Step-by-step explanation:
To solve this problem, we can use the law of cosines. The law of cosines states that for any triangle with sides a, b, and c, and an angle C opposite side c,
c² = a² + b² - 2abcos(C)
In this problem, we can consider the man's starting point as the origin, and the distance he travels in the first leg as the first side of the triangle (a = 4km). The distance he travels in the second leg is the second side of the triangle (b). The angle between the two legs is the angle opposite side c, which is 90 degrees since the man changes direction from due west to southwest.
Therefore, we can use the law of cosines to find the distance he traveled in the second leg:
c² = a² + b² - 2abcos(90)
c² = 4² + b²
c = √(4² + b²)
c = √(16 + b²)
We know that the bearing of the second leg is 197 degrees, which is equivalent to a bearing of -163 degrees, since bearing measurements are taken clockwise from due north.
So we can use the law of cosines to find the distance he traveled in the second leg:
b = √(c² + a² - 2ac cos (-163))
We can now plug in the values we know:
b = √(c² + 4² - 24c*cos(-163))
We can now solve for c:
c = √(b² + 16 - 8bc)
The man is then southwest of his starting point, so the distance from his starting point to the final point is c.
The path of a fast moving particle traces a circle with equation (x-3)² + (y-4)² = 25. It starts at point (3,-1), moves counter clockwise, and passes the point (8,4) for the first time after traveling 7 microseconds. Where is the particle after traveling for 20 microseconds.
The particle is at the point (-1.112,3.909) after traveling for 20 microseconds.
We have been given a circle,
(x-3)²+(y-4)²=25
whose center is (3,4)
and with a radius of 5 units.
The particle starts at (3,-1) which is the 6 o'clock position in the circle, and ends at (8,4) after 7 microseconds which are at the 3 o'clock position in the circle.
So, the particle traveled 1/4 of the circumference of the circle in 7 microseconds
therefore according to the unitary method it will travel 5/7 of the circumference of the given circle.
so it will subtend 2π×5/7 of the circle from (3,-1)
from the polar form of the circle and the shifting of center of the circle we can conclude
that it's location will be
(5 × cos (10π/7) - 3 , 5 × sin (10π/7) - 4)
= (-1.112,3.909)
Learn more about the equation of a circle on
https://brainly.com/question/29288238?referrer=searchResults
#SPJ4
Andy buys x cakes
Betty buys 4 times as many cakes as andy
colin buys 3 more cakes than andy
each cake costs 65p
the total cost of the cakes is £52.65
How many cakes did each person buy?
Andy:
Betty:
Colin:
Each person buys a number of cakes
Andy: 13Betty: 52Colin:16What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Andy buys x cakes, Betty buys 4 times as many cakes as andy, and colin buys 3 more cakes than andy
So,
Andy has = x Cakes
Betty have = 4x Cakes
Clin has = x +3 Cakes
Since each cake costs 65p and the total cost of the cakes is £52.65
thus,
0.65( x + 4x + x +3) = 52.62
x + 4x + x +3 = 81
6x = 78
x = 13
Therefore,
Andy has = 13 cakes
Betty has = 4x = 4*13 = 52 cakes
Colin has = x + 3 = 16 cakes
Learn more about Mathematical operations here:
https://brainly.com/question/20628271
#SPJ1
Which function represents the reflection over the x-axis of f(x)=x
The reflected function is the one below:
g(x) = -√x
This function is represented by the last table.
Which one represents the reflected fucntion?For a general function y = f(x), we define a reflection over the x-axis as:
g(x) = -f(x)
In this case f(x)= √x, then the reflected function will be:
g(x) = -f(x) = -√x
Now we can evaluate this function to get some pairs of values.
Then when x = 1
g(1) = -√1 = -1
g(2) = -√2 = -1.41
And so on.
Then the correct option is the last table.
Learn more about reflections at:
https://brainly.com/question/26494295
#SPJ1
15/4 + 7/2 = ????????
Answer:
29/4 or as a mixed fraction 7 1/4
Step-by-step explanation:
Due today!! Please help me with this question asap!
Answer:
30
Step-by-step explanation:
Because it is an isosceles triangle, then only two sides of the triangle are of the same length and since it said one angle of the triangle is 120° there are still 60° left, so split that into two, and it equals 30° for both equal sides
Which is a correct solution for the following system of Inequalities
A correct solution for the following system of Inequalities is; (-2, 6)
What is the solution to the inequality graph?From the graph, it represents two inequalities and we can say that the solution of the two inequalities is the coordinate of the point where both lines of the inequalities intersect each other.
In the given graph, the coordinate of the point where both lines intersect each other is expressed as;
(-0.5, 4.2)
Now, that coordinate is not among the options but then the solution to the inequality graph will be the region shaded purple which in this case the only correct one is the coordinate (-2, 6)
Read more about Inequality Solution Graph at; https://brainly.com/question/11234618
#SPJ1
The electronics department is having a no sales tax scale in addition all of the items in the department are on sale for 24% off Wyatt is looking at a music player that normally costs $120 he has $ 95 to spend and he is wondering if he has enough money to but it. A. Find 25% of $120 is this the price he will pay? B. Does Wyatt have enough
25 percent of $120 is $30 and yes, he has enough money to buy the music player.
A) Find 25% of $120:
To find 25% of $120, we divide $120 by 100 and then multiply by 25:
$120 / 100 * 25 = $30
So, 25% of $120 is $30.
B) Does Wyatt have enough:
To find the sale price of the music player, we need to apply the 24% discount:
$120 - $120 * 24% = $120 - $120 * 0.24 = $120 - $28.80 = $91.20
So, the music player will be sold for $91.20.
Wyatt has $95, so he has enough money to buy the music player.
To learn more about percent here:
https://brainly.com/question/16242050
#SPJ4
One of the tables shows a proportional relationship.
Graph the line representing the proportional relationship from this table.
Keyboard Instructions
Initial graph state
The horizontal axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
The vertical axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
x 1 2 3 5
y 2 3 4 6
x 2 4 6 8
y 0 2 3 4
x 0 2 4 6
y 1 3 5 7
x −2 1 2 3
y −6 3 6 9
Two variables are primarily linked when there is a proportionate relationship, which means that as 1 variable rises or falls, the other rises or falls at the same rate.
What factors determine if one relationship is proportional?The ratios between both the two variables should be considered in order to determine whether a relationship is proportional. The relation is proportional if the ratio remains constant. The relationship is indeed not proportional if the ratio shifts.
What are the two proportional relationships principles?When two or more items are directly proportionate or change in size according to equivalent ratios, the relationship is said to be proportional. This proportional relationship can be expressed using the formula y = kx.
To know more about ration visit:
https://brainly.com/question/13419413
#SPJ1
Answer:
Two variables are primarily linked when there is a proportionate relationship, which means that as 1 variable rises or falls, the other rises or falls at the same rate.
What factors determine if one relationship is proportional?
The ratios between both the two variables should be considered in order to determine whether a relationship is proportional. The relation is proportional if the ratio remains constant. The relationship is indeed not proportional if the ratio shifts.
What are the two proportional relationships principles?
When two or more items are directly proportionate or change in size according to equivalent ratios, the relationship is said to be proportional. This proportional relationship can be expressed using the formula y = kx.
To know more about ration visit:
brainly.com/question/13419413
Step-by-step explanation:
A square painting has a diagonal of 44 in. Lorraine wants to frame the picture. The framing material is sold by the inch.
What is the minimum amount of framing she needs?
The minimum amount of framing Lorraine needs for the square painting is 31 inches.
We can use the Pythagorean theorem to calculate the length of the side of the square given the length of its diagonal. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
We know that the diagonal of the square painting is 44 inches, and since the diagonal of a square bisects its angles, the square can be divided into two congruent right-angled triangles. Therefore, the length of one side of the square can be calculated using the Pythagorean theorem:
44 inches^2 = x^2 + x^2
x^2 = 11*11
x = 11 inches
Since the square painting has a side length of 11 inches, and the framing material is sold by the inch, Lorraine will need a minimum of 11 inches of framing on each side, for a total of 44 inches.
5.
Find the coordinates of B, C, and D given that AB = 5 and BC
= 10.
The coordinates of B, C, and D are (3,-5), (3,5), and (-7,5) respectively.
Given point A (-2,-5) and the lengths of the sides AB = 5 and BC = 10, we can use this information to determine the coordinates of B, C, and D.
Using the information provided, we know that B is 5 units away from A in the positive x-direction. Therefore, the x-coordinate of B is (-2) + 5 = 3 and the y-coordinate of B is the same as that of A, which is -5. So point B is (3,-5).
Next, we know that C is 10 units away from B in the positive y-direction. Therefore, the x-coordinate of C is the same as that of B, which is 3, and the y-coordinate of C is (-5) + 10 = 5. So point C is (3,5).
Finally, we know that D is 10 units away from C in the negative x-direction. Therefore, the x-coordinate of D is 3 - 10 = -7 and the y-coordinate of D is the same as that of C, which is 5. So point D is (-7,5).
To learn more about the coordinates at
https://brainly.com/question/16634867?referrer=searchResults
#SPJ4
The question is -
Find the coordinates of B, C, and D given that AB = 5 and BC = 10 where A = (-2,-5).
rsti is a parallelogram. what is the value of x 2x+15 x+15
For x = 0, the sides of parallelogram are equal.
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
There are six crucial parallelogram characteristics to be aware of:
Congruent sides are those when AB = DC.
Congruent opposite angels are D = B.
(A + D = 180°) Consecutive angles are supplementary.
All angles are correct if just one of them is.
A parallelogram's diagonals cut each other in half.
A parallelogram is a four-sided, two-dimensional form in geometry. This particular quadrilateral example has equal and parallel opposite sides.
As the sides of parallelogram are parallel and equal,
2x + 15 = x + 15
2x = x
x = 0
To learn more about Parallelogram from given link
https://brainly.com/question/2680995
#SPJ1
Cedric and Insha solved the same equation using the calculations below.
Cedric’s Work
Insha’s Work
z minus 4.5 = negative 1.5. z minus 4.5 + 4.5 = negative 1.5 + 4.5. z = 3.
z minus 4.5 = negative 1.5. z minus 4.5 + (negative 4.5) = negative 1.5 + (negative 4.5). z = negative 6.
Which statement is true about their work?
Cedric is correct because he used the inverse of subtraction and added 4.5.
Cedric is incorrect because he should have subtracted 4.5 from both sides instead of adding.
Insha is correct because she added the opposite if 4.5, which is Negative 4.5, to both sides.
Insha is incorrect because she did not add Negative 1.5 + (negative 4.5) correctly.
Answer:d
Step-by-step explanation:
can somebody help me with this pls:Simplify: 8-2
Answer:
Step-by-step explanation:
I think it's 6 but I am not positive. I would double check it
(n^4-14n^3+51n^2-19n-30)/(n-8) Synthetic Division
The solution of (n⁴ - 14n³ + 51n² - 19n - 30) / (n - 8) using synthetic division is n³ - 6n² + 3n + 5 + 10/n - 8.
What is the solution of (x³ - 5x² -24x) / (x + 8) using synthetic division?The solution of (n⁴ - 14n³ + 51n² - 19n - 30) / (n - 8) using synthetic division is given below:
(n⁴ - 14n³ + 51n² - 19n - 30) / (n - 8)
The divisor is 8
The coefficients are:
1 -14 51 -19 -30
Using synthetic division:
the first coefficient is 1
the second coefficient = 1 * (8) + (-14)
the second coefficient = -6
the third coefficient = -6 * (8) + (51)
the third coefficient = 3
the fourth coefficient = 3 * (8) + (-19)
the third coefficient = 5
the remainder = 5 * (8) + (-30)
the remainder = 10
Therefore, the solution = 1(n⁴/n) -6(n³/n) + 3(n²/n) + 5(n/n) + 10/n - 8
The solution = n³ - 6n² + 3n + 5 + 10/n - 8
Learn more about synthetic division at: brainly.com/question/18788426
#SPJ1
What happens to the energy in the pendulum as it swings from point A to point B?
Potential energy is converted to kinetic energy.
Kinetic energy is converted to potential energy.
Kinetic energy is converted to chemical energy.
O Chemical energy is converted to thermal energy.
The energy in the pendulum as it swings from point A to point B
Potential energy is converted to kinetic energy.
Now, According to the question:
Energy is defined as the ability of an object to do work. Energy can be classified in two different types of energy, Kinetic and potential energy. This two may be the principal ones, but we can see how energy manifests in different ways in nature, like heat, chemical potential energy, solar energy, electric potential energy, and so on.
Energy is constantly changing from kinetic to potential energy, and vice-versa in a pendulum. At the lowest point of the pendulum swing, the pendulum will have reach a state of maximum kinetic energy. This due to it attaining the maximum speed the pendulum can reach due to it's movement. As the pendulum start to rise again, it will start to lose kinetic energy and will gain potential energy. This loss in kinetic energy will cause the pendulum to slow down until it reaches it's max height. At this point the pendulum will have converted all of it's kinetic energy to potential energy.
Hence, Potential energy is converted to kinetic energy.
Learn more about Energy at:
https://brainly.com/question/6614962
#SPJ4
DATA COLLECTION Rafaella collected data to determine the number of
books her schoolmates were bringing home each evening. Her data is
shown in the mapping. She let x be the number of textbooks brought
home after school and y be the number of students with x textbooks.
a. Express the relation as a set of ordered pairs.
b. What is the domain of the relation?
c. What is the range of the relation?
The relation as a set of ordered pairs is expressed below.
The domain of the relation is {0, 1, 2, 3, 4, 5}.
The range of the relation is {8, 11, 12, 23, 28}.
What is an ordered pair?In Mathematics, an ordered pair can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph such as the following:
Mathematically, the set of ordered pairs which represents the relation include the following:
Ordered pair = (0, 12)Ordered pair = (1, 8).Ordered pair = (2, 23).Ordered pair = (3, 38).Ordered pair = (4, 11).Ordered pair = (5, 11).Based on the mapping diagram (see attachment), the domain and range of the relation is given by:
Domain = {0, 1, 2, 3, 4, 5}.
Range = {8, 11, 12, 23, 28}.
Read more on domain here: brainly.com/question/18176333
#SPJ1
consider the random variable that assigns the number 0 to red and white, the number 1 to green and blue, and the number 2 to yellow and violet. what is the distribution of this random variable?
A variable whose value is decided by a random process or experiment is known as a random variable.
Depending on how the experiment or random process turns out, it may have a range of distinct numerical values. Random variables come in two varieties: discrete and continuous. A continuous random variable can take on any value within a specific range, such as real numbers, but a discrete random variable can only take on a countable number of values, such as integers.
This random variable has the following distribution and is discrete in nature:
P(X=0) = probability of red or white = P(red) + P(white)
P(X=1) = probability of green or blue = P(green) + P(blue)
P(X=2) = probability of yellow or violet = P(yellow) + P(violet)
P(X=x) must have a sum of all possible values of 1, which indicates that
P(red) + P(white) + P(green) + P(blue) + P(yellow) + P(violet) = 1
Therefore ,with a probability of 1/3 for each value, this random variable has a discontinuous uniform distribution over the set of values 0, 1, and 2.
To know more about random variable at :
brainly.com/question/22236950
#SPJ4
WRITE Why are all rectangles parallelograms, but all parallelograms are not rectangles? Explain.
Answer:
because they are not equal in size
Pls answers this I need help on homework
The equation of the trend line, can be found to be y = - 25 + 250
How to find the equation of the trend line ?To find the equation of the trend line, you first need to find the slope. To do this, pick two points on the trend line. ( 4, 150) and ( 8, 50 ).
The slope is:
= ( Y2 - Y1 )/ ( X 2 - X 1 )
= ( 50 - 150 ) / ( 8 - 4 )
= - 100 / 4
= - 25
The equation of the trend line takes the form:
y = mx + b
m = slope
b = y - intercept
The slope allows you to find the y - intercept :
y = mx + b
50 = - 25 ( 8 ) + b
b = 250
The equation is:
y = - 25 + 250
Find out more on equations at https://brainly.com/question/2589459
#SPJ1
Amanda and Marvin are going to a movie this evening. Marvin wants to have at least $60 in his wallet.
He currently has $15. Write and solve an inequality to find how much more cash Marvin should put in his wallet.
Marvin should put at least $45 more cash in his wallet in order to have at least $60.
Solving inequality questionsLet x be the amount of cash that Marvin needs to put in his wallet. We know that he wants to have at least $60, and he currently has $15, so we can write the inequality as:
x + 15 ≥ 60
To solve for x, we need to subtract 15 from both sides of the inequality:
x ≥ 60 - 15
x ≥ 45
Marvin should put at least $45 more cash in his wallet in order to have at least $60.
learn more on inequality questions here:https://brainly.com/question/29300322
#SPJ1
11 (4 - 6) + 5 (13 + 1) = 9
Answer: False because 20 doesn't equal to 9. Have a nice day ;)
Answer: the answer is false
Step-by-step explanation:
In the year 2016, the total number of metric tons of
copper produced in the world was 495,000.
Each year since, the total number of metric tons of
copper produced has increased on average by about
3.25% over the amount produced the previous year.
Which function models the total number of metric tons
of copper produced in the year that is x years since
2016?
c(x) = 495,000(1.0325)^x
c(x) = 495,000(0.9675)^x
c(x)=495,000(1.325)^x
c(c)=2010(3.25)^x
Answer:
A. C(x) = 495,000 (1.0325)^ x
Step-by-step explanation:
c(x) = 495,000 x (1+3.25%)^x
= 495,000(1.0325)
what is the solution of the system of equations for a graph that intersects at (0,6)
The solution of a system of equations for a graph that intersects at (0, 6) is given by the ordered pair (0, 6).
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines representing a system of linear equations cross each other (intersect), which is depicted by an ordered pair containing the point that corresponds to the x-axis and y-axis on a cartesian coordinate.
By critically observing the graph of the lines representing the system of linear equations, you would notice that the correct solution set lies on Quadrant I and it represents the y-intercept of the graph.
In conclusion, the ordered pair (0, 6) represents the point of intersection and solution set to the system of linear equations represented by the graph.
Read more on a graph here: brainly.com/question/4546414
#SPJ1
I'LL WRITE A GOOD REVIEW AND 5 STARS!
The original length is 250 meters and the scale drawing width is 0.67 cm
The original length of the landFrom the question (see attachment), we have the following parameters that can be used in our computation:
Scale length = 0.5 meters
So, we have
Original length = 0.5/(1/500)
Evaluate
Original length = 250
This means that the original length is 250 meters
The scale drawing widthHere, we have
Scale drawing width = 335 cm * 1/500
Scale drawing width = 0.67 cm
Hence, the scale drawing width is 0.67 cm
Read more about scale at
https://brainly.com/question/15891755
#SPJ1
g the radius of a sphere is increasing at a rate of 4 mm/s. how fast is the volume increasing when the diameter is 100 mm?
Answer:
125,664 mm³/s
Step-by-step explanation:
V = (4/3)πr³
dV/dt = (4π/3) × 3r² × dr/dt
dV/dt = 4πr² × dr/dt
dr/dt = 4 mm/s
d = 100 mm; r = 50 mm
dV/dt = 4π(50 mm)² × 4 mm/s
dV/dt = 125,664 mm³/s
I need help with this proof
The proof that shows that triangles ABC and EDC are similar is explained in the table below.
How to Write a Proof?A proof is a logical argument that demonstrates the truth of a statement. So, each step must be justified and flow logically from the previous step.
The proof that shows that the triangles are similar is explained as shown below.
Statement Reason
1. AB || DE 1. Given
2. <A ≅ <E 2. Alternate interior <s theorem
3. <B ≅ <D 3. Alternate interior <s theorem
4. ∆ABC ~ ∆EDC 4. AA Similarity theorem
Learn more about AA Similarity Proof on:
https://brainly.com/question/21247688
#SPJ1
are the responses to the survey question quantitative or categorical? quantitative b. how many of the respondents said that they expect driverless cars to be common in the next years? round your answer to nearest whole number. 79659 c. how many respondents answered in the range years? round your answer to nearest whole number. 15030
The responses to the survey question are quantitative, as the respondents were asked to provide a numerical answer.
Out of the 79,659 respondents, 79,659 said that they expect driverless cars to be common in the next years.
Out of the 79,659 respondents, 15,030 answered in the range of years. This means that 15,030 respondents provided a numerical answer that was within the range of years.
It is important to note that the survey question was quantitative, so the responses provided by the respondents were numerical. This means that the responses were not categorical, as categorical responses would have been in the form of words or phrases.
To learn more about quantitative or categorical:
https://brainly.com/question/24401930
#SPJ4
Sammi plans on selling Christmas tree ornaments. She figured a profit of $2. 00 for each item. She thinks one item out of every fifty may be defective and returned for exchange. That will cost her $7. 00
because of shipping and cost of the replacement. Calculate the expected value.
The expected value for each set of 50 items that Sammi sells is $1.82.
The expected value can be calculated by multiplying the profit from each successful sale by the probability of making that sale, and then subtracting the expected cost of each defective item.
Expected value = (Profit from each successful sale * Probability of making that sale) - (Expected cost of each defective item)
Let's assume that Sammi plans to sell 50 items. So, the probability of a successful sale is 49/50 = 0.98. The expected cost of each defective item is $7.
Expected value = ($2 * 0.98) - ($7 * 1/50) = $1.96 - $0.14 = $1.82
So, the expected value for each set of 50 items that Sammi sells is $1.82.
To learn more about expected value here:
https://brainly.com/question/18523098
#SPJ4
what is 30 x 8/12+18
Need HELP ASAP PLEASE HELP ME
MARKING BEST ANSWER BRAINLIST.
Please help!!
Seven friends accept the invitation to the twins' birthday party. At the last minute, Tomas and Emilio learn that their neighbor also wants to attend. The twins realize that they can stay within their budget by buying different amounts of popcorn.
Small popcorn that serves 1 = $4. 50,
Medium popcorn that serves 2 = $5. 75,
Large popcorn that serves 2-3 = $6. 50.
Describe a different popcorn scenario that will allow the twins to bring 8 friends, including their neighbor, and still stay within their budget.
Your description must be able to be proven mathematically and make sense
The equation for Tomas and Emilio birthday party's celebration is 200 = 45.99 + 17p
In math the term called equation is defined as a mathematical statement that shows that two mathematical expressions are equal.
Here we have know that seven friends accept the invitation to the twins' birthday party.
Where the possible equation that can be set up will have the total budget equal to total expenses.
So it can be written as the Total Cost of party is 200,
Then the amount can be divided as
=> Cost of Party Room + Cost of Movie Tickets + Cost of popcorns
Let us consider that if p people attend the party, then the cost of movie tickets will be $12.50p and cost of popcorns will be $4.50p, assuming that each person get a small popcorn bag.
Hence the equation will be written as
=> 200 = 45.99 + 12.50p + 4.50p
=> 200 = 45.99 + 17p
To know more about equation here.
https://brainly.com/question/10413253
#SPJ4