Classify the quadrilateral and explain the reasoning

Classify The Quadrilateral And Explain The Reasoning

Answers

Answer 1
This is a rectangle because there are two pairs of parallel equilateral sides and each corner is perpendicular to each other ;)

Related Questions

I WILL GIVE BRAINLIEST TO WHOEVER ANSWER THIS FOR ME

I WILL GIVE BRAINLIEST TO WHOEVER ANSWER THIS FOR ME

Answers

Answer:

\( \frac{12}{x} = \frac{20}{25} \\ 20x = 25 \times 12 \\ x = 15\)

Hello! answer: 15

25 ÷ 20 = 1.25

1.25 × 12 = 15 so 15 is the answer Hope that helps!

A truck traveling at 52 mph brakes to a stop in 145 feet. what was the average acceleration and stopping time?

Answers

The Average acceleration is -4.39 fps^2 and the stopping time is 3.96 seconds

We know that

Average acceleration formula is: a = ( v - u ) / t

Stopping distance formula is: s = ( u * t ) + ( 0.5 * a * t ^ 2)

where v => initial velocity

u => final velocity

t => time taken

Initial velocity, u = 52 mph

Final velocity, v = 0 mph

Stopping distance, s = 145 feet

Initial velocity (u) = 52 mph = 52 * 1.47 fps (1 mph = 1.47 fps) ≈ 76.44 fps

s = (u * t) + (0.5 * a * t^2)

145 = (76.44 * t) + (0.5 * a * t^2)   --> ( Equation1 )

v = u + (a * t)

0 = 76.44 + (a * t) --> ( Equation2 )

Now, from equation2, at = -76.44

Placing at value in equation1, 145 = ( 76.44 + 0.5 * (-76.44) ) * t

t = 3.96

Placing t value in at = -76.44,

a = 4.39

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7) What is the SECOND step in simplifying the equation below?
4 - 3y = 31

Answers

Answer:

subtract 4 from both sides

Step-by-step explanation:

you will then get -3y=27 as your equation then you just divide each side by -3 and your answer will be y = -9

Answer:

Step-by-step explanation:

4 - 3y = 31

Step 1:  Subtract 4 from both sides

        -3y =  31 -4

         -3y = 27

Step 2:  Divide both sides by (-3)

\(\dfrac{-3y}{-3}=\dfrac{27}{-3}\)

 y = -9

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 2, and the given zeros. -4,0,2,4

Answers

Answer:

A least degree polynomial, having rational coefficients and a leading coefficient of 2, with,-4, 0, 2, and 4 as the zeros of the polynomial is;

f(x) = 2·x⁴ - 4·x³ - 32·x² + 64·x

Step-by-step explanation:

The given parameters of the polynomial are;

The leading coefficient of the polynomial = 2

The zeros of the polynomial = -4, 0, 2, 4

We note that zeros of -4, and 4 gives a factor of the form, (x² - 4²)

For a zero of the polynomial equal to 0, one of the factors of the polynomial is equal to 'x'

To have a leading coefficient of 2, we can add '2' as a factor of the polynomial

Therefore, we can have the factors of the polynomial as follows;

(x² - 4²)·2·x×(x - 2) = 0

From the above equation, using a graphing calculator, we get the following possible polynomial;

(x² - 4²)·2·x×(x - 2) = 2·x⁴ - 4·x³ - 32·x² + 64·x = 0

Therefore, a polynomial, function of least degree that has rational coefficients, a leading coefficient of 2,and the zeros, -4, 0, 2, and 4 is  f(x) = 2·x⁴ - 4·x³ - 32·x² + 64·x.

Find the distance between the two points S(–5, –2) and T(–3, 4).

Find the distance between the two points S(5, 2) and T(3, 4).

Answers

Answer:

10 units

Step-by-step explanation:

this is right answer

Find the distance between the two points S(5, 2) and T(3, 4).

find the slope of the following lines ​

find the slope of the following lines

Answers

Answer:

The slope to the question provided is -2.

Hey there!

The slope of the given line is -2

We can solve this by doing rise over run. Pick a point and see how much it goes up (positive number) or down (negative number) - numerator - and put it over the number it goes left (negative number) or right (positive number) - denominator. For example, in this situation, we can start at the point (2, -1), and we can see that we go up 2 and left 1, until we get to the next point (1, 1). Therefore, our fraction would be \(\frac{2}{-1}\), or -2.

Hope it helps and have a great day!

List the characteristics of a proportinonal relationship

Answers

Answer:

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

The two requirements for a proportional relationship are: The ratio of the two variables maintain the same ratio.

Precalculus Compound Interest/Annuities Name: 1. Abby is saving for a vacation to Europe. She has budgeted $40 a month to put towards the trip. She researched travel costs and found that the trip will cost her $9000 if she wants to stay for two weeks. Abby found an annuity that would give her 7.5% on her investment compounded daily to help her achieve her goal. If Abby starts right now, how many years until she can afford her vacation?​

Answers

Answer:

  11.7 years

Step-by-step explanation:

You want the number of years it takes for an annuity of $40 per month earning 7.5% interest compounded daily to achieve a value of $9000.

Annuity

The formula for the future value of an ordinary annuity is ...

  FV = P((1 +r)^n -1)/(r -1)

where P is the periodic payment, r is the periodic interest rate, and n is the number of periods.

This problem is a bit tricky in that the payment period is 1 month, but the compounding of interest is done daily. That means the effective monthly interest rate (r) is ...

  1 +r = (1 +0.075/365)^(365/12) ≈ 1.00626892594

This is the 12th root of the effective annual rate.

Solution

Solving for n, we get ...

  9000 = 40(1.0063^n -1)/0.0063

  0.0063·225 = 1.0063^n -1

  log(0.0063·225 +1)/log(1.0063) = n ≈ 140.7885 . . . . . . months

We want the time in years, so we need to divide by 12:

  years = 140.7885/12 ≈ 11.7324 ≈ 11.7

It will be about 11.7 years until Abby can afford her vacation.

Precalculus Compound Interest/Annuities Name: 1. Abby is saving for a vacation to Europe. She has budgeted




A data set has 20 elements. A second data set of 20
ciements is obtained by adding 7 to each element of the
first set. A third data set of 20 elements is obtained by
multiplying each element of the second data set by 3.
The median of the third data set is 63. What is the medi-
an of the first data set?


A.7
B.14
C.21
D.196
E.210

Answers

Answer:

B.14

Step-by-step explanation:

Goodluck guys sa sagot

A triangle has a base length of 3.1 cm and corresponding height of 4.2 cm, correct to
one decimal place. Calculate the upper and lower bounds for the area of the triangle as
accurately as possible.

Answers

Answer:

The upper bound of the area is 6.69375 cm²

The lower bound of the area is 6.32875 cm²

Step-by-step explanation:

The question relates to measurements and accuracy

The given information are;

The base length of the triangle = 3.1 cm

The height of the triangle = 4.2 cm correct to one decimal place

The lower bound for the base length of the triangle = 3.05 cm

The upper bound for the base length of the triangle = 3.15 cm

Similarly, the lower bound for the height of the triangle = 4.15 cm

The upper bound for the height of the triangle = 4.25 cm

The formula for calculating the area of a triangle is given by the following formula;

Area of a triangle = 1/2 × Base × Height

The upper bound of the area = 1/2 × The upper bound of the base × The upper bound of the height

The upper bound of the area = 1/2 × 3.15 × 4.25 = 6.69375 cm²

The upper bound of the area = 6.69375 cm²

The lower bound of the area = 1/2 × The lower bound of the base × The lower bound of the height

∴ The lower bound of the area = 1/2 × 3.05 × 4.15 = 6.32875 cm²

The lower bound of the area = 6.32875 cm²

the length (in km) of a random sample of new zealand (nz) rivers that travel to the pacific ocean and the lengths (in km) of a random sample of new zealand rivers that travel to the tasman sea are given in the table below. do the data provide enough evidence to show on average that the rivers that travel to the pacific ocean are longer than the rivers that travel to the tasman sea?

Answers

The data provide enough evidence to show on average that the rivers that travel to the Pacific Ocean are longer than the rivers that travel to the Tasman Sea.

How to calculate the value

The test statistic is:

t = (209 - 76) / (™(19 * 78.95² + 22 * 33.29²))

= 3.263

The p-value is:

p-value = 0.0024

Since the p-value is less than 0.05, we reject the null hypothesis. This means that there is sufficient evidence to conclude that the mean length of the rivers that travel to the Pacific Ocean is greater than the mean length of the rivers that travel to the Tasman Sea.

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the length (in km) of a random sample of new zealand (nz) rivers that travel to the pacific ocean and

there are two ducks in front of a duck, two ducks behind a duck and a duck in the middle. how many ducks are there?

Answers

Answer:

3 Ducks

Step-by-step explanation:

Two ducks are in front of the last duck; the first duck has two

ducks behind; one duck is between the other two

Hence , there are 3 ducks

Hope it is correct

Answer: I think 7

Step-by-step explanation: Sorry if its wrong.

In 2020, a total of 9559 Nissan Leafs were sold in the US. For the 12-month period starting January 2020 and ending December 2020, the detailed sales numbers are as follows: 651, 808, 514, 174, 435, 426, 687, 582, 662, 1551, 1295 and 1774 units.

before the Nissan plant in Smyrna, Tennessee, started to produce the Nissan Leaf they were imported from Japan. Although cars are now assembled in the US, some components still imported from Japan. Assume that the lead time from Japan is one weeks for shipping. Recall that the critical electrode material is imported from Japan. Each battery pack consists of 48 modules and each module contains four cells, for a total of 192 cells. Assume that each "unit" (= the amount required for an individual cell in the battery pack) has a value of $3 and an associated carrying cost of 30%. Moreover, assume that Nissan is responsible for holding the inventory since the units are shipped from Japan. We suppose that placing an order costs $500. Assume that Nissan wants to provide a 99.9% service level for its assembly plant because any missing components will force the assembly lines to come to a halt. Use the 2020 demand observations to estimate the annual demand distribution assuming demand for Nissan Leafs is normally distributed. For simplicity, assume there are 360 days per year, 30 days per month, and 7 days per week.

(a) What is the optimal order quantity?
(b) What is the approximate time between orders?

Answers

(a)The optimal order quantity is  4609 units.

(b)The time between orders is  1.98 months.

To determine the optimal order quantity and the approximate time between orders, the Economic Order Quantity (EOQ) model. The EOQ model minimizes the total cost of inventory by balancing ordering costs and carrying costs.

Optimal Order Quantity:

The formula for the EOQ is given by:

EOQ = √[(2DS) / H]

Where:

D = Annual demand

S = Cost per order

H = Holding cost per unit per year

calculate the annual demand (D) using the 2020

sales numbers provided:

D = 651 + 808 + 514 + 174 + 435 + 426 + 687 + 582 + 662 + 1551 + 1295 + 1774

= 9559 units

To calculate the cost per order (S) and the holding cost per unit per year (H).

The cost per order (S) is given as $500.

The holding cost per unit per year (H)  calculated as follows:

H = Carrying cost percentage × Unit value

= 0.30 × $3

= $0.90

substitute these values into the EOQ formula:

EOQ = √[(2 × 9559 × $500) / $0.90]

= √[19118000 / $0.90]

≈ √21242222.22

≈ 4608.71

Approximate Time Between Orders:

To calculate the approximate time between orders, we'll divide the total number of working days in a year by the number of orders per year.

Assuming 360 days in a year and a lead time of 1 week (7 days) for shipping, we have:

Working days in a year = 360 - 7 = 353 days

Approximate time between orders = Working days in a year / Number of orders per year

= 353 / (9559 / 4609)

= 0.165 years

Converting this time to months:

Approximate time between orders (months) = 0.165 × 12

= 1.98 months

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I WILL GIVE BRAINLYEST

I WILL GIVE BRAINLYEST

Answers

The anser is .93 , Im 100% sure.
I used my Graphing calculator and even had my algebra teacher go over it and she said it was correct!

Answer:

0.93

Step-by-step explanation:

A hospital can increase the dollar amount budgeted for nurses' overtime wages during the
next year by only 3%. The nurses union has just won a 5% hourly rate increase for the next
year. By what percentage must the hospital cut the number of overtime hours in order to
stay within budget?

Answers

The hospital must cut the number of overtime hours by approximately 2.91% in order to stay within budget.

To determine the required percentage reduction in overtime hours, we need to consider the impact of the nurses' hourly rate increase and the limited budget increase for overtime wages.

Let's assume the current budget for nurses' overtime wages is denoted by B, and the total number of overtime hours worked is denoted by H. The current overtime rate per hour is R.

With the 5% hourly rate increase, the new overtime rate per hour becomes 1.05R. Considering the limited budget increase of 3%, the new budget for overtime wages is 1.03B.

To calculate the required percentage reduction in overtime hours, we can set up the following equation:

(1.05R) * (1 - x) * H = 1.03B

where x represents the required percentage reduction in overtime hours.

Simplifying the equation, we have:

(1 - x) * H = (1.03B) / (1.05R)

Now, let's solve for x:

1 - x = (1.03B) / (1.05R * H)

x = 1 - [(1.03B) / (1.05R * H)]

Here, we can see that the required percentage reduction in overtime hours, represented by x, depends on the values of B, R, and H.

It's important to note that without knowing the specific values of B, R, and H, we cannot calculate the exact percentage reduction. However, based on the provided information, we can determine the maximum percentage reduction that the hospital must make to stay within budget.

By assuming that B, R, and H are constant, we can use the given constraints to calculate an approximate percentage reduction. Based on the constraints of a 3% budget increase and a 5% hourly rate increase, the hospital would need to reduce the number of overtime hours by approximately 2.91% to maintain a balanced budget.

Please keep in mind that this approximation may vary depending on the specific values of B, R, and H.

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What other information is needed to prove that FGE Ijh by the SAS?

Answers

To prove that triangle FGE and triangle IJH we need information like the two sides of each triangle and the included angle to be congruent.

To prove two triangles are similar by the SAS is that you need to show that two sides of one triangle are proportional to two corresponding sides of another triangles, with the included corresponding angles being congruent.

For the SAS postulate you need two sides and the included angle in both triangles.

Side-Angle-Side (SAS) postulate:-

If two sides and the included angles of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. SAS postulate relate two triangles and says that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

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0.72...0.702 put < or > between the numbers in each pair​

Answers

Answer:

0.72>0.702

Step-by-step explanation:

Janie's rectangular backyard measures 1.84 × 102 ft by 98 ft. What is the approximate area of Janie's backyard?

Answers

Answer: 5.64 x 10^2 ft^2

Step-by-step explanation: Figure out what 1.84 x 10^2 equals- 184- then add 184+184+98+98 and get 564. then put it in Scientific Notation 5.64 x 10^2 ft^2

find cos2a; the angle a is in the 4th quadrant, and sin a= -0.75.A) 0.2800B) 0.4050C) 0.5950D) 0.3450

Answers

If the angle is in the 4th quadrant, its sine is negative and its cosine is positive.

First, let's calculate the cosine of a, using the trigonometrical identity below:

\(\begin{gathered} \sin^2a+\cos^2a=1\\ \\ (-0.75)^2+\cos^2a=1\\ \\ 0.5625+\cos^2a=1\\ \\ \cos^2a=1-0.5625\\ \\ \cos^2a=0.4375\\ \\ \cos a=0.6614 \end{gathered}\)

Now, we can use the formula below to calculate the cosine of 2a:

\(\begin{gathered} \cos2a=\cos^2a-\sin^2a\\ \\ \cos2a=0.4375-0.5625\\ \\ \cos2a=-0.125 \end{gathered}\)

math question pls help will mark brainiest!!!

math question pls help will mark brainiest!!!

Answers

Answer:

second option

Step-by-step explanation:

Using the rule of exponents/ radicals

\(a^{\frac{m}{n} }\) ⇔ \(\sqrt[n]{a^{m} }\), then

\(80^{\frac{x}{4} }\)

= \(\sqrt[4]{80^{x} }\)


AB has endpoints A (4, 6) and B (2, -14). What are the coordinates of midpoint M?

Answers

The coordinates of midpoint M is (3,-4)

It is given that AB is a line segment whose end points A ( 4,6) and B (2.-14) and M is the midpoint

We need to find out the coordinates of midpoint  M which can be found out using the mid point formula  which is (x1 + x2/2 , y1 +y2/2)

the x coordinate of the midpoint M of line segment AB = 4 + 2/2

                                                                                               = 6/2

                                                                                                = 3

the y coordinate of the midpoint M of line segment AB = 6+ (-14) /2

                                                                                               = -8/2

                                                                                               = -4

Hence the coordinates of the midpoint M of line segment AB is (3,-4)

In geometry, the midpoint is the center point of a line section. it's far equidistant from each endpoints, and it's far the centroid each of the segment and of the endpoints. It bisects the section.

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find the number degree of freedom, Critical value X², X² Given 95% confidence; n = 25, s = 0.24 Degree of freedom, df = 24 Critical value: X= [Select] X²= [Select] [Select] 39.364 32.852 12.401

Answers

The number of degrees of freedom is 24, and the critical value X² for a 95% confidence level and 24 degrees of freedom is approximately 36.415.

To find the number of degrees of freedom and the critical value X² for a 95% confidence level with n = 25 and s = 0.24, we need to determine the appropriate values based on the chi-square distribution.

The number of degrees of freedom (df) is equal to n - 1, where n is the sample size. In this case, df = 25 - 1 = 24.

To find the critical value X² for a 95% confidence level and 24 degrees of freedom, we need to consult a chi-square distribution table or use statistical software. The critical value corresponds to the chi-square value that leaves 5% (0.05) in the right tail.

Looking up the chi-square distribution table or using software, we find that the critical value for a 95% confidence level and 24 degrees of freedom is approximately 36.415.

Therefore, the number of degrees of freedom is 24, and the critical value X² for a 95% confidence level and 24 degrees of freedom is approximately 36.415.

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a plane left Atlanta at 11:30 a.m and flew to an airport near boston. the plane was due at boston at 3:15 pm

Answers

The elapsed time during the trip is 4 hours 10 minutes.

With that in mind,

the plane left Atlanta at 11:30 am for an airport near Boston. The plane was scheduled to arrive in Boston at 3:15 pm.

Mathematics is about a number of operations based on information.

because the plane leaves Atlanta at 11:30 am and he lands at Boston airport 25 minutes later than the actual arrival time.

The arrival time was 3:15 PM, but due to a delay, the plane landed at Boston Airport at 3:40 PM. 15:40 is 15:40 on a 24-hour clock. So

Elapsed Time = 15:40 - 11:30

= 4 : 10

means 4 hours and 10 minutes

So the elapsed time during the trip is 4 hours and 10 minutes.

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A store is offering a 25% discount on all electronics during a special weekend sale. Marcia wants to buy a television that regularly costs p dollars. She has written the expression 0. 75p to represent the sale price. Which is the best description for her expression?.

Answers

Marcia has written the expression 0. 75p to represent the sale price. The best description for her expression is she multiplied p by 0.25 then subtracted that from p.

How to express the sale price?

The sale price is the price after discount. Discount is the amount by which the origin price of an item is reduced. In this case, Marcia wants to buy a television with the origin prices is p dollars. The store is offering 25% discount.

p = the origin price

25% discount = 0.75p

The sale price = p - (0.25p)

So, the best description for Marcia's expression is  multiplied p by 0.25 then subtracted that from p.

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A store is offering a 25% discount on all electronics during a special weekend sale. Marcia wants to

6. Write the parametric equations of the line through the point P (-6, 4, 3), that is perpendicular to both the lines with equations: [3 marks]
L1: (x, y, z) = (0, -10, -2) + s(4,6,-3)
L2: (x, y, z)=(5, 5, -5) + t(3, 2, 4)

Answers

The parametric equations of the line through the point P (-6, 4, 3), that is perpendicular to both the lines with equations  L1: (x, y, z) = (0, -10, -2) + s(4,6,-3) and L2: (x, y, z)=(5, 5, -5) + t(3, 2, 4) is given by: x= -6 + 18t,y= 4 - 39t, and z= 3 - 10t.

Let us first find the direction vector of the lines L1 and L2.

From line L1, the direction vector is given by:

d1= 4i + 6j - 3k

From line L2, the direction vector is given by:

d2= 3i + 2j + 4k

Now, let us find the vector that is perpendicular to both d1 and d2 by taking their cross product:

n= d1×d2= (4i + 6j - 3k)×(3i + 2j + 4k)

Simplifying this gives:

n= 18i - 39j - 10k

This is the normal vector of the plane that contains both lines L1 and L2.

Now, we want to find a line that passes through the point P(-6, 4, 3) and is perpendicular to this plane.

A line that is perpendicular to this plane is parallel to the normal vector.

So we can use this normal vector as the direction vector of the line we want to find.

The parametric equations of the line are:

x= -6 + 18t,y= 4 - 39t,z= 3 - 10t,where t is a parameter.

Thus, the answer is that the parametric equations of the line through the point P (-6, 4, 3), that is perpendicular to both the lines with equations:

L1: (x, y, z) = (0, -10, -2) + s(4,6,-3) and

L2: (x, y, z)=(5, 5, -5) + t(3, 2, 4) is given by:

x= -6 + 18t,y= 4 - 39t, and z= 3 - 10t.

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How do i solve this paper?
I feel like my answers are gone and i need help.

How do i solve this paper?I feel like my answers are gone and i need help.

Answers

Answer:

you have it correct sir

Step-by-step explanation:

i need help to know all three steps of decimal place value decimal:______________ decimal point:__________________ place value:____________________ help please i need my dba done!!!!!!!!

Answers

The three steps of decimal place value are the decimal, decimal point, and place value.

The decimal is a number that is expressed using place value, with each digit representing a different power of 10. Decimals are used to represent parts of a whole or a fraction, and can be expressed as a fraction or a percentage.

The decimal point is a symbol used to separate the whole number part from the decimal part of a number. It is placed after the ones place in a whole number, and the position of the decimal point determines the value of the digits to its left and right.

The place value is the value of a digit in a number based on its position from the decimal point.

Each digit to the left of the decimal point represents a power of 10 that is greater than the previous digit, while each digit to the right of the decimal point represents a power of 10 that is smaller than the previous digit.

For example, in the number 123.45, the decimal is the number 5, the decimal point is the symbol between 3 and 4, and the place value of the digits are as follows:

1 is in the hundreds place

2 is in the tens place

3 is in the ones place

4 is in the tenths place

5 is in the hundredths place

Understanding decimal place value is important for performing mathematical operations with decimals, such as addition, subtraction, multiplication, and division.

By knowing the value of each digit in a decimal number, we can correctly place the decimal point and obtain the correct result.

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How many unique 4 digits integers ( excluding leading zeros) are there that the sum of the 4 digits is 6?

Answers

There are 84 unique 4-digit integers (excluding leading zeros) whose sum of the digits is 6.

To find the number of unique 4-digit integers (excluding leading zeros) where the sum of the digits is 6, we can use a combinatorial approach.

Let's consider the four digits as four distinct positions: A, B, C, and D. The sum of the four digits is 6, so we need to distribute these six units among these four positions.

We can solve this problem using stars and bars. Imagine we have six stars (representing the six units) and three bars (representing the three dividers between the positions). The bars help us separate the units into four distinct positions.

For example, if we have the configuration "* | * * | * * | *," it represents the digits 1, 2, 2, and 1. The sum of these digits is 6.

The number of ways to arrange the six stars and three bars is given by the binomial coefficient (6 + 3 choose 3). Using the formula for combinations, we have:

(6 + 3) C 3 = (9 C 3) = 9! / (3! * (9 - 3)!) = 84.

So, there are 84 unique 4-digit integers (excluding leading zeros) whose sum of the digits is 6.

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An airplane travels at a bearing of 100° (clockwise from North) at 180 km/hr. A wind redirects the plane, blowing at 30 km/hr at a bearing of 42°. Find the true speed of the plane and its new direction by modeling the speeds and directions as vectors.

Answers

The true speed of the plane is given as follows: 197.54 km/h.The direction of the plane is given as follows: 59.87º clockwise from north.

How to obtain the velocity and the direction of the plane?

The first step is converting both the velocity and the wind in vector form, as follows:

Velocity: \(\vec{v_1} = 180 \text{ km/hr} \angle 100^\circ\)Wind: \(\vec{v_2} = 30 \text{ km/hr} \angle 42^\circ\)

Then the true speed of the plane is given by the addition of these two vectors, as follows:

\(\vec{v_1} + \vec{v_2} = \sqrt{|v_1|^2 + |v_2|^2 + 2 \cdot |v_1| \cdot |v_2| \cdot \cos(\theta)}\)

The magnitudes of each vector are given as follows:

\(|v_1| = 180\).\(|v_2| = 30\).

The angle between these two vectors is given as follows:

\(\theta = 100^\circ - 42^\circ = 58^\circ\)

Thus the resulting speed is obtained as follows:

\(\vec{v_1} + \vec{v_2} = \sqrt{180^2 + 30^2 + 2 \cdot 180 \cdot 30 \cdot \cos(58^\circ)} = 197.54\)

The resulting angle of the plane is then obtained as follows:

\(\angle = \arctan\left(\frac{|v_1| \cdot \sin(\theta) + |v_2| \cdot \sin(\theta_2)}{|v_1| \cdot \cos(\theta) + |v_2| \cdot \cos(\theta_2)}\right)\)

Hence:

\(\angle = \arctan\left(\frac{180 \cdot \sin(58^\circ) + 30 \cdot \sin(42^\circ)}{180 \cdot \cos(58^\circ) + 30 \cdot \cos(42^\circ)}\right)\)

\(\angle = 59.87^\circ\)

More can be learned about vectors at https://brainly.com/question/25705666

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Answer:

  197.5 km/h

Step-by-step explanation:

You want the resultant speed with an airplane at a speed of 180 km/h at 100° is acted upon by a wind at a speed of 30 km/h at 42°. Angles are bearings CW from north.

Solution

A vector calculator makes short work of this. The resultant speed is ...

  197.5 km/h at 92.6°

Law of cosines

The law of cosines can be used to find the side opposite the known angle in the triangle with sides 30 km/h and 180 km/h. The known angle is ...

  180° -(100° -42°) = 122°

So, the resultant speed is ...

  c = √(a²+b²-2ab·cos(C))

  = √(30² +180² -2(30)(180)·cos(122°)) ≈ √39023.13

  c ≈ 197.543

The true speed of the plane is about 197.5 km/h.

__

Additional comment

You will notice that we used bearing angles directly in the calculator computation. As long as angles are consistently measured, it doesn't matter how they're measured.

When plotting the vectors on the Cartesian plane, we need to subtract the bearing angles from 90° to make them correspond to the vectors plotted on a map with north at the top.

An airplane travels at a bearing of 100 (clockwise from North) at 180 km/hr. A wind redirects the plane,
An airplane travels at a bearing of 100 (clockwise from North) at 180 km/hr. A wind redirects the plane,

Use combining like terms to simplify the expression: 7x+2−5x+4

Answers

Answer:

2x+6

Step-by-step explanation:

add the numbers:7x+6-5x

combine the like terms:7x+6-5x

2x+6

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