A large helium balloon is tethered to the ground by two taut lines. One line is 100 ft. Long and makes an 80 degree angle with the ground. The second line makes a 40 degree angle with the ground. How long is the second line?
Answers
The second line is 153ft long.
We are making a figure out of the given statment. Where we have the Triangle ABC and other two Triangle ADB and ADC inside Triangle ABC. Here Angle ADC = 80 degress and Angle ACD = 40 egress.
According to given statement and figure,
In triangle ABO, AD= 100 ft
Hence, BD/AD = Cos80
or, BD = (100 * Cos80)
or, BD = 17.36 ft
Now, AB/AD = Sin80
or, AB = (100* Sin 80)
or, AB = 98.48
Now, In case of triangle ABC
AB/AC = Sin40
or, AC = AB/ Sin 40
or, AC = 98.48/ Sin40
or, AC = 153.2 ft (nearly equal to 153 ft)
The second line is 153ft long.
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Related Questions
1. Cameron ran 3 miles in 24 minutes. Identify the equivalent ratio that represents Cameron's run. *
Answers
The equivalent ratio that represents Cameron's run is 1 : 8
Equivalent Ration:
In mathematics, the definition of equivalence ratio says: The equality of two ratios is also called a ratio. Front and follow have different values, but reducing them to their simplest form gives the same value.
For example, to find out if 2:3 and 16:24 are equivalent ratios, we need to reduce both ratios to their simplest form. The HCF of 2 and 3 is 1, so 2:3 is already in the simplest form. The HCF for 16 and 24 is 8. Divide these two numbers by 8 to get the reduced form. This means (16÷8):(24÷8) = 2:3. It's clear that 2:3 and 16:24 are the same value, equivalent ratios.
Based on the question :
Cameron ran 3 miles in 24 minutes.
Now,
Therefore we can say that :
Cameron ran 1 miles in 8 minutes;
Therefore, the equivalent ration is 1 : 8.
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When you use substitution What are the steps used to find the solution to a system of linear equations?
Answers
In one of the equations, separate one of the two variables. In the other equation, replace the expression with the value of the isolated variable from Step 1. Consequently, a linear equation with just one variable ought to emerge.
What constitutes the substitution system's solution?The one y-value in the substitution method is replaced with the other. We'll give an example to illustrate this. Since y = y, we can replace y in the second equation with y from the first equation. The linear system's solution is (1, 6).
What are the three possible types of solutions for a linear equation?Numerous solutions, no solutions, and a singular solution.
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Which represents the solution set of 5(x+5) <85?
Ox< 12
O x> 12
O x < 18
O x> 18
Answers
Answer: O x<12
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
5x+25<85
Step 2: Subtract 25 from both sides.
5x+25−25<85−25
5x<60
Step 3: Divide both sides by 5.
5x/5 < 60/5
x<12
3) Camile offers you a challenge. Are the triangles below similar? Examine them and tell how
you know.
a) Use a flowchart to organize your explanation.
b) Camile says, "These triangles aren't just similar-they're congruent!" Is Camile
correct? What special value in your flowchart indicates that the triangles are
congruent?
Answers
a) The flowchart for the congruency of triangles is given below.
b) The triangles are congruent as DQ ≅ XZ, PQ ≅ XY, and ∠PQD ≅ ∠ZXY.
What is congruency?
The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal.
In the given diagram, it can be seen that -
Line segment DQ = Line segment XZ.
Similarly, Line segment PQ = Line segment XY.
Since, the two sides of the triangle are equal, hence the third side must also be equal.
Line segment PD = Line segment ZY.
Also, in the diagram it can be seen that ∠PQD ≅ ∠ZXY.
Therefore, the triangles PDQ and ZXY are equal and congruent.
The flowchart for the same is given below.
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x^2=Σ(o-e)^2/e
17. A candidate for mayor is discussing the crime rate in the city. She asks the police department to provide some statistics on how many people out of a group of 500
people were victims of four specific crimes. She expects that she can verify this information by doing her own survey. She then asks a group of 500 people to identify
whether they were victims of the same crimes. Her results are the observed quantities, and the police data are the expected quantities. The following is a table of the
results.
Category: observed/ expected
Robbery
24/18
Assault
15/21
Discrimination
79/56
Theft
124/138
Calculate the chi-square value for her survey. Remember, to calculate the chi-square value, use the formula shown.
A. 12.68
B. 8.56
C. 8.15
D. 14.58
Answers
On solving the provided question we cans ay that - the value of the following exponent is
what are exponents?Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where
here,
= [tex]10^2 X 10^-3[/tex] X 32
= 100 X 1/1000 X 32
=1/10 X 32
=3.2
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Select the correct answer.
Which phrase best describes the relationship indicated by the scatter plot?
A. constant correlation
B. negative correlation
C. positive correlation
D. no correlation
Answers
Answer: B
Step-by-step explanation:
Correlation tells us the relationship of 2 variables. Looking at the graph, the data appears to going down, as we read graphs from left to right. We can automatically eliminate C and D, since we have determined going down. We know it's also not A because if the correlation is constant, then all the dots would be lined up, and not scattered around. Since the dots are going down, this tells us that it is a negative correlation. Hence, B is the answer.
Answer:
B. negative correlation
Step-by-step explanation:
Which of the following chocies is not a function?
A {(0, 0), (1, 4), (2,8)}
B {(0, 0), (3, 16), (16, 49)}
C {(1, 1), (2, 2), (3, 3), (4,4)}
D {(7, 1), (6, 2), (5, 3), (5,4)}
E All of these choices are functions.
Answers
C has x values that repeat.
expand this expression using the distributive property. 4(-2g+4-3t)
Answers
Answer:
-8g+16-12t is the answer
Step-by-step explanation:
multiply everything by 4
In this course, we'll begin to
explore "opposite" function types. For example, think about
a quadratic function and its key features. What key features do you think its opposite
function will have? Why?
Answers
Answer:
Some key features quadratic functions have are:
Axis of symmetryx and y-interceptsZeroesvertexPoint symmetric to y-interceptStep-by-step explanation:
Answer: You could say something like this ''I think the opposite function of a quadratic function would have an inverted parabolic curve that always opens upwards, since a quadratic function can open upwards or downwards. It would also have a single maximum or minimum point, depending on the coefficient of the quadratic term, since a quadratic function has a single vertex. Finally, the opposite function would have either no real roots or two real roots with opposite signs, depending on the discriminant, since a quadratic function can have either two distinct real roots or two complex roots.''
Find the value of x.
2x-8
6
Answers
Answer:
[tex]x=7[/tex]
Step-by-step explanation:
Angles opposite congruent sides in a triangle are congruent.
[tex]6=2x-8 \\ \\ 2x=14 \\ \\ x=7[/tex]
Nathan had 58 pieces of gum that he wants to make last six days how much can he chew each day so that the gum last him six days between what two whole numbers does your answer lie
Answers
Natha can chew between 9 to 10 chewing gum each day so that it could last for 6 days.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Nathan had 58 pieces of gum that he wants to make last six days.
Therefore, The number of chewing gums he can chew is the total number of chewing gums he has divided by the total number of days which is,
= (58/6).
= 9.66 chewing gums but it should be a whole number.
So, Nathan can chew between 9 to 10 chewing gums each day.
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Is 4x² 3x 7 a polynomial?
Answers
As all the exponents of x are whole numbers, the expression 4x² – 3x + 7 is a polynomial in one variable.
What is exponents?The exponent of a number shows how many times the original value of the number has been multiplied. For example, the number 34 indicates that we have multiplied three by four. 3 × 3 × 3 × 3 × 3 is its expanded form. Exponent is another term for a number's power. It might be a decimal, a fraction, a negative number, or a whole number.
Exponents are important because without them, writing the product when a number was repeated many times on its own would be very difficult. For example, it is much easier to write 57 than it is to write 5 × 5 × 5 × 5 × 5.
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Find the measure of the indicated angle to the nearest degree.
Answers
Answer:
? ≈ 20°
Step-by-step explanation:
using the cosine ratio in the right triangle
cos ? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{16}{17}[/tex] , then
? = [tex]cos^{-1}[/tex] ( [tex]\frac{16}{17}[/tex] ) ≈ 20° ( to the nearest degree )
Why is triangle always 180 degrees?
Answers
Triangle is always 180 degrees because the sum of all angles in a triangle is 180 degrees. This is known as the "Triangle Angle Sum Theorem." The theorem states that the sum of all angles in a triangle is equal to 180 degrees.
1. A triangle is a three-sided polygon with three angles.
2. The sum of the three angles in any triangle must be 180 degrees.
3. This is known as the Triangle Angle Sum Theorem.
4. The Triangle Angle Sum Theorem states that the sum of the angles in a triangle must equal 180 degrees.
5. It does not matter which angles the triangle has, the sum will always equal 180 degrees.
6. This theorem is based on the fact that the sum of the angles in any triangle is equal to two right angles or 180 degrees.
7. The Triangle Angle Sum Theorem can be proven by drawing a triangle, and then measuring and adding the three angles.
8. The sum of the three angles will always equal 180 degrees.
9. Therefore, triangle is always 180 degrees.
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What number should be added to the polynomial 2x³ − 3x² − 8x so that the resulting polynomial leaves the remainder 12 when divided by 2x 1?
Answers
The number that should be added to the polynomial 2x³ - 3x² - 8x is 12x
When a polynomial is divided by a linear factor, the remainder is equal to the constant term of the polynomial multiplied by the reciprocal of the linear factor.
In this case, the polynomial is 2x³ - 3x² - 8x, and the linear factor is 2x-1.
To find the remainder when this polynomial is divided by 2x-1, we need to multiply the constant term of the polynomial, which is -8, by the reciprocal of 2x-1, which is 1/(2x-1).
So the remainder should be -8*(1/(2x-1)) = -8/(2x-1) = -4/(x-0.5)
To make the remainder 12, we will add 12x to the polynomial so that the new constant term is 12.
The polynomial 2x³ - 3x² - 8x + 12x will have a remainder of 12 when divided by 2x-1.
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Let n be the least positive integer for which 149^n-2^n is divisible by 3^3.5^5.7^7.$ Find the number of positive integer divisors of n.
Answers
Calculating the LCM of all these, one gets 2^2. 3^2 . 5^4 .7^5. Using the factor counting formula, the answer is 3.3.5.6 = {270}
Step-by-step explanation:
Note that for all n, 149^n-2^n is divisible by 149-2=147 by difference of nth powers. That is 3.7^2, so now we can clearly see that the smallest n to make the expression divisible by 3^3 is just 3^2 Similarly, we can reason that the smallest n to make the expression divisible by 7^7 is just 7^5.
Finally, for 5^5, take (mod {5}) and ( mod {25} )of each quantity (They happen to both be -1 and 2 respectively, so you only need to compute once). One knows from Fermat's theorem that the maximum possible minimum n for divisibility by 5 is 4, and other values are factors of 4. Testing all of them(just 1,2,4 using mods-not too bad), 4 is indeed the smallest value to make the expression divisible by 5, and this clearly is NOT divisible by 25. Therefore, the smallest (n) to make this expression divisible by 5^5 is $2^2 .5^4.
Using the factor counting formula, 2^2. 3^2 . 5^4 .7^5 = 3.3.5.6 = {270}
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Dave can clean pools at a constant rate of 3/5 pools/hour. How long does it take Dave to clean 15 pools?
Answers
9 hours will it take to clean the 15 pools.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Dave can clean pools at a constant rate of 3/5 pools per hour.
This also means that he cleans 3 pools in 5 hours
So, the time taken to clean 15 pools is
= 15×3/5
= 9 hours.
Hence, the time taken is 9 hours.
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At summer camp this year, Clare is leading the beadwork class. Each of the 9 craft tables has a bucket of beads. The graph shows the weight of the beads in each bucket.
If Clare distributes all of the beads equally among the 9 buckets, how much will the beads in each bucket weigh?
Answers
The beads in each bucket will weigh 1 pound
How to determine the weight of the beads in each bucket?
A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.
From the graph, we have weights of 0, 1/2, 1 1/2 and 2 pounds.
In order for Clare to distributes all of the beads equally among the buckets, she need to add up weight of the beads and divide by 5.
weight in each bucket = (0 + 1/2 + 1 1/2 + 2)/5 = 5/5 = 1 pound
Thus, each bucket weighs 1 pound
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Please help ASAP this is for a final test
A line which is perpendicular to this line would have a slope of ___.
Write your answer as a whole number or simplified fraction or improper fraction (not a decimal or mixed number). Use a / for a fraction bar.
Answers
Answer: I'm sorry bro i don't know
Step-by-step explanation:
Amrita divides a circular disc of radius 7 cm in two equal parts. What is the perimeter of each semicircular shape disc? (USE π=22/7 )
Answers
The perimeter of each semicircular shape disc created by Amrita by dividing a circular disc of radius 7 cm into two equal parts is 44 cm. This is calculated by multiplying the circumference of the circle (2πr = 2 × 22/7 × 7 = 44 cm) by half.
Amrita divided a circular disc of radius 7 cm into two equal parts. This created two semicircular shape discs
Step 1: Calculate the circumference of the original circle.
Circumference of a circle = 2πr
Circumference of the circle with a radius of
7 cm = 2πr = 2 × 22/7 × 7 = 44 cm
Step 2: Calculate the perimeter of each semicircular shape disc.
The semicircular shape discs are created by dividing the original disc into two equal parts. Therefore, the perimeter of each semicircular shape disc is half of the circumference of the original circle.
Perimeter of each semicircular shape disc
= 44 cm/2
= 22 cm
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The red line on this graph is y=-2x-1
The dotted line is y=x.
Write the equation of the inverse of this function
Answers
Answer:
Step-by-step explanation:
Consider rigid-body physics in a higher or lower dimension than three. How many coordinates are required to specify the location and orientation of a rigid body:If the space is two-dimensional?a. 2b. 3c. 4d. 5
Answers
In two-dimensional space, only two coordinates are required to specify the location and orientation of a rigid body.
In two-dimensional space, a rigid body can only move in two directions (up/down and left/right) and rotate around a single axis. As a result, only two coordinates are needed to specify the location and orientation of a rigid body in two-dimensional space. The two coordinates needed to specify the rigid body's position are the x-coordinate and y-coordinate, which define the position of the body in the plane. The orientation of the rigid body can be determined by determining the angle between the x-axis and the body's orientation, which is referred to as the angle of rotation. The combination of these two coordinates (position and rotation) specify the full state of the rigid body in two-dimensional space.
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One of the legs of a right triangle measures 2 cm and its hypotenuse measures 5 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth."
Answers
When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm, [tex]\sqrt{21}[/tex] is the measurement of the other leg.
what is Pythagoras theorem ?Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides. The Pythagorean Theorem demonstrates how to calculate the side lengths of a right triangle by adding the areas of three intersecting squares. As the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite, this theorem is a very helpful tool. Given a triangle ABC with sides measuring a, b, and c, and the equation a2 + b2 = c2, Make another triangle with sides of lengths a and b and a right angle.
given
by Pythagoras theorem
[tex]c^{2} = a^{2} + b^{2} \\5^{2} = 2^{2} + b^{2} \\5^{2} - 2^{2} = b^{2} \\25 - 4 = b^{2} \\21 = b^{2} \\b =\sqrt{21}[/tex]
When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm, [tex]\sqrt{21}[/tex] is the measurement of the other leg.
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need help on both these , preciate it .
Answers
Therefore ,we can conclude from answering the offered question that the region of the circle, triangle, and square is where the darkest area is. A=210-123 = 87 square units
Triangle - what is it?A triangle is a polygon since it has three sides plus three vertices. It is one of the basic geometric forms. An illustration of a triangle with the sides A, B, and C is Triangle ABC. A distinct plane or triangle in Geometrical are discovered when the three aspects are not collinear. Three sides & three corners define a triangle as a polygon. The triangle's corners are defined as the locations where three sides converge. 180 degrees is the result of multiplying three triangle angles.
Here,
The total of the circle, triangle, and square's surface areas.
The region of the darkish area is comprised of the areas of the Circle, Triangle, and Square.
=>A = 210 – 123 = 87 square units
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The manufacturer's price for a Jinko car is $x
Ben was given a 7% discount on the manufacturer's price when he bought a Jinko.
Ben paid $23 622 when he bought his Jinko.
(a) Calculate the value of x.
Answers
Answer:
x = $25,400 [the original price of the Junko car]
Step-by-step explanation:
The price Ben paid, $23,622, is after the 7% discount. Let x be the original price of the Jinko car. Ben's prices reflect a 7% discount:
x*(1-0.07) = $23,622 [The expression (1-0.07) means the original price, 1, is reduced by 7%, -0.07, to give the final price]
(0.93)x = $23,622
x = $25,400
Find the value of x.
2x-8
6
Answers
Answer:
[tex]x=7[/tex]
Step-by-step explanation:
Angles opposite congruent sides in a triangle are congruent.
[tex]6=2x-8 \\ \\ 2x=14 \\ \\ x=7[/tex]
Given: △ACE,BD¯¯¯¯¯∥AE¯¯¯¯¯ Prove: BACB=DECD A triangle with vertices labeled as A, C, and E, with base A E. Sides C A and C E contain midpoints B and D, respectively. A line segment parallel to base A E is drawn from point B to D. Angle C A E is labeled as 4 and angle C E A is labeled as 3. Angle C B D is labeled as 1 and angle C D B is labeled as 2. Drag an expression or phrase to each box to complete the proof. Statement Reason △ACE,BD¯¯¯¯¯∥AE¯¯¯¯¯ Given Response area Corresponding Angles Postulate △ACE∼△BCD Response area CACB=CECD Definition of similar triangles CA=CB+BACE=CD+DE Segment Addition Postulate CB+BACB=CD+DECD Substitution Property of Equality CBCB+BACB=CDCD+DECD Addition of fractions 1+BACB=1+DECD Simplification of fractions Response area Subtraction Property of Equality
Answers
For triangle ACE, if BD ∥AE , then BA/CB = DE/CD is proved.
For given triangle ACE,
BD || AE ...............(Given)
∠4 ≅ ∠1 and ∠3 ≅ ∠2 ..............(Corresponding Angles Postulates)
ΔACE ~ ΔBCD .............(Angle-Angle Similarity Postulate)
CA/CB = CE/CD ............(Definition of similar triangles)
CA = CB + BA, CE = CD + DE ..........(Segment Addition Postulate)
(CB + BA)/CB = (CD + DE)/CD ..........(Substitution Property of Equality)
CB/CB + BA/CB = CD/CD + DE/CD .........(Addition of Fractions)
1 + BA/CB = 1 + DE/CD .............(Siplification of fractions)
BA/CB = DE/CD ...............(Subtraction Property of equality)
Hence proved.
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Which of the following constructions can be accomplished with paper
folding?
Check all that apply.
A. Constructing a line segment of length 2 and then finding the
midpoint
B. Drawing a perpendicular line segment through a given point on a
given segment
C. Drawing a line through a given point parallel to a given line
D. Drawing a perpendicular line segment from a given point to a
given segment
Answers
Answer: Constructions A, B, and D can be accomplished with paper folding.
Construction A involves constructing a line segment of length 2 and then finding the midpoint, which can be done by folding the paper in half.
Construction B involves drawing a perpendicular line segment through a given point on a given segment, which can also be done by folding the paper.
Construction D involves drawing a perpendicular line segment from a given point to a given segment, which can also be done by folding the paper.
Construction C, drawing a line through a given point parallel to a given line, cannot be accomplished with paper folding. To do this construction, you would need a straightedge, such as a ruler.
Step-by-step explanation:
The following constructions can be accomplished with paper folding -
Drawing a perpendicular line segment through a given point on a given segment.Drawing a line through a given point parallel to a given line.Drawing a perpendicular line segment from a given point to a given segment. What is construction in mathematics?Constructions are accurate drawings of shapes, angles and lines in geometry. Some basic constructions -
Constructing bisectors of lines and angles.Constructing regular polygons inscribed in circles.Constructing circumcircles and incircles.Constructing a line tangent to a circle.Given is to find which of the following constructions can be accomplished with paper folding.
The following constructions can be accomplished with paper folding -
Drawing a perpendicular line segment through a given point on a given segment.Drawing a line through a given point parallel to a given line.Drawing a perpendicular line segment from a given point to a given segment.Therefore, the following constructions can be accomplished with paper folding -
Drawing a perpendicular line segment through a given point on a given segment.Drawing a line through a given point parallel to a given line.Drawing a perpendicular line segment from a given point to a given segment.To solve more questions on constructions, visit the link-
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Stacy wants to buy a tree to decorate her apartment. Her living room has 8 foot high ceilings. The height of each tree she is interested in buying is given below. Which tree(s) can she buy so that they fit in her living room? Choose all that apply
A. 108 inches
B. 114 inches
C. 94 inches
D. 79 inches
or other you can type what you got
Answers
Answer:
C And D
Step-by-step explanation:
94 Inches Is 7.8 Feet Tall & 79 Inches is 6.5 Feet Tall
Answer:
C and D
Step-by-step explanation:
You should start by changing the inches to feet
(there are 12 inches in foot [ 12 inch = 1 foot ])
A. 9 foot
B. 9.5
C. about 7 feet
D. about 6 feet
C and D are correct. Hope this helps!
As part of an experiment to test different liquid fertilizers, a sprinkler has to be set to cover an area of 140 square yards in the shape of a sector of a circle of radius 50 yards. Through what angle should the sprinkler be set to rotate? If necessary, round the answer to two decimal places
Answers
The sprinkler should be set to rotate through the angle 6.42 degrees.
What is an angle?
Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.
r = 50 yards
Area, A = 140 square yards
Θ = angle
A= (Θ /360) πr²
140 = (Θ /360) * 3.14 * 50*50
Θ = (140*360)/(3.14*25*100) = 6.42 degrees
The sprinkler should be set to rotate through the angle 6.42 degrees.
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