Two people stand on opposite ends of a bridge that crosses a river. Both can see an island located in the river. The angle
formed at the location of the first person is 37' and the angle formed at the second person is 55'. If the bridge is 5280 feet
long, how far is the first person from the island?
Answers
Answer:
The first person is about 4327.76 feet away from the island.
Step-by-step explanation:
We can draw a diagram to represent the situation. This is attached below.
Essentially, we want to find the value of x.
We are given that ∠A is 37° and ∠B is 55°.
The interior angles of a triangle must total 180°. Hence:
[tex]m\angle A+m\angle B+m\angle C=180[/tex]
Substitute:
[tex](37)+(55)+m\angle C=180[/tex]
Thus:
[tex]\displaystyle m\angle C=88^\circ[/tex]
We are also given that the length of the bridge is 5,280 feet. Since we want to find x, we can use the Law of Sines:
[tex]\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}[/tex]
The variables do not really matter. It is more important that we align the angles with their respective (i.e. opposite) sides.
The respective side to ∠C is AB which measures 5280.
The respective angle to x is ∠B, which is 55°.
Hence:
[tex]\displaystyle \frac{\sin(55)}{x}=\frac{\sin(88)}{5280}[/tex]
Solve for x. Cross-multiply:
[tex]x\sin(88)=5280\sin(55)[/tex]
Thus:
[tex]\displaystyle x=\frac{5280\sin(55)}{\sin(88)}[/tex]
Use a calculator:
[tex]\displaystyle x\approx 4327.76\text{ feet}[/tex]
The first person is about 4327.76 feet away from the island.
Related Questions
What is the perimeter of a square with an area of 256
cm2?
a. 16 cm
b. 32 cm
C. 64 cm
d. 128 cm
Answers
Answer:
C
Step-by-step explanation:
Since we know that squares have all equal sides the area of a square is just a side². So, we would square root 256 in order to find one side. And we know that there are 4 sides of a square so 16+16+16+16= 64. so the answer is C
Of the last 20 balloons sold at a party store, 2 were red. What is the experimental probability that the next balloon sold will be red? Write your answer as a fraction or whole number.
Answers
| ||||||||
I dont know sorry 2/4 or 18
Determine whether quadrilateral EFGH is similar to quadrilateral QRST. If so, give the similarity statement. (ASAP PLS HELP!! no spam pls)
A)
QRST ∼ EFGH
B)
QRST ∼ FEHG
C)
Impossible to determine.
D)
The quadrilaterals are not similar.
Answers
Answer:
D) The quadrilaterals are not similar
Step-by-step explanation:
The given parameters are;
In quadrilateral EFGH, the sides are;
[tex]\overline {EF}[/tex] = [tex]\overline {HG}[/tex] = 8, [tex]\overline {EH}[/tex] = [tex]\overline {FG}[/tex] = 7
In quadrilateral QRST, the sides are;
[tex]\overline {QR}[/tex] = [tex]\overline {ST}[/tex] = 32, [tex]\overline {QT}[/tex] = [tex]\overline {RS}[/tex] = 36
The ratio of the lengths of the corresponding parallel sides on quadrilaterals EFGH and QRST are;
For the horizontal sides, we have;
[tex]\overline {EF}[/tex]/[tex]\overline {QR}[/tex] = 8/32 = 1/4 = 0.25
For the inclined parallel sides, we have;
[tex]\overline {EH}[/tex]/[tex]\overline {QT}[/tex] = 7/36 = 0.19[tex]\overline 4[/tex]
Therefore, given that the ratio of the corresponding sides on quadrilaterals EFGH and QRST are not equal, we have;
The quadrilaterals (EFGH and QRST) are not similar.
7 1/2 / (4 1/2 - 5 1/8) =
Answers
Answer:
Negative twelve aka -12
Answer:
-12
Step-by-step explanation:
15/2 ÷ (9/2 - 41/8)
= 15/2 ÷ (36/8 - 41/8)
= 15/2 ÷ (-5/8)
= 15/2 × (-8/5)
= -120/10 or -12
If (3, 7) and (7, −3) are the endpoints of the segment, find the equation of the perpendicular bisector of .
Answers
Answer:
[tex]y = \frac{2}{5}x[/tex]
Step-by-step explanation:
Concepts⭐Perpendicular bisector of a segment
another line or segment that splits the segment in half and forms 90 degree anglesthe perpendicular bisector cuts through the midpoint of the segmentthe perpendicular has a slope that is the opposite reciprocal of the segment⭐Midpoint formula
[tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex][tex](x_1,y_1)[/tex] is one coordinate on the line[tex](x_2,y_2)[/tex] is another coordinate on the line⭐Point-slope form
[tex]y-y_1 = m(x-x_1)[/tex]m is the slope[tex](x_1,y_1)[/tex] is a coordinate on the linea way to write the equation of a line⭐Slope
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex][tex](x_1,y_1)[/tex] is a coordinate[tex](x_2, y_2)[/tex] is another coordinate⭐Slope-intercept form
[tex]y = mx + b[/tex]m is the slopeb is the y-intercept (the y-value for when x=0)StrategyFind the midpoint of the given segmentFind the slope of the given segmentWrite the equation of the bisector equation in point-slope formSubstitute the opposite-reciprocal of the given segment's slope into the bisector equationSubstitute the midpoint of the given segment into the bisector equationExpand & simplify the bisector equation to convert it into slope-intercept formWorking1. Find the midpoint of the given segment
[tex]midpoint = (\frac{(x_1+x+2)}{2}, \frac{(y_1+y_2)}{2})[/tex]
[tex](x_1,y_1)[/tex] = (3,7)
[tex](x_2,y_2)[/tex] = (7,-3)
∴ midpoint [tex](\frac{3+7}{2}, \frac{7+(-3)}{2})\\= (\frac{10}{2}, \frac{4}{2})\\= (5,2)[/tex]
2. Find the slope of the given segment
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex](x_1,y_1)[/tex] = (3,7)
[tex](x_2,y_2)[/tex] = (7,-3)
∴ slope [tex]m = \frac{-3-7}{7-3}\\= \frac{-10}{4}\\= \frac{-5}{2}[/tex]
3. Write the equation of the bisector equation in point-slope form
[tex]y - y_1 = m(x-x_1)[/tex]
4. Substitute the opposite-reciprocal of the given segment's slope into the bisector equation
The slope of the given segment is -5/2.
Therefore, the opposite-reciprocal of the given segment's slope is 2/5.
[tex]y - y_1 = \frac{2}{5}(x-x_1)[/tex]
5. Substitute the midpoint of the given segment into the bisector equation
midpoint = (5, 2)
[tex]y -2 = \frac{2}{5}(x-5)[/tex]
6. Expand & simplify the bisector equation to convert it into slope-intercept form
We need to convert [tex]y -2 = \frac{2}{5}(x-5)[/tex] into [tex]y = mx + b[/tex] form.
[tex]y -2 = \frac{2}{5}x - \frac{2 * -5}{5}[/tex] . . . . . . . distribute the 2/5 into the parentheses
[tex]y -2 = \frac{2}{5}x - 2[/tex] . . . . . . . compute
[tex]y = \frac{2}{5}x[/tex] . . . . . . add 2 to the LHS and RHS to isolate y
⭐if this response helped you, please mark it the "brainliest"!⭐
PLEASE I NEED THIS!! Which quadrilateral(s) have the same attributes as a rhombus
Answers
Answer:
The correct answer is square and parallelogram
Explanation:
If you turn the rhombus around it will turn into a squarewhich choice is a correct congruence statement for the triangles?
Answers
The reason why is because the order is important when it comes to congruent statements. I'm referring to the order of the letters of ACB and CAD.
Each answer choice has "ACB" in that exact order shown on the left hand side of each congruent statement. We have "A" listed first, then "C" next. In short, segment AC is the first thing mentioned of ACB. This means that we need to list out segment AC as the first thing for the other triangle as well, in order to have a match. Segment AC is the same as segment CA, which is the first segment mentioned in triangle CAD. That's why choice 3 is the answer.
Note how something like triangle CDA won't work since segment CD is listed first, which doesn't pair up with segment AC. This allows us to rule out the first answer choice. Choices 2 and 4 can be eliminated for similar reasons.
Put another way: let's assume choice 1 was the answer. That would mean that AC = CD as they are the first pair of letters of ACB and CDA respectively. But the diagram shows that AC = CD is not true; otherwise, the segments would have similar tickmarks to show they are the same length. This is an alternative way to see why choices 1, 2, and 4 can be crossed off the list.
What is sec 0 when tan 0 = V3? Đ. (1, 0) sec 0 = [?]
Answers
Answer:
secθ = - 2
Step-by-step explanation:
Using the identity
sec²θ = 1 + tan²θ
= 1 + ([tex]\sqrt{3}[/tex] )² = 1 + 3 = 4 ( take the square root of both sides )
secθ = ± [tex]\sqrt{4}[/tex] = ± 2
Since secθ < 0 in the third quadrant , then
secθ = - 2
Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answers
Given:
The given quadratic equation is:
[tex]12a^2+9a+7=0[/tex]
To find:
The solution for the given quadratic equation in simplest form by using the quadratic formula.
Solution:
Consider a quadratic equation is defined as [tex]ax^2+bx+c=0[/tex], then the quadratic formula is:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
The given quadratic equation is:
[tex]12a^2+9a+7=0[/tex]
We have, [tex]a=12,b=9,c=7[/tex]. Using the quadratic formula, we get
[tex]x=\dfrac{-(9)\pm \sqrt{(9)^2-4(12)(7)}}{2(12)}[/tex]
[tex]x=\dfrac{-9\pm \sqrt{81-336}}{24}[/tex]
[tex]x=\dfrac{-9\pm \sqrt{-255}}{24}[/tex]
[tex]x=\dfrac{-9\pm i\sqrt{255}}{24}[/tex] [tex][\because \sqrt{-a}=i\sqrt{a}][/tex]
The solutions of the given equations are [tex]x=\dfrac{-9-i\sqrt{255}}{24}[/tex] and [tex]x=\dfrac{-9+i\sqrt{255}}{24}[/tex].
Hence, the correct option is B.
y=5/4x-2 y=5/4x-1 !HELP ME GRAPH AND ANSWER THE QUESTION!!
Answers
Answer:
Y=54x−2y=54x−1
I hope this helps you!
A pendulum of length 1m and period 2.01s is placed at the top of Mount Everest
having an altitude of 8849m. Calculate the value of ‘g’ at that point.
Answers
Answer: A pendulum of length 1m and period 2.01s is placed at the top of Mount Everest having an altitude of 8849m. Calculate the value of 'g' at that point.
The period of this pendulum can be solved using the formula shown in the picture below. T is the period in seconds; L is the length in meters and g is the acceleration due to gravity which is equal to 9.81 m/s²near the equator.
T = 2 × π × (square root of 1.00 m / 9.81 m/s²)
T = 2 * 3.1416 * (square root of 0.101936799)
T = 6.2832 * 0.319275428
T = 2.00 seconds
The period of this pendulum correct to 3 significant figures is 2.00 seconds.
The frequency of this pendulum is solved by the formula f = 1/T
f = 1/2.00 seconds
f = 0.500 hertz
Answer: 9.76 m/s^2
Step-by-step explanation:
Mr. Brust can eat 3/4 of a bucket of wings in 3/4 hour. How many wings does Mr. Brust eat in one hour?
Answers
Answer:
1 bucket
Step-by-step explanation:
3/4 buckets = 3/4 hours
multiply both sides by 4/3 to get one hour
(4/3) * (3/4) buckets = (4/3) * (3/4) hours
1 bucket = 1 hour
1. A school held several events last month- a music concert, a basketball game, a drama play, and
literacy night. The music concert was attended by 250 people. How many people came to each of
the events? 250 people attended the events.
a. The attendance to the basketball game was 30% of attendance at the concert. 75 people
attended the basketball game.
b. Attendance at the drama play was 140% of attendance at the concert.
C. Attendance at the literacy night was 44% of the attendance at the concert.
Answers
70% of those who went to the music concert and the play also did so.
What is meant by percentage?A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a percentage. Divide the number by the total and multiply by 100 to find the percent of a given number. A portion per hundred is what the percentage denotes. Percentage refers to one in a hundred. The word "%" stands in for it.
In addition to being stated as a decimal or a fraction, a percentage is a number that indicates how many out of 100 it is. Three for the price of one! Simply enter the % as the numerator and 100 as the denominator to convert the percentage to a fraction.
We know that 350 people attended the drama play.
50% of 350 = (0.5) · 350 = 175 people attended both the drama play and music concert.
We know that 250 people attended the music concert.
The percentage of the people who attended the music concert even attended the drama play would be 175 ÷ 250 · 100% = 70%
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70% of those who went to the music concert and the play also did so.
Hence, the option A is correct.
What is meant by percentage?In mathematics, a value or ratio that can be expressed as a fraction of 100 is known as a percentage. In order to get the percentage of a given number, divide the number by the total and multiply by 100. The percentage is a chunk out of one hundred. One out of 100 is referred to as a percentage. The symbol for it is "%".
A % is a number that, in addition to being expressed as a decimal or a fraction, also specifies how many out of 100 it is. For the price of one, get three! To convert a percentage to a fraction, just enter the% as the numerator and 100 as the denominator.
We know that 350 people attended the drama play.
50% of 350 = (0.5) · 350 = 175 people attended both the drama play and music concert.
We know that 250 people attended the music concert.
The percentage of the people who attended the music concert even attended the drama play would be 175 ÷ 250 · 100% = 70%
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What will be the output of 7 by 2?
Answers
The resultant output of the given question is 7 by 2 is 14.
This is because 7 multiplied by 2 is equal to 14
When you multiply two numbers, the result is the product of the two numbers. In this case, 7 multiplied by 2 is equal to 14.
Mathematicians use the process of multiplication to calculate the product of two or more given numbers. It is a fundamental mathematical operation in maths that is frequently utilised in everyday life. When we need to combine groups of similar sizes or values , we utilise multiplication.
Hence the correct answer to the given question is 14 .
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if you Decrease £200 by 12.5% what do you get?
Answers
Answer:
175
Step-by-step explanation:
Find how much is left by multiplying 200 by 0.875, since this will give you the remaining 87.5%:
200(0.875)
= 175
So, the answer is 175.
Consider the line =−−8x6y1.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answers
Answer:
Below
Step-by-step explanation:
Well I can't really see the equation but I can tell you how to do it.
Parallel slopes are the same slope as the equation.
For example, y = mx + b
The slope of a line parallel to it is m
Perpendicular slopes are the opposite reciprocal as the equation.
For example, y = mx + b
The slope of a line perpendicular to it is[tex]-\frac{1}{m}[/tex]
Answer:
parallel: -8
perp: +1/8
Step-by-step explanation:
parallel lines have the same slopes
perp lines have opposite reciprocal slopes
Given that AB is a line segment and the angle
y
= 67°, work out the value of the angle marked
x
Answers
Answer:
x = 113°
Step-by-step explanation:
AB is a line segment and hence it is a straight line which means it is a straight angle, so it is 180° .
y = 67°
x = ?
So, x + y = AB
=> x + 67° = 180°
=> x = 180° - 67°
=> x = 113°
Therefore, x = 113°
Hope it helps :)
Given right triangle ABC with altitude BD drawn to hypotenuse
AC. If AC = 27 and DC = 3, what is the length of BC?
27
D
3
B
X
Answers
Answer:
x=9
Step-by-step explanation:
Answer: 9
Step-by-step explanation:
i got it right
2) The function f(t) - 5t2 + 200 + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?
Answers
Answer:
8 seconds
Step-by-step explanation:
if you graph the function, the difference between the zeros is 8
In a survey of 2000 people who owned a certain type of car, 1200 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answers
The percentage of people who are satisfied with the car are 60%.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".Given is that in a survey of 2000 people who owned a certain type of car, 1200 said they would buy that type of car again.
The percentage of people who are satisfied with the car are -
{x}% = (1200/2000) x 100
{x}% = (12/20) x 100
{x}% = 12 x 5
{x}% = 60
Therefore, the percentage of people who are satisfied with the car are 60%.
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Central Park in New York City is rectangular with a length of 2.5 miles and a width of 0.5 mile. During an afternoon, its population density is about 15 people per acre. Find the number of people in the park that afternoon. One acre is equal to 1640 square mile.
Answers
On solving the provided question, we can say that Surface Area of central park = 2.5 × 0.5 = 1.25 square mile
what is surface area ?An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).
Surface Area of central park = 2.5 × 0.5 = 1.25 square mile
1 acre = 1/640 square mile
1.25 square mile = 1.25 ÷ 1/640 = 800 acre
Number of people in the park = 800 ÷ 15 = 53.3 ≈ 53 people
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PLEASE HELP!!! WILL GIVES BRAINIEST!! PLEASE SHOW YOUR WORK!!
Answers
Explanation: 3% × y = 1.86 =>
y =
1.86 ÷ 3% =
1.86 ÷ (3 ÷ 100) =
(100 × 1.86) ÷ 3 =
186 ÷ 3 =
62
Please mark me brainiest
Answer:
0.0558
Step-by-step explanation:
3% is out of hundred so we multiply
3%×1.86=0.0558
Checking:
0.0558÷1.86=0.03
0.03=3%
What is the 2 step rule in math?
Answers
The Two steps equation in mathematics are the equations that can be solved within exactly two steps.
What is a Two Step Equation ?
The Two Step Equation are the algebraic problems that just take two steps to solve. It is a linear equation in one variable.
When solving the two step equation, we have to perform operation on both sides of the equation .
For Example : Solve [tex]2x+6=12[/tex] ;
Step1 : we Subtract -6 from both sides to isolate variable x.
⇒ [tex]2x + 6 - 6 = 12 - 6[/tex]
⇒ [tex]2x = 6[/tex]
Step2 : We Divide both the sides of equation by 2 and solve for x.
⇒ [tex]\frac{2x}{2} =\frac{6}{2}[/tex]
⇒ [tex]x = 3[/tex] ;
Therefore , the equation is solved in two steps .
The given question is incomplete , the complete question is
What is the two step equation in math ?
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The graph of a proportional relationship contains the point (-12, 3)
What is the corresponding equation?
Enter your answer as a fraction in simplest form by filling In the boxes.
y= __/__ x
Answers
The corresponding equation of the proportional relationship will be;
⇒ y = - 1/4x
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The graph of a proportional relationship contains the point (-12, 3).
Now,
Let the equation of the proportion is,
⇒ y = kx
Where, 'k' is constant of proportion.
Since, The graph of a proportional relationship contains the point (-12, 3).
Hence, Substitute x = 0 12 and y = 3 in above equation we get;
⇒ 3 = k × - 12
⇒ 3 / (-12) = k
⇒ k = - 1/4
Thus, The equation of the proportion is,
⇒ y = - 1/4x
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6(u+3) Use the distributive property to remove the parentheses 6(u+3
Answers
Answer:
6u+18
Step-by-step explanation:
6*u=6u and 6*3=18
solve -2 ( x+2)=-12 help me plsssssssssssssssss
Answers
Answer:
x = 4
Step-by-step explanation:
-2 ( x+2)=-12
-2x - 4 = -12
-2x = -8
x = 4
Kendra is choosing bouquets of flowers for table centerpieces. She decides to buy 40 bouquets for $120 because she thinks that price is a better value than 40 bouquets for $2.50 each. Explain Kendra’s error.
Which statement is correct?
Which statement is correct?
Answers
Answer:
To find the unit cost of her choice, divide $120 by 40 to get $3.00 per bouquet. This unit cost is more than the other deal.
Step-by-step explanation:
Is the following graph proportional or non proportional?
PLS HELP:((
Answers
Answer:
Proportional
Step-by-step explanation:
Proportional, because the graph goes through (0, 0). If the line crossed the y-axis elsewhere, the function would NOT be proportional.
6 = x +2y solve for y
Answers
PLEASE HELP I HAVE NO CLUE WHAT IM DOING. Parents finna ground me if I don't do this tonight.
Answers
Answer:
First find x and y at given parameters:
x = (v₀cosθ)t = (123 cos60°)t = 61.5ty = h + (v₀sinθ)t - 16t² = 0 + (123 sin 60°)t - 16t² = 106.52t - 16t²Maximum height is at vertex. Time is:
t = -106.52/-32 = 3.3 secondsMaximum height is:
y = 106.52*3.3 - 16(3.3)² = 177.3 ftHorizontal distance:
x = 61.5*3.3 = 203 feetTime to hit the ground:
106.52t - 16t² = 016t = 106.52 (t = 0 is discounted)t = 106.52/16t = 6.7 seconds