In an orienteering competition, Jada walks 70 degrees north of west for 200 meters. She then walks due east for 90 meters. How far and at what bearing is Jada from her starting point?
Answers
c²=a²+b²-2abCos C
a=200, b=90, C=70°
thus plugging in our values we get:
c²=200²+90²-2×200×90×cos70
c²=40000+8100-36000(0.3420)
c²=35788
hence
c=189.1772 m'
therefore the distance Jada is from the starting point is 189.1772 m
Answer:
N55.0679°W
Step-by-step explanation:
Check the attachment for detailed explanation.
Related Questions
Please help:
In a right triangle ABC, tan(A) = 3/4. Find sin(A) and cos(A).
In a right triangle ABC with angle A equal to 90 degrees, find angle B and C so that sin(B) = cos(B).
Answers
To make sine and cos equal the opposite and adjacent sides must be equal. By corresponding angles it is isosceles so b and c must be 45
solve for y. triangle PQR is congruent to triangle DEF, PQ= 15, QR= 10, RP=8, and EF = 6y +4
Answers
looking at the order of the letters in the triangles EF are the last 2 and QR are the last 2
so EF should equal QR
we are told QR = 10 so EF needs to equal 10
so we have 6y+4 = 10
now solve for Y
6y +4 = 10
subtract 4 from each side:
6y = 6
divide each side by 6
y = 1
Circle 1 is center at (-4,5) and has a radius of 2 centimeters. Circle 2 is centered at (2,1) and has a radius of 6 centimeters. What transformations can be applied to Circle 1 to prove the circles are similar?
Answers
1) Draw a vector from point A to B
2)Dilate circle A to circle B. It means translating mapping circle A to circle B.
3)By this way, we can claim that circles A and B are similar.
And the similarity ratio is [tex] \frac{ r_{2} }{ r_{1} } = \frac{6}{2} =3[/tex]
16. Supposes that y varies inversely with x and that y-10 whenx-7. Which of the following equations models this relationship?
A. Y=70x
B. Y=-10x
C. Y=x/70
D. Y=70/x
Answers
Hope that helped!;)
The equation that models this relation is y = 70/x. So, option (D) is the correct answer.
What is constant of proportionality?The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant.
For the given situation,
The values are y = 10 and x = 7
y varies inversely with x.
⇒ [tex]y[/tex] ∝ [tex]\frac{1}{x}[/tex]
To remove proportionality we introduce a constant 'k'.
⇒ [tex]y=\frac{k}{x}[/tex]
Substitute the values of x and y,
⇒ [tex]10=\frac{k}{7}[/tex]
⇒ [tex]k=70[/tex]
Now substitute the value of k = 70 in y,
⇒ [tex]y = \frac{70}{x}[/tex]
Hence we can conclude that the equation that models this relation is y = 70/x. So, option (D) is the correct answer.
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If I’m 17 1/2 do I still have to wait a year to get my provisional license after I get my permit in Florida
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PLEASE HELP ME!!!! Thank you
Answers
a store is selling uniform shirts for 18.95 each. if samuel has a coupon for 1/4 off the price, how much would he pay for the shirt, excluding tax??
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jane's salary is increased by 2% to £39474. how much is her salary before the rise?
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x + 0.02x = 39474
1.02x = 39474
x = 39474 / 1.02 = £38,700 answer
A large truck and a small car have a head-on collision. Which scenario is true?
A) The truck has the greater acceleration because it has the greater mass
B) The car has the greater acceleration because it has the smaller mass
C) Both the truck and car have the same magnitude of acceleration
(Edit: This was meant to go in the Physics section, I'm so sorry about this, if anyone here could still answer that's be amazing)
Answers
In a collision, both the car and truck experience the same force due to Newton's Third Law. However, due to Newton's Second Law, the car, with its smaller mass, experiences a greater acceleration.
Explanation:According to Newton's Third Law of Motion, 'for every action, there is an equal and opposite reaction', both the truck and the car would experience the same magnitude of force. However, let's recall Newton's Second Law, 'force equals mass times acceleration' (F=ma). Using these physics principles, we can deduce that the car with the smaller mass would experience a greater acceleration, and the large truck would experience a lesser acceleration. This is because when the same force is applied to both objects, an object with a smaller mass will have a greater acceleration compared to an object with a larger mass. Hence, option B) 'The car has the greater acceleration because it has the smaller mass' would be the correct answer based on Newton's laws of motion.
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You have a bag of chocolate candy. Ten of them are red, 7 are brown, 12 are green, and 9 are blue. What is the probability that you pick a red candy, given that you have already picked a red candy and have not replaced it?
Answers
9/37 is the correct answer.
A cone and a cylinder have the same base and height, as shown below.
(please see attached picture)
The volume of the cylinder is 84(3.14) in^2 What can be concluded about the volume of the cone? Check all that apply.
The volume of the cone is 1/3 the volume of the cylinder.
The volume of the cylinder is 2 times the volume of the cone.
The volume of the cone is less than the volume of the cylinder.
The expression 84(3.14)/3 finds the volume of the cone.
The expression 84 (3.14)/2 finds the volume of the cone.
Answers
Answer with Step-by-step explanation:
We know that volume of a cylinder with radius r and height h is:
πr²h
and volume of cone with radius r and height h is:
πr²h/3
Volume of cone=Volume of cylinder/3 < Volume of cylinder
Volume of cylinder=84π in² where π=3.14
Volume of cone=84π/3 in²
= 84(3.14)/3 in²
Hence, correct options are:
The volume of the cone is 1/3 the volume of the cylinder.
The volume of the cone is less than the volume of the cylinder.
The expression 84(3.14)/3 finds the volume of the cone.
the answer is: A, C, and D
The sales tax in the city of Taxemalot is 8.1%. What is the growth factor for any item purchased at your local Tarmart? a.8.1 c.1.081 b.0.81 d.81
Answers
Two mechanics worked on a car. the first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. together they charged a total of $1775 . what was the rate charged per hour by each mechanic if the sum of the two rates was $100 per hour?
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x = amount of $ / hr that the mechanic obtains 1.
y = amount of $ / hr obtained by mechanic 2.
We write the system of equations:
x + y = 100
20x + 15y = 1775
Solving the system of equations we have:
x = 55 $ / hr
y = 45 $ / hr
Answer:
the rate charged per hour by each mechanic was:
x = 55 $ / hr
y = 45 $ / hr
Calculate the area of the shaded sector in square inches.
Answers
The larger square has area of 400 square inches. the areas of the two squares have a ratio of 1:4. what is the side lengh of the smaller square?
Answers
A= s²
(400)1/4 = area of the smaller square.
100=s²
10²=s²
s= 10, so the smaller side is 10 inches.
Final answer:
To find the side length of the smaller square, we take the square root of the larger square's area (400 sq inches) to get 20 inches, then halve it to align with the 1:2 scale factor of the sides for a correct length of 10 inches.
Explanation:
To solve this problem, we first acknowledge that the ratio of the areas of the two squares is 1:4. Since area is a function of the side length squared, we look for a scale factor of the side length that when squared will give us this ratio. In this case, the scale factor is 1:2, meaning the side length of the smaller square is half that of the larger square.
The area of the larger square is given as 400 square inches. To find the side length, we take the square root of the area, which is 20 inches. Therefore, the side length of the smaller square is half of this, which is 10 inches. However, given that the statement seems to expect an 8-inch side for the larger square, there might be a misunderstanding in the problem, assuming that area scales directly with side length rather than its square. Nonetheless, based on area and scale factor, the correct side length is 10 inches.
Subtract 8 + 7i from 4 − 16i. -4 − 23i 4 − 23i 4 + 9i 4 − 11i
Answers
Answer:
-4-23i
Step-by-step explanation:
Above answer didn't quite understand what the question was asking. It's asking to SUBTRACT 8+7i from 4-16i. So it would be written like this:
(4-16i) - (8+7i).
Simplify it from there and you'd get -4-23i
To subtract 8 + 7i from 4 - 16i, subtract the real parts and the imaginary parts separately, resulting in -4 - 23i.
Explanation:To subtract 8 + 7i from 4 − 16i, you treat the real and imaginary parts separately.
Subtract the real parts: 4 − 8 = −4.
Subtract the imaginary parts: (−16i) − (7i) = −16i − 7i = −23i.
Combine the results to get the final answer: −4 − 23i.
Therefore, subtracting 8 + 7i from 4 − 16i gives −4 − 23i.
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Zack borrowed $1,087 for 12 months at 11 percent interest. If he must pay 11.00 per $100, what is Zack's monthly payment?
Answers
[tex] \frac{1087}{100} =10.87[/tex]
Now we know that he must pay $11.00 10.87 times each month, so the last thing we are going to do to find his monthly payment is multiply both quantities:
[tex]11.00*10.87=119.57[/tex]
We can conclude that Zack's monthly payment is $119.57
How do you simplify x^2+y^2?
Answers
You may think this is a trivial response, but it is a good one. It teaches you not to destroy plus signs by combining unlike terms. You should treat this as a "can you combine apples and oranges" problem.
In other words, is there any similarity between apples and oranges other than both are fruits? You should answer no there is no similarity.
Same with xs and ys. There is no similarity. until you are told there is.
Answer<<<<< nothing can be done.
A waitress works 1.75 hours less in the afternoon than in the evening. If she works 5 1/8
hours in the afternoon, how many hours does she work in the evening?
Answers
We know for our problem that she works [tex]5 \frac{1}{8} [/tex] in the afternoon and that she works 1.75 hours less in the afternoon than in the evening, so:
[tex]x=5 \frac{1}{8} -1.75[/tex]
Since [tex] \frac{1}{8} =0.125[/tex], we can rewrite our expression:
[tex]x=5.125-1.75[/tex]
[tex]x=3.375[/tex]
We can conclude that she works 3.375 hours in the evening, or expressed as a mixed fraction: [tex]3 \frac{3}{8} [/tex] hours.
Answer: The waitress works:[tex]\[{6 \frac{7}{8}}[/tex] hours in the evening
Let us denote the number of hours the waitress works in the evening as E and the number of hours she works in the afternoon as A.
Given that:
[tex]\[A = 5 \frac{1}{8} \text{ hours}\][/tex]
We can convert the mixed number to an improper fraction:
[tex]\[5 \frac{1}{8} = 5 + \frac{1}{8} = \frac{40}{8} + \frac{1}{8} = \frac{41}{8}\][/tex]
So, [tex]\( A = \frac{41}{8} \)[/tex] hours.
The waitress works 1.75 hours less in the afternoon than in the evening. Thus, we have:
[tex]\[A = E - 1.75\][/tex]
[tex]\[\frac{41}{8} = E - 1.75\][/tex]
Converting 1.75 to a fraction:
[tex]\[1.75 = \frac{7}{4} = \frac{14}{8}\][/tex]
Now, the equation becomes:
[tex]\[\frac{41}{8} = E - \frac{14}{8}\][/tex]
[tex]\[E = \frac{41}{8} + \frac{14}{8}\]\[E = \frac{41 + 14}{8} = \frac{55}{8}\][/tex]
Convert the improper fraction back to a mixed number:
[tex]\[\frac{55}{8} = 6 \frac{7}{8}\][/tex]
Therefore, the waitress works:
[tex]\[{6 \frac{7}{8}}[/tex] hours in the evening
The perimeter of a rectangular garden is 100 feet (ft). the area of the rectangular garden area is 600 ft2. find the length and width of the garden. let the length of the garden be the shorter side, of necessary.
Answers
Area=x*y=600
thus
x=600/y
Perimeter=2(L+W)
100=2(x+y)
substituting the value of x we obtain:
100=2(600/y+y)
solving for y we shall have:
50=600/y+y
50y=600+y^2
thus
y^2-50y+600=0
solving the quadratic we obtain:
y=20 or y=30
thus the length=30 ft and the width=20 ft
The length of the garden is 20 feet and the width is 30 feet.
To solve this problem, we will use the formulas for the perimeter and area of a rectangle. The perimeter (P) of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. The area (A) of a rectangle is given by the formula A = lw.
Given the perimeter of the garden is 100 feet, we can set up the following equation:
[tex]\[ 2(l + w) = 100 \][/tex]
[tex]\[ l + w = 50 \][/tex]
[tex]\[ w = 50 - l \][/tex]
This equation relates the length and width of the garden.
Next, we are given that the area of the garden is 600 square feet:
[tex]\[ lw = 600 \][/tex]
Substituting the expression for w from the first equation into the area equation, we get:
[tex]\[ l(50 - l) = 600 \][/tex]
[tex]\[ 50l - l^2 = 600 \][/tex]
Rearranging the terms, we have a quadratic equation:
[tex]\[ l^2 - 50l + 600 = 0 \][/tex]
To solve this quadratic equation, we can factor it:
[tex]\[ (l - 20)(l - 30) = 0 \][/tex]
This gives us two possible solutions for the length: l = 20 feet or l = 30 feet.
Since we are asked to let the length be the shorter side, if necessary, we choose the smaller value for the length:
[tex]\[ l = 20 \text{ feet} \][/tex]
Now we can find the width by substituting the length back into the equation for the perimeter:
[tex]\[ w = 50 - l \][/tex]
[tex]\[ w = 50 - 20 \][/tex]
[tex]\[ w = 30 \text{ feet} \][/tex]
Therefore, the length of the garden is 20 feet and the width is 30 feet.
The number of tropical fish that an aquarium can hold depends on the volume of the fish tank. the interior dimensions of the fish tank are 25 cm, 30 cm, and 39 cm. each fish requires 10,000 cubic centimeters of water. how many tropical fish will this fish tank hold?
Answers
A summer camp manager wants to order 500 bag lunches for a field trip. Each lunch will have a piece of fruit. The manager is deciding on ordering apples, oranges, bananas, or plums. The camp manager surveys 50 random campers, and the results are given in this table.
Based on the results, which fruit should the manager order?
A- Apples
B- Oranges
C- Plums
D- Bananas
Answers
If I get 3 problems wrong on a 12 question math paper, what grade would I get?
Answers
If you got 3 questions wrong on a 12 problem math paper, to figure out how many you got right you must subtract the number you got incorrect (3) from the total number (12).
12-3=9
To figure out your grade, you have to divide how many you got correct (9-see above) by the total number of questions (12).
9/12 = 0.75
If you multiply this decimal by 100, you get the equivalent percentage of 75%.
Therefore, you would have gotten a 75% on the paper.
Hope this helps!
Doug can paint the living room in 4 hours. it would take elaine 6 hours to paint the same room. how long would it take doug and elaine, working together, to paint the living room?
Answers
You can get this by setting up the equation:
x/4 + x/6 = 1
Where x is equal to the amount of hours spent working. In this equation x/4 would be Doug. In 4 hours he would paint on room. x/6 would be Elaine. When you add them together using common denominators, you can find x.
Phillip watched a beach volleyball game from 1:45pm to 2:00pm.how many degrees did the minutes hand turn?
Answers
We have then:
2:00 - 1:45 = 15 minutes
Then, the amount of degrees is given by:
(15/60) * (360) = 90 degrees
Answer:
the minutes hand did turn about:
90 degrees
Answer:
90 degrees
Step-by-step explanation:
8 MIN LEFT anyone know this?
Answers
Chris took a vacation trip to maine, where sales tax on taxable items is 5%. in maine, prepared food and lodging are taxed an additional 2%, for a total of 7% tax, while auto rentals are taxed an additional 5%, for a total of 10% tax.chris bought $70 worth of souvenirs, taxable at the general rate. he also spent $580 on prepared food and lodging and $620 for a rental car, all before tax. how much did he spend in total after tax was included?
a.$1333.50
b.$1316.10
c.$1270.00
d.$1376.10
Answers
$70 of souvenirs mean the tax is 5% since it is not prepared food, lodging, or auto rentals.
$580 on prepared food means that has 7% tax because it is special.
$620 on the car has a 10% tax, as stated in the problem.
So do 70(1.05)+580(1.07)+620(1.1) to get $1376.1.0
For anyone with the “TRICIA” problem: $1202.30
if you enjoy math and science, the career cluster that might be best for you is
Answers
Information Technology and Engineering
Step-by-step explanation:Mathematics is also a branch of Science. A person who is good in mathematics can take the analytical view of anything and convert ideas into practical form by using mathematical models. There are a lot of applications that can be used for converting analog models into digital models by using mathematics. So all of these models require mathematical backgrounds and engineers are the people who bring ideas to reality. The same is applied on IT field too.
Use the following information to answer the next two questions
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y=abˣ
where:
a=initial value
b=growth factor
y=number of years
thus using point (1,63) and (2,226)
the growth factor will be:
b=(226/63)=3.587~3.6
a=63
thus the formula for the function will be:
A(y)=a(3.6)^y
substituting (1,63) in the equation and solving for a.
63=a(3.6)^1
thus
a=63/3.6=17.5
hence the formula will be:
A(y)=17.82(3.6)^y
Answer: D] 17.5(3.6)^y
2] The number of acres defoliated after 5 years will be as follows:
y=5 years
A(y)=17.82(3.6)^y
plugging in the value we get:
A(y)=17.82(3.6)^5
simplifying the above
A(y)=10775.07
A(y)=10775
Answer: D
An in-ground pond has the shape of a rectangular prism. The pond has a depth of 24 inches and a volume of 72,000 cubic inches. The length of the pond is two times its width. Find the length and width of the pond to the nearest tenth.
Answers
The length of the pond is 77.4 inches, and the width of the pond is 38.7 inches.
What is the rectangular prism?In geometry, a rectangular prism can be defined as a 3-dimensional solid shape that has six faces that are rectangles. A rectangular prism is also a cuboid.
Let,a be the length of the pond and b be the width of the pond.
The volume of the pond is;
[tex]\rm Volume \ of \ the \ pond= Area\ of\ the\ base\times deep\\\\Area\ of\ the\ base=\dfrac{Volume \ of \ the \ pond}{base}\\\\Area\ of\ the\ base=\dfrac{72000}{24}\\\\Area\ of\ the\ base=3000 in^2[/tex]
The length of the pond is two times its width.
a = 2b
The area of the base = a × b
3000 = ab
ab = 3000
Substitute the value of a in equation 2
[tex]\rm ab=3000\\\\2b \times b = 3000\\\\b^2=\dfrac{3000}{2}\\\\b^2=1500\\\\b=38.7[/tex]
Substitute the value of b in equation 1
[tex]\rm a=2b\\\\a=2 \times 38.7\\\\a=77.4[/tex]
Hence, the length of the pond is 77.4 inches, and the width of the pond is 38.7 inches.
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The width of the pond is approximately 38.7 inches and the length is approximately 77.4 inches.
Explanation:To find the length and width of the pond, we can use the formula for the volume of a rectangular prism: length × width × depth. We are given that the depth is 24 inches and the volume is 72,000 cubic inches.
Let's denote the width as w.
Since the length is two times the width, we can express the width as w and the length as 2w.
Therefore, the equation for the volume becomes:
2w × w × 24 = 72,000
48w^2 = 72,000
w^2 = 1,500
w ≈ 38.7
Therefore, the width is approximately 38.7 inches and the length is approximately 77.4 inches.
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