A boat travels 8 miles north from point A to point B. Then it moves in the direction S 40°W and reaches point Finally, it turns S 40°E and returns to point A
The total distance covered by the boat is______miles
A. 14.95
B. 18.44
C. 20.04
D. 25.88
Answers
Answer:
B.18. 44 miles
Step-by-step explanation:
We are given that
Distance between A and B=8 miles
Angle B=Angle BCQ=40 degree (Alternate interior angles)
Angle ACB=180-Angle ACP-Angle BCQ
Angle ACB=180-40-40=100 degree
In triangle ABC
Angle A+ Angle B +Angle C=180 degree using sum of angles of triangle property
Substitute the values
[tex]\angle A+40+100=180[/tex]
[tex]\angle A+140=180[/tex]
[tex]\angle A=180-140[/tex]
[tex]\angle A=40[/tex] degree
Angle A=Angle B
When two angles are equal of a triangle then the triangle is isosceles triangle.
Therefore, triangle ABC is an isosceles triangle.
[tex]\implies BC=AC [/tex]
Now, Sine law
[tex]\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}[/tex]
Using the sine law
[tex]\frac{BC}{sin 40}=\frac{AB}{sin 100}[/tex]
[tex]\frac{BC}{sin 40}=\frac{8}{sin 100}[/tex]
[tex]BC=\frac{8\times sin40}{sin 100}[/tex]
BC=5.22
AC=BC=5.22 miles
Now, total distance covered by the boat=AB+BC+AC
Total distance covered by the boat=8+5.22+5.22=18.44 miles
Hence, option B is correct.
Related Questions
. A ride at a county fair spins in a circle of radius (in meters). The centripetal force experienced by one of the passengers on the ride is modeled by the equation below, where is the number of seconds the ride takes to complete one revolution and is the mass (in kilograms) of the passenger. Tom, whose mass is kilograms is on a ride that is spinning in a circle at a rate of seconds per revolution. The radius of the circle is meters. Letting , how much centripetal force does Tom experience
Answers
Answer:
150 Newtons
Step-by-step explanation:
Given
[tex]t = \sqrt{\frac{4\pi^2mr}{F}}[/tex]
[tex]t = 12[/tex]
[tex]r =6.5[/tex]
[tex]\pi = 3.14[/tex]
[tex]m = 84.4[/tex]
See attachment
Required
Find F
We have:
[tex]t = \sqrt{\frac{4\pi^2mr}{F}}[/tex]
Square both sides
[tex]t^2 = \frac{4\pi^2mr}{F}[/tex]
Multiply both sides by F
[tex]Ft^2 = 4\pi^2mr[/tex]
Divide both sides by [tex]t^2[/tex]
[tex]F = \frac{4\pi^2mr}{t^2}[/tex]
Substitute known values
[tex]F = \frac{4*3.14^2*84.4*6.5}{12^2}[/tex]
[tex]F = \frac{21635.90624}{144}[/tex]
[tex]F = 150.249348889[/tex]
[tex]F = 150N[/tex]
solve similar triangles (advanced)
solve for x
Answers
Answer:
27/2 =x
Step-by-step explanation:
We can write a ratio to solve
3 2
----- = ---------
3+x 11
Using cross products
3*11 = 2(3+x)
33 = 6+2x
Subtract 6 from each side
33-6 = 6+2x-6
27 = 2x
27/2 = 2x/2
27/2 =x
Will give brainliest answer
Answers
Answer:
Step-by-step explanation:
A(1) is the amount after 1 decade.
A(0.1) is the amount after 1 year.
Every year, the amount of CO₂ increases by a factor of 1.06^(0.1) ≅ 1.0058
PLEASE HELP ILL GIVE BRAINLIEST !!!!
Answers
Answer:
y=3x-2
Step-by-step explanation:
The slope of the equation is (-2-(-5))/(0-(-1))=3. The y intercept is - 2. So y=3x-2
A number increased by a% and decreased by 80% is 400. What is the number?
Answers
Answer:
[tex]x = \frac{2000 }{(\frac{a+100}{100})}[/tex]
updated response , given that you confirmed the question....
if the percent is the variable a% then ....
[tex]x*(\frac{a+100}{100}) = 2000[/tex]
[tex]x = \frac{2000 }{(\frac{a+100}{100})}[/tex]
I think that there is missing information here ....
you can make any number work here the result of the number being increased by the percent has to be 2000...
so if if the number is 1000 then the percent would be 100%
if you make the number 1500 then the percent would be 33 1/3 %
Step-by-step explanation:
The number is [tex]\frac{2000}{(1+\frac{a}{100})}[/tex]
What will be the new number when the original number is increased by a% and decreased by 80%?Let us assume that the number be x.
When the number x is increased by a% the new number will be,
[tex]x(1+\frac{a}{100})[/tex]
Now, this number is decreased by 80%. So, the new number will be,
[tex]x(1+\frac{a}{100})*(1-\frac{80}{100} )\\=x(1+\frac{a}{100})*(1-0.8 )\\=x(1+\frac{a}{100})*0.20[/tex]
By the given condition,
When x increased by a% and decreased by 80% it becomes 400
Therefore, we can write
[tex]x(1+\frac{a}{100})*0.20=400[/tex]
[tex]x(1+\frac{a}{100})=\frac{400}{0.20}[/tex]
[tex]x(1+\frac{a}{100})=2000[/tex]
[tex]x=\frac{2000}{(1+\frac{a}{100})}[/tex]
So, the number will be [tex]\frac{2000}{(1+\frac{a}{100})}[/tex].
Learn more about the percentage change of a number please follow: https://brainly.com/question/26527346
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james invested some money at 13% interest. James also invested $199 more than 3 times that amount at 12%. How much is invested at each rate if James receives $1561.50 in interest after one year? (Round to two decimal places if necessary.)
Answers
9514 1404 393
Answer:
$3138 at 13%9613 at 12%Step-by-step explanation:
Let x represent the amount invested at 13%. Then (3x+199) is the amount invested at 12%. The total interest earned in 1 year is ...
(13%)(x) +(12%)(3x+199) = 1561.50
0.49x +23.88 = 1561.50 . . . . simplify
0.49x = 1537.62 . . . . . . . . . . subtract 23.88
x = 3138 . . . . . . . . . . . . . . . . divide by 0.49
3x+199 = 9613
$3138 was invested at 13%; $9613 was invested at 12%.
Determine the dimension of the vector space. M4,2
STEP 1: Determine the number of linearly independent vectors needed to span M4,2. The basis for M4,2 has linearly independent vectors.
STEP 2: Using the result from Step 1, determine the dimension of M4,2.
Answers
Answer:
STEP 1
M_{4,2} is set of 4x2 matrices hence each matrix has 4*2=8 entries. Each entry can be filled independently.
Hence its basis has 8 linearly independent vectors.
STEP 2
Dimension= cardinality of basis = 8.
10-d=34-5d[tex]10-d=34-5d[/tex]
Answers
Answer:
d = 6
Step-by-step explanation:
10 - d = 34 - 5d
add d to both sides to make all the d's on one side
10 = 34 - 4d
subtract 34 from both sides to isolate the d and its coefficient
-24 = -4d
divide both sides by -4 to isolate d
d = 6
A survey showed that, in one city, 20.7% of the population used
product X, 50% use product Y and among users Y, 36.5% use X. Randomized interview
However, a resident in that city, calculate the probability that that person
a) Use both X and Y;
b) Neither X nor Y
Answers
Answer:
Step-by-step explanation:
a) 0.5*0.365=18.25%
b) (100%-20,7%-50%)=29.3
What is the area of my lawn if it measures 4m x 4.5m
Answers
Answer:
18m squared
Step-by-step explanation:
4m x 4.5m = ?
find the first quartile form the following data 73,58,39,46,61,52,32
Answers
Answer:
----------------------------
quartile first = 73
----------------------------
Find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it. Use 3.14 as an
approximation for
90 m
40
2,794 square meters
1,256 square meters
974 square meters
O 6,844 square meters
Answers
The approximate area of the shaded region is 2794 m². The correct option is the first option 2794 square meters
From the question, we are to determine the approximate area of the shaded region
The area of the shaded region = Area of the triangle - Area of the circle
Area of triangle = 1/2 × base × height
Area of the triangle = 1/2 × 90 × 90
Area of the triangle = 4050 m²
Area of a circle = πr²
Where r is the radius
In the diagram,
Diameter = 40 m
∴ Radius = 40/2 = 20 m
Thus,
Area of the circle = π × 20²
Area of the circle = 3.14 × 400
Area of the circle = 1256 m²
Therefore,
The area of the shaded region = 4050 m² - 1256 m²
The area of the shaded region = 2794 m²
Hence,
The darkened area covers about 2794 m²
Learn more on Calculating area here: https://brainly.com/question/14989383
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In a certain year Congress debated a bill. A poll of 1000 Americans indicated 401 opposed 293 favored 306 not sure. What is the probability that random person was in favor
Answers
401 + 239 + 306 = 1000
Now 293 from the 1000 is favored,
So in pregnant is 293/1000 = 0.293
That’s also the probability to random person is favor (or 29.3% chance)
in the box of Stones ,the ratio of red marbles is 2:5. the ratio of green stones to the total stones is 3:10 .if the stones that are neither red nor green are blue ,how many blue are in the box.if there are 40 marbles in the box?.
Answers
Do this please helpppp
Answers
Answer:
y = [tex]\frac{20}{9}[/tex]
Step-by-step explanation:
Since the figures are similar then the corresponding sides are in proportion, that is
[tex]\frac{JH}{PQ}[/tex] = [tex]\frac{FM}{ST}[/tex] , substitute values
[tex]\frac{6}{4}[/tex] = [tex]\frac{7}{3y-2}[/tex] ( cross- multiply )
6(3y - 2) = 28
18y - 12 = 28 ( add 12 to both sides )
18y = 40 ( divide both sides by 18 )
y = [tex]\frac{40}{18}[/tex] = [tex]\frac{20}{9}[/tex]
Answer:
20/9
Step-by-step explanation:
since the 2 are similar,
JH/PQ = FM/ST
6/4 = 7/(3y-2)
6(3y-2) = 7*4
18y-12=28
18y = 40
y = 40/18 = 20/9 = 2 2/9
What will be the reciprocal of 4/9 × 45/36
Answers
Answer:
[tex]\frac{9}{5}[/tex]
Step-by-step explanation:
[tex]\frac{4}{9}[/tex] × [tex]\frac{45}{36}[/tex]
= [tex]\frac{4}{9}[/tex] × [tex]\frac{5}{4}[/tex] ( cancel 4 on numerator/ denominator )
[tex]\frac{5}{9}[/tex]
Given a number n then its reciprocal is [tex]\frac{1}{n}[/tex]
Then the reciprocal of [tex]\frac{5}{9}[/tex] is
[tex]\frac{1}{\frac{5}{9} }[/tex] = [tex]\frac{9}{5}[/tex]
Reciprocal of 5/9 is 9/5
Fifty three million, eight hundred thousand and thirteen
Answers
Answer:
53,800,013
need brainliest!!!
An unknown number becomes 30 when rounded to the nearest ten. Which could NOT be the unknown number?
A. 24
B. 25
C. 28
D. 31
Answers
Answer:
A. 24
Step-by-step explanation:
Five and above rounds up
so 25,26,27,28,29 rounds up to 30
We leave it alone when 4 or less
34,33,32,31,30 remains at 30
24 would not round to 30
If the sum of two numbers is 4 and the sum of their squares minus three times their product is 76, find the numbers.
Answers
I'll be referring to each of these numbers as x and y.
x + y = 4
(x^2) + (y^2) - 3(x)(y) = 76
x = 4 - y
(4 - y)^2 + (y^2) - 3(4 - y)(y) = 76
(4 - y)(4 - y) + y^2 - (3y)(4 - y) = 76
16 - 4y - 4y + y^2 + y^2 - 12y + 3y^2 = 76
16 - 20y + 5y^2 = 76
5y^2 - 20y - 60 = 0
y^2 - 4y - 12y = 0
(y - 6)(y + 2) = 0
y = 6 or -2
x = 4 - 6 = -2
x = 4 - - 2 = 6
As you can see, we got the same numbers for both x and y, -2 and 6. Therefore, the two numbers are -2 and 6. But, we can check our work to ensure that the answer is correct.
x = -2
y = 6
6 - 2 = 4
4 = 4
(-2)^2 + (6^2) - 3(-2)(6) = 76
4 + 36 - 3(-12) = 76
40 + 36 = 76
76 = 76
Hope this helps!
Answer:
X and y = -2 or 6
Step-by-step explanation:
A hot air balloon descends 200 feet per
minute from an altitude of 1000 feet. Write a expression
Answers
y=90x+2,000
Step-by-step explanation:
90 is the rate of change because the hot air balloon descends 90 feet per minute.
And 2,000 is the starting point because the hot air balloon started the descent at 2,000 feet.
HEYYYYYYYYYYYYYYY
PLEASE HELP AND BE CORRECT ANSWER AT THE BOTTOM
TELL ME WHERE TO PUT THE POINTS
Answers
Answer:
y = -3 (you have to draw an horizontal line that passes for the point (0,-3)
Step-by-step explanation:
We have to find the middle points of the segments that unite the corrispettive points.
We are lucky because the images of the points have the same x coordinate of the original ones, so we have just to find the y coordinates.
Segment CC‘
(y1 + y2)/2 = (-1-5)/2 = -3
Segment AA’
(0-6)/2 = -3
Segmet BB’
(1-7)/2 = -3
Segment DD’
(1-7)/2 = -3
In conclusion we can say that the points of the reflection have all the y coordinate equal to -3.
the line is horizontal and its equation is : y = -3
The probability of A is 7/20, the probability of A intersection B is 49/400 what is the probability of B?
Answers
Answer:
n(A)+n(B)-49/400=n(AUB)
n(B)=1-7/20+49/400
n(B)=(400+49-140)/400
n(B)=309/400
Plz help I need this last question
Answers
Step-by-step explanation:
[tex]v = \frac{\pi r {}^{2}h }{3} [/tex]
[tex]3v = \pi {r}^{2} h[/tex]
[tex] \frac{3v}{\pi h} = {r}^{2} [/tex]
[tex] \sqrt{ \frac{3v}{\pi h} } = r[/tex]
How far from "0 is the green rectangle?
Answers
3 1/2
Step-by-step explanation:
Rectangle is located at 3 but 2/4 between 3 & 4.
Simplify 2/4
1/2
The polynomial P is graphed.
5+
P
4+
3
→
-3
-2
-1
1
-2+
-3+
-4-
What is the remainder when P(x) is divided by (x + 2)?
Answers
Answer:
-4
Step-by-step explanation:
The remainder when P(x) is divided by (x + 2) is P(-2) which is - 4
1
What is the perimeter of a rectangle
whose length is 5 feet and whose width
is 3.5 feet?
O 8.5 ft.
O 16.5 ft.
O 17 ft.
O 17.5 ft.
Answers
Answer:
17ft
Step-by-step explanation:
5*2 + 3.5*2=17
Explanation
Perimeter of rectangle = 2(l+b)
As length = 5 ft and breadth/width = 3.5 ft
So,
=2 ( 5+3.5)
=2 ( 8.5 )
= 17 feet
I hope it helps!
pls mark me brainliest :)
find the surface area of the prism
Answers
Answer:
Base area=5*12=60
Height is 4
Perimeter or the base is 2*(12+5)=34
Surface area is 2B+Ph=120+136=256
40pts and a brainliest to the person who can help me with this stock problem. PLEASE show all steps in detail so I can learn how to do this!
What is the rate of return when 20 shares of Stock A, purchased for $30/share, are sold for $710? The commission on the sale is $6. Give your answer as a percent rounded to the nearest tenth.
Answers
Answer:
Rate of Return is 14.8%
Step-by-step explanation:
We know that 20 shares of Stock are purchased for $30 per share.
This gives us a total value of: 20 × 30 = $600.
Now, the shares are sold for $710 with a commission sale of $6. This means the final money going to the seller is; 710 – 6 = $704.
Thus, the rate of return percentage is = (704 – 600)/704) × 100% = 14.7727%
To the nearest tenth gives us 14.8%
find the missing side. round your answer to the nearest tenth. PLEASE HURRY!
Answers
Answer:
44.8
Step-by-step explanation:
Using the Cosine formula, we first have Cos 48 = 30/x. So then we just solve for x and get 44.8342965, which rounds to 44.8
I hope this helped! :D
Richland's Real GDP per person is #10b and poorland's Real GDP per person is #5b. However, Richland's Real GDP per person is growing at 1% per year and poorland's Real GDP per person is growing at 3% per year. Compare real GDP per person in the two countries after ten years and after twenty years. Approximately how many years will it take poorland to catch up with Richland?
Answers
Answer:
after 5 years, rich : poor = 11.0 : 6.7after 10 years, 12.2 : 9.035.3 yearsStep-by-step explanation:
It is convenient to let a graphing calculator show the answers to these questions.
The exponential equation modelling the growth will be of the form ...
f(x) = (initial value) × (1 +growth rate)^x
Richland's GDP/person can be modeled by r(x) = 10·1.01^x
Poorland's GCP/person can be modeled by p(x) = 5·1.03^x
The attached graph shows values for x=5, 10 and r(x)=p(x).
It will take about 35.3 years for Poorland to catch up.
