The distance from point A to the boat is approximately 23.3 meters, and the distance from point B to the boat is approximately 26.7 meters, rounded to the nearest foot.
Describe Distance?Distance can be calculated using a variety of methods, depending on the context. For example, the distance between two points in a straight line can be calculated using the Pythagorean theorem in two dimensions or the distance formula in three dimensions. In more complex situations, such as when the two points are not in a straight line, distance may be calculated using other mathematical methods or by estimating the distance based on contextual information.
Distance is often used in everyday life to describe how far apart objects or locations are from each other, such as the distance between two cities, the distance from home to work, or the distance between two landmarks. It is also used in many scientific fields to describe the separation between celestial objects, the distances traveled by particles in a chemical reaction, or the distances between neurons in the brain.
We can solve this problem using the Law of Sines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C:
a/sin A = b/sin B = c/sin C
Let's label the distance from point A to the boat as a, the distance from point B to the boat as b, and the distance from point C to the opposite bank as c. We are given that AB = 50 meters, angle ABC = 68 degrees, and angle BCA = 73 degrees. We want to find a and b.
First, we can find the measure of angle ACB by using the fact that the sum of angles in a triangle is 180 degrees:
angle ACB = 180 - angle ABC - angle BCA
angle ACB = 180 - 68 - 73
angle ACB = 39 degrees
Next, we can use the Law of Sines to find a and b:
a/sin 68 = c/sin 39
b/sin 73 = c/sin 39
Solving for c in both equations gives:
c = a sin 39 / sin 68
c = b sin 39 / sin 73
We can set these two equations equal to each other and solve for b:
a sin 39 / sin 68 = b sin 39 / sin 73
b = a (sin 39 / sin 73) * (sin 68 / sin 39)
b = a (sin 68 / sin 73)
We know that a + b = 50, so we can substitute the expression for b into this equation:
a + a (sin 68 / sin 73) = 50
Solving for a gives:
a = 50 / (1 + sin 68 / sin 73)
a ≈ 23.3 meters
Substituting this value of a into the expression for b gives:
b ≈ 26.7 meters
So the distance from point A to the boat is approximately 23.3 meters, and the distance from point B to the boat is approximately 26.7 meters, rounded to the nearest foot.
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The complete question is
Two landing points, A and B, lie on the straight bank of a river and are separated by 50 meters. Find the distance from each landing point to a boat pulled ashore on the opposite bank at a point C if angle ABC=68 degree and angle BCA=73 degree. Round to the nearest foot.
IXL
An equilateral triangle with center C is shown below.
(HELP!!)
The area of the equilateral triangle is 36√3 square units
What is area of the equilateral triangle?
Area of an equilateral triangle is equal to(√3/4)a², where an is the length of the triangle's side.
In an equilateral triangle, the center, the centroid, and the circumcenter coincide.
The distance between the center and a vertex is 6cm, which is also the radius of the circumcircle.
The side length is [tex]6(3)^{1/2}[/tex], which is twice the length of the radius.
So, the radius of the circumcircle is 6 cm, and the length of each side of the equilateral triangle is 12 cm.
The area of an equilateral triangle with side length s is given by:
A = (s² * √3) / 4
Substituting s = 12, we get:
A = (12² * √3) / 4
= 36√3
Therefore, the area of the equilateral triangle is 36√3 square units.
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Write an equation in point-slope form of the line that passes through the given
point and with the given slope m.
8. (3, -4); m = 6
9. (4, 2); m= -=
10. (-2, -7); m=1
11. (4, 0); m =
-1
Answer:
y - (-4) = 6(x - 3)
y - 2 = -3(x - 4)
y - (-7) = 1(x - (-2))
y - 0 = -1(x - 4)
Given an integer n and a base b, we can find the last digit of the base-b expansion of n by performing the division algorithm to find n = qb + r. The remainder r is the last digit. By repeating the process with q instead of n, we find the next digit, and so on.
The base-10 expansion after calculations, of 123 comes up as -: 123 = 1 x 10^2 + 2 x 10^1 + 3 x 10^0.
The given statement is about finding the last digit of the base-b expansion of an integer n, and a base b. We can find the last digit of the base-b expansion of n by performing the division algorithm to find n = qb + r. The remainder r is the last digit. By repeating the process with q instead of n, we find the next digit, and so on.
That means we can determine all the digits one by one by repeating this process. Let's take an example: Suppose we need to find the last digit of 123 in base 10. We can use the division algorithm to find 123 = 12 x 10 + 3. Here, the remainder 3 is the last digit. Now, to find the second-last digit, we repeat the process with q=12 instead of n=123.
That is, 12 = 1 x 10 + 2. Here, the remainder 2 is the second-last digit. Finally, to find the third-last digit, we repeat the process with q=1 instead of n=12. That is, 1 = 0 x 10 + 1. Here, the remainder 1 is the third-last digit.
Therefore, the base-10 expansion of 123 is 123 = 1 x 10^2 + 2 x 10^1 + 3 x 10^0.
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Draw a graph of a line with a NEGATIVE slope. Draw two slope triangles formed by the line. Show that the simplified ratio of the rise/run of each triangle is equivalent
to the slope.
Answer:
Step-by-step explanation:
Here's a graph of a line with a negative slope:
| /
| /
| /
| /
|/
------->
The line descends from left to right.
To draw the slope triangles, we can choose any two points on the line and draw a triangle with one vertex at each point. Let's choose the points (0, 4) and (3, 0):
| /
| /
| / T1
| /
|/
----/-------
/|
/ |
/ |
/ |
T2
The height of the first triangle, T1, is the difference between the y-coordinates of the two points: 4 - 0 = 4. The base of T1 is the difference between the x-coordinates: 3 - 0 = 3. So the rise/run ratio for T1 is 4/3.
The height of the second triangle, T2, is the difference between the y-coordinates of the two points: 0 - 4 = -4. Note that because the slope of the line is negative, the height of the triangle is negative as well. The base of T2 is the difference between the x-coordinates: 3 - 0 = 3. So the rise/run ratio for T2 is (-4)/3, which simplifies to -1.33.
The slope of the line is defined as rise divided by run. In this case, the rise is -4 (because the line is descending) and the run is 3. So the slope is (-4)/3, which is approximately -1.33. We can see that the simplified ratio of the rise/run of each triangle is indeed equivalent to the slope of the line.
A function passes through the points (1,6) and (3,54) select all of the equations that could represent this function
Therefore, the equation of the function in slope-intercept form is: y = 24x - 18.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions, often containing variables. It typically consists of two expressions separated by an equal sign. The expressions on either side of the equal sign may contain constants, variables, operators (such as +, -, ×, ÷), and functions.
Here,
We can use the two given points to find the slope and y-intercept of the function, and then write the equation of the function in slope-intercept form y = mx + b.
The slope of the function can be found using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (1, 6) and (x2, y2) = (3, 54):
m = (54 - 6) / (3 - 1) = 24
So the slope of the function is 24.
To find the y-intercept, we can use one of the two given points and the slope of the function:
y = mx + b
6 = 24(1) + b
b = -18
So the y-intercept of the function is -18.
Therefore, the equation of the function in slope-intercept form is:
y = 24x - 18
Any equation in this form with the same slope and y-intercept will represent the same function passing through the given points.
For example, y = 24x - 18, y = 24x - 20, and y = 24x - 16 are all equations that could represent the function passing through the points (1, 6) and (3, 54).
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Would a line through these two points A and B be a good fit for the data? Why or why not?
(Please don’t mind the other words! TvT
an airplane 32,000 feet above the ground begins to descend at a rate of 2,250 feet per minute .Assuming the plane continues the descend at the same rate write an equation to model the height h of the plane ,t minutes after it began its descent. Then find the height of the plane after 6 minutes
After answering the presented question, we can conclude that equation Therefore, the height of the plane after 6 minutes of descending is 19,500 feet.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
h(t) = 32,000 - 2,250t
h(6) = 32,000 - 2,250(6) = 19,500 feet
Therefore, the height of the plane after 6 minutes of descending is 19,500 feet.
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The triangle below is equilateral. Find the length of the side x to the nearest tenth.
To the nearest tenth, the length of each side of the equilateral triangle is roughly [tex]10(\sqrt{(3) - 1)[/tex].
What characteristics define equilateral?An equilateral triangle has the following three characteristics: identical lengths on all three sides. The three angles are identical. Three symmetry lines may be seen in the figure.
All of the triangle's sides are equal in length since it is equilateral. Call this length "s" for short.
The distance from vertex A to side x, measured in altitude, is equal to the length of side x. Call the intersection of the altitude and side x "P" for short.
The length of AP is [tex](s/2) * \sqrt{}[/tex] because we know that the altitude from vertex A creates a triangle with sides of 30-60-90. (3).
Since side BP is half the length of side AB, we also know that its length is (s/2).
As a result, x's length equals the product of AP and BP:
x = AP + BP
= (s/2) * [tex]\sqrt{(3) + (s/2)[/tex]
= [tex](s/2)(\sqrt{(3) + 1)[/tex]
We are told that x equals 10. We may put the formula we discovered for x equal to 10 and do the following calculation to find s:
[tex](s/2)(\sqrt{(3) + 1)[/tex] = 10
The result of multiplying both sides by two is:
[tex]s(\sqrt{(3) + 1) = 20[/tex]
When you divide both sides by [tex](\sqrt{(3) + 1)[/tex], you get:
[tex]s = 20/(\sqrt{3) + 1)[/tex]
The result of multiplying the numerator and denominator by the conjugate of [tex](\sqrt{(3) + 1), (\sqrt{(3) - 1)[/tex], is as follows:
s = [tex]20(\sqrt{3) - 1)/(3 - 1)[/tex]
= [tex]10(\sqrt{(3) - 1[/tex]
As a result, to the nearest tenth, the length of each side of the equilateral triangle is about [tex]10(\sqrt{(3) - 1[/tex].
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Three divided by six hundred twenty two (remainder included
the answer is 207 Remainder 1
Which number line best represents the solution to the problem below -x-8<16
The solution set of the inequality -x - 8 < 16 is graphed in the number line at the end of the answer.
Which number line represents the solution of the inequality?Here we want to see which number line represents the solution set of the inequality:
-x - 8 < 16
First, let's solve the inequality by isolating x, then we will get:
-x - 8 < 16
-8 - 16 < x
-24 < x
That is the inequality solved, the graph of this will be an open circle at x = -24 and then a line that goes to the right, like in the image posted at the end of this answer.
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GUYS PLEASE HELP
* I’LL GIVE YOU BRAINLIEST
Compare the maximum values and the end behavior of the functions of f and g.
Therefore , the solution of the given problem of function comes out to be even though the two functions' maximum numbers are different, their final behavior is the same.
What is function?On the midterm exam, there will be inquiries about design, mathematics, each topic, and both actual and hypothetical locations. a summary of the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input. Each post also has a particular location, that could be the enclave, an area, or even something completely different.
Here,
When x = 2, the maximum value of function f is 6, and
when x = -2, the highest value of function g is 3.
Both functions result in the same action in the end.
Both functions move closer to positive infinity as x gets closer to positive or negative infinity.
This is due to the positive quadratic component that dominates the behavior of the leading term in both functions as x increases in magnitude.
As a result, even though the two functions' maximum numbers are different, their final behavior is the same.
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what is the radical equivalent to s^3/2
Answer:
√1.5
Step-by-step explanation:
As a fraction, the square root of 3/2 can be expressed as √1.51 or just as √1.5.
The figure below is made of 2 rectangular prism.
What is the volume of this figure?
Total volume of the shape is 124 cm³
What is a cuboid?A cuboid is a three-dimensional solid shape that has six rectangular faces or sides, where each face meets at a right angle with its adjacent faces.
The formula for the volume of a cuboid is:
Volume = Length x Width x Height
So, the Volume of first cuboid = 3 × 4 × 5 = 60 cm³
and the Volume of second cuboid = 2 × 4 × 8 = 64 cm³
Total volume of the shape = Volume of first cuboid + Volume of second cuboid
Total volume of the shape = 60 cm³ + 64 cm³
Total volume of the shape = 124 cm³
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What is the value of the missing side
length?
5.6
x
3.4
Answer:
the missing value of the side length is 19.04
A small circle is centered inside of a larger circle. The large circle has a radius of 10 inches. The small circle has a radius of 3 inches.
Answer: 126in
Step-by-step explanation:
ftc6yhunum8im
huju7kt6r
5+10=24
g5ghykn
Find the missing base of the parallelogram described.
I need help with this please
Work Shown:
1 km = 1000 m
5*(1 km) = 5*(1000 m)
5 km = 5000 m
Step-by-step explanation:
let x= m
1 km=1000m
5km= x.m
1km.x/1km=5000.km/1km
x=5000m
therefore 5km=5000m
what is the center of dilation
The center of a dilation is a fixed point in the plane about which all points are expanded or contractedAnswer:
Step-by-step explanation:
the square region shown has been partitioned into 5 identical rectangular regions. if the perimeter of each of the rectangular regions is 30, what is the perimeter of the square region?
Given that the square region has been partitioned into 5 identical rectangular regions, and the perimeter of each rectangular region is 30. We are to find the perimeter of the square region.
As we know that the perimeter of a rectangle is given by P= 2 (l + b)
Let's say the length of the rectangle is 'l' and the breadth of the rectangle is 'b'. Since the five rectangular regions are identical, all of them will have the same length and breadth. Let's take the length and breadth of each rectangular region as x and y respectively. So, the perimeter of each rectangular region is given by P = 2(x + y) = 30Given P = 30, we get2(x + y) = 302x + 2y = 30x + y = 15... equation (1)
We know that the square region is partitioned into 5 identical rectangular regions. Therefore, the length of the square region will be 5 times the length of the rectangular region and the breadth of the square region will be the same as the breadth of the rectangular region. So, length of the square region = 5x, and breadth of the square region = y.
The perimeter of the square region = 2(5x + y) = 10x + 2yAs we know that x + y = 15 (from equation 1)So, 10x + 2y = 10(x + y) + 8y= 10(15) + 8y= 150 + 8y. Therefore, the perimeter of the square region is 150 + 8y.
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what is the polynomial of the shaded region?
The polynomial that represents the area of the shaded region is 7x-1 ( optionA)
What is area of a shape?The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares
Therefore, the area of the shaded region = area of the big rectangle - area of the small rectangle
area of the big rectangle = l×b
= (x-1)(x+5)
= x²+5x -x -5
= x²+4x-5
area of the small rectangle = l×b
=( x+1)(x-4)
= x²-4x+x-4
= x²-3x-4
therefore area of the shaded part
= x²+4x-5 - (x²-3x-4)
= x²+4x-5-x²+3x+4
collect like terms
x²-x²+4x +3x+4-5
= 7x -1
therefore the polynomial that represents the area of the shaded part is 7x-1
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The assets and liabilities of a local surf shop are listed below. Building Mortgage $100,650 Other Debt $45,780 Accounts Receivable $11,261 Property Value $181,975 Long Term Investments $138,000 Small Business Loan $22,698 Long Term Liabilities $35,000 Owned Inventory $32,990 Cash $219,783 Savings Account $148,321 Owned Equipment $35,872 The surf shop owner receives notice that the property value has increased by $20,000. What is the net worth of the surf shop?
The net worth of the surf shop is $585,074.
What is total cost?The variable and fixed cost of providing commodities are combined to create a total using the total cost formula.
First, we need to add the $20,000 increase in property value to the existing value to get the new property value:
$181,975 + $20,000 = $201,975
Next, we can add up the values of all the assets:
Owned inventory + Cash + Savings account + Accounts receivable + Owned equipment + Property value + Long-term investments
= $32,990 + $219,783 + $148,321 + $11,261 + $35,872 + $201,975 + $138,000
= $788,202
Then we can add up the values of all the liabilities:
Building mortgage + Small business loan + Other debt + Long-term liabilities
= $100,650 + $22,698 + $45,780 + $35,000
= $203,128
Finally, we can subtract the total liabilities from the total assets to find the net worth of the surf shop:
Net worth = Total assets - Total liabilities
= $788,202 - $203,128
= $585,074
Therefore, the net worth of the surf shop is $585,074.
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123000000 as a power of 10
Answer:
123,000,000 as a multiple of a power of 10 is
1.23 x 10⁸ .
write the center of radius of the circle
To write the center and radius of a circle, we need to have the equation of the circle in standard form, which is: (x - h)² + (y - k)² = r² where (h, k) is the center of the circle and r is the radius.
What is circle?A circle is a geometrical figure that is defined as a closed shape where all the points on the boundary of the shape are at an equal distance from the center point. The center of a circle is the point which is equidistant from all points on the circumference of the circle. To determine the center of a circle, we need to follow some steps:
Step 1: Identify the coordinates of three points on the circle
To find the center of a circle, we need to know the coordinates of at least three points on the circumference of the circle. The coordinates of these points can be determined by measuring the distance of the points from the x-axis and y-axis.
Step 2: Find the perpendicular bisectors of two chords
Once we have identified three points on the circle, we need to find the perpendicular bisectors of two chords. A chord is a line segment that connects two points on the circumference of the circle. The perpendicular bisector of a chord is a line that is perpendicular to the chord and passes through the midpoint of the chord.
Step 3: The intersection of perpendicular bisectors is the center of the circle
The perpendicular bisectors of two chords will intersect at a single point. This point is the center of the circle. To verify that this point is indeed the center, we can measure the distance from the center point to the three points on the circle. If the distances are equal, then the point is indeed the center of the circle.
In summary, to find the center of a circle, we need to identify the coordinates of at least three points on the circumference of the circle, find the perpendicular bisectors of two chords, and then find the intersection of the two perpendicular bisectors. This point is the center of the circle.
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there are 75 people at the city swim park today. everyone in the park was wearing swim suits or sunglasses, some people had both. how many people had swim suits on but not sunglasses, if you know 63 people have swim suits on and 43 have sunglasses?
If you know 63 people have swim suits on and 43 have sunglasses, 32 people have swim suits on but not sunglasses.
To find out how many people have swim suits on but not sunglasses, we can use the principle of inclusion-exclusion.
We know that there are 75 people in the park, and 63 of them have swim suits on. We also know that 43 people have sunglasses. However, some people have both swim suits and sunglasses. Let's denote the number of people who have both by x. Then we can use the formula:
total = swim suits + sunglasses - both
Substituting in the given values, we get:
75 = 63 + 43 - x
Simplifying, we get:
x = 31
Therefore, 31 people have both swim suits and sunglasses, and the number of people who have swim suits on but not sunglasses is:
63 - 31 = 32
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That answer is wrong
Answer: why is it wrong
Step-by-step explanation:i said so
Factor:
[tex]8 {x}^{2} + 2x - 3[/tex]
Please show the steps on how you got it!
Answer:
(2x - 1) (4x + 3)
Step-by-step explanation:
8x² + 2x - 3
= 8x² - 4x + 6x - 3
= 4x (2x - 1) + 3 (2x - 1)
= (2x - 1) (4x + 3)
So, the factor is (2x - 1) (4x + 3)
The 15 Chihuahua puppies ate 63 cups of food last week. If each puppy ate the same amount of food, how many cups of puppy food did each puppy eat?
15 StartLongDivisionSymbol 63.0 EndLongDivisionSymbol minus 60 = a remainder of 30 and a quotient of 4.blank.
How many cups of food did each puppy eat?
4 cups
4.1 cups
4.2 cups
4.ModifyingAbove 2 with bar cups
Answer:c 4.2 cups
Step-by-step explanation:
just do 63 divided 15
Keith took a four question test. He got 1 and a half of a question wrong. What is his final score?
Keith took a four question test and got 1 and a half questions wrong. His final score is 2.5 out of 4, or 62.5%.
To calculate Keith's final score, you need to divide the number of correct answers by the total number of questions. In this case, Keith answered 2.5 out of 4 questions correctly. Therefore, his final score is 2.5 divided by 4, which equals 0.625. This is equal to 62.5%.
To summarize, Keith took a four question test and got 1 and a half questions wrong, giving him a final score of 62.5%.
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What inequality describes the number of weeks for which halimah will put money in the bank
The inequality "w < 30" describes the weeks for which Halimah will put money in the bank instead of buying an oud. It means she must save for less than 30 weeks to have less than $300 saved.
Let's assume the number of weeks Halimah saves money is represented by the variable "w".
Halimah saves $10 per week, so the total amount of money she saves after "w" weeks is:
Total amount saved = $10 x w
According to the problem, Halimah will put the money in the bank instead of buying an oud if she saves less than $300. Therefore, the inequality that describes the number of weeks for which Halimah will put money in the bank is:
$10 x w < $300
Simplifying the inequality:
w < 30
Therefore, the inequality that describes the number of weeks for which Halimah will put money in the bank is "w < 30".
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Complete question:
Halimah saves $10 per week for w weeks to buy an oud. If she saves less than $300, she will put the money in the bank instead of buying an oud.
What inequality describes the number of weeks for which Halimah will put money in the bank?
you toss 3 distinguishable dice with 6 sides each, numbered from 1 to 6 and sumn them. how much more likely is it to get a sum of 17 than a sum of 18\
Bytaking the quotient between the probabilities we can see that Getting a 17 is three times more likely to get a 18.
How much more likely is it to get a sum of 17 than a sum of 18?If you toss 3 dices with 6 sides each, then the total number of combinations is:
6*6*6 = 216
Now, the outcomes that add up to 18 are:
dice 1, dice 2, dice 3, sum:
6 6 6 , 18
The outcomes that add up to 17 are:
dice 1, dice 2, dice 3, sum:
5 6 6 , 17
6 5 6 , 17
6 6 5 , 17
So the probabilities are:
P(18) = 1/216
P(17) = 3/16
The quotient gives:
P(17)/P(18) = 3
Getting a 17 is 3 times more likely to get a 18.
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