The tallest lighthouse in the world is the Jeddah Light. It is 133 m tall. A dhow is sailing away from this lighthouse. From the top of the lighthouse, the angle of depression to the dhow is 65° Later, the angle of depression has changed to 40°.
How far did the dhow travel during that time?
To solve this problem, we can use trigonometry and the fact that the angles in a triangle add up to 180°.
Let's call the distance between the lighthouse and the dhow "d".
We know that the angle of depression from the top of the lighthouse to the dhow is 65°, and the angle of depression later changed to 40°.
Let's call the angle between the horizontal and the line of sight from the lighthouse to the dhow, "x"
Since the angles in a triangle add up to 180°, we can say that:
x + 65 + 40 = 180
x = 75
Now, we can use the tangent function to find the distance d. We know that:
tan(x) = d / h
tan(75) = d / 133
d = 133 * tan(75)
Therefore, the dhow traveled 133 * tan(75) distance during that time.
5 = –6x2 + 24x
5 = –6(x2 – 4x)
inside the parentheses and
.
–19 = –6(x – 2)2
StartFraction 19 Over 6 EndFraction = (x – 2)2
Plus or minus StartRoot StartFraction 19 Over 6 EndFraction EndRoot = x – 2
The two solutions are
Plus or minus StartRoot StartFraction 19 Over 6 EndFraction EndRoot
Answer:I apologize, but I am not able to understand your question as it is written in a mix of mathematical notation and text that is not clear. Could you please rephrase your question or provide more context? I'll be happy to help you with your question.
Step-by-step explanation:
What i the range of the variable x
X 2 4 6 8 10 12
p (x) 0. 10 0. 20 0. 15 0. 10 0. 12 0. 25
A. 2
B. 10
C. 8
D. 12
Answer:
B.10
Step-by-step explanation:
Because it increases by 10
I need help i cant figure out what im doing wrong, im confused (just number 15)
the length of the sections will be 24 and 18 respectively.
What are parallel lines?Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.
Given, Some pair of lines in that three lines are parallel and two of them are intersecting them.
Since, these are the the section made by two parallel lines. Thus, these given section will be Proportional to each other.
Thus,
20/15 = ( 7x - 11)/(4x - 2)
4/3 = ( 7x - 11)/(4x - 2)
16x - 8 = 21x - 33
5x = 25
x = 5
therefore, the length of the sections will be 24 and 18 respectively.
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2. If 60 adults ages 18 - 29 made resolutions, how many people were surveyed?
picture is the percentages of people that age
ex: 10% of adults are ages 18-29
If 60 adults ages 18-29 made resolutions, and 10% of adults are ages 18-29, we can infer that 600 people were surveyed.
How to calculate percentages?
Percentages are a way to express a number as a fraction of 100. To calculate a percentage, you can use the following formula:
(Part/Whole) x 100 = Percentage
The question states that 60 adults ages 18-29 made resolutions, but does not provide information about the total number of people surveyed. In order to determine the total number of people surveyed, we would need additional information about the percentage of adults that fall within the age range of 18-29.
If the percentage of adults ages 18-29 is 10%, and 60 adults in that age range made resolutions, we can use that information to determine the total number of people surveyed.
We can use the following formula:
(Total number of people surveyed) = (Number of adults ages 18-29 who made resolutions) / (Percentage of adults ages 18-29)
(Total number of people surveyed) = (60) / (0.10) = 600
Hence. If 60 adults ages 18-29 made resolutions, and 10% of adults are ages 18-29, we can infer that 600 people were surveyed.
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Use the distributive property to write an expression that is equivalent to . 6−9x
The distributive property states that for any real numbers a, b and c, the following is true:
a(b + c) = ab + ac
To use the distributive property to write an expression that is equivalent to 6 - 9x, we can factor out the -9x from the second term:
6 - 9x = 6 - 9x + 0 - 0x = 6 - 9x + (-9x) = 6 + (-9x)
Therefore, using the distributive property, we can write an expression that is equivalent to 6 - 9x as:
6 + (-9x)
Answer:
-3 ( 3x - 2 )
Step-by-step explanation:
- 9x + 6
x(-2.54y+6y-3.77)+x
pls help asap it’s already 2 days late
Answer: To find the answer to the expression x(-2.54y+6y-3.77)+x, I followed these steps:
Distribute the x coefficient:
x(-2.54y+6y-3.77) = -2.54xy + 6xy - 3.77x
Combine like terms:
-2.54xy + 6xy - 3.77x + x = -2.54xy + 6xy - 2.77x
Simplify the expression:
-2.54xy + 6xy - 2.77x
The result is a polynomial with x and y as variables, and the coefficients -2.54, 6, -2.77.
It is a good practice to check the work by substituting the variables with some numbers to see if the output is correct.
Step-by-step explanation:
Answer:
he given expression can be simplified as:
X(-2.54y+6y-3.77)+x
= X(-2.54y + 6y) + X(-3.77) + x
= X(3.46y) - 3.77X + x
= 3.46xy - 3.77X + x
So, the simplified form of the given expression is 3.46xy - 3.77X + x.
whats x-8< -2?x−8<−2?
you get 15 points for solving
The solution to the inequality is x < 6
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
x - 8 < -2
Add 8 to both sides of the inequality
So, we have the following representation
x - 8 + 8 < -2 + 8
Evaluate the sum in the expression
x < -2 + 8
Evaluate the other sum
x < 6
Hence, the solution is x < 6
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Please help me again, part 3
Answer:
c
Step-by-step explanation:
c
Choose Efficient Methods Determine whether b = 6 is a solution or is not a solution of each equation. please help!!
Here, b = 6 is a solution for the equations 8b = 48, b + 3 = 9 and 54 ÷ b = 9 but not a solution for 4 = b + 11 - 3b.
What is the solution of equation?Finding an equation's solutions, which are values (numbers, functions, sets, etc.) that satisfy the equation's condition and typically consist of two expressions connected by an equals sign, is known as solving an equation in mathematics.
One or more variables are designated as unknowns when looking for a solution. An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution.
To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself. The term "equation's root" is frequently used to refer to an equation's solution, especially but not exclusively for polynomial equations.
Given to prove b = 6
a. 8b = 48
b = 48/8
b = 6
b = 6 is a solution
b. 4 = b + 11 - 3b
3b - b = 11 - 4
2b = 7
b = 7/2
b = 3.5
b = 6 is a not solution
c. b + 3 = 9
b = 9 - 3
b = 6
b = 6 is a solution
d. 54 ÷ b = 9
9b = 54
b = 54/9
b = 6
b = 6 is a solution
Thus, b = 6 is a solution for the equations 8b = 48, b + 3 = 9 and 54 ÷ b = 9 but not a solution for 4 = b + 11 - 3b.
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Sandy used a virtual coin toss app to show the results of flipping a coin 50 times, 400 times, and 2,000 times. Explain what most likely happened in Sandy's experiment.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 400 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 50 flips.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The most likely happened in Sandy's experiment is that,
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
Option D is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Tossing a coin:
The probability of getting a head = 1/2
The probability of getting a tail = 1/2
This is the theoretical probability.
Now,
Experiment probability:
Virtual coins too have the same probability of getting a head and a tail as compared to the theoretical probability.
Thus,
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
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Answer:Not Sure but it is not D at all so please don't use that!
Step-by-step explanation:
What kind of triangle is this 90 29 61?.
The triangle with angles of 90 degrees, 29 degrees, and 61 degrees is a general right triangle that does not belong to any specific type of triangle and it has no specific ratios between the sides.
The triangle with angles of 90 degrees, 29 degrees, and 61 degrees is not a special type of triangle. It is a general right triangle because it has one right angle (90 degrees) and two acute angles (29 degrees and 61 degrees).
This triangle is not a 30-60-90 triangle because it does not have the specific angle measurements of 30-60-90 degrees. Similarly, it's not a 45-45-90 triangle because the angles don't match the specific angles of 45-45-90 degrees. There are no specific ratios between the sides of this triangle.
In general, right triangles are triangles that have one right angle (90 degrees), and the other two angles can take any value between 0 and 90 degrees. The sides of a right triangle have a relationship known as the Pythagorean Theorem. This theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Therefore, In short, the triangle with angles of 90 degrees, 29 degrees, and 61 degrees is a general right triangle that does not belong to any specific type of triangle and it has no specific ratios between the sides.
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If 10 people hare 3 brownie o each peron get the ame amount, how much brownie will each peron get
If 10 people share 3 brownies equally, each person will get the same amount. To find out how much each person will get, you can divide the total number of brownies by the number of people.
Unitary Method:
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
3 brownies / 10 people = 0.3 brownies per person
So, each person will get 0.3 of a brownie. Since a brownie is a solid object, it is not possible for each person to get 0.3 of a brownie, It would be best to cut the brownies into 10 equal pieces.
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5x+20+3x-8 please help!
Answer:
29x+20
Step-by-step explanation:
7th grade math questoion will give bring list thingy pls answer asap
Answer: Expression - 10.2x
The weight carried by each hiker is 10.2 pounds.
Step-by-step explanation:
Hello! To find the answer, you have to add all of the weight together. Do 3.4 + 4.6 + 2.2 = 10.2. You know the total combined weight that all hikers will have to carry is 10.2 pounds. The expression will be 10.2x. You can check this by putting a random number in for x to represent the number of hikers. 10.2 (2) = 20.4. 20.4 would be the total weight that two hikers would have to carry, so the expression is correct. You already know the weight each hiker will have to carry, 10.2 pounds, so you can put that in for the second question.
What is inverse of a number?.
In common inverse meaning is “something that is contrary or reverses”. When we define inverse meaning we will talk mostly from the mathematics point of view where we find the inverse of different operations and functions
The inverse of a given number is equal to number that is obtained by solving the operation 1/x where x is the initial number.
The inverse operation of subtraction is addition, the inverse operation of division is multiplication.
The inverse of a number should not be muddled with its opposite. While the inverse is 1/x, the opposite is equal to -x. That is, the inverse of 3 is equal to 1/3 while its opposite will be equal to -3.
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Derek bought a pack of 8 baseball cards for $16. He bought I football card for $11.
How much more did Derek spend on I football card than on I baseball card? Enter the answer in the box.
Answer:
9
Step-by-step explanation:
16 divided by 8 equals 2
11-2=9
Where is the vertex of the graph of the quadratic function f/x )= x² located?.
The vertex of the graph of the quadratic function f(x )= x² located at the origin of the graph.
The function f(x)=x² looks like a quadratic equation.
The most basic quadratic function is f(x) = x², Its shape should look familiar from Intermediate Algebra – it is called a parabola. The point (0,0) is called the vertex of the parabola.
To find the vertex of a quadratic function on a graph:
Get the equation in the form y = ax²+bx+c.
Calculate -b/2a. This is the x-coordinate of the vertex.
To find the y-coordinate of the vertex, simply plug the value of -b/2a into the equation for x and solve for y. This is the y-coordinate of the vertex.
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What is the corresponding point on the unit circle for the given radian measure?
0=5pi/3
The corresponding point on the unit circle for the angle θ = 5pi/3 is given by: (0,5, -0.866).
What is the unit circle?
Basically, the unit circle is a circle with a radius of 1. It is used in trigonometry to help define and understand angles and their associated trigonometric values. The unit circle is centered at the origin (0, 0) of the coordinate plane, and each point on the circle is defined by its distance from the origin and its angle from the positive x-axis.
What is area of circle ?
The area of circle can be defined as the product of pi and square of radius of a given circle.
In this problem, we have that θ = 5pi/3 , hence:
cos θ = 0.5
sin θ = -0.866
Thus the point is (0,5, -0.866).
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Helen has 687 acres of corn. She expects a yield of 188 bushels per acre. Estimate the total yield.
Answer:
129,156
Step-by-step explanation:
Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.
Outcome Frequency
Green 4
Black 6
Orange 5
Based on the given frequency, determine the experimental probability of selecting an orange marble.
0.27
0.33
0.40
0.67
The probability of selecting an orange marble is 0.33.
Option B is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
The number of times each marble is selected.
Green = 4
Black = 6
Orange = 5
Total number of times all marbles are selected.
= 4 + 6 + 5
= 15
Now,
The probability of selecting an orange marble.
= 5/15
= 1/3
= 0.33
Thus,
The probability of selecting an orange marble is 0.33.
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Sam ha 3. 50 le than junhao and 2. 30 le than Nora. Junhao ha 4. 25. How much money doe Nora have
Nora will have $ 4.05 money.
Given that, Sam has 3. 50 less than Junho and 2. 30 less than Nora. Junhao has 4. 25.
By using the unitary method
The unitary approach is a methodology for problem-solving that involves first determining the value of a single unit and then determining the necessary value by multiplying the single unit value.
The unitary method's formula is to get the value of a single unit and then multiply that value by the number of units to obtain the required value.
Junhao has $4.25
so, Sam has =$4.25-3.50
= $1.75
::NORA HAS = $ 1.75 +2.30
= $ 4.05
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If a: b = 1:2 and b; c = 3:4, find a : c.
Answer:
Step-by-step explanation:
b:c= 3:6
Answer:
Step-by-step explanation:
We know that:
a : b = 1 : 2 (or a = (1/b)*b)
b : c = 3 : 4 (or b = (3/4)*c)
So, we can substitute the value of b from the second equation into the first equation to get the ratio of a : c:
a = (1/b)*b = (1/((3/4)c))((3/4)c) = (4/3)(1/c)*c = (4/3)*1 = 4/3
So, the ratio of a : c is 4 : 3.
Alternatively, we can use the cross-multiplication method to find the ratio.
a : b = 1 : 2, and b : c = 3 : 4
so a4 = b3, and b4 = c3
so a4 = c3
so a:c = 3:4
In this way also we got the ratio of a:c as 3:4
Write it using this format (example): △ABC = △DEC due to AAS
Angle A = Angle D Given
Angle C1 = Angle C2 Vertically Opposite
AB=DE
Shapes that are identical to each other are considered congruent. There are no differences in the matching sides or angles.
What is a congruent shape?
Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.
Congruent refers to something that is "absolutely equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them.
Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.
Here is the format you requested:
△ABC = △DEC due to AAS
Angle A = Angle D Given
Angle B = Angle E Alternate Interior
Angle C1 = Angle C2 Vertically Opposite
AB = DE Congruent Sides
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I need some help on this question please
Answer:
m1 = 4, m2 = 176
Step-by-step explanation:
Using complementary angle rule you know the total angle is 180 thus:
[tex]180 - (x-18) = 8x\\198 - x = 8x\\198 = 9x\\x = 22[/tex]
m1 = (22 - 18) = 4
m2 = 8(22) = 176
The Rose department store chain was closing one of its stores so they had to sell most of the inventory in the store. In the final markdown, they
marked all items 1/3
off the ticketed price. How much would a shirt that was ticketed at $24.99 cost?
The cost of the shirt given the ticketed price is $16.66.
What is the cost of the shirt?When the price of an item is marked down, it means that the price of the item is reduced. The item would become cheaper after the mark down. The shirt would become cheaper after it is marked down.
Price of the shirt after the mark down = (1 - fraction of mark down in price) x ticketed price
= (1 - 1/3) x $24.99
= 2/3 x $24.99
= $16.66
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How do I do this problem?
No, these statements are not needed to prove that ABCD is a parallelogram.
What is parallelogram?A parallelogram is a type of four-sided geometric shape with two pairs of opposite sides that are parallel. Each side of the parallelogram is a line segment, and all four of the interior angles are equal. The opposite sides of a parallelogram are also equal in length. Parallelograms can be found in a variety of applications, including engineering, architecture, and other fields. The most common types of parallelograms are squares, rectangles, and rhombuses.
A parallelogram is defined as a four-sided shape with opposite sides that are equal in length and with opposite angles that are equal in measure.
To prove that ABCD is a parallelogram, it is necessary to show that two of its sides are parallel and that its opposite sides are equal in length.
The statements provided do not show any of these properties, and so are not needed to prove that ABCD is a parallelogram.
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Find An Equation Of The Plane Consisting Of All Points That Are Equidistant From (1, 4, 4) And (-4, 1, 2). Note: You Have To Enter The Full Equation.This problem has been solved!You'll get a detailed solution from a subject matter expert that helps you learn core concepts.See AnswerFind an equation of the plane consisting of all points that are equidistant from (1, 4, 4) and (-4, 1, 2).Note: you have to enter the full equation.
An equation for the plane consisting of all points that are equidistant from the points (1,4,4) and (-4, 1, 2) is 5x+3y+2z-6=0
Given, the points are (1, 4, 4) and (-4, 1, 2).
We have to find an equation for the plane consisting of all points that are equidistant from the given points.
Let the parametric point be (x, y, z) on the plane which is equidistant from the given points.
Using the distance formula:
[tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2+(z_{2}-z_{1} )^2 } }[/tex]
Distance between the points (x, y, z) and (1, 4, 4)
=[tex]\sqrt{(x-1)^2+(y-4)^2+(z-4)^2}[/tex]
Distance between the points (x, y, z) and (-4, 1, 2)
=[tex]\sqrt{(x-(-4)^2+(y-1)^2+(z-2)^2}\\\\ \sqrt{(x+4)^2+(y-1)^2+(z-2)^2}[/tex]
Given, [tex]\sqrt{(x-1)^2+(y-4)^2+(z-4)^2}=\sqrt{(x+4)^2+(y-1)^2+(z-2)^2}[/tex]
By using algebraic identity,
(a-b)² = a²-2ab+b²
(a+b)² = a²+2ab+b²
(x² - 2x + 1)+(y²-8y+16)+(z²-8z+16)=(x²+8x+16)(y²-2y+1)+(z²-4z+4)
x²+y²+z²-2x-8y-8z+1+16+16=x²+y²+z²+8x-2y-4z+16+1+4
By grouping,
-2x-8x-8y+2y-8z+4z+33-21
-10x-6y-4z+12=0
Dividing by -2 into both sides,
5x+3y+2z-6=0
Therefore, the equation of the plane is 5x+3y+2z-6=0
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The sum of the first four terms of an arithmetic progression is 14. If the sum of the first eight terms is 108, find the sixth term of this progression.
The sixth term of the arithmetic progression is 94.
An arithmetic progression is a sequence of numbers such that the difference between any two successive members of the sequence is a constant.
Let's call the first term of the arithmetic progression "a" and the common difference "d". Then the nth term of the progression can be found using the formula:
an = a + (n-1)d
We know that the sum of the first four terms is 14, so we can set up the following equation:
a + (a+d) + (a+2d) + (a+3d) = 14
We also know that the sum of the first eight terms is 108, so we can set up another equation:
a + (a+d) + (a+2d) + (a+3d) + (a+4d) + (a+5d) + (a+6d) + (a+7d) = 108
Now we can use the first equation to substitute for the first four terms of the second equation:
14 + (a+4d) + (a+5d) + (a+6d) + (a+7d) = 108
This gives us:
a + 4d = 94
So the sixth term can be found by substituting n = 6 into the first formula:
a + (6-1)d = a + 5d = 94
Therefore, the sixth term of the arithmetic progression is 94.
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Complete the ratio table.
145 52
290 104
435 156
580
725
Step-by-step explanation:
since a ratio is a fraction with all calculation and comparison rules (but with a special overall meaning), we need to observe the main rule for transforming fractions : when multiplying one part of the fraction by a factor, we also need to multiply the other part by the same factor to keep the value of the fraction unchanged.
the basic ratio is here
145/52 (or written 145:52 - it has the same meaning)
290/104 is just (145×2)/(52×2)
435/156 is just (145×3)/(52×3)
to complete the table we simply have to keep following that structure :
580 = 145×4
so, 52×4 = 208
and the ratio is
580/208
725 = 145×5
52×5 = 260
and the ratio is
725/260
PLEASE HURRRY I NEED HELP!
From the given angles of the triangle, it was possible to find the angle x=29°.
TrianglesTriangles are geometric figures with three (3) sides. They present different classifications regarding their sides or angles.
Like a classification for angles, it is possible to cite, a right triangle. A triangle is classified as a right triangle when it presents one of your angles equal to 90º.
For another side, an equilateral triangle whose classification is associated with the sides. An equilateral triangle presents the three equal sides.
Regardless of its classification, the sum of the a triangle's angles will always be 180°.
The question gives two angles: 50° and 101°. And, it asks the value of angle x.
Therefore,
50+101+x=180
x+151=180
x=180-151
x=29°
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