaying quantitative data. Option B.

An ogive is a graph that represents a cumulative distribution function (CDF) of a frequency distribution. It shows the cumulative relative frequency or cumulative frequency of each class plotted against the upper limit of the corresponding class. In other words, an ogive can be used to represent data through graphs by plotting the upper limit of each class interval on the x-axis and the cumulative frequency or cumulative relative frequency on the y-axis.

An ogive is used to display the distribution of quantitative data, such as weight, height, or time. It is also useful when analyzing data that is not easily represented by a histogram or a frequency polygon, and when we want to determine the percentile or median of a given set of data. Based on the information given above, option B: "Cumulative frequency or cumulative relative frequency of each class against the upper limit of the corresponding class" is the correct answer.

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Answer:

16000=140x

It will take 90 minutes to hit 12,600 ft above ground.

Step-by-step explanation:

Just swap out 16000 for 12600. Then solve from there.

Hope it helped!

Part A: The point (2, 80) represents that when the number of hours is 2, the number of miles of water in the tank is 80.

Part B: y = 40x

The theory used in this question is the concept of proportional relationships.

A proportional relationship between two variables is one in which one variable is a constant multiple of the other.

In this case, the number of miles of water in the tank is a constant multiple of the number of hours.

The equation y = mx is used to describe a proportional relation, where m is the constant of proportionality.

The equation for the proportional relationship between hours, x, and number of miles, y, of water in a tank can be written in the form of y = mx. To find the value of m, we can use the point (2, 80) from the graph. We know that when x = 2, y = 80. We can use this information to solve for m.

m = y/x

m = 80/2

m = 40

Therefore, the equation for the proportional relationship is y = 40x.

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1. A∪B = {b, c, d, e, f, g}

A∩B = {d, f, g}

2. B' = { a, b, h , l)

From the information given, we have that:

A∪B = {The sum of sets in A and B without repetition}

Then we have:

A∪B = {b, c, d, e, f, g}

A∩B = {Sets found in both A and B}

Then, we have:

A∩B = {d, f, g}

2. B' = { sets found in the universal set and not in B}

We have:

B' = { a, b, h , l)

Thus, we can see that union and intersection of sets give different subsets from the two original sets.

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