Pls answer fast!!! Whoever gets it correct first gets a brainly!!!!

Pls Answer Fast!!! Whoever Gets It Correct First Gets A Brainly!!!!

Answers

Answer 1

Answer: B

Step-by-step explanation:

The answer is 9x^2 + 14xy -19y^2


Related Questions

what is the difference between -3 - 6

Answers

Answer: -9

Step-by-step explanation: When you’re subtracting with negative numbers, the subtraction sign changes to an addition sign. Also, negatives and positives always turn out as negatives.

Therefore, -3 - 6 = -9

Which of the following functions has a graph with a vertex that is a translation 5 units horizontally to the right of the vertex of the graph of g(x) = (x + 2)^2 + 2?

Answers

Answer:

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

Step-by-step explanation:

The function with a graph that has a vertex 5 units horizontally to the right of the vertex of the graph of g(x) = (x + 2)^2 + 2 is f(x) = (x - 3)^2 + 2, which can be obtained by subtracting 5 from x + 2 to get x - 3 inside the parentheses of (x - 3)^2 and translating the vertex horizontally to (3, 2).

help please so I can play on my ps4. 50 points for simple question.

Answers

Answer:

area: 100km

Explanation:

Answer:

Step-by-step explanation:

S(square) = Area, if it's true ===> 10km * 10 km = 100 km^2
Because u need just (10km)^2

-2p^2+7p-6
factor the polynomial I NEED ASAP

Answers

Factored: -(2p - 3)(p - 2)

Take out the negative in front of the first term, which is just -1;
-(2p^2 - 7p + 6)

Now we need factors of 2 times 6 that have a sum of -7.
The factors are -4 and -3.
-(2p^2 - 4p - 3p + 6)

Now we can basically split it into two using common factors:
- 2p(p - 2) - 3(p - 2)

Since (p-2) is repeated, the terms outside the parentheses get combined;
-(2p - 3)(p-2)

A Purse is discounted at 45% off. The original price is $275.
What is the sales price?
O $146.25
O $142.50
O $151.25
O $136.25

Answers

Therefore, the sales price is $151.25. So, the answer is (C) $151.25.

What is sale price?

Sale price refers to the price of a product or service that has been reduced from its original or regular price. It is usually offered as a discount or promotion to attract customers and increase sales. The sale price can be expressed as a percentage or a dollar amount off the regular price. For example, a shirt with a regular price of $50 might be put on sale for 20% off, making the sale price $40.

To find the sales price, we need to apply the discount to the original price:

Discount amount = 45% of $275 = 0.45 x $275 = $123.75

[tex]Sales price = Original price - Discount amount[/tex]

[tex]Sales price = $275 - $123.75 = $151.25\[/tex]

Therefore, the sales price is $151.25. So, the answer is (C) $151.25.

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from its 32 regions, the faa selects 6 regions, and then randomly audits 25 departing commercial flights in each region for compliance with legal fuel and weight requirements. this is an example of group of answer choices judgment sampling. cluster sampling. stratified random sampling. simple random sampling.

Answers

The FAA selects 6 regions from its 32 regions, and then randomly audits 25 departing commercial flights in each

region for compliance with legal fuel and weight requirements. This is an example of stratified random sampling.

Stratified random sampling is a type of probability sampling method that involves dividing the population into smaller

groups, or strata, and then selecting samples from each stratum. This sampling technique is used when the population

is too large to sample as a whole, and it is necessary to divide it into smaller, more manageable groups.

Stratified random sampling is designed to ensure that each stratum within the population is adequately represented in

the sample. This is achieved by selecting a random sample from each stratum, with the size of the sample determined

by the proportion of the population that it represents.

By selecting a sample from each stratum, stratified random sampling allows for a more accurate representation of the

population as a whole.

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suppose you've been given the sample information in the following chart. what would be the correct value for the upper control limit (ucl) for the corresponding control chart? calculate your answer using values to three decimal places. unanswered suppose you've been given the sample information in the following chart. what would be the correct value for the upper control limit (ucl) for the corresponding control chart? calculate your answer using values to three decimal places.

Answers

The correct value for the upper control limit (ucl) for the corresponding control chart for the informations contained in table is equals to the 706.232.

We have a chart table present in above figure and shows the sample informations for making a control chart. Now, control Limits are Calculated by:

Estimating the standard deviation, σ, of the sample data.Multiplying that number by three.Adding (3 x σ to the average) for the UCL and subtracting (3 x σ from the average) for the LCL.

For a Sample size, n = 10

Average = 705

Range, R = 4

Formula for calculating upper control limit, UCL= Average + mean factor(A) × range (R), here, x and R are known. The value of A is corresponding value of sample size in the table. The sample size here is 10. Therefore value of A is 0.308. So, UCL = 705 + 0.308(4)

= 706.232

Similarly, LCL = Average - mean factor(A) × range (R)

=> LCL = 705 - 0.308(4)

= 703.778

In case 3-sigma control chart, the Upper control limit is calculated as, Average +3σ

Lower control limit= Average - 3σ. Hence, required value is equals to 706.232 .

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Complete question:

The above figure completes the question.

Suppose you've been given the sample information in the following chart. what would be the correct value for the upper control limit (ucl) for the corresponding control chart? calculate your answer using values to three decimal places.

Consider the equation and the graph. f(x)=(1/2)^x+1 g(x)=log (x-1)+1

Answers

With this information, we can now sketch the graphs of the functions f(x) and g(x) or analyze them further as needed.

Determine the behavior of each function as x increases:
  - f(x) decreases as x increases
  - g(x) increases as x increases.

To analyze the graphs of the given functions, let's first understand each function and their properties.
1. [tex]f(x) = (1/2)^x + 1[/tex]:

This is an exponential function with base (1/2) and a vertical shift of 1 unit up.

The graph of this function will have a horizontal asymptote at y = 1 and will decrease as x increases.

2. [tex]g(x) = log(x-1) + 1[/tex]:

This is a logarithmic function with a horizontal shift of 1 unit to the right and a vertical shift of 1 unit up.

The graph of this function will have a vertical asymptote at x = 1 and will increase as x increases.
Analysis:
1. Identify the type of each function:
  - f(x) is an exponential function
  - g(x) is a logarithmic function
2. Determine the transformations of each function:
  - f(x) has a vertical shift of 1 unit up
  - g(x) has a horizontal shift of 1 unit to the right and a vertical shift of 1 unit up

3. Identify the asymptotes for each function:
  - f(x) has a horizontal asymptote at y = 1
  - g(x) has a vertical asymptote at x = 1
4. Determine the behavior of each function as x increases:
  - f(x) decreases as x increases
  - g(x) increases as x increases.

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Mamadou and his children went into a restaurant and will buy hotdogs and drinks. Each hotdog costs $4.50 and each drink costs $3. Mamadou has a total of $70 to spend on hotdogs and drinks. Write an inequality that would represent the possible values for the number of hotdogs purchased, ℎ h, and the number of drinks purchased, � . d.

Answers

Considering the definition of an inequality, an inequality that represent the possible values for the number of hotdogs purchased and the number of drinks purchased is [tex]\bold{4.50h + 3d \leq 70}[/tex].

Definition of inequality

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.

An inequality contains one or more unknown values, in addition to certain known data.

Inequality in this case

In this case, you know that:

Each hotdog costs $4.50 and each drink costs $3.

Mamadou has a total of $70 to spend on hotdogs and drinks.

Being:

"h" the number of hotdogs purchased."d" the number of drinks purchased.

the inequality that expresses the previous relationship is

[tex]\bold{4.50h + 3d \leq 70}[/tex]

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Final answer:

The inequality that represents the possible values for the number of hotdogs and drinks purchased is 4.50ℎ + 3d ≤ 70.

Explanation:

To write an inequality that represents the possible values for the number of hotdogs purchased, ℎ h, and the number of drinks purchased, �, we can use the following equation:

4.50ℎ + 3d ≤ 70

This inequality states that the sum of the cost of the hotdogs (4.50 multiplied by the number of hotdogs) and the cost of the drinks (3 multiplied by the number of drinks) should be less than or equal to 70, which is the total amount of money Mamadou has to spend.

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How do i solve this problem: -12-(-40+18)

Answers

Answer:

Add −40 and 18 to get −22.

−12−(−22)

The opposite of −22 is 22. (because of the two negatives it makes a positive)

−12+22

Add −12 and 22 to get 10.

Step-by-step explanation:

Find the probability of exactly 5 successes
in 6 trials of a binomial experiment in
which the probability of success is 95%.
P = [?]%
Round to the nearest tenth of a percent.
Enter

Answers

The probability of exactly 5 successes in 6 trials of a binomial experiment when we round to the nearest tenth of a percent is 29.2%.

What is probability?

The likelihood or chance of an event occurring is measured by probability. Usually, it is stated as a number between 0 and 1, where 0 denotes an event's impossibility and 1 denotes its certainty.

According to question:

The probability of exactly k successes in n trials of a binomial experiment with probability of success p is given by the binomial probability formula:

P(k) = (n choose k) * [tex]p^k[/tex] * [tex](1-p)^(n-k)[/tex]

the number of ways there are to select k things from a group of n objects, where (n choose k) is the binomial coefficient.

In this problem, we are given that n = 6, p = 0.95, and we want to find the probability of exactly 5 successes.

P(5) = (6 choose 5) * 0.95⁵ * [tex](1-0.95)^(6-5)[/tex]

Simplifying the expression inside the parentheses:

P(5) = 6 * 0.95⁵ * 0.05¹

P(5) = 0.2915

Therefore, the probability of exactly 5 successes in 6 trials of a binomial experiment with probability of success 95% is approximately 0.2915, when we round to the nearest tenth of a percent. So we can write:

P = 29.2% (rounded to one decimal place).

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Why did the cube root erase the cubic functions math homework? its a riddle

Answers

Radical can also mean "basic" or "far-reaching," therefore it's possible that the cube root's radical shift involved erasing the cubic functions maths homework.

what is function ?

A function in mathematics is a relationship between a set of possible outputs (the range) and a set of inputs (the domain), with the property that each input is associated to exactly one outcome. A rule or procedure that transforms an input value into an output value is referred to as a function. Typically, the variable x represents the input value, while the object y or f represents the output value (x). A formula or equation that explains the relationship here between values of the input and output is frequently used to express functions.

given

The riddle's solution is: Since it desired a profound transformation!

Expressions using cubic functions can be made simpler by using the cube root, a kind of radical function.

Radical can also mean "basic" or "far-reaching," therefore it's possible that the cube root's radical shift involved erasing the cubic functions maths homework.

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Two years ago, Estelle reserved 24 books in 4 months. Then last year, Estelle reserved books in 36 months. Finally, this year, Estelle reserved 18 books in 3 months. Write this proportional relationship as an equation in the form , where is the unit rate between books and months.

Answers

Answer: To write the proportional relationship between books and months, we can use the formula:

unit rate = (total books) / (total months)

Let's calculate the total books and months for Estelle's reservations:

Two years ago: 24 books in 4 months

Last year: unknown number of books in 36 months

This year: 18 books in 3 months

To find the total number of books for last year, we can use a proportion:

24 books / 4 months = x books / 36 months

Cross-multiplying, we get:

24 * 36 = 4 * x

x = 24 * 9

x = 216

So Estelle reserved 216 books in 36 months last year.

Now we can calculate the unit rate:

unit rate = (total books) / (total months)

unit rate = (24 + 216 + 18) / (4 + 36 + 3)

unit rate = 258 / 43

unit rate = 6

Therefore, the proportional relationship between books and months is:

books = 6 * months

Step-by-step explanation:

P and Q are two points at a distance of 5 units from the origin on the line 3x + 4y + 15 = 0. Find the area of triangle POQ. ​

Answers

Answer: First, we need to find the coordinates of points P and Q. Since both P and Q lie on the line 3x + 4y + 15 = 0 and are equidistant from the origin, we can set up two equations:

3x + 4y + 15 = 0 (equation of the line)

x^2 + y^2 = 5^2 (equation of the circle with radius 5)

Solving these two equations simultaneously, we get:

x = -3, -12/5

y = -4, 3/5

Since P and Q lie on the same line, we can find the midpoint of PQ as:

(((-3) + (-12/5))/2, ((-4) + (3/5))/2) = (-33/10, -37/10)

Let O be the origin. Then the length of PO is the distance between O and P, which is:

sqrt((-3 - 0)^2 + (-4 - 0)^2) = 5

Similarly, the length of QO is also 5. Thus, we have a right triangle POQ with hypotenuse of length 5 and legs of length 5. Therefore, the area of triangle POQ is:

(1/2) * base * height

= (1/2) * 5 * 5

= 12.5 square units.

Step-by-step explanation:

The area of triangle POQ is approximately 17.32 square units.

How do we calculate?

We will apply  the formula for the distance between a point and a line to find their coordinates.

The formula for the distance between a point (x0, y0) and a line Ax + By + C = 0 is:

d = |Ax0 + By0 + C| / √t(A^2 + B^2)

Here we have, A = 3, B = 4, and C = 15.

5 = |3x0 + 4y0 + 15| / sqrt(3^2 + 4^2)

Solving for |3x0 + 4y0 + 15|, we get:

|3x0 + 4y0 + 15| = 5 * sqrt(3^2 + 4^2) = 25

This gives us two equations, solving these equations simultaneously, we get two points:

3x0 + 4y0 + 15 = 25

3x0 + 4y0 + 15 = -25

P = (-5, 0)

Q = (5, 0)

PO = √((-5 - 0)^2 + (0 - 0)^2) = 5

QO = √((5 - 0)^2 + (0 - 0)^2) = 5

PQ = √((5 - (-5))^2 + (0 - 0)^2) = 10

Using Heron's formula to find the area of triangle POQ:

s = (5 + 5 + 10) / 2 = 10

Area = √ (s(s-5)(s-5)(s-10)) = √(300)

=17.32

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read the story. zack planted an assortment of tulip bulbs in his garden. half of them were pink tulips. this morning, he noticed that 3 of the tulips had started to sprout. how likely is it that all of them will be pink? zack simulates the situation by flipping a coin 3 times. each time the coin lands on heads, it represents a pink tulip. this table shows the results of 100 trials: number of heads flipped 0 1 2 3 number of trials 12 37 38 11 based on zack's results, what is the probability that all of the tulips will be pink?

Answers

The probability of getting all heads in three-coin tosses is 1/8 or 0.1251. This means that there is a 12.5% chance that all of Zack’s tulips will be pink.

We know that the formula for finding a probability for any outcome is:

Probability = Number of favorable outcomes ÷ Total number of outcomes.

We know that, when a coin is tossed one time then, there are two sample space: {H,T}.

This means that we can get either a head or a tail when a coin is tossed once. Now, since the coin has been tossed 3 times, hence:

The total number of possible outcomes = 2³ =8

This is due to the fact that there are a total of 2ⁿ possible outcomes when a coin is tossed n times.

The eight outcomes would be as follows:

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

We are asked to find the probability of getting three heads, or tulips be pink. Therefore,

Probability = 1/8.

Therefore, there are 12.5% chances that all of the Zack's tulips would be pink.

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Complete question is:

Read the story. Zack planted an assortment of tulip bulbs in his garden. half of them were pink tulips. this morning, he noticed that 3 of the tulips had started to sprout. how likely is it that all of them will be pink? Zack simulates the situation by flipping a coin 3 times. Each time the coin lands on heads, it represents a pink tulip.

This table shows the results of 100 trials:

number of heads flipped   0   1   2   3

number of trials                  12 37 38 11

Based on zack's results, what is the probability that all of the tulips will be pink?

The table shows the amount of rainfall recorded over the first 10 months of a year. Draw a line plot, if needed.


Amount of Rainfall (inches)

1

3

4

,


2

1

2

,


3

4

,


1

1

4

,


2

,


1

1

2

,


2

3

4

,


3

1

4

,


1

,


2

3

4


Part A

What is the difference between the greatest and least amounts of rainfall in a month?


A.

1

1

4

inches


B.

1

1

2

inches


C.

2

1

2

inches


D.

2

3

4

inches


Part B

What fraction of the

10

months had more than

2

inches of rainfall?


A.

2

10

B.

3

10

C.

4

10

D.

5

10

Answers

The answer is (D) 5/10.

what is data?

Data refers to any set of observations, measurements, or facts that can be collected, analyzed, and interpreted to gain insights or knowledge about a particular subject or phenomenon. It can be in the form of numbers, text, images, audio, or any other type of information that can be recorded.

To create a line plot, we need to represent each value in the data set with a point on a number line and then connect the points with a line. Here is the line plot for the given data:

 4|              ●

 3|        ●     ●

 2|  ●     ●     ●

 1|  ●  ●  ●  ●  ●

  +-----------------

     1  2  3  4  5  6

Part A:

From the line plot, we can see that the greatest amount of rainfall in a month is 4 inches, and the least amount of rainfall is 1 inch. Therefore, the difference between the greatest and least amounts of rainfall in a month is:

4 - 1 = 3 inches

The answer is not given as one of the options provided.

Part B:

To determine the fraction of the 10 months that had more than 2 inches of rainfall, we count the number of months that had more than 2 inches and divide by the total number of months:

There are 6 months with more than 2 inches of rainfall: 1st, 2nd, 3rd, 7th, 8th, and 10th.

So, the fraction of the 10 months with more than 2 inches of rainfall is:

6/10 = 3/5

Therefore, the answer is (D) 5/10.

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Use the given information to find the number of degrees of​ freedom, the critical values x 2/L and x 2/R​, and the confidence interval estimate of sigma. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Nicotine in menthol cigarettes ​98% ​confidence; n​=25, s=0.27 mg.

Answers

The true standard deviation of nicotine in menthol cigarettes is believed to be between 0.044 and 0.102 mg, with a 98% confidence level.

To find the number of degrees of freedom for the confidence interval estimate of sigma, we need to use the formula:

df = n - 1

where n is the sample size. In this case, n = 25, so:

df = 25 - 1 = 24

Next, we need to find the critical values x2/L and x2/R using a chi-square distribution table or calculator. For a 98% confidence interval and 24 degrees of freedom, the critical values are:

x2/L = 10.643

x2/R = 41.337

Finally, we can use the formula for the confidence interval estimate of sigma:              

s/√(x2/R) < σ < s/√(x2/L)

Plugging in the values we have, we get:

0.27/√(41.337) < σ < 0.27/√(10.643)

0.044 < σ < 0.102

Therefore, we can say with 98% confidence that the true standard deviation of nicotine in menthol cigarettes is between 0.044 and 0.102 mg.

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For the function below, describe how its graph is a sequence of translations and reflections of the graph of a simpler function.
f(x) = e-x + 5

Answers

The graph of a simpler function, in this case, e-x, allows us to visualize how changes to the function, such as translations and reflections, impact the graph.

The graph of f(x) = e-x + 5 is a sequence of translations and reflections of the graph of a simpler function, namely the graph of f(x) = e-x. To understand this, let's first consider the graph of e-x. This is an exponential function that starts at 1 when x=0 and approaches zero as x goes to infinity. The graph is always decreasing and asymptotic to the x-axis.

Now, when we add 5 to e-x, we shift the entire graph upward by 5 units. This is a translation of the graph. Next, we take the negative of e-x, which reflects the graph across the x-axis. This gives us a decreasing function that starts at 6 (since e0 = 1) and approaches 5 as x goes to infinity.

So, the graph of f(x) = e-x + 5 is a translation of the graph of e-x by 5 units upward, followed by a reflection across the x-axis. This sequence of translations and reflections results in a decreasing function that starts at 6 and approaches 5.

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In circle M, MN = 6 and the area of shaded sector = 11pie. Find m/NMO.
M
N

Answers

The value of m∠NMO is 110°.

What is the area of the shaded sector?

A sector is an area that is enclosed by the arc of the circle that lies between two radii and two radii. A sector's area is a portion of the circle's total area. This region is inversely proportional to the principal angle. This suggests that the sector's area increases with increasing central angle.

Here, we have

Given: In circle M, MN = 6 and the area of the shaded sector = 11π

We have to find the value of m∠NMO.

area of the shaded sector = πr²× m∠NMO/360°

11π = π(6)²× m∠NMO/360°

11 = 36× m∠NMO/360°

11 = m∠NMO/10°

11×10° = m∠NMO

m∠NMO = 110°

Hence, the value of m∠NMO is 110°.

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I need help asap !!!!

Answers

Answer:

To find the area of the rectangle, you would do length times width, so it would be (4+√3)(2-√3)

Then the area would be 5.732050808 which would round up to 5.73.

To find the perimeter you would do P=2(l+w), so you would have 2(4+√3)(2-√3)

Then you would get 11.46, which you would round up to 11.5.

All in all:

Area = 5.73

Perimeter = 11.5

Step-by-step explanation:

The assessed value of the kreiner family house is 457,000 the annular property tax rate is 2.66% of assed value what is the annular property tax on the kreiners home

Answers

Answer:

To calculate the annual property tax on the Kreiner family house, we can use the formula:

annual property tax = assessed value x annual tax rate

where the annual tax rate is given as a percentage. We first need to convert the tax rate from a percentage to a decimal:

2.66% = 0.0266

Then, we can plug in the given values and calculate:

annual property tax = 457,000 x 0.0266

annual property tax = 12,157.80

Therefore, the annual property tax on the Kreiner family house is $12,157.80.

Hope This Helps!

solve using quadratic formula

6x²2x-4=0

Answers

the answers would be x = 1 and x = -2/3.

please help!!!!!! ………

Answers

So the answer is going to be $27,162.54

The number 55 is decreased to 53. What is the percentage by which the number was decreased, to the nearest tenth of a percent?

Answers

Answer is 96.4% decrease

Explanation

We know 55 times x % = 53

Our equation

55x = 53

53/55 = .9636…

Change to percent 96.36%

Round to tenth = 96.4%

Now check your work

55 x .964 = 53.02 rounded to 53

Answer proved correct

determine the expected value of the amount that could be paid to mark ross in a settlement. use the 67% probability figure that the plaintiff wins and is awarded 60% of the amount requested. also, determine a maximum and minimum expected value for the settlement figure based on the confidence interval above. be sure to include all the damages mark ross will be able to recover. how would you interpret your expected values?

Answers

As per the probability, to interpret these expected values, we can say that on average, Mark Ross could expect to receive $40,200 if he wins the case and is awarded 60% of the amount requested.

.

To calculate the expected value, we need to multiply the probability of each outcome by the value of that outcome and then add them up. In this case, the outcome is the settlement amount that could be paid to Mark Ross. Let's assume that the amount requested by Mark Ross is $100,000.

The probability that the plaintiff wins and is awarded 60% of the amount requested is 67% * 60% = 40.2%. Therefore, the expected value of the settlement amount is:

Expected Value = 40.2% * $100,000 = $40,200

This means that on average, Mark Ross could expect to receive $40,200 if he wins the case and is awarded 60% of the amount requested.

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Sandy works at a clothing store. She makes $6 per hour plus earns 10% commission on her sales. She worked 74 hours over the last two weeks and had a total of $2,250 in sales before taxes.

Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?
A.
$225
B.
$444
C.
$669
D.
$269

Answers

Answer:

$701.20

Step-by-step explanation:

1.  If she earns $6 per hour and worked 79 hours, how much, in the form of pay, did she earn?

2.  If she sold $2292 in merchandise, she receives 10% of that as a bonus.  How much is this bonus?

3.  Add the results of (1) and (2) together.  The result will be her total earnings.

Question 18
Is 21, 22, or 23 the solution of the equation 29.7 = y + 7.7?
+ - x ÷
品电台台
= = < ><>

Answers

It’s 22.
Explanation:
You want to get y by itself so therefore you would do 29.7 - 7.7 which is 22.
The reason you subtract the 7.7 from the 29.7 is because it was positive next to the y so you have to change it when moving it to the other side of the equal sign.
Hope this helped!

EREGENT PLEASE HURRY DONT LIE 40 POINTS

Answers

Step-by-step explanation:

Using the rules of PEDMAS :

32  ÷  10 - 8  ÷ 2 - 3 = 5

32 ÷ (10-8)   ÷  2  -3  = 5

32 ÷ 2  ÷  2  -3  = 5  

       With multiple divisions or multiplications go from L to right in order

16  ÷  2  - 3 = 5

  8 - 3 = 5

1/2 x 12 ÷2-2+11 = 13

1/2 x (12 ÷ 2 - 2) + 11 = 13

1/2 x (6-2) + 11 =13

1/2 (4) + 11 = 13

   2 + 11 = 13

X, Y and Z are three points on a map.

Y is 80km and on a bearing of 190° from X.

Z is on a bearing of 140°, from Y.

Z is due south of X.

Calculate the distance between X and Z rounded to 1 DP.

Answers

So the distance between X and Z is simply 80 km. Rounded to one decimal place, this is 80.0 km.

What is trigonometry?

Trigonometry is a branch of mathematics that focuses on the relationships between the sides and angles of triangles. It involves the study of trigonometric functions, which relate angles and sides of a right triangle, as well as the application of these functions to various real-world problems such as navigation, physics, and engineering. Trigonometry has a wide range of applications in fields such as science, engineering, architecture, and more.

Here,

First, we need to find the coordinates of each point. Let's assume that X is located at the origin (0,0) on the map. From X, we know that Y is 80 km away on a bearing of 190°. This means that Y is located 80 km to the southwest of X. To find the coordinates of Y, we need to use trigonometry. Let's define angle A as the angle between the positive x-axis and the line XY. Then we can use the cosine and sine functions to find the x and y coordinates of Y:

cos(A) = adjacent/hypotenuse = x/80

sin(A) = opposite/hypotenuse = -y/80 (note the negative sign because Y is southwest of X)

Solving for x and y, we get:

x = 80 cos(A)

y = -80 sin(A)

Now we need to find the coordinates of Z. We know that Z is due south of X, which means it lies on the y-axis. We also know that Z is on a bearing of 140° from Y, which means it forms a 40° angle with the negative y-axis. Let's call this angle B. Using trigonometry again, we can find the distance between Y and Z (which we'll call d) and the coordinates of Z:

cos(B) = adjacent/hypotenuse = x/d

sin(B) = opposite/hypotenuse

= -y/d (again note the negative sign)

We want to find d, so we can rearrange the cosine equation:

d = x/cos(B)

Substituting in the expressions for x and y in terms of A, we get:

d = (80 cos(A))/cos(B)

Finally, we need to eliminate the variables A and B. We know that A + B = 180° because angle AYX + angle BYZ = 180°. Rearranging, we get:

B = 180° - A

Substituting into the expression for d, we get:

d = (80 cos(A))/cos(180°-A)

Simplifying using the cosine difference identity, we get:

d = (80 cos(A))/(-cos(A))

= -80

This negative distance means that Z is actually due north of X, which makes sense because it is "directly south" of X on the map. So the distance between X and Z is simply 80 km.

To know more about trigonometry,

https://brainly.com/question/26719838

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I need help with this question please

Answers

Answer:

the answer is C

Step-by-step explanation:

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