Answer:
distance island dock to Dock A = 4.99 km
distance island dock to Dock K = 6.35 km
Step-by-step explanation:
Always make a scetch to visualize the situation.
You need to construct two triangle both with a streight angle, so you can use Pythagoras to calculate the unknown distances between the island dock L, and each of the other two docks A an K.
I chose to introduce an extra letter, the letter C. In total you have the letters A K L and the letter C.
The letter C has a streight angle of 90° between ACL and it has the same streight angle of 90° with KCL. It is crucial that you see that the distance of LC is exactly the same in triangle LAC and that LC has exactly the same distance in the other triangleLKC.
The distance between AK = 2.3 km.
I define the distance between K and point C as 2.3 + x, because the distance x is unknown.
KC = 2.3 + x
Further more, when you make a picture, you can see that the distance between A and point C = x.
From such a picture, it would show clearly, that K is further away in respect to L then point A. From the picture it would be clear that the angle of LKC is smaller then the angle of LAC, so LKC = 45° and LAC = 64°.
Because angle LKC = 45° and we choose C to have an angle of 90°, the TRIANGLE LKC must be a special triangle... In any triangle, the sum of the three angles together, must add up to 180° .
If that is true, then we have 45 + 90 + 45 (because that adds up to 180). Now that means triangle LKC must have two equal sides (because of the same angels of 45° ).
So we know the distance KC = LC and we already defined KC = 2.3 + x.
Now we know enough to solve the problem.
AK = 2.3 km
angle of LKC = 45°
angle of LAC = 64°
AC = x
KC = 2.3 + x
LC = KC
LC = 2.3 + x
Try to calculate the distance x by using tan. After that you can use Pythagoras to find the other distances.
tan(LKC) = ( LC ) / ( KC )
tan(LKC) = ( x+2.3 ) / ( x+2.3 )
That is not helpful. Let's try the other triangle...
tan(LAC) = LC / AC
tan(LAC) = ( x+2.3 ) / x
tan(64) = ( x+2.3 ) / x
Solve the equation which means you try to find the value for x.
x * tan(64) = ( x+2.3 )
tan(64) * x -x = 2.3
tan(64) * x - 1* x = 2.3
Try to get x outside of the braquets...
x* ( tan(64) - 1 ) = 2.3
x* (2.0503038415793 - 1 ) = 2.3
1.0503038415793 * x = 2.3
x = 2.3 / 1.0503038415793
x = 2.19
Now use Pythagoras a² + b² = c² in triangle LAC to find distance LA.
LA² = AC² + LC²
AC = x = 2.19
LC = 2.3 + x = 4.39
LA² = 2.19² + 4.39²
LA = SQRT( 4.79 + 20.16 )
LA = SQRT( 24.95 )
LA = 4.99 km
Now use Pythagoras a² + b² = c² in triangle LKC to find distance LK.
LK² = KC² + LC²
KC = 2.3 + x = 4.39
LC = 2.3 + x = 4.39
LK² = 4.39² + 4.39²
LK = SQRT( 20.16 + 20.16 )
LK = SQRT( 40.32 )
LK = 6.35 km
A pair of shoes is originally priced at $120.00 It is on sale for 35% off. What is the price that you would pay?
[tex]answer = $78 \\ solution \\ marked \: price = $120 \\ discount \: percent = 35 \\ discount \: amount = discount \: percent \: of \: mp \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 35 \: of \: 120 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ = $42 \\ selling \: price = mp - discount \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 120 - 42 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = $78 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]..
The price of a bicycle was decreased by 40% to £96. What was the price before the decrease?
Answer:
£160
Step-by-step explanation:
£160 times 0.6 equals £96
since £96 is 60% of the original price since 40% was taken off
The price of the bicycle before decrease is obtained as £160.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100. And to convert a fraction or a decimal into percentage, they are multiplied by 100.
The new price of the bicycle is £96.
And, the percent of decrease is 40%.
Suppose the original price be x.
Then, the following equation can be written for the given case as,
x - 40% × x = 96
⇒ x - 40/100x = 96
⇒ 60/100x = 96
⇒ x = 160
Hence, the original price of the bicycle is given as £160.
To know more about percentage click on,
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What is the value of the exponential expression below 161/2
A.2
B.8
C.6
D.4
Answer:
D
Step-by-step explanation:
I'm taking this to mean 16^(1/2)
If I am correct, then the answer is the square root of 16 which among the answers given is 4
So the answer is D
Solve the inequality. 3p+7<31
Answer:
p < 8
Step-by-step explanation:
3p+7<31
Subtract 7 from each side
3p+7-7<31-7
3p <24
Divide each side by 3
3p/3 <24/3
p < 8
what is the circumference of the circle? Use 3.14 for Pi
Answer:
The answer is, B. 40.192
Step-by-step explanation:
The formula for circumference is, C=2(pi)r.
2×3.14=6.28
6.28×6.4=40.192
psllslsslslslsl help ASAP BRAINLIST
Answer:
24.94
Step-by-step explanation:
To find shipping and handling take the price and multiply by the shipping and handling percent
464 * 5.375%
Change to decimal form
464 * .05375
24.94 for shipping and handling
Solve the following formula for the specified variable.
B =1/2m(r + k) for r
Answer:
(2B/m) - k = r
Step-by-step explanation:
B =1/2m(r + k)
Multiply each side by 2
2B =m(r + k)
Divide each side by m
2B/m = m/m (r+k)
2B/m =(r+k)
Subtract k from each side
(2B/m) - k = r+k-k
(2B/m) - k = r
!!!PLEASE HELP!!!
the exponential function g, represented in the table, can be written as g(x)=a•b^x.
complete the equation for g(x).
please and thank you
Answer:
g(x) = [tex]12.(\frac{3}{4})^x[/tex]
Step-by-step explanation:
Exponential function g has been represented by the table attached,
Equation of the exponential function is,
g(x) = [tex]a.(b)^x[/tex]
Now we substitute the values of x and g(x) from the table,
For a point (0, 12),
12 = [tex]a(b)^0[/tex]
a = 12
For another point (1, 9),
9 = [tex]a.(b)^1[/tex]
9 = a × b
9 = 12 × b
b = [tex]\frac{9}{12}[/tex]
b = [tex]\frac{3}{4}[/tex]
Therefore, equation of the exponential function will be,
g(x) = [tex]12.(\frac{3}{4})^x[/tex]
please answer the question in the picture!
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v
Answer:
B is correct
Step-by-step explanation:
Hope I helped you and have an amazing day
x² - 36 = 0
solve for x
Answer: +6
Explanation: The equation x² - 36 = 0 is called a quadratic equation because he have a squared term as our highest power.
Our first step in this problem is to get the x²
term by itself by adding 36 to both sides.
That gives us x² = 36.
Next we must get the x by itself and in order to do
that we do the opposite of what is happening to x.
Since x is being squared, the opposite
of squaring is square rooting.
So to get x by itself, we square
root both sides of the equation.
On the left the square root of x² is x and on
the right, remember the following rule.
When square rooting both sides of
an equation, always use plus or minus.
So the answer to this problem would be +6.
So our solution to this equation is +6.
Please help I only need part b and part c
Answer:
Here is the answer.
Step-by-step explanation:
b) students are the frequency. so we need to add all the frequency.
5 + 4 + 7 + 10 + 4=30 students
c) here we need to use the summation.
total/ frequency= mean
6*5=30
7*4=28
8*7=56
9*10=90
10*4=40
we need to add them all= 244
total frequency= 30
mean = 244/30= 8.133333333...≈ 8 (this is a rounded of value as in 0.13, 3 goes on repeating.
type a is 5 feet tall and grows at a rate of 18 inches per year Type B is 10 feet tall and grows at a rate of 8 inches per year. How many years will it take for these trees to be the same height
Answer:
The height will be same in 6 years time
Step-by-step explanation:
Since we do not know the years it would take, we can call this x
Kindly note that 12 inches is 1 feet, so 5 ft would be 60 inches and 10 feet will be 120 inches
Now, the height of tree A after x years would be;
60 + 18x
For tree B, height would be 120 + 8x
Now, we were made to know that they have equal height at the xth year.
Thus;
60 + 18x = 120 + 8x
10x = 120-60
10x = 60
x = 60/10 = 6
NEED HELP ASAP!!!
A six-sided number cube is rolled twice.
What is the probability that the first roll is an even number and the second roll is a number greater than 4?
One-sixth
One-third
Two-thirds
Five-sixths
Answer:
1/6
Step-by-step explanation:
an even number has a 1/2 chance of being rolled and a number greater than 4 has a 1/3 chance of getting rolled. multiply 1/2 and 1/3 together and you get 1/6 for your answer.
What is the simplified form of each expression? a. 108 b. (0.2)5
Answer:
a. 108
b. 2.5
Step-by-step explanation:
a. ex: 108 = 108
b. ex: 5/2 = 5/2
convert to a decimal
2.5
. . .
Please help me with my homework!!!!!
8th grade word problem... Can someone please help if you don’t know then please don’t answer...
Answer:
30 of each type sold.
Step-by-step explanation:
It would be 30 since the LCM of 10 and 3 is 30.
If you need further explanation, reply to this answer but that's about it.
2. A map scale is 2 in = 400 miles. If the actual distance between Virginia 10 points
Beach and San Diego is 2,335 miles, approximately how many inches
apart is it on a map? *
9 in
10 in
11 in
a
12 in
hadow that is 9 feet long. At the same time, a 6 ft tall
10 points
Answer:
800
Step-by-step explanation:
I believe it its 800 inches Mark me brainliest
PLEASE THIS IS TIMED, PLEASE HELP ME ANSWER THIS QUESTION!
A power failure on the bridge of a Great Lakes freighter has resulted in the ship's navigator having to do her own calculations. She measures the angle between the ship's course and a lighthouse on shore as 32°. After the ship has travelled 1500 m, she measures the angle to be 72°. Determine if the ship was closer to or farther from the lighthouse at the second sighting, and by what distance
Answer:
I think the ship was farther by 40°
alguien me ayuda
5 (x-3) - 2 = 23
Write as a fraction in lowest terms:
Answer:
[tex]\frac{79}{100}[/tex]
Step-by-step explanation:
Question:
Write as a fraction in lowest terms:
Answer:
a = 79
b = 99
What is x+r if x =4 and r=5
Answer:
9
Step-by-step explanation:
x + r. Substitute
4 + 5 Add
9
10>j+5
What are the inequalities of j?
Answer:
j < 5
Step-by-step explanation:
=> 10 > j+5
Subtracting both sides by 5, we get
=> 10-5 > j
=> 5 > j
OR
=> j < 5
Square RSTU is translated to form R'S'T'U', which has vertices R'(–8, 1), S'(–4, 1), T'(–4, –3), and U'(–8, –3). If point S has coordinates of (3, –5), which point lies on a side of the pre-image, square RSTU?
(–5, –3)
(3, –3)
(–1, –6)
(4, –9)
please help
Answer:
The answer is A on Edge
Step-by-step explanation:
Two teammates were comparing data from five basketball games.
Andrew scored 10, 14, 8, 12, and 11 points. Leroy scored 2, 12, 9, 11, and 16
points. Who has the higher mean?
Answer:
The answer is andrew!
Step-by-step explanation:
andrew 10 + 14 + 8 + 12 + 11/ 5 = 11
leroy 2 + 12 + 9 + 11 + 16/5 = 10
does the equation y=4.2x represent a proportional relationship
Answer:
A proportional relationship is one in which two quantities vary directly with each other.We say the variable varies directly .If y=k.x then as x increases y also increases.Here k is called the constant of proportionality.
The given equation y = 4.2x is of the form y=k.x where k= 4.2 as x increases y value will also increase. The relation is called a proportional relationship.
Step-by-step explanation:
state of the triangles in each pair are similar. If so State how you know they are similar and complete the similarity statement.
Answer: a) similar, AA similarity, ΔKQR
Step-by-step explanation:
Given: QR || ML therefore,
∠KLM ≡ ∠KQR by Alternate Interior Angles Theorem
∠KML ≡ ∠KRQ by Alternate Interior Angles Theorem
also, ∠RKQ ≡ ∠MKL by Vertical Angles Theorem
Since the angles are congruent then
ΔKLM ≅ ΔKQR by Angle-Angle Similarity Theorem
WILL MARK BRAINLIEST!! Help ASAP PLEASE!!! A cone has a radius of 6 inches and a height of 11 inches. What is the volume of the cone? Show your work.
Answer:
414.69inches
Step-by-step explanation:
V=pr^2h/3. r^2=36.36xpi=113.097335529. h/3=3.66666666667. 113.097335529x3.66666666667=414.69 inches
Step-by-step explanation:
PARA UN CONO DE BASE REDONDA ES:
V = π[tex](6 in)^{2}[/tex](11 in)/3 = [tex]414.7 in^{2}[/tex]
at 5% commision, an agent received rs.32,500 by selling a second-hand car. At what price did he/she sell tha car?
Solution,
Let the price of car be X.
Rate(R)=5%
Here,
Commission % of price of car=32500
or,5% of X=32500
or,5/100*X=32500
or,X=32500*20
X=Rs 650000
Hope it helps
Good luck on your assignment........
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!!
Step-by-step explanation:
h(x) = (x-11)(x+3)
= x^2 + 3 - 11x - 33
= x^2 - 11x -30
Answer:
11 seconds
Step-by-step explanation:
did it on khan
A school must select one student from the honors program to send to the annual math convention. Which of the following is NOT a mathematically fair way to select the student?
A) Use a random number generator to choose a student ID number.
B) Have the students play a game that involves flipping a coin. Heads is worth 2 points and tails is worth 1 point. The first student to reach 40 points wins the trip.
C) Have each teacher select their favorite student and then randomly draw one of those names.
D) Line the students up alphabetically. Each student selects a playing card. A card is then drawn from another deck. The student with the matching card wins.
Answer:
Answer is option C.
Step-by-step explanation:
This is because it does not take into account "random selection" (probability). Thus the mode of selection is biased. The mere fact that a teacher selects his favourite student means the experiment is biased.
