Answer:
The value of x is 4.
Step-by-step explanation:
-5(x-1)-x+1= -18
or, -5x+5-x+1=-18
or, -6x+6= -18
or, -6(x-1)=-18
or, x-1=3
or, x=4
A plane flies 545 kilometers with a bearing of 316° from Naples to Elgin (see figure). The plane then flies 680 kilometers from Elgin to Canton (Canton is due west of Naples). Find the bearing of the flight from Elgin to Canton. (Round to the nearest whole number.)
Answer:
235°Step-by-step explanation:
Use of low of sinesConsider triangle CENBearing of angle counted from zero to the vector of flightWe have
∠CNE = complementary with 44° ⇒ m∠CNE = 90° - 44° = 46°NE = b = 545 kmEC = a = 680 km∠ECN = xFind the measure of angle x:
sin 46° / a = sin x / bsin 46° / 680 = sin x / 545sin x = 545 sin 46 deg / 680x = arcsin (545 sin 46 deg / 680)x = 35° (rounded)Bearing of the flight from Elgin to Canton is:
270° - 35° = 235° as the vector is in the third quadrantAnswer:
235°
Step-by-step explanation:
Bearing: The angle (in degrees) measured clockwise from north.
The given scenario can be modeled as a triangle.
Given sides of the triangle:
a = 680 kmb = 545 kmAs due north is at a right angle to due west, the angle in the right corner of the triangle is:
⇒ 90° - 44° = 46°
Use the Sine Rule to find angle y marked on the attached diagram (the angle opposite side b).
Sine Rule
[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
[tex]\implies \sf \dfrac{\sin 46^{\circ}}{680}=\dfrac{\sin y}{545}[/tex]
[tex]\implies \sf \sin y= \dfrac{545\sin 46^{\circ}}{680}[/tex]
[tex]\implies \sf y= \sin^{-1} \left(\dfrac{545\sin 46^{\circ}}{680}\right)[/tex]
[tex]\implies \sf y=35.20682806...^{\circ}[/tex]
Interior angles of a triangle sum to 180°
⇒ x° + y° + 46° = 180°
⇒ x° + 35.2068...° + 46° = 180°
⇒ x° = 98.79317194...°
Consecutive Interior Angles Theorem
When a straight line intersects two parallel straight lines, the consecutive interior angles formed sum to 180°. Therefore the angle between due north and side a of the triangle is:
⇒ 180° - 44° = 136°
To find the bearing of the flight from Elgin to Canton, find the angle labelled green on the attached diagram:
[tex]\implies \sf Bearing =136^{\circ}+ 98.79317194...^{\circ}[/tex]
[tex]\implies \sf Bearing = 234.7931719...^{\circ}[/tex]
[tex]\implies \sf Bearing = 235^{\circ}[/tex]
As bearings are usually given as a three-figure bearings, the bearing of the flight from Elgin to Canton is 235°.
Learn more about bearings here:
https://brainly.com/question/27928951
Every Month the average number of books borrowed by a class of 24 from a library is 4.What is the total number of books borowed by the class for the month
Answer:
96
Step-by-step explanation:
24*4=96
What is the measure of each angle of a regular pentagon? If necessary, round to the nearest tenth.
Answer: Find the measures of an exterior angle and an interior angle given the number of sides of each regular polygon. Round to the nearest tenth, if necessary. 24 b 15, 345 24, 156 7.5, 172.5 15, 165
Step-by-step explanation: sum, S, of the measure of the interior angles of a polygon with n sides is: ... The sum of the interior angles of a 24 -gon is 3960. ... angles of a polygon is (n−2)⋅180 , where n is the number of sides. ... Each exterior angle measures 36024=15 . ... The sum of the 24 interior angles is then 24⋅165=3960 .
On a later day, he asked the same group of 10 friends to throw a ball again and collected another set of data. The median of the second data set is 49 feet, and the IQR is 6 feet.
a. Did the 10 friends, as a group, perform better (or throw farther) in the second round compared to the first round?
(Worse or better)
b. Were the distances in the second data set more variable or less variable compared to those in the first round?
(More variable or less variable)
Answer:
a
Step-by-step explanation:
0 What is A U B?
Set A = 1, 2, 3, 4
Set B = 2, 3, 6, 10, 11
Answer:
A U B= 1,2,3,4,6,10,11
Step-by-step explanation:
because A union B is all number from set A and set B together without repeating
Quadrilateral KLMN is dilated by a scale factor of 2/3 to form quadrilateral K'L'M'N'. What is the measure of side NK?
Answer:
NK = 42
Step-by-step explanation:
Scale factor of dilating KLMN to form K'L'M'N' = ⅔. This fraction implies there was a reduction of the original shape to form the new image/shape.
NK corresponds to N'K'
N'K' = 28
To get the NK, divide 28 by the scale factor.
28 ÷ ⅔ = 28*³/2 = 42
NK = 42
A football team incurred a 10 yard penalty for being off sides. Write an integer to represent this situation?
Answer:
sir u can try looking up on internet, we do not do homeworks/assignemnts for people
Step-by-step explanation:
4 1/6 divided by 1 1/8
Answer:
3.7037037037
Step-by-step explanation:
Answer:
5 35/48
Step-by-step explanation:
25/6x11/8=275/48=5 35/48
4) Evan bought 6 roses for his mother. 2/3 of the roses were red. How many red roses were there?
Answer:
4 roses were red.
Step-by-step explanation:
(2/3)*6=4
A lighthouse is located on a small island 5 km away from the nearest point P on a straight shoreline and its light makes six revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? (Round your answer to one decimal place.)
Answer:
The beam of light is moving along the shoreline at a velocity of approximately 196 kilometers per second.
Step-by-step explanation:
The statement is described geometrically in the image attached below by means of a right triangle. All variables are described below:
[tex]OP[/tex] - Minimum distance between lighthouse and the straight shoreline, in kilometers.
[tex]PP'[/tex] - Distance along the straight shoreline, in kilometers.
[tex]\theta[/tex] - Angle of rotation of the lighthouse, in sexagesimal degrees.
To find the rate of change of distance along the straight shoreline ([tex]\frac{dPP'}{dt}[/tex]), in kilometers per minute, we use the following trigonometric relationship:
[tex]PP' = OP \cdot \tan \theta[/tex] (1)
Then, we differentiate this expression in time:
[tex]\frac{dPP'}{dt} = OP\cdot \dot \theta \cdot \sec^{2}\theta[/tex] (2)
Where [tex]\dot \theta[/tex] is the rate of change of the angle of rotation of the lighthouse, in radians per minute.
The angle at the given instant is calculated by (1): [tex]OP = 5\,km[/tex], [tex]PP' = 1\,km[/tex]
[tex]\theta = \tan^{-1} \left(\frac{PP'}{OP} \right)[/tex]
[tex]\theta \approx 11.310^{\circ}[/tex]
If we know that [tex]\dot \theta = 37.699\,\frac{rad}{min}[/tex], [tex]\theta \approx 11.310^{\circ}[/tex] and [tex]OP = 5\,km[/tex], then the rate of change is:
[tex]\frac{dPP'}{dt} \approx 196,035\,\frac{km}{min}[/tex]
The beam of light is moving along the shoreline at a velocity of approximately 196 kilometers per second.
When x = 4 and y = 3, find the value of:
a) 2x + 7y - 10
b) y(x - 2y)
c) (5y - 3x)/12
PLEASE HELP
PLEASEE
Answer:
a-8x+21y-10=19
b-3(x-6y)=6
c-(15-12)=4
Step-by-step explanation:
how to solve 46 divide by 6 and change it to a multiplication equation
Answer:
46/6 is approximately 7.667.
To change it to a multiplication problem, I can do 46 = 6*7.667. The answer is not exact, just an estimated approximation.
You can also try to divide yourself.
Write an expression equivalent to 5(3m+n)
Answer:
15m+5n
Step-by-step explanation:
5(3m+n) In this case you need to multiply. 5x3m is 15m; 5xn is 5n. 15m+5n
A circular swimming pool has a radius of 3.5 meters. Liz is placing a piece of rope around the
edge of the pool. If Liz has exactly enough rope, which measurement is dosest to the length
of the piece of rope in meters?
Answer:
220m
Step-by-step explanation:
2 pie r=2*22/7*3.5=220 m
pls someone anwser quick
You purchase a car for $20,000. It depreciates 30% each year. Which formula calculates how much your car will be worth in 10 years?
Answer:6722.8(sorry if i'm wrong)
Step-by-step explanation:
Which of the following choices lists the values of the side longths of a triangle with 45-45-90 degree angles and a hypotonuso - 247? Need help
Answer:
D 12rad2 12rad2 24
Step-by-step explanation:
in class of 24 pupils, 4 need additional support
Answer:
1 out of ever PUPILS need support
Step-by-step explanation:
4/24=1/6
Solve using Cramer's rule. 3x + 2y = 5
x + 3y = 4
i need an answer ASAP
By applying Cramer's rule as solution method, the solution of the linear system 3 · x + 2 · y = 5 and x + 3 · y = 4 is equal to the set (x, y) = (1, 1).
How to solve a system of two linear equations with two variables
Determinants are constructions studied in linear algebra and related to matrices, one of the most common applications of determinants is the solution of linear equations, whose simplest form is known as the Cramer's rule.
Now we proceed to use this rule to get the solution of the linear system:
[tex]x = \frac{\left|\begin{array}{cc}5&2\\4&3\end{array}\right| }{\left|\begin{array}{cc}3&2\\1&3\end{array}\right|}[/tex]
[tex]x = \frac{(5)\cdot (3)-(4)\cdot (2)}{(3)\cdot (3) -(1)\cdot (2)}[/tex]
x = 1
[tex]y = \frac{\left|\begin{array}{cc}3&5\\1&4\end{array}\right| }{\left|\begin{array}{cc}3&2\\1&3\end{array}\right|}[/tex]
[tex]y = \frac{(3)\cdot (4) - (5)\cdot (1)}{(3)\cdot (3) - (1)\cdot (2)}[/tex]
y = 1
By applying Cramer's rule as solution method, the solution of the linear system 3 · x + 2 · y = 5 and x + 3 · y = 4 is equal to the set (x, y) = (1, 1).
To learn more on Cramer's rule: https://brainly.com/question/12682009
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3.1 Simplify the following ratios:
3.1.1 500g: 3 kg
- 15
Answer:
1g:6g-15
Step-by-step explanation:
I need help ASAP will mark the brainliest
Answer:
hhffuutxu da ruzrxtoxotx suzs txyfyfxkfzfjzrzjrzurzi f2f jfizeyUrYsU
Step-by-step explanation:
that boi sus fo real nfcgxjfxiffxdkhdkydkgzxd lux kygksktskgxkhxyzjrztjztkxlyslyskt
Write an exponential function in the form y=ab^xy=ab
x
that goes through points (0, 18)(0,18) and (2, 1152)(2,1152).
Answer:
Step-by-step explanation:
let y=ab^x
x=0,y=18
18=ab^0=a
a=18
y=18b^x
when x=2,y=1152
[tex]1152=18b^{2}\\b^{2}=\frac{1152}{18}=64=8^2\\b=8\\so~y=18(8)^x[/tex]
9. square
A =
s= 15 ft
Answer:
225 square feet
Step-by-step explanation:
If one side = 15 ft, and it's a square, you do 15 x 15 = 225 square feet
Hope that helps!
I need help can any on help me
Answer:
Simplify 3log3(-5) = undefined?
Step-by-step explanation:
The question that is asked
Answer:
THE ANSWER IS B BECAUSE I AM BIG BRAIN
Step-by-step explanation:
A park has a triangular sandbox. Todd wants to create a smaller sandbox at his backyard having the same angles as the park sandbox.
What is the perimeter in feet of Todd’s sandbox?
For what values of x and y is PQRS a parallelogram?
Answer:
[tex]y =2[/tex]
[tex]x =3[/tex]
Step-by-step explanation:
Given
The attached parallelogram
Required
Find x and y
Opposite sides are equal
So:
[tex]PQ = SR\ and\ QR = PS[/tex]
This gives:
[tex]2y + 3 = y + 5[/tex] -- (1)
[tex]4x - 3 = 4y + 1[/tex] -- (2)
[tex]2y + 3 = y + 5[/tex]
Collect like terms
[tex]2y - y= 5 - 3[/tex]
[tex]y =2[/tex]
[tex]4x - 3 = 4y + 1[/tex]
Substitute [tex]y =2[/tex]
[tex]4x - 3 = 4 * 2 + 1[/tex]
[tex]4x - 3 = 9[/tex]
Collect like terms
[tex]4x = 3 + 9[/tex]
[tex]4x = 12[/tex]
[tex]x =3[/tex]
I need help on the griding for (1/2,2). Please explain. :(
Which of the following can be used to prove that AABC = AADC?
Answer:
AAS postulate
Step-by-step explanation:
Answer:
i hope it help u:))
Step-by-step explanation:
i think that it will be ASA postulate
5x+2y=10
x+ay=4
Which value of a makes these equations have no solution.
Answer:
2
Step-by-step explanation:
Rearrange to same form:
2y = -5x + 10
y = -5/2x + 10
ay = -5x + 4
Parallel lines have no intersection and solution, thus a = 2
Answer:
Step-by-step explanation:
For there to be no solution the lines must be parallel and have different y intercepts. To be parallel they must have the same slope.
Solving each for y
y=(10-5x)/2 and y=(4-x)/a
So the slopes are
-5/2 and -1/a, if they are equal
-5/2=-1/a
-5a=-2
a=2/5