A cyclist set out from a town P on a bearing of to a town Q, 5 km away. He then moves on a bearing of to a town R, 6km from Q.
1. Represent the information on a diagram
Calculate, correct to two decimal places
2. the bearing of R from P
3. |PR|
Answers
The bearing of R from P is 019 and the distance |PR| is 8.75
The complete questionA cyclist set out from a town P on a bearing of 060 to a town Q, 5 km away. He then moves on a bearing of 345 to a town R, 6km from Q.
The diagram that represents the informationSee attachment
The bearing of R from PStart by calculating the distance PR using the following cosine ratio
PR² = PQ² + QR² - 2 * PQ * PR cos(Q)
Substitute known values
PR² = 5² + 6² - 2 * 5 * 6 cos(105)
Evaluate
PR² = 76.53
Take the square root of both sides
PR = 8.75
Next, calculate angle R using the following sine ratio
PQ/sin(R) = PR/sin(Q)
Substitute known values
5/sin(R) = 8.75/sin(105)
Evaluate the quotient
5/sin(R) = 9.06
Multiply both sides by sin(R)
9.06 * sin(R) = 5
Divide both sides by 9.06
sin(R) = 0.5519
Take the arc sin of both sides
R = sin⁻¹(0.5519)
Evaluate
R = 34
Calculate angle P using:
P = 180 - 34 - 105
P = 41
The bearing of R from P is then calculated as:
Bearing = 060 - 41
Evaluate
Bearing = 019
Hence, the bearing of R from P is 019
The distance |PR|In (b), we have:
PR = 8.75
Hence, the distance |PR| is 8.75
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Related Questions
A metronome is a device that ticks at adjustable intervals to help keep time when playing music. The metronome on Ryan’s piano has the basic shape below.
A square pyramid. The base is 9 centimeters by 9 centimeters. The triangular sides have a base of 9 centimeters and height of 20.5 centimeters. The pyramid has a height of 20 centimeters.
If the metronome was created out of a piece of solid wood, what is the minimum amount of solid wood that was used?
Answers
Answer:
[tex]540cm^{3}[/tex]
Step-by-step explanation:
Chin was shown the graph of a line that contained point (1, 7). He wrote f(x) = 4x + 3 to correctly represent the line. Which of these equations could represent the same line?
Answers
A line is a distance between two points. The possible equation of the line will be g(x) = 4x - 7
Equation of a lineA line is a distance between two points. The equation of a line in slope-intercept form is expressed as y = mx + b
where:
m is the slopeb is the y-interceptGiven the equation of the line graphed by Chin expressed as f(x) = 4x + 3, the equation similar the line must have the same slope. The possibe equation of the line will be g(x) = 4x - 7
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Answer:
C. y – 7 = 4(x – 1)
Step-by-step explanation:
I did the test and got it correct.
Which statement describes the vertical asymptotes of the graph of f(x)=x^2-64/8x-64
O The graph has no vertical asymptote.
O The graph has a vertical asymptote at x = 8 only.
O The graph has a vertical asymptote at x = -8 only.
O The graph has vertical asymptotes at both x = 8 and x = -8.
Answers
The graph has no vertical asymptote
===========================================================
Explanation:
Let's simplify the function by factoring each piece.
[tex]f(x) = \frac{x^2-64}{8x-64}\\\\f(x) = \frac{(x-8)(x+8)}{8x-64}\\\\f(x) = \frac{(x-8)(x+8)}{8(x-8)}\\\\f(x) = \frac{x+8}{8}\\\\[/tex]
In the 2nd step, I used the difference of squares rule to factor the numerator. In the 4th step, the (x-8) terms cancel.
The simplified version doesn't have any variables in the denominator. This indicates the denominator is always 8, and never 0. So it's impossible to divide by zero in this simplified form. Consequently it means this graph has no vertical asymptotes.
However, there is a hole at x = 8 because this input causes a division by zero error in the original non-simplified function. Why? Because the calculator will use PEMDAS to evaluate the expression after replacing every copy of x with 8. It likely won't attempt to simplify like shown in the steps above. This is what causes the hole at x = 8.
The value x = -8 is perfectly fine in either the original function or the simplified one. It doesn't cause the denominator to be zero.
2- Answer the following question:
a. What are the four different ways to solve a quadratic function? (5 points)
b. Solvex² - 4x - 11 = 0 using completing the square. You must show all the steps. (10 points)
c. Solve 2x² + 16x + 24 = 0 using the quadratic formula. You must show all the steps. (10 points)
Answers
A. Four ways to solve a quadratic equation
---Factoring
---Completing the square
---Quadratic equation
---Graphing
B. Solve the equation by completing the square
x^2 - 4x - 11 = 0
x^2 - 4x = 11
x^2 - 4x + 4 = 11 + 4
(x - 2)^2 = 15
x - 2 = +/- 15
x - 2 = 15 || x = 17
x - 2 = -15 || x = -13
C. Solve the equation using the quadratic formula
Quadratic formula = [tex]\frac{-b +/-\sqrt{b^2 - 4ac} }{2a}[/tex]
Equation = 2x^2 + 16x + 24 = 0
a = 2
b = 16
c = 24
[tex]\frac{-16 +/- \sqrt{16^2 - 4(2)(24)} }{2(2)}[/tex]
[tex]\frac{-16 +/- \sqrt{256 - 192} }{4}[/tex]
[tex]\frac{-16 +/- \sqrt{64} }{4}[/tex]
[tex]\frac{-16 +/- 8 }{4}[/tex]
[-16 + 8] / 4 = -2
[-16 - 8] / 4 = -6
x = -6, -2
Hope this helps!
Determine whether triangles EFG and PQR are congruent
Plsss help
Answers
Answer:
B
Step-by-step explanation:
Because it flipped over the x axis
Spot the coordinates
E(-3,1)P(-3,-1)F(1,1)Q(1,-1)G(4,4)R(4,-4)Yes it's reflection along x axis
.(x,y)=(x,-y)Option B
5x-4y=10
slope intercept form
Answers
Answer:
5x-4y=10
solution
first find x intercept is the graph cross x-axis.to find the x intercept,we set y¹=0 and the Solve x.
5x-4y=10
5x-4(0)=0
x¹ =2 y¹=0
y intercept
5x-4y=10
5(0)-4y=10
y²=2.5 x²=0
The weights of packs of chewing gum for a certain brand have a mean of 47.1 grams and a standard deviation 2.4 grams. The weight of a randomly selected pack of gum has a z-score of 3.11. Which of the following statements is the best interpretation of the z-score?
The weight of this pack of gum is lighter than the mean weight by 3.11 standard deviations.
The weight of this pack of gum is heavier than the mean weight by 3.11 standard deviations.
The weight of this pack of gum is lighter than the mean weight by 2.4 standard deviations.
The weight of this pack of gum is heavier than the mean weight by 2.4 standard deviations.
Answers
The weight of this pack of gum is heavier than the mean weight by 3.11 standard deviations.
Why is the above statement appropriate ?The supplied z-score of 3.11 can be best translated as "This pack of gum weighs 3.11 standard deviations more than the mean weight." A z-score indicates how many standard deviations an observation is from the population mean. When an observation has a positive z-score, it is above the mean; when it has a negative z-score, it is below the mean. The selected pack of gum weighs more than the population's mean weight because the specified z-score is positive. Furthermore, a z-score of 3.11 means that the pack of gum weighs 3.11 standard deviations more than the population's mean weight.
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what is the mean median and mode of 201,201,200,199,199
Answers
Answer:
the median will be 200.
the mode will be 402 n 398.
the mean will be 400.
The UAE has very specific guidelines set out for the use and display of the UAE flag. One of
the rules regards the dimensions of the flag. The rule is that the ratio of the length of the flag
to the width must be 2: 1.
The length and width of the flag is 37 cm and 18.5 cm
It is divided into four rectangular parts. The first is red in colour, its length being equivalent to
the height of the flag, while its width is 0.25 of the length of the entire flag. The other three
parts constitute the remaining area of the flag which are in the shape of three equal horizontal
rectangles, width of these rectangles should be 0.33 of the width of the entire flag . The top
most rectangle part is green, the middle is white and the lower is black in colour.
Answers
Find the measure of angle VOQ
Answers
Answer:
124
.........................
PLEASE HELP!
Martha and Emily had to sew dresses with beads. Emily had 20% more beads than Martha. Then Emily gave 25% of her beads to Martha. Now Martha has 80 beads more than Emily. How many beads did each dressmaker had at the start?
Answers
Answer:
Emily has about 73 beads and Martha has about 62
Step-by-step explanation:
E = M · 1.2
M + ( .25 · E ) = m
m = 80
Now work backwards to find the answer.
Note that to find the answer you must get rid of the variable E, so you must use the expression M · 1.2 to represent E.
M + ( .25 · M · 1.2 ) = 80
M + .3M = 80
1.3M = 80
Divide both sides by 1.3
M = 61.5
Round to the nearest one
M = 62
Now use this to find E
E = 62 · 1.2
E = 74.4
Round to nearest one
E = 73
This might be confusing but I hope it was helpful!
Also, can I get brainliest because this took a lot of work to figure out.
(-17,-5), (15,-13)
Slope of the line through each pair of points
Answers
Using -17 ,15
And, 15 , -13
Hope this helps!
From a hot-air balloon, Ian measures a 30^{\circ}
∘
angle of depression to a landmark that’s 1250 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.
Answers
The balloon’s vertical distance above the ground is 721.7 f
Angle of elevation and depressionIn order to determine the balloon's vertical distance, we will use the SOH CAH TOA identity
Given the following parameters
Angle of depression = 30 degrees
Horizontal distance =1250 feet
Required
vertical distance H
Using the SOH CAH TOA identity
tan 30 = H/1250
H = 1250tan30
H = 721.7 feet
Hence the balloon’s vertical distance above the ground is 721.7 feet
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Answer:
721.7
Step-by-step explanation:
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If LN = 12x + 16, what is the length of Line segment L N in units?
Answers
Answer:
LN = 64 units
Step-by-step explanation:
Given M lies on LN, so LN = LM + MN --------------(1)
LN = 12x + 16
LM = 10x + 8
MN = 5x - 4
Substituting the values in equation 1, we get:
12x + 16 = (10x + 8) + (5x - 4)
12x + 16 = 15x + 4
15x - 12x = 16 -4
3x=12
Therefore x=4
LN= 12(4) + 16 = 64 units
The Broad Street subway line express train stops at city hall every 9 minutes. The local train stops at the station every 12 minutes. If you arrived at the station just as both trains left, how long will you have to wait until they both arrive at the same time again?
Answers
Answer:
36 Minutes
Step-by-step explanation:
You have to find the lowest common multiple which you can do by listing the times tables for each number.
9,18,27,36,45,54
12,24,36,48,60,72
and finding the lowest multiple that matches.
Both the train will meet after 36 minutes.
Concept:To find when both the train will meet again at the same time, we need to find the LCM of the frequency.How to solve the given question?Frequency of express train = 9 minutes = 3 × 3Frequency of local train = 12 minutes = 2 × 2 × 3LCM = 2 × 2 × 3 × 3 = 36Thus, both the train will meet after 36 minutes.
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Which of the following is a factor of both f(x)=x^2-4x-45 and g(x)=x^2-25
Answers
Answer:
-5
Step-by-step explanation:
x² - 4x - 45 = 0
(x - 9)(x + 5) = 0
x = 9 or -5
x² - 25 = 0
(x + 5)(x - 5) = 0
x = 5 or -5
-5 is a common factor between both of them
6)( b)write down the ratio of white chocolates to milk chocolates 3/8
Answers
Answer:
white chocolates = 3
milk chocolates = 8
ratio= 3:8
[tex] \frac{3}{8} [/tex]
0.375
Sanjay has ordered 30 slices of pizza for 7 people, including himself. If everyone gets an equal share, how many slices will each person get and what is the remainder? Choose the answer in the form (quotient)r (remainder).
please help i'm retaking a test because i don't have my head in the game! :C
Answers
Answer:
Each person get 4 slice of pizza and 2 is remaining
help me I need the answer on paper help me now
Answers
Answer:
x = 144
Step-by-step explanation:
Angle sum of heptagon = 900
5x + 90 + 90 = 900
5x + 180 = 900
5x + 180 - 180= 900 - 180
5x = 720
Divide both sides by 5
x = 144
Each section of a spinner is labeled with a unique number and is the same size and shape as the other sections. the spinner is spun two times. the number of possible outcomes is 16. how many sections is the spinner divided into? 2 4 8 16
Answers
By counting the total number of outcomes, we conclude that the spinner has 4 sections.
How many sections does the spinner has?Let's say that the spinner has N sections.
If we spin it twice, for the first outcome we have N possible outcomes and for the second spin there are N possible outcomes.
Then for the experiment of spinning the spinner twice, the number of outcomes is:
O = N*N
And we know that the number of possible outcomes for spinning the spinner twice is 16, then we have:
16 = N*N = N^2
Solving for N, we have:
N = √16 = 4
Then we conclude that the spinner has 4 sections.
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A group of students from your school is part of the audience for a TV game show. The total number of people in the audience is . What is the theoretical probability of students from your school being selected as contestants out of possible contestant spots?
Answers
A group of students from your school is part of the audience for a TV game show, the theoretical probability of students is mathematically given as
P=2.7%
What is the theoretical probability of students from your school being selected as contestants out of possible contestant spots?Generally, the equation for Probability is mathematically given as
[tex]P=\frac{Desired outcomes}{Total outcomes}[/tex]
Where Desired outcomes
D=40C5 *110C3
D=1420112865560
And Total outcomes
T=150C8 *
T=5.2572*10^10{12}
Hence, Probability
[tex]P=1420112865560/ 5.2572*10^10{12}[/tex]
P=0.0270
P=2.7%
In conclusion, the theoretical probability
P=2.7%
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A price is divided into 1:11. If the difference between the shares is £180, what is the total prize
Answers
Answer:
£216
Step-by-step explanation:
The total prize will be the sum of the divisions of the prize. The difference of those divisions is given.
__
divisionsLet P represent the value of the prize. The 1:11 ratio of the parts tells us there are 1 +11 = 12 total parts, and their ratio is P/12 : 11P/12. The sum of these divisions is the whole prize:
P/12 +11P/12 = 12P/12 = P
differenceThe difference of the two divisions of the prize is ...
11P/12 -P/12 = £180
10P = £2160 . . . . . . . . multiply by 12 and simplify
P = £216 . . . . . . . . divide by 10
The total prize is £216.
_____
Additional comment
The divisions of the prize are
£216/12 = £18 and 11×£18 = £198
The sum of those divisions is the total prize: £18 +198 = £216.
The total price (prize)the difference between the shares is £180 is £216.
How to determine the total prizeLet's represent the total price as "P." According to the information given, the price is divided into a ratio of 1:11.
The total number of parts in the ratio is 1 + 11 = 12 (1 part for the first share and 11 parts for the second share).
Let the first share be "x" and the second share be "11x" (since the ratio is 1:11).
Now, the difference between the shares is £180:
11x - x = £180
Simplifying:
10x = £180
Now, divide both sides by 10 to find the value of "x":
x = £180 / 10
x = £18
Now, we can find the total price "P" by adding the shares together:
P = x + 11x
P = £18 + £198
P = £216
So, the total price (prize) is £216.
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2x – y = 3
ayuda por favor
Answers
i really need help will give brainliest
Answers
Answer:
You would put 11y-22+7y-6+3x+12+5x and that will give you the answer. Hope this helps!
PLEASE HELP Which statement about the answer to this problem is most accurate?
5/6−3/8=19/24
The answer 19/24 is reasonable because both fractions are closer to 1/2 than they are to 1, making the difference close to 0.
The answer 19/24 is reasonable because 5/6 and 3/8 are both closer to 1 than to 1/2, making the difference close to 0.
The answer 19/24 is not reasonable because 5/6 is closer to 1 than to 1/2, and 3 is close to 1/2, making the difference close to 1/2.
The answer 19/24 is not reasonable because 5/6 is closer to 1/2 than to 1, and 3/8 is closer to 0 than to 1/2, making the difference close to 1/2.
Answers
The answer 19/24 is not reasonable because 5/6 is closer to 1 than to 1/2, and 3 is close to 1/2, making the difference close to 1/2.
Step-by-step explanation:
the third answer.
5/6 is almost 1, 3/8 is almost 1/2, so their difference is close to 1 - 1/2 = 1/2.
and 19/24 is much bigger than 1/2 (which would be 12/24).
in real numbers
5/6 - 3/8 = 5×4/24 - 3×3/24 = 20/24 - 9/24 = 11/24.
which is indeed very close to 1/2 (or 12/24).
write (4 x 100) + (3 x 10) + (6 x 1/10) + (7 x 1/100) in standard form.
Answers
Answer:
430.67
Step-by-step explanation:
(4 x 100) + (3 x 10) + (6 x 1/10) + (7 x 1/100)l
(400) + (30) + (6×0.1) + (7×0.01)
400 + 30 + 0.6 + 0.07
430.67
If Cyrus knows that △ABC∼△EDC and AB¯¯¯¯¯¯¯¯∥ED¯¯¯¯¯¯¯¯, how can he prove that line m passing through AB¯¯¯¯¯¯¯¯ has the same slope as line l passing through ED¯¯¯¯¯¯¯¯?
Brainliest and 5 Stars to Best Answer and Explanation!
Answers
As AB and ED are parallel, they have the same slope. This means that since lines that are colllinear with parallel segments are parallel, lines l and m are parallel.
please help, 30 points, will give brainly
Answers
Answer:
∠ABC = 39°
Step-by-step explanation:
Since ED bisects ∠CBD :
∠EBD = ∠CBE = 30°
Now, ∠ABD = ∠ABC + ∠CBE + ∠EBD = 99°
Solving :
99° = ∠ABC + 30° + 30°∠ABC = 99° - 60°∠ABC = 39°Two circles lying one inside the other. The inner circle is shaded purple and the outer circle is shaded yellow. The diameter of the inner circle is labeled 9 feet. The distance between the outer and the inner circle is circle is labeled 2.5 feet.
Answers
Answer:
what are you asking for? the area of the inner circle? the area of the outer circle? the area shaded only yellow?
Need the answer to the question
Answers
Answer:
The graph is wider and is reflected across the x axis.
Step-by-step explanation:
See attached image.