For part (b), you are told that John must make at least $80,000 to pay bills. That can be rephrased as $80,000 is less than or equal to John’s profit. You also know that John’s profit is less than or equal to $250,000

Answer: the three consecutive integers are 18, 19, and 20.

Step-by-step explanation:

Answer:

18, 19, and 20

Step-by-step explanation:

let the first integer be 'x'.

Thus, the three consecutive integers are:

x, (x+1), (x+2).

Therefore, if 4 × x added to (x+2) = 92, then:

[tex](x+2)+4x=92\\5x+2=92\\5x=90\\x=18[/tex]

Hence x = 18, and thus, the three consecutive integers are 18, 19, and 20.

Nothing can be said about the curve, for the parametric equations where the range of is [-1, 9] and the range of is [-1, 9]. Option B is the correct answer.

The parametric equations define the curve in terms of the parameter t. The given ranges for t and u indicate the domain of the curve. Without additional information, it is difficult to say much about the curve.

Option A is incorrect because there is no reason to assume that the curve lies inside a circle with a center (-1, -1) and radius of 0.5.

Option C is incorrect because the range of u is greater than 3.

Option D is incorrect because the given range of t is not sufficient to define a line segment between (-1, 1) and (7, 3). Option E is incorrect because there is no reason to assume that the curve lies outside the rectangle [-1, 7] by [1, 3].

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The question is -

Suppose a curve is given by the parametric equations where the range of is [-1, 9] and the range of is [-1, 9]. what can you say about the curve? you must select all correct choices to get full credit on this problem.

A. The curve must lie inside a circle with a center (-1, -1) and radius of 0.5.

B. Nothing can be said about the curve.

C. The curve is completely contained in the rectangle [-1, 1] by [1, 3].

D. The curve is the line with endpoints (-1, 1) and (7, 3).

E. The curve must lie outside the rectangle [-1, 7] by [1, 3].

D. The curve is a circle with a center (-1, -1) and a radius of 3.

Answer:

The answer is 1×10⁶ to the nearest whole number

Step-by-step explanation:

7.6×10⁰/5.4×10‐⁶

7.6×10^(0-(-6)/5.4

7.6×10^(0+6)/5.4

7.6×10⁶/5.4

=1×10⁶ to the nearest whole number

In linear equation, 4,000 guest nights did the hotel have during this period.

What is a linear equation in mathematics?

A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables. 

According to question,

Guest nights = Number of guests × Number of nights

                       = 2,000 × 2

                       = 4,000

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Answer:

Roots = (1, 0) and (-5, 0)

Vertex = (-2, -9)

Two additional points = (-4, -5) and (0, -5)

Step-by-step explanation:

The given equation y = x² + 4x - 5 is a quadratic equation with a positive leading coefficient. Therefore, the shape of the curve is a parabola that opens upwards.

The roots of a quadratic equation are the x-values that satisfy the equation y = 0. They are the points at which the curve crosses the x-axis.

To calculate the roots of the given equation, set it to zero and solve for x.

[tex]\begin{aligned}x^2+4x-5&=0\\x^2+5x-x-5&=0\\x(x+5)-1(x+5)&=0\\(x-1)(x+5)&=0\\\\\implies x-1&=0 \implies x=1\\\implies x+5&=0 \implies x=-5\end{aligned}[/tex]

Therefore, the roots of the equation are (1, 0) and (-5, 0).

The x-value of the vertex of a quadratic function in the form ax² + bx + c is -b/2a.

For the given equation y = x² + 4x - 5, a = 1 and b = 4.

To find the x-value of the vertex, substitute these values into the formula:

[tex]x_{\sf vertex}=\dfrac{-b}{2a}=\dfrac{-4}{2(1)}=-2[/tex]

To find the y-value of the vertex, substitute the x-value of the vertex into the given equation:

[tex]y_{\sf vertex}=(-2)^2+4(-2)-5=-9[/tex]

Therefore, the vertex is (-2, -9).

To find two other points on the curve, substitute two values of x into the equation.

[tex]\begin{aligned}x=-4 \implies y&=(-4)^2+4(-4)-5\\&=16-16-5\\&=0-5\\&=-5\end{aligned}[/tex]

[tex]\begin{aligned}x=0 \implies y&=(0)^2+4(0)-5\\&=0+0-5\\&=0-5\\&=-5\end{aligned}[/tex]

The axis of symmetry of a quadratic equation is the vertical line that divides the parabola into two mirror images. The x-value of the vertex is the axis of symmetry. Therefore, the axis of symmetry is x = -2.

To graph the given equation:

Level of advertisement expenditure when x < 300, Q'(x) >0 units of product sold is increasing and when x > 300 ,Q'(x) < 0 product sold in decreasing.

Function is equal to ,

Q(x) = -x² + 600x + 25

'Q' represents the firm estimated number of units sells its product with an advertising expenditure.

To get the critical point get the first derivative of Q(x) ,

Q'(x) = -2x + 600

Now equate it to zero.

Q'(x) = 0

This implies

⇒ -2x + 600 = 0

⇒ 2x = 600

⇒ x = 300

For x < 300 , Q'(x) is positive.

Number of units of product sold is increasing for the level of advertising expenditure.

For x > 300, Q'(x) is negative .

Number of units of product sold is decreasing for the level of advertising expenditure.

Therefore, the level of advertising expenditure is x  < 300 then the number of units of product is increasing and when x > 300 then it is decreasing.

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The solutions to the expressions 1 to 17 are shown below

The expressions 1 to 17 are solved below

3x - 12 = 6

3x = 6 + 12

3x = 18

x = 6

2x + 4 = 8

2x = 8 - 4

2x = 4

x = 2

12s - 12 = 12

12s = 12 + 12

12s = 24

s = 2

14s + 7 = 35

14s = 35 - 7

14s = 28

s = 2

3s - 12 = 6

3s = 6 + 12

3s = 18

s = 6

18t + 9 = 34

18t = 34 - 9

18t = 25

t = 25/18

21x + 7 = 28

21x = 28 - 7

21x = 21

x = 1

50y + 3 = 103

50y = 103 - 3

50y = 100

y = 2

(1/4)x - 6 = 18

(1/4)x = 18 + 6

(1/4)x = 24

x = 24/(1/4)

x = 96

26x + 2 = 18

26x = 18 - 2

26x = 16

x = 16/26

6 - 2x = 18

-2x = 18 - 6

-2x = 12

x = -6

14 + s = 21

s = 21 - 14

s = 7

16x - 4 = 28

16x = 28 + 4

16x = 32

x = 2

19x - 1 + 3 = 40

19x + 2 = 40

19x = 40 - 2

19x = 38

x = 2

100t = 194

t = 194/100

500x + 100 = 1100

500x = 1100 - 100

500x = 1000

x = 2

60 - 3x + 3 = 114

-3x = 114 - 60 - 3

-3x = 51

x = -17

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It is true to say that when utilizing MATLAB's built-in ode solver, the function for one's states the variable for the state derivatives must be set as column vectors.

The Ordinary Differential Equation (ODE) solvers in MATLAB solve initial value problems with a varient state of properties. They consider state spaces as a column vector. For example, two solve a second degree ODE, It's two states in state space has to be arranges in a 1x2 column vector to pass it into a ODE solver.

ODE solvers in MATLAB.

It used to compare methods of orders four and five to determine an estimate error.

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The probability of drawing a face card followed by condition of drawing non face card is equal to 18% ( approximately).

In a standard deck of cards,

There are 12 face cards 4 jacks, 4 queens, and 4 kings

And 40 non-face cards 10 numbered cards each for the 4 suits.

The probability of drawing a face card on the first draw is

=  12/52

= 3/13.

Assuming a face card was drawn on the first draw,

There are now 51 cards remaining in the deck.

Of which 40 are non-face cards.

Probability of drawing a non-face card on the second draw is

= 40/51.

Probability of both events happening drawing a face card followed by a non-face card

= Multiply the probabilities of the individual events

= (3/13) x (40/51)

= 120/663

=  0.181approximately  

= 18% (rounded to the nearest whole number).

Therefore,  the probability of drawing a face card followed by drawing a non-face card in a standard deck of cards is approximately 18%.

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The slope of the line in the reduced form is 4 / 7.

The slope of a line is the change in the dependent variable with respect to the change in the independent variable.

Therefore,

slope = m = change in y / change in x

slope = m = y₂ - y₁ / x₂ - x₁

P = (2, 3)

Q = (9, 7)

x₁ = 2

x₂ = 9

y₁ = 3

y₂ = 7

Therefore,

slope = 7 - 3 / 9 - 2

slope = 4 / 7

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The section for piano will have 60 degrees in the circle graph.

To find out how many degrees the section for piano will have in the circle graph, we first need to find the fraction of the circle that the piano represents.

The total degrees in a circle is 360 degrees. We can use the given fraction of piano (1/6) and multiply it by 360 degrees to find out the degrees of the section for piano.

Degrees for piano = (Fraction of piano) × 360

Degrees for piano = (1/6) × 360

Now, multiply the fraction by 360:

Degrees for piano = 60

So, the section for piano will have 60 degrees in the circle graph.

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→ 60° ( btw, ° means degrees )

— if a WHOLE circle is 360° and the piano is 1/6 of the circle, then all you have to do is multiply 1/6 by 360° which gives you 60 OR 60°

HEY- you look hungry, eat up !! →

A) Their graphs will be different from the graph of the linear parent function. B) In real-world context, comparing functions can be useful in many scenarios, such as predicting sales or analyzing trends.

The y-intercept is the point where the graph of a function intersects with the y-axis. It is the point at which the value of x is 0.

Part A:

The linear parent function is represented by y = mx + b, where m is the slope and b is the y-intercept. The slope of the linear parent function is constant, while the y-intercept can vary.

In Jack's function, d = 0.05t, the slope is 0.05, which means that for every minute he runs, he travels 0.05 miles. The y-intercept is 0, which means that he starts at 0 miles.

In Jill's function, d = 0.04t + 0.5, the slope is 0.04, which means that for every minute she runs, she travels 0.04 miles. The y-intercept is 0.5, which means that she starts at 0.5 miles.

Both functions are linear, but they have different slopes and y-intercepts. Therefore, their graphs will be different from the graph of the linear parent function.

Part B:

Comparing Jack and Jill's functions to the linear parent function can give us insights into their race. The fact that their functions are linear means that they are running at a constant rate. However, the different slopes and y-intercepts mean that they are running at different rates and starting at different distances.

For example, we can see from their functions that Jack is running faster than Jill since his slope is larger. We can also see that Jill has a head start since her y-intercept is larger. By comparing their functions, we can make predictions about who will win the race or how far ahead one person will be at a certain time.

In real-world context, comparing functions can be useful in many scenarios, such as predicting sales or analyzing trends. By understanding the relationship between variables, we can make informed decisions and predictions.

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27 cubic in is he Volume of a Cube.

What is a Cube in Mathematics?

In mathematics or geometry, a cube is a solid three-dimensional figure with 6 square faces, 8 vertices, and 12 sides. Also called a hexahedron. Examples of common dice are:

                          Cubes, square ice cubes, Rubik's cubes, square tissue boxes, sugar cubes. A cube has six equal square sides. Also, the dice has 8 vertices (corners) and 12 sides, all of equal length. All the corners of the cube are right angles. Cubic objects include blocks and cubes. 

S = 3 in

volume of cube

                          V=SXSXS

                           V=3x3x3

                           V=27 cubic in

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Step-by-step explanation:

+ 1.25

every new term is the previous term + 1.25.

with starting value -1.75

f(n) = 1.25n - 1.75

Answer: 13 non-apple phone to 12 apple phone

Step-by-step explanation:

48 are apple phone

100-48=52   52 are non-apple phones

52:48

simplify

13:12

we can reject the null hypothesis at the 5% significance level since the p-value is less than 0.05.

To calculate the p-value, we need to perform a hypothesis test.

Let's assume the null hypothesis is that the proportion of defective systems produced by x-game is equal to or less than the industry standard of 0.02, while the alternative hypothesis is that the proportion is greater than 0.02.

We can use the normal approximation to the binomial distribution since we have a large sample size (n=120) and np and n(1-p) are both greater than or equal to 10.

The test statistic can be calculated as:

[tex]z = (p_hat - p) / \sqrt{(p*(1-p)/n)}[/tex]

where [tex]p_hat[/tex]  is the sample proportion of defective systems, p is the hypothesized proportion under the null hypothesis, and n is the sample size.

Using the values given in the question, we have:

[tex]p_hat = 6/120 = 0.05[/tex]

p = 0.02

n = 120

Plugging these values into the formula, we get:

[tex]z = (0.05 - 0.02) / \sqrt{(0.02*(1-0.02)/120) = 2.041}[/tex]

The p-value can be calculated as the probability of getting a test statistic as extreme or more extreme than 2.041 under the null hypothesis.

Since this is a one-tailed test (the alternative hypothesis is one-sided), we look up the area in the right tail of the standard normal distribution table.

Using a standard normal distribution table, we find that the area to the right of 2.041 is 0.0207.

Therefore, the p-value is 0.0207.

Therefore, we can reject the null hypothesis at the 5% significance level since the p-value is less than 0.05.

This means that there is strong evidence that the proportion of defective systems produced by x-game exceeds the industry standard of 0.02.

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Answer:

The answer is 3

Step-by-step explanation:

x×108=y

x×2²×3³=y

3×108=324

The total hours that the school had someone on site at the local home is 186.5 hours.

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organised in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.

Given that, 1 students and chaperones participated on the day of the event thus we have:

Total time = (4.5 hours) x (41 people) = 184.5 hours

Now,

Total time spent on site by teacher sponsor = 120 minutes / 60 = 2 hours

Thus,

Total time credit received by school = 184.5 hours + 2 hours = 186.5 hours

Hence, the total hours that the school had someone on site at the local home is 186.5 hours.

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Angle ACB = 180 degrees - angle ADC . AXB and angle ACB are supplementary

Supplementary angles are  angles whose sum is 180 degrees. For example, an angle of 130° and an angle of 50° are supplementary angles, because the sum of 130° and 50° is  180°. Similarly, complementary angles add up to 90 degrees.

 To show that angle AXB and angle ACB are supplementary, we must show that their sum is  180 degrees.  

First, we can use the fact that angle AXB is a circumscribed angle of circle C to say that XA and XB are the ears of the circle that intersect at  B. Let O be the center of  circle C. Then, by the inscribed angle theorem, we get:

angle AOB = 2 * angle AXB

Similarly, we can say that AC is a chord of a circle that intersects  XB at  D. Then, using the inscribed angle theorem again, we get:

angle AOC = 2 * angle ADC

Since the angles AOB and AOC are both subtended by the arc AC, they are equal. Therefore, we can equate the expressions  AOB and AOC:

2 * angle AXB = 2 * angle ADC

Simplifying this expression, we get:

angle AXB = angle ADC

Now we can use this fact to show that angle AXB and angle ACB are supplementary. Since the angles AXB and ADC are opposite angles of the cyclic quadrilateral AXDC, we know that they add up to 180 degrees:

angle AXB + angle ADC = 180 degrees

Replacing angle AXB with angle ACB (since they are equal), we get:

angle ACB + angle ADC = 180 degrees

In the reorganization, we have:

angle ACB = 180 degrees - angle ADC

So angle ACB and angle ADC are also supplementary. Therefore, we have shown that angle AXB and angle ACB are supplementary by necessity.

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The monthly interest rate is the annual interest rate divided by 12

To calculate the monthly interest rate, we need to divide the annual interest rate by 12 (since there are 12 months in a year).

So if the annual interest rate is 8%, the monthly interest rate can be calculated as:

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 8% / 12

Monthly interest rate = 0.6667%

Therefore, the monthly interest rate would be 0.6667%.

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The amplitude of angle A is 113.4° and the amplitude of angle B is 189° if angle c is 35° and 20°.

Let x be the amplitude of angle A, and y be the amplitude of angle B.

We know that half of the amplitude of angle A is equal to 3/5 of the amplitude of angle B, so we can write the equation: x/2 = 3/5 × y.

We also know that angle B is three times the size of angle C, where angle C measures 43° and 20, so angle B is equal to 3 × (43° + 20).

We can use equation (3) to find the amplitude of angle B: y = 3 × (43° + 20) = 189°.

Now that we know the value of y, we can substitute it into equation (2) to find the amplitude of angle A: x/2 = 3/5 × y = 3/5 × 189° = 113.4°.

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The question is -

MARCIA IS GOING TO LIGHT UP A THEATRICAL SPACE WITH LIGHTS THAT HAVE DIFFERENT ANGLES OF ILLUMINATION, AND TO DO SO SHE NEEDS TO CALCULATE TWO OF THOSE ANGLES. THE GIVEN DATA IS: HALF OF THE AMPLITUDE OF "A" IS EQUAL TO 3/5 OF THE MEASURE OF ANGLE "B," AND ANGLE "B" IS THREE TIMES THE SIZE OF ANGLE "C." IF ANGLE "C" MEASURES 43° AND 20, WHAT IS THE AMPLITUDE OF ANGLE "A" AND "B"?

The minimum possible diameter of a soccer ball is 8.60 inches, and the maximum possible diameter is 8.70 inches.

What is equations?

Equivalent equations are algebraic equations that are having identical roots or solutions.

The soccer ball specifications require a diameter of 8.65 inches, with an allowable margin of error of 0.05 inch.

This means that the actual diameter of any new soccer ball should be within the range of 8.60 inches to 8.70 inches. The equation that can be used to find the diameter of a new soccer ball is d = 8.65 ± 0.05, where d represents the diameter. The symbol "±" indicates that the diameter can be either 0.05 inches larger or smaller than the specified diameter of 8.65 inches.

It is important to ensure that the diameter of a soccer ball falls within this allowable range to comply with the specifications and ensure fair play.

Therefore, The minimum possible diameter of a soccer ball is 8.60 inches, and the maximum possible diameter is 8.70 inches.

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The margin of error for the school's claim  is 0.055 or approximately 5.5%.

To find the margin of error, we need to use the formula:

Margin of error = Critical value x Standard error

For a sample size of 500, the critical value can be found by:

critical value = 1.96

Next, we need to find the standard error. The formula for the standard error is:

standard error = sqrt(p_hat * (1 - p_hat) / n)

In this case, the sample proportion is 150/500 = 0.3.

standard error = sqrt(0.3 * (1 - 0.3) / 500) = 0.028

Finally, we can calculate the margin of error:

Margin of error = 1.96 x 0.028 = 0.055

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--The complete Question is, What is the margin of error for the school's claim that 30% of grade 3 pupils stay in the playground after their classes, given the results of the survey of 500 grade 3 pupils, which revealed that 150 of them stay in the playground after their classes? Assume a confidence level of 95%.--

The total number of probability options will be 8 options.

1. Red plain and Red striped.

2. Blue plain and Blue striped.

3. Yellow plain and Yellow striped.

4. Green plain and Green striped.

5. Red plain and Blue striped.

6. Blue plain and Yellow striped.

7. Yellow plain and Green striped.

8. Green plain and Red striped.

There are 8 socks in the basket, and you can choose 1 plain sock and 1 striped sock.

This means that there are 8 possible combinations of socks you could choose.

Count the number of socks in the basket. There are 8 total socks (4 plain and 4 striped).

The number of options: There are 8 possible combinations of socks you could choose, so you have 8 options for wearing a plain sock on your left foot and a striped sock on your right foot.

Therefore,

You have 8 options for wearing a plain sock on your left foot and a striped sock on your right foot.

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The proof of the above parallelogram is given as follows.

Statement                                                                   Reason

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Therefore, the solution to the system of equations is (x, y) = (-3, 4).

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can be composed of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems in various fields such as physics, engineering, economics, and mathematics.

To solve the system of equations using elimination, we need to manipulate one or both equations so that one of the variables has the same coefficient with opposite signs. Here's how we can solve the system:

Multiply the first equation by -2 to get -4x - 10y = -28.

Add the second equation to the new equation to get -8y = -32.

Divide both sides by -8 to get y = 4.

Substitute y = 4 into either equation to solve for x.

Using the first equation:

[tex]2x + 5(4) = 14[/tex]

[tex]2x + 20 = 14[/tex]

[tex]2x = -6[/tex]

[tex]x = -3[/tex]

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The probability that a randomly chosen part is defective is 0.16, or 16%.

The probability that a randomly chosen part is defective, we need to use the law of total probability.

Let [tex]$D$[/tex] be the event that a part is defective and let [tex]$M_i$[/tex] be the event that the part came from machine [tex]$i$[/tex], for [tex]$i = A, B, C$[/tex].

Then we have:

[tex]$P(D) = P(D|M_A)P(M_A) + P(D|M_B)P(M_B) + P(D|M_C)P(M_C)$[/tex]

60% of the products come from machine A, 30% from machine B, and 10% from machine C.

Therefore:

[tex]$P(M_A) = 0.6$[/tex]

[tex]$P(M_B) = 0.3$[/tex]

[tex]$P(M_C) = 0.1$[/tex]

The probability of a part being defective is 10% if it comes from machine A, 30% if it comes from machine B, and 40% if it comes from machine C.

Therefore:

[tex]$P(D|M_A) = 0.1$[/tex]

[tex]$P(D|M_B) = 0.3$[/tex]

[tex]$P(D|M_C) = 0.4$[/tex]

Substituting these values into the law of total probability, we get:

[tex]$P(D) = 0.1 \cdot 0.6 + 0.3 \cdot 0.3 + 0.4 \cdot 0.1 = 0.16$[/tex]

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The bearing of C from A is 90 degrees when B is equidistant from A and C.

In navigation and geometry, bearing refers to the direction or angle between two points, measured clockwise from a fixed reference direction. Typically, bearings are measured in degrees, with 0 degrees indicating a direction due north, 90 degrees indicating a direction due east, 180 degrees indicating a direction due south, and 270 degrees indicating a direction due west. Bearings can be expressed as either magnetic bearings or true bearings, depending on the reference direction used.

Let's assume that the distance from B to A and from B to C is the same.

To find the bearing of C from A, we can use the fact that the interior angles of a triangle sum up to 180 degrees. Therefore, we can first find the bearing of A from C:

180 - 129 = 51

This means that the bearing of C from A is 51 degrees in the opposite direction of the bearing of A from C. Since the bearing of A from C is 219, the bearing of C from A is:

219 - 180 + 51 = 90 degrees

Therefore, the bearing of C from A is 90 degrees.

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Answer:

x = 3

Step-by-step explanation:

given two intersecting chords , then the product of the parts of one chord is equal to the product of the parts of the other chord, that is

4(2x) = 4(x + 3) ← divide both sides by 4

2x = x + 3 ( subtract x from both sides )

x = 3