a passenger in an airplane at an altitude of 53 km sees two towns directly to the east of the plane the angles of depression to the towns of 28° and 55°. How far apart are the towns? round Answer to two decimal places.
Answers
Answer:
The two towns are 62.57km apart.
Explanation:
A diagram representing the problem is redrawn and attached below:
From trigonometric ratios:
\(\begin{gathered} \tan 55\degree=\frac{53}{OA} \\ OA\times\tan 55\degree=53 \\ OA=\frac{53}{\tan 55\degree} \\ OA=37.11\operatorname{km} \end{gathered}\)Similarly:
\(\begin{gathered} \tan 28\degree=\frac{53}{OB} \\ OB\times\tan 28\degree=53 \\ OB=\frac{53}{\tan 28\degree} \\ OB=99.68\operatorname{km} \end{gathered}\)Therefore, the distance between the two towns is:
\(\begin{gathered} AB=OB-OA \\ =99.68-37.11 \\ =62.57\operatorname{km} \end{gathered}\)The two towns are 62.57km apart.
Related Questions
what’s the answer for this problem????
Answers
The inequality on the number line is 5x -2 > -22 or 6x-7 < 11.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
The open circles on the number line shows that it does not include those value i.e., the values have less than and greater than.
So, from the number line the inequality is -4 < x < 3.
Now, 5x -2 > -22 and 6x-7 < 11
5x > -20 and 6x < 18
x > -4 and x<3.
x+5 >8 and 3+ 2x < -5
x >3 and x < -4.
so, the inequality is 5x -2 > -22 or 6x-7 < 11.
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What is 9.25% tax of $27.26?
Answers
Answer:
$29.78
Step-by-step explanation:
1. make the % into a decimal
9.25% = 0.0925
2. multiply amount by the decimal to get the tax amount
$27.26 × 0.095 = $2.52
3. take the original amount and add the tax to get your final total
$26.27 + $2.52 = $29.78
A textbook store sold a combined total of 445 biology and history textbooks in a week. The number of history textbooks sold was 45 less than the number of biology textbooks sold. How many textbooks of each type were sold?
Answers
Equations to use:
x = biology
y = history
x + y = 445.
x - 45 = y
Step-by-step explanation:
hope you understand..........
Solve for x. Leave your answer in simplest radical form.
Answers
Answer:
√122
Step-by-step explanation:
first we have to find the missing side with x on the 5 and 9 triangle by using the theorem
a^2+b^2=c^2
9^2+5^2=c^2
81+25=c^2
106=c^2
√106=c
and now we can use this as a side to find x
4^2+√106^2=x^2
16+106=x^2
122=x^2
√122=x
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What is the current temperature in Fahrenheit on the thermometer below?
A.
B.
C.
D.
Answers
Answer:
the answer is D just did the quiz hope this helps!!!!!
Step-by-step explanation:
Please tell me how much it would be for 1
Answers
Answer: tall is 12 dollars
Step-by-step explanation:
1. You are given the 3rd and 5th terms of a geometric sequence. Describe how to determine the 10th term without finding the general term.
Answers
The 10th term of the geometric sequence is given as follows:
\(a_{10} = a_5\left(\sqrt{\frac{a_5}{a_3}}\right)^{n-5}\)
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
\(a_n = a_1q^{n-1}\)
In which \(a_1\) is the first term.
Using the mth term as the reference, we have that:
\(a_n = a_mq^{n-m}\)
Hence:
\(a_5 = a_3q^2\)
\(q = \sqrt{\frac{a_5}{a_3}}\)
And then the 10th term is given as follows:
\(a_{10} = a_5\left(\sqrt{\frac{a_5}{a_3}}\right)^{n-5}\)
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could someone help me with this and show work?
Answers
The volume of the shape is 490cm³
What is volume of prisms?A prism is a solid shape that is bound on all its sides by plane faces. prism is named after the shape of these bases.
The base of this prism is rectangular. The volume of a prism is expressed as;
V = base area × height
base area = 7 × 10 = 70cm²
height = 7cm
the volume of the shape = 70× 7 = 490cm²
therefore the volume of the shape is 490cm³.
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AB and AD are tangent to circle C. Find the length of AB, if AB = 8x and AD = x + 9. Round your answer to 2 decimal places.
Answers
When a line is tangent to a circle, it forms a right angle with the radius drawn to the point of tangency. This means that triangle ABD is a right triangle with AB as the hypotenuse.
We can use the Pythagorean theorem to find the length of AB:
AB^2 = AD^2 + BD^2
Since AD = x + 9 and BD = 8x - (x + 9) = 8x - x - 9 = 7x - 9, we can substitute these values into the equation:
(8x)^2 = (x + 9)^2 + (7x - 9)^2
64x^2 = x^2 + 18x + 81 + 49x^2 - 126x + 81
64x^2 = 50x^2 - 108x + 162
14x^2 + 108x - 162 = 0
Dividing the equation by 2, we get:
7x^2 + 54x - 81 = 0
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
a = 7, b = 54, c = -81
x = (-54 ± √(54^2 - 4 * 7 * -81)) / (2 * 7)
x = (-54 ± √(2916 + 2268)) / 14
x = (-54 ± √5184) / 14
x = (-54 ± 72) / 14
Now we solve for x:
Case 1: x = (-54 + 72) / 14 = 18 / 14 = 9 / 7
Case 2: x = (-54 - 72) / 14 = -126 / 14 = -9
Since the length of a segment cannot be negative, we discard the second case and focus on the positive solution.
Therefore, x = 9/7.
Substituting this value back into AB = 8x:
AB = 8 * (9/7) = 72/7 ≈ 10.29
Rounding to 2 decimal places, the length of AB is approximately 10.29 units.
Answer:
To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:
8x = x + 9
Solving for x, we get:
x = 1.5
Therefore, AB = 8x = 8(1.5) = 12.
To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:
AB^2 + BD^2 = AD^2
Substituting the values, we get:
12^2 + BD^2 = (1.5 + 9)^2
Simplifying, we get:
BD^2 = 56.25
Taking the square root of both sides, we get:
BD = 7.5
Hence, the length of AB is 12 and the length of BD is 7.5.
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Solve the inequality below. Use the drop-down menus to describe the solution and its graph. 7 13 11 Click the arrows to choose an answer from each menu. The solution to the inequality is Choose.... Choose... A graph of the solution should have Choose.... and be shaded to the
Answers
Answer:
\(x \leq -4\)
There will be a filled-in hole at -4.
Step-by-step explanation:
We can solve an inequality the same way we do for equations. The only thing to keep in mind, is that multiplying by a negative number will result in flipping the inequality sign (< to > and vice versa)
\(-7x + 13 \geq 41 \text{ //}-13\\-7x \geq 28 \text{ //}:-7 \text{ (Notice we multiply by a negative number.)}\\x \leq -4\)
The difference between a filled-in and an empty hole in terms of inequality graphs, is whether or not the number limiting the inequality is included in it.
For example, in x > 3, 3 is limiting the inequality, however, it is not included in it, therefore, x would always be greater than 3.
In another example, \(x \leq -4\), -4 is limiting inequality and is included in it. Therefore, x would always be less than or equal to -4.
A filled-in hole means the number is included in the inequality, while an empty one means it isn't.
In our cases, -4 is included in the inequality (notice the line under the inequality sign that resembles "less than or equal to"), therefore there will be a filled-in hole at -4.
Rationalize the denominator of the fraction and enter the new denominator below.
Answers
Answer:
7/19
Step-by-step explanation:
7/19=square root of 11=22-3 19
please explain the reasoning!!
Answers
Answer:
No, the rectangles are not proportional.
Step-by-step explanation:
I say this because the area of the first one is 10ft x 12ft = 120 ft
But, the answer to the second rectangle is 9ft x 8ft = 72ft
Proportional means corresponding in size
So, the rectangles above are not proportional.
Hope this helps!
PLEASE PLEASE HELP MEEE :(
Select the correct point on the coordinate plane.
Which point can be used to form a right triangle to derive the distance formula to find the length of the line segment?
Answers
(-3, 3) and (4, -1) are the points that can be used to form a right triangle to derive the distance formula to find the length of the line segment
Determining the distance between two points.Given the line on the xy-plane, we are to determine the points on the line that can be used to determine the distance between the two points.
The required points on the line will be the two endpoints on the line. The end points are (-3, 3) and (4, -1). The distance between this points is expressed as:
D = √(-1-3)²+(4+3)²
D = √14 + 49
D = √63
Hence the points that can be used to form a right triangle to derive the distance formula are (-3, 3) and (4, -1)
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Answer: It’s -1,-3
Step-by-step explanation:
got 100 on the test
The value of 8 units is 11. What is the value of 1 unit?
Answers
Please answer this question:
1.)
\( {3}^{n + 2} + \: ({3}^{n + 3} - \: {3}^{n + 1})\)
2.)
\( \frac{( {25}^{ - 1} + ( {25}^{ - 2})}{( {625}^{0} + ( {25}^{ - 2} )}\)
hope you can help me. thank you in advance. I'll give the brainliest.
Answers
Answer:
\( {3}^{n + 2} + \: ({3}^{n + 3} - \: {3}^{n + 1} ) \\{ 3 }^{n + 2} + {3}^{n + 1} ({3}^{2} + 1) \\ {3}^{n + 2} + {3}^{n + 1} (9 + 1) \\ {3}^{n + 1} (3 + 10) \\ {3}^{n + 1} 30 \\ {3}^{n} \times 3 \times 30 = 90 \times {3}^{n}\)
second one 13/313
![Please answer this question:1.) [tex] {3}^{n + 2} + \: ({3}^{n + 3} - \: {3}^{n + 1})[/tex]2.) [tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/IFR8v9sScYJgWbUXplLZuIDz0GjjoJli.jpeg)
Please help if good at math
An isosceles trapezoid has a perimeter of 49 centimeters. Its shorter base measures 8
centimeters and its longer base measures 11 centimeters. The two remaining sides have the
same length
what is that length?
Answers
Answer:
15
Step-by-step explanation:
11+8=19
49-19=30
because its an isosceles trapezoid the missing sides are equal to each other so we just have to divide 30 by 2
30/2=15
the answer is 15
have a great day :D
Steve watched television for 3/4 hour on Monday and 5/6 hour on Tuesday. How much longer did he watch television on Tuesday than on Monday?
_______ hour
Answers
What is the equation of the graph below?
y = sec(x) + 2
y = csc(x) + 2
y = csc(x + 2)
y = sec(x + 2)
Answers
Answer:
y = csc(x) + 2
Step-by-step explanation:
The equation for the given graph is y = csc(x) + 2
What is an equation of a graph?'In graph theory, Graph equations are equations in which the unknowns are graphs. One of the central questions of graph theory concerns the notion of isomorphism. The graphs are expressed differently in terms of graph equations.'
According to the given problem,
We know, periodicity of a.csc( bx + c ) + d = \(\frac{periodicity of cscx}{[b]}\)
The periodicity of csc(x) is 2π,
⇒ \(\frac{2\pi }{1}\)
= 2π
Hence, we can conclude, the equation y = csc(x) + 2 represents the given graph.
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In an examination, 500 students appeared. Out of these students; 25 % got first division, 35 % got second division and 5 students failed, find the number of students who just passed and didn't get any division.
Answers
The number of students who just passed and didn't get any division is 195.
How to find the number of students got division?We can start by finding the number of students who got first or second division:
Number of students who got first division = 25% of 500 = 0.25 * 500 = 125Number of students who got second division = 35% of 500 = 0.35 * 500 = 175Next, we can find the total number of students who got a division:
Total number of students who got a division = Number of students who got first division + Number of students who got second division
= 125 + 175 = 300
Now, we can find the number of students who failed:
Number of students who failed = 5
Finally, we can subtract the number of students who got a division and the number of students who failed from the total number of students to find the number of students who just passed and didn't get any division:
Number of students who just passed and didn't get any division = Total number of students - Number of students who got a division - Number of students who failed
= 500 - 300 - 5
= 195
Therefore, the number of students who just passed and didn't get any division is 195.
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For the question of total area of the cuboid is 200cm^.
I understand where we divide 150 by 4.
But why do I need to multiply by 5, when there are 6 faces.
Answers
You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.
When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.
A cuboid has six faces, but each face has a pair that is identical in size and shape.
Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.
To find the surface area of a cuboid, you can add up the areas of all its faces.
However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:
(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.
By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.
Essentially, you are considering one face from each pair and then summing their areas.
Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.
When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.
Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.
Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.
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which of the following is equivalent to x^2 -5x +6
Answers
Hello!
x² - 5x + 6
= (x² - 2x) + (-3x + 6)
= x(x - 2) - 3(x - 2)
= (x - 2)(x - 3)
image is below, please help me fast i have 2 minutes left, thank you very much
Answers
Answer:
45
Step-by-step explanation:
1/3 of 90
= 1/3 * 90
= 90/3
= 30
Let the missing number be x.
2/3 of x
= 2/3 * x
= 2x/3
30 = 2x/3
Cross multiply,
2x = 30 * 3
2x = 90
x = 90/2
x = 45
Hence,
the missing number is 45.
A line passes through the points (-1, -8) and (3, 12). Compute the slope of
the line. Show your steps. *
Your answer
This is a required question
A line passes through the points (-1, -8) and (3, 12). Write the equation for
the line that passes through these points in the form y=mx + b. (Hint: you
already computed m in the previous problem.) *
Answers
Answer:
y = 5x - 3
Step-by-step explanation:
The Slope of a Line
Suppose it's given a line that passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the formula:
\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)
The equation of the line in slope-intercept form is:
y=mx+b
Where:
m = slope
b = y-intercept.
We are given the points (-1,-8) and (3,12). Compute the slope:
\(\displaystyle m=\frac{12+8}{3+1}=\frac{20}{4}=5\)
The equation of the line now has one known value:
y = 5x + b
Let's use the point (3,12) to find the value of b:
12 = 5(3) + b = 15 + b
Solving for b:
b = 12 - 15 = -3
The required equation of the line is:
y = 5x - 3
what is the nth term in a cube number sequence
Answers
Answer:
cube numbers: 1, 8, 27, 64, 125, ... - the nth term is. triangular numbers: 1, 3, 6, 10, 15, ... (these numbers can be represented as a triangle of dots).Step-by-step explanation:
IF IT HELPED UH PLEASE MARK ME A BRAINLIEST :-)Need help with the question below.
Answers
Answer:
A
Step-by-step explanation:
r=10 and the angle bln 5√3 and -5 is 330 or 11π/6
What is the solution to the inequality below?
−8m ≥ 40
Answers
2. m < -5
Question 9 of 10 If two triangles are congruent, which of the following statements must be true? Check all that apply. A. The triangles have the same size, but not the same shape. B. The triangles have the same size and shape. C. The corresponding angles of the triangles are congruent. D. The corresponding sides of the triangles are congruent.
Answers
Answer:
ACD
Step-by-step explanation:
All statements are correct for two congruent trianglesStep-by-step explanation:If two triangles are congruent than the rules states thatTriangles are congruent when all corresponding sides and interior angles are congruent. The triangles will have the same shape and size, but one may be a mirror image of the other.As the fig shows two triangleΔ PQRΔ LMNAll three corresponding sides of triangle are congruentall three corresponding angles are congruentBoth triangle are of same sizeBoth are of same shapehence all the statements are CORRECT Keywords:Geometry
find the missing measure in each triangle with the given angle measures
Answers
We are asked to find the missing angle in each of the given triangles.
Recall the fact that the sum of interior angles of a triangle must be equal to 180°.
7)
\(45\degree+35\degree+x=180\degree\)Let us solve the above equation for the unknown angle x.
\(\begin{gathered} 45\degree+35\degree+x=180\degree \\ 80\degree+x=180\degree \\ x=180\degree-80\degree \\ x=100\degree \end{gathered}\)Therefore, the missing angle is 100°
8)
Similarly, sum the angles and equate them to 180°
\(\begin{gathered} 100\degree+x+40\degree=180\degree \\ 140\degree+x=180\degree \\ x=180\degree-140\degree \\ x=40\degree \end{gathered}\)Therefore, the missing angle is 40°
9)
Similarly, sum the angles and equate them to 180°
\(\begin{gathered} x+90\degree+16\degree=180\degree \\ x+106\degree=180\degree \\ x=180\degree-106\degree \\ x=74\degree \end{gathered}\)Therefore, the missing angle is 74°
Javier bought a painting for
$
150
$150dollar sign, 150. Each year, the painting's value increases by a factor of
1.15
1.151, point, 15.
Which expression gives the painting's value after
7
77 years?
Choose 1 answer:
Choose 1 answer:
(Choice A)
(
150
⋅
1.15
)
7
(150⋅1.15)
7
left parenthesis, 150, dot, 1, point, 15, right parenthesis, start superscript, 7, end superscript
A
(
150
⋅
1.15
)
7
(150⋅1.15)
7
left parenthesis, 150, dot, 1, point, 15, right parenthesis, start superscript, 7, end superscript
(Choice B)
150
⋅
1.1
5
7
150⋅1.15
7
150, dot, 1, point, 15, start superscript, 7, end superscript
B
150
⋅
1.1
5
7
150⋅1.15
7
150, dot, 1, point, 15, start superscript, 7, end superscript
(Choice C)
(
150
+
1.15
)
⋅
7
(150+1.15)⋅7left parenthesis, 150, plus, 1, point, 15, right parenthesis, dot, 7
C
(
150
+
1.15
)
⋅
7
(150+1.15)⋅7left parenthesis, 150, plus, 1, point, 15, right parenthesis, dot, 7
(Choice D)
150
+
1.15
⋅
7
150+1.15⋅7150, plus, 1, point, 15, dot, 7
D
150
+
1.15
⋅
7
150+1.15⋅7
Answers
The correct expression is \($(150 \cdot 1.15)^7$\) (Choice A).
The problem states that the painting's value increases by a factor of 1.15 each year. This means that the value at the end of each year is 1.15 times the value at the beginning of the year. Therefore, after one year, the value of the painting is\($150 \cdot 1.15 = 172.50$\).
To find the value after 7 years, we need to multiply the value of the painting each year by 1.15 a total of 7 times. This can be represented mathematically as \($(150 \cdot 1.15)^7$\). This expression is equal to the starting value of the painting, 150, multiplied by 1.15$ raised to the 7th power, which represents the 7 years of appreciation.
If we were to choose expression B, it would give an incorrect result because it uses a value of 1.1 instead of 1.15 to represent the yearly increase in value.
Expressions C and D are also incorrect because they are not taking into account the compounding effect of the yearly increase. Expression C adds the initial value and the total years together, and expression D adds the initial value to the yearly increase multiplied by 7, neither of which correctly reflects the exponential growth of the painting's value.
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Is there a difference between shapes when plotting Uniform acceleration towards (+)directtion,Uniform acceleration towards (-)direction, Uniform deceleration towards (+) direction and Uniform deceleration towards (-) direction in displacement time graph
Answers
Yes, there is a difference in the shapes of the displacement-time graphs for uniform acceleration towards the positive direction, uniform acceleration towards the negative direction, uniform deceleration towards the positive direction, and uniform deceleration towards the negative direction.
Uniform acceleration towards the positive direction:
In this case, the object's velocity increases in the positive direction over time. The displacement-time graph will have a concave-upward shape, forming a curve that starts with a small slope and gradually becomes steeper as time progresses.
Uniform acceleration towards the negative direction:
Here, the object's velocity increases in the negative direction, meaning it accelerates in the opposite direction to its positive direction.
The displacement-time graph will have a concave-downward shape, forming a curve that starts with a steep slope and gradually becomes less steep as time progresses.
Uniform deceleration towards the positive direction:
In this scenario, the object's velocity decreases in the positive direction, but it still moves towards the positive direction.
The displacement-time graph will show a curve with a decreasing slope, forming a concave-downward shape, indicating that the object is slowing down.
Uniform deceleration towards the negative direction:
Here, the object's velocity decreases in the negative direction, opposing its initial direction.
The displacement-time graph will have a curve with a decreasing slope, forming a concave-upward shape, indicating that the object is slowing down but still moving in the negative direction.
In summary, the shapes of the displacement-time graphs differ based on the direction and type of acceleration (positive or negative) and whether the object is undergoing uniform acceleration or uniform deceleration. These differences can be observed through the concavity and slope of the graphs.
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