Answer:
44.5 km on a bearing of 134.1°
Step-by-step explanation:
A suitable vector calculator will tell you the location of the ship from port is ...
21∠32° +45∠287° = 44.5∠-45.9°
The bearing of the port is in the reverse direction, so 180° added to this:
180° +(-45.9°) = 134.1°
The distance from port is 44.5 km. The bearing of the port is 134.1°.
_____
Additional comment
The distance from port is perhaps most easily found using the Law of Cosines. It is the third side of a triangle with sides 21 and 45. The included angle is (287° -(180° +32°)) = 75°. The distance is then ...
c = √(a² +b² -2ab·cos(C)) = √(21² +45² -2·21·45·cos(75°)) ≈ √1976.83
≈ 44.5 km
The angle between the 32° bearing and the bearing from the port to the ship can be found using the Law of Sines.
B = arcsin(b/c·sin(C)) = arcsin(45/44.5sin(75°)) ≈ 77.9°
so, the bearing angle from the ship to the port is ...
180° +(32° -77.9°) = 134.1°
__
Bearings are measured clockwise from north. A diagram can be helpful.
BRAINLIEST
Can you help me finish these
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Which postulate or theorem proves that these two triangles are
congruent?
O HL Congruence Theorem
ASA Congruence Postulate
O SAS Congruence Postulate
• AAS Congruence Theorem
Answer:
AAS Congruence Theorem
Step-by-step explanation:
the lines in the angle show similarity. so angle FGJ= angle HJG, similarly, angle F= angle H.GJ is the same as JG so this side of both triangles is congruent. since the order of congruency is the same (triangle GHJ: angle H, angle HJG, then JG; triangle JFG: angle F, angle FGJ, then GJ) and the congruent side length isn't between the congruent angles, it's AAS
Jasmine got a new puppy for her birthday. He's full of energy, so she takes him for a walk along a 1.2-mile loop in a nearby park. If they walked a total of 3.6 miles, how many loops did they do?
Answer:
3 loops
Step-by-step explanation:
1.2x = 3.6 [Setting up an equation]
x = 3 [dividing both sides by 1.2]
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
In how many years will Rs 1200 at the rate of 15% interest amount to Rs 1740?
Answer:
3 years.
Step-by-step explanation:
Answer
3 years
Step by step explanation
Interest = 1740 - 1200
= 540
SI = prt/100
540 = 1200*15*t/100
540 = 12*15*t
540 = 180*t
t = 540/180
t = 3 yrs
plss help me with this:(((((
The answer for the first question is A
The answer the second question is D
Step-by-step explanation:
so, let's look at the options.
A. (x+3)/x = 3
that hurts already by just looking at it.
but let's check anyway :
x + 3 = 3x
3 = 2x
and that is only true for one value of x (3/2), but not in general.
so, this is wrong.
B. (x²+5)/5 = x² + 1
x² + 5 = 5x² + 5
x² = 5x²
that is only true for one value of x (0), but not in general.
so, this is wrong.
C. (2x+7)/(2x+9) = 7/9
9(2x+7) = 7(2x+9)
18x + 63 = 14x + 63
4x = 0
that is only true for one value of x (0), but not in general.
so, this is wrong.
D. (-5x - 10)/(x+2) = -5
-5x - 10 = -5(x + 2) = -5x - 10
now this is true in all cases, so this is correct.
make simple :
(a² - 4a + 4) / (a² - 4)
with a little bit of experience you see right away that
a² - 4a + 4 = (a - 2)²
as we know from the generic squaring
(a - b)² = a² - 2ab + b² : a perfect fit.
and
(a² - 4) = (a + 2)(a - 2)
as we know from the generic factor multiplying
(a+b)(a-b) = a² + ab - ab - b² = a² - b² : a perfect fit.
so, the given expression is actually
(a - 2)² / ((a - 2)(a + 2)) = ((a-2)(a-2)) / ((a-2)(a+2))
and so, after eliminating one (a-2) term in the numerator and in the denominator the following remains :
(a - 2) / (a + 2)
and that is answer A
Answer this for alot of piontsssssss plssssssssss I need it by today please have a good day
Answer:
Can anyone agree this image is blurry? Can you send it again but not blurry this time? Sorry!
Step-by-step explanation:
In Dominic’s classroom, there are 5 rows of desks. There are 5 desks in each row. In all, 5 classrooms in his school have the desks set up the same way. Write an expression with an exponent that shows the total number of desks in these 5 classrooms.
Use words, numbers, and/or pictures to show your work. Write your answer on the paper provided.
Answer:
5^(3) is the exponent form which equals 125desks
Step-by-step explanation:
A row has 5 desks
A classroom has 5 rows of desks= 5*5 desks
The school has 5 classrooms
=5*5+5*5+5*5+5*5+5*5 desks
=5^(2)+5^(2)+5^(2)+5^(2)+5^(2)
=5[5^(2)]
=5^(3) = 125 desks
Please, If you can help i will be grateful and give brainliest.
Answer:
To complete the square, you always want to add [tex](\frac{a}{2} )^{2}[/tex], where a is the coefficient of x.
In this case, the coefficient of x is -1.
Thus,
[tex]y=x^2-x+1[/tex]
[tex]y=x^2-x+(\frac{-1}{2})^2 +1-(\frac{-1}{2})^2[/tex]
[tex]y=(x-\frac{1}{2})^2+1-\frac{1}{4}[/tex]
[tex]y=(x-\frac{1}{2})^2+\frac{3}{4}[/tex]
2x+3y=15
x+y=6
work out the values of x and y.
Answer:
Step-by-step explanation:
Elimination sounds the easiest for y:
[tex]I - 2II: 2x+3y -2x -2y = 15-12 \rightarrow y= 3[/tex]
Now we got one value, let's replace in one of the two and find the second
[tex]II: x+(3)=6 \rightarrow x=3[/tex]
Answer:
[tex]2x + 3y = 15...(1) \\ x + y = 6...(2) \\ 2 \times (2) \\ 2x + 2y = 12...(3) \\ (1) - (3) \\ 0 + 3y - 2y = 15 - 12 \\ \color{red} \boxed{ y = 3 }\\ sub \: in \: (2) \\ x + 3 = 6 \rightarrow \: x = 6 - 3 \\ \color{green} \boxed{ x = 3 }[/tex]
Can someone please explain what x is over here? And solve a part with working please :). Eternally grateful
Answer:
[tex]\frac{1}{9}[/tex] , 3 , 10
Step-by-step explanation:
Using the rules of exponents
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
[tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^m}[/tex]
[tex]a^{0}[/tex] = 1
(a)
[tex]6^{-x}[/tex] = [tex]\frac{1}{6^{x} }[/tex] = [tex]\frac{1}{9}[/tex]
(b)
[tex]6^{\frac{x}{2} }[/tex] = [tex]\sqrt{6^{x} }[/tex] = [tex]\sqrt{9}[/tex] = 3
(c)
[tex]6^{0}[/tex] + [tex]6^{x}[/tex] = 1 + 9 = 10
If you can walk 3/8 of a mile in 1/9 hour, how far could you walk in one hour
9514 1404 393
Answer:
27/8 = 3 3/8 miles
Step-by-step explanation:
To find the rate in miles per hour, divide miles by hours.
(3/8 mi)/(1/9 h) = (3/8)·(9/1) mi/h = 27/8 mi/h = 3 3/8 mi/h
You can walk 3 3/8 miles in 1 hour at that rate.
6 (3j + 5 + 4j) simplified with the commutative property
(25 points)
(this is 6th grade second-semester math)
Answer:
6 x (3j + 5+ 4j)
6 x(8j+4j)
6 x 12
72
Step-by-step explanation:
hope this helps
Translate the sentence into an equation.
Nine more than the quotient of a number and 8 is equal to 5.
Answer:
x/8 + 9 =5
Step-by-step explanation:
Quotient is division and I decided to use x as my number so the first part is x/8. Then you do the nine more because more is addition to whatever is after it in our case it is x/8 so now you have x/8 + 9. Then it says equals 5 so the equation is x/8 + 9 = 5
I hope this helps!
please help! with work please Zeroes of polynomials. will give brainliest!
Answer: 4k^2 - 9k - 9 = 0
Step-by-step explanation:
lmk if i was right please and ty
Help me I don’t understand please explain the answer to me
Answer:
a
Step-by-step explanation:
r and t are same- side exterior angles and sum to 180 , so
t + r = 180 , that is
t + 91 = 180 ( subtract 91 from both sides )
t = 89
t and u are vertically opposite angles and are congruent , so
u = t = 91
Then
t + u = 89 + 89 = 178 → a
A reflection over the x axis moves the point (-2, 5) to which quadrant?
I
Hiiii!!! Can someone please help mee!! I will give you double points!!!
Answer:
II quadrant
Step-by-step explanation:
Looking at the drawing, you can determine that the point with
coordinates (-2 ; 5) is in the II quadrant
Tayla purchased a large box of comic books for $300. She gave 15 of the comic books to her brother and then sold the rest on an Internet website for $330, making a profit of $1.50 on each one. How many comic books were in the box
Answer:
Number of comic books is 75.
Original price of each comic book is 4$.
Step-by-step explanation:
There were 75 comics in the box originally.
What is an equation?An equation is the statement of equality between two expressions consisting of variables and/or numbers.
Given that, Tayla purchased a large box of comic books for $300. She gave 15 of the comic books to her brother and then sold the rest on an internet website for $330, making a profit of $1.50 on each one.
Let x be the number of comics originally
(x - 15) is the number of comics sold.
Original price of each comic = 300/x
Price of comics which she gave to brother = 15*300/x
Original price of all the books that has been sold = 300 - 15*300/x
Tayla's profit = 330 - (300 - 15*300/x) = 30 + 15*300/x
Number of comics sold = (30 + 15*300/x)/1.5
Equation will be,
(30 + 15*300/x)/1.5 = x - 15
20 + 3000/x = x - 15
(x² - 15x - 3000)/x = 20
x² - 35x - 3000 = 0
On factorizing the quadratic equation, we get,
x = 75 or -40 (Neglecting -40, because number of books can't be negative)
Hence, there were 75 comic books in the box originally.
For more references on Equations, click;
https://brainly.com/question/10413253
#SPJ5
Leah bought 3/4 pound of trail mix to make snack bags. She put 1/8 pound of trail mix into each snack bag. Which expression can be used to find how many snack bags Leah made? (Show work and simplify pls)
Answer:
3/4 ÷ 1/8 = 6
Step-by-step explanation:
first you would have to figure out how to make them even factors.
6/8 ÷ 1/8
Then you would divide, and get 6.
Can you please help I’ll give you points I need help if I can’t pass this I can’t play in my basketball game Sunday
Answer:
m∠X = 70°
Step-by-step explanation:
In congruent triangles, corresponding parts have the same measures. In ΔABC and ΔXYZ, the corresponding parts are ...
∠A = ∠X = 70° . . . . . . . . . . . matches choice A
∠B = ∠Y = (90° -70°) = 20°
∠C = ∠Z = 90°
AB = XY = √(3.5² +9.6²) ≈ 10.22 cm
BC = YZ = 9.6 cm
AC = XZ = 3.5 cm
Answer:
m∠X = 70°
Step-by-step explanation:
In congruent triangles, corresponding parts have the same measures. In ΔABC and ΔXYZ, the corresponding parts are ...
∠A = ∠X = 70° . . . . . . . . . . . matches choice A
∠B = ∠Y = (90° -70°) = 20°
∠C = ∠Z = 90°
AB = XY = √(3.5² +9.6²) ≈ 10.22 cm
BC = YZ = 9.6 cm
AC = XZ = 3.5 cm
Number line fractions
Answer:
-7/4 is between -2 and -1 1/2
11/4 is in between 2 1/2 and 3
Step-by-step explanation:
-7/4 is -1.75 which means its right before -2
11/4 is 2.75 which means it's right before 3
DesBest Granola bars are now 25% longer. if the original bar was 20 centimeters long, how long is the new granola bar?
Answer:
25
Step-by-step explanation:
25% is a 4th of the whole number, the whole number is 20 so a 4th of 20 is 5 because 5 times 4 equals 20.
due to the fact that 25% of 20 is 5 we now have to add that to the whole number which is 20.
20 + 5 = 25
help please !!!!!!!!!
help me please on my math I need All of this FACTORS and the LCM
Answer:
the LCM is :
1. 144
2.40
3.870
4. 63
5.216
6.150
7. 112
8.162
9. 96
10. 40
The expression 3(x + 4) - (2x + 7) is equivalent to
Answer:
Why don't know wt is equal to..
Step-by-step explanation:
3(x + 4) - (2x + 7)
3x + 12 - 2x - 7
1x + 5
x + 5
helpp pleaseeeeeeeeee
Given triangle MTW is congruent to triangle BGK,find y.
Answer:
y = 8
Step-by-step explanation:
As MTW and BGK are congruent
angle T = angle G
4x - 3 = 45
in triangle MTW
angle M = 180 - (T + W)
= 180 - (45 + 41)
= 180 - 86
= 94
and angle M = B
11y + 6 = 94
11y = 94 - 6
11y = 88
y = 8
If i can get 6 poland spring water 3-liter for $6. How much would it be if i get 3 poland water?
Explain
Answer:
$3
if we wanted to find how much 1 bottle would cost we would do 6/6=1 and from that we now know that 1 bottle of water costs $1 so if we times that by 3 to find out how much 3 bottles will cost we get $3.
Use a number line to add or subtract.
3−(-1)=
Answer:
4
Step-by-step explanation:
rule 1 positive + positive= positive
rule 2 negative plus negative = negative
how do I solve this linear inequality?
5x - 7 > 4x + 8
Step-by-step explanation:
just like an equation.
5x - 7 > 4x + 8 | -4x + 7
x > 15
and that is your result.
in contrast to an equation, an inequality delivers a range as result and not a single point.
Answer:
[tex]\huge\boxed{\sf x > 15}[/tex]
Step-by-step explanation:
5x - 7 > 4x + 8
Subtract 4x to both sides, and Add 7 to both sides
5x - 4x > 8 + 7
x > 15
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807A water pipe can fill an empty pool in 3 hours. When the pool is full, an open drain can empty the pool in 4 hours. Using the water pipe with the drain open, how many hours will it take to fill the empty pool? I give brainliest
Answer:
Step-by-step explanation:
Even though this seems like a crazy trick question it isn’t. An empty pool with a closed drain takes 3 hours to fill. A full pool with and open drain takes 4 hours to empty. So to fill and empty pool with an open drain, i’d say in my opinion it’d either take 7 hours or you wouldnt be able to fill it at all. I mean it’s an open drain
hope this helped :3
:3 byeeeeeeeeeeeeeeeee