Answer:
The answer is "[tex]\bold{\frac{x^{'}^2}{17}-\frac{y^{'}^2}{31}=1}[/tex]"
Step-by-step explanation:
In the given question there is some mistyping error if the given value is this. so, its solution can be defined as follows:
[tex]19x^2 + 24\sqrt{3} xy - 5y^2 - 527 = 0...................(1) \\\\ \theta = 30^{\circ}[/tex]
Formula:
[tex]\bold{x=x'\cos \theta -y' \sin \theta}[/tex] [tex]_{where} \ \ \ \ \theta =30[/tex]
[tex]=x' \cos 30- y' \sin 30\\\\ =x' \frac{\sqrt{3}}{2}- y' \frac{1}{2}\\\\ =\frac{1}{2}(x' \sqrt{3}- y')....(a)\\\\[/tex]
[tex]\bold{y=x'\sin \theta +y' \cos \theta}[/tex] [tex]_{where} \ \ \ \ \theta =30[/tex]
[tex]=x' \sin 30+y' \cos 30\\\\ =x' \frac{1}{2}+y' \frac{\sqrt{3}}{2}\\\\ =\frac{1}{2}(x'+ y'\sqrt{3})....(b)\\\\[/tex]
put the equation (a) and equation (b) value in equation 1:
equation:
[tex]\to 19x^2 + 24\sqrt{3} xy - 5y^2 - 527 = 0...................(1) \\\\[/tex]
[tex]\to 19(\frac{1}{2}(x'\sqrt{3}- y'))^2+24\sqrt{3}(\frac{1}{2}(x'\sqrt{3}- y))( \frac{1}{2}(x'+y'\sqrt{3}))- 5(\frac{1}{2}(x'+y'\sqrt{3}))^2-527= 0\\[/tex]
[tex]\to \frac{19}{4}(3x^{'}^2+ y^{'}^{2}-2\sqrt{3}x' y')+6\sqrt{3}(\sqrt{3}x^{'}^{2}+2x'y'-\sqrt{3}y^{'}^2)-\frac{5}{4}(x^{'}^2+ 3y^{'}^{2}-2\sqrt{3}x' y')-527=0[/tex]
[tex]\to \frac{57}{4}x^{'}^2+\frac{19}{4}y^{'}^2-\frac{19 \sqrt{3}}{2}x^{'}^2y^{'}^2+18x^{'}^2+12\sqrt{3}x^{'}^2y^{'}^2-18y^{'}^2-\frac{5}{4}x^{'}^2-\frac{15}{4}y^{'}^2-\frac{5\sqrt{3}}{2}x^{'}^2y^{'}^2-527=0\\\\\to 31x^{'}^2-17y^{'}^2-527=0\\\\\to 31x^{'}^2-17y^{'}^2=527\\\\\to \frac{x^{'}^2}{17}-\frac{y^{'}^2}{31}=1\\\\[/tex]
Answer:The answer is The answer is ""
Step-by-step explanation:
Sally invested some money at 15 % interest. Sally also invested $172 more than 3 times that amount at
14%. How much is invested at each rate if Sally receives $1398.35 in interest after one year? (Round to
two decimal places if necessary.)
Answer:
Amount at 15%=$2,411
Amount at 14%=$7,405
Step-by-step explanation:
let
x= the amount at 15% rate.
y=amount at 14% rate
y= x times 3 plus $172
y= 3x + $172 (1)
x times 15% plus y times 14% equals a return of $1,398.35 after one year
0.15x + 0.14y= $1,398.35 (2)
Recall,
y= 3x + $172
Substitute (1) into (2)
0.15x + 0.14y= $1,398.35
0.15x + 0.14(3x+172)=1398.35
0.15x + 0.42x + 24.08=1398.35
Collect like terms
0.15x + 0.42x=1398.35 - 24.08
0.57x=1374.27
Divide both sides by 0.57
x=2,411
x=$2,411
Find y
y= 3x + $172
=3(2,411) + 172
=7,233+172
=7,405
y=$7,405
Amount at 15%=$2,411
Amount at 14%=$7,405
Check:
$2,411*0.15=$361.65
$7,405*0.14=$1036.70
Total=$361.65 + $1036.70
=$1,398.35
Question no. e. and f. please help me !!!!!
Answer: see proofs below
Step-by-step explanation:
Proofs are like a puzzle that you have to unravel.
You can manipulate the left side to get the right side (LHS → RHS)
or
You can manipulate the right side to get the left side (RHS → LHS)
You will need to use Pythagorean Identities, Sum and Difference Identities, and/or Double Angle Identities when manipulating one of the sides.
Use the following Identities:
cos 2A = cos²A - sin²A
sin 2A = 2 cosA · sinA Note that A can be substituted with 2A
sin 3A = 3 sinA - 4sin³A
cos 3A = 4cos³A - 3cosA
***********************************************************************************
e) Prove: 4 sin A · cos³A - 4 cos A · sin³A = sin(4A)
LHS → RHS
Given: 4 sin A · cos³A - 4 cos A · sin³A
Factor: 4 sin A · cos x (cos²A - sin²A)
2(2 sin A · cos A)(cos²A - sin²A)
Double Angle Identity: 2(sin 2·A)(cos 2·A)
2 sin (2A) · cos (2A)
Double Angle Identity: sin (2·2A)
sin 4A
Proven: sin 4A = sin 4A [tex]\checkmark[/tex]
*****************************************************************************************
f) Prove: 4 sin³A · cos 3A + 4 cos³A · sin 3A = 3 sin(4A)
LHS → RHS
Given: 4 sin³A · cos 3A + 4 cos³A · sin 3A
Triple Angle Identity: 4sin³A (4cos³A - 3 cosA) + 4cos³A (3sinA - 4sin³A)
Expand: 16sin³A · cos³A - 12sin³A · cosA + 12cos³A · sinA - 16sin³A · cos³A
Simplify: 12cos³A · sinA - 12sin³A · cosA
Expand: 6cos²A(2cosA · sinA) - 6sin²A(2cosA · sinA)
Double Angle Identity: 6cos²A(sin 2A) - 6sin²A(sin 2A)
Factor: 6sin 2A (cos²A - sin²A)
Double Angle Identity: 6sin 2A (cos 2A)
3(2sin 2A · cos 2A)
Simplify: 3sin (2·2A)
3 sin 4A
Proven: 3sin 4A = 3sin4A [tex]\checkmark[/tex]
Evaluate the expression. *
23 – (12 + 6) + 8
Please help
Answer:
13
Step-by-step explanation:
23-(12+6)+8
23-18+8
31-18
13
answer is 13
Step-by-step explanation:
Using the BODMAS rule,bracket of division or multiplication, addition or subtraction.
This applies the rule:
therefore,
23- (12+6)+8 ,calculate within bracket first
=23-(18)+8
now remove the bracket,by multiply by the -1
=23-18+8
the start calculate from the left to right
=23-10
=13
therefore the answer is 13
COME ON!! What’s the answer 53 points!
Answer:
X : -6, 3, 15, -12
Y : 11, 5, -3, 15
Step-by-step explanation:
Hey there!
To find the y values we need to plug the x values into th given equation,
y = -2/3x + 7
-6 ⇒ 11
15 ⇒ -3
Now we have a x value missing to that that we work backwards,
we plug in 15 for y in the given equation,
15 ⇒-12
Hope this helps :)
Step-by-step explanation:
[tex]y = - \frac{2}{3} x + 7[/tex]
Substituting the values of x into the expression we have
For x = - 6[tex]y = - \frac{2 }{3} ( - 6) + 7[/tex]
y = 11 For y = 5Make x the subject
[tex]5 = - \frac{2}{3} x + 7[/tex]
Multiply through by 3
15 = - 2x + 21
-2x = 15 - 21
- 2x = - 6
Divide both sides by - 2
x = 3For x = 15[tex]y = - \frac{2}{3} (15) + 7[/tex]
y = - 10 + 7
y = - 3For y = 15[tex]15 = - \frac{2}{3} x + 7[/tex]
Multiply through by 3
45 = - 2x + 21
- 2x = 45 - 21
- 2x = 24
Divide both sides by - 2
x = - 12Hope this helps you
L-Lcosθ=v^2/2 solve for L
Answer:
[tex]$L=\frac{v^2}{2-2\cos(\theta)}$[/tex]
Step-by-step explanation:
Solve for [tex]L[/tex] in
[tex]$L-L \cos(\theta)=\frac{v^2}{2} \Longrightarrow L(1-\cos(\theta))=\frac{v^2}{2}$[/tex]
[tex]$L=\frac{v^2}{2(1-\cos(\theta))}=\frac{v^2}{2-2\cos(\theta)}$[/tex]
Please help me on this question
Answer:
The area can be expressed as: [tex]\pi r^2+lw[/tex].
We have l=10, because 18-2(4)
We have w=8, as given.
Thus, the rectangle area is 80.
There are two semicircles, but they add to form a full circle, which makes things a lot easier. We have the circle area formula, and substituting the values gives us 50.24 as the circle volume
80+50.24=130.24.
Rounded to 1 decimal place that is 130.2
Hope this helps :)
Jovie is maintaining a camp fire. She has kept the fire steadily burning for 10 hours with 15 logs. She wants to know how many hours (h)left parenthesis, h, right parenthesis she could have kept the fire going with 9 logs. She assumes all logs are the same.
Answer:
6 hours
Step-by-step explanation:
We can use ratios to solve
10 hours x hours
-------------- = -------------
15 logs 9 logs
Using cross products
90 = 15x
Divide by 15
90/15 = 15x/15
6 = x
6 hours
Answer:
Below
Step-by-step explanation:
Jovie has maintained the fire burning with 15 logs for 10 hours.
● 15 => 10
Let's find how many hours do 9 logs keep the fire burning.
Let x be that time
● 9 => x
■■■■■■■■■■■■■■■■■■■■■■■■■■
● 15 => 10
● 9 => x
● 15 * x = 9×10
● 15x = 90
● x = 90/15
● x = 6
So the time that the fire will keep burning is 6 hours.
Describe the end behavior of the graph of f(x) = x^3 (x + 3)(-5x + 1) using limits.
Answer: Rises to the left and falls to the right
Step-by-step explanation:
Use the degree and the leading coefficient to determine the behavior.
There is a good video called "Describing End Behavior Using Limit Notation" by Mario's Math Tutoring, and it helps to show you how to find the end behavior with limits.
If a triangle has two of its shorter sides measuring 7 and 12, what is a possible length of the longest side of the triangle to make it acute?
Answer:
13
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
How to do 18b ? pls explain too thanks
Answer:
m² + 9n² + 4m - 12n - 6mn + 4
Step-by-step explanation:
18b
(2+m-3n)² = (2+m-3n)(2+m-3n)
= 2*2 + 2*m + 2*-3n + m*2 + m*m + m*-3n - 3n*2 -3n*m - 3n*-3n
= 4 + 2m - 6n + 2m + m² - 3mn - 6n - 3mn + 9n²
= m² + 9n² + 2m + 2m - 6n - 6n - 3mn - 3mn + 4
= m² + 9n² + 4m - 12n - 6mn + 4
Answer:
(2+m-3n)(2+m-3n)
Step-by-step explanation:
Here's solution:
(2+m-3n)(2+m-3n)
4 + 2m - 6n + 2m + m^2 - 3mn - 6n - 3mn + 9n^2
4 + 4m - 12n + m^2 - 9mn + 9n^2
I hope this is right, I'm a bit tired.
Hope this helps, and have a good day :)!
Help please will give brainliest
Answer:
18.
a) 6k + 2y
b) 2x^2 + 2x
c) 16h
19. 4.5 cm
20.
a) x > 4.5
b) x >= 32
Step-by-step explanation:
does the following table shows a proportional relationship between the variables g & h
*the table being referred to is attached below
Answer:
The table does not show a proportional relationship between variable g and h.
Step-by-step explanation:
For a proportional relationship to exist between two variables, there must be a constant, of which serves like a unit rate, when comparing two variables.
Thus, in the table attached below, there is no obvious constant of proportionality between variable g and variable h.
Thus, [tex] \frac{9}{3} [/tex] ≠ [tex] \frac{36}{6} [/tex] ≠ [tex] \frac{81}{9} [/tex]
What is the area of a regular hexagon with perimeter 24? A) 8sqrt3 B) 12sqrt3 C) 16sqrt3 D) 24sqrt3
Answer: C) 16
Step-by-step explanation:
A Hexagon has 6 Sides and Since the perimeter is 24, each side has a length of 4.
4 * 4 = 16
Tyler and Jamie decide to share a box of 50 candy bars. To their pleasant surprise, there are 5 extra candy bars in the box. They agree that Tyler gets at least eight more candy bars than Jamie. What is the minimum number of candy bars that Tyler gets. Can I get a step by step explanation please? Thank you!
Answer:
Minimum candy Tyler gets = 32
Step-by-step explanation:
Given:
Number of candy in box = 50
Extra candy = 5
Find:
Minimum candy Tyler gets
Computation:
Assume.
Number of candy Tyler gets = x
Number of candy Jamie gets = x - 8
Total number of candy in box = 50 + 5 = 55
So,
Number of candy Tyler gets + Number of candy Jamie gets = Total number of candy in box
x + x - 8 = 55
2x = 63
x = 31.5
So,
Minimum candy Tyler gets = 32
T(d) is a function that relates the number of tickets sold for a movie to the number of days since the movie was
released. The average rate of change in Td) for the interval d = 4 and d = 10 is 0. Which statement must be true?
O The same number of tickets was sold on the fourth day and tenth day.
O No tickets were sold on the fourth day and tenth day.
O Fewer tickets were sold on the fourth day than on the tenth day.
O More tickets were sold on the fourth day than on the tenth day.
Answer: The same number of tickets was sold on the fourth day and tenth day.
Step-by-step explanation:
Given, T(d) is a function that relates the number of tickets sold for a movie to the number of days since the movie was released.
The average rate of change in a function with respect to the independent variable gives the value of change in a particular period.
If average rate of change in T(d) for the interval d = 4 and d = 10 is is 0 , that means nothing has been changed in the number of tickets sold on 4th day and 10th day after the film release.
Hence, the correct statement is "The same number of tickets was sold on the fourth day and tenth day."
The correct option is (A).The same number of tickets was sold on the fourth day and tenth day.
Given,
T(d) is a function that relates the number of tickets sold for a movie to the number of days since the movie was released.
The Average rate of change in T(d) for the interval d = 4 and d = 10 is 0.
We have to find which statement is true.
Since the average rate of change in T(d) for the interval d = 4 and d = 10 is 0, it means nothing has been changed in the number of tickets sold on day 4 and day 10 after the film release.
Hence, the correct statement is The same number of tickets was sold on the fourth day and tenth day.
Thus The correct option is A.
For more details follow the link:
https://brainly.com/question/8011401
4(3r+2)-3r= -10? need help thanks
Answer: -2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
please help me find the nth term of this sequence 0, 3, 8, 15, 24
Answer:
80
Step-by-step explanation:
0, 3, 8, 15, 24, 35, 48, 63, 80 which is the nth term
first step you have to find how many steps the sequence was going with.
examples= from 0 to 3 the steps were 3
=from 3 to 8 the steps were 5
= from 8 to 15 the steps were 7
you will recognize that the steps the sequence is going with is odd numbers.
so you will use the odd numbers until you find what you need. which leads you to 80 which is the nth number in the sequence.
Answer:
80
Step-by-step explanation:
Change 06:00 to 12 hour clock time using a.m. and p.m.
I will mark you as brainlist
Answer:
06:00 a.m.
Step-by-step explanation:
That very simble, from 0:00 to 11:59 you use am, from 12:00 to 23:59 you use p.m :)
In January 2008, the temperature in parts of Minnesota fell from 48 F degrees to -12 F degrees over a 24 hour period. What was the average temperature change per hour?
Answer:
The average temperature per hour:
-2.5 °F
Step-by-step explanation:
(-12-48) / 24 = -60/24
-60/24 = -2.5
In average decrease:
2.5°F
per hour
!50 POINTS! GIVE REAL ANSWER OR I REPORT PLZ NO TROLLS! An executive drove from his home at an average speed of 35 mph to an airport where a helicopter was waiting. The executive then boarded the helicopter and flew to the corporate offices at an average speed of 78 mph. The entire distance from his home to the office was 169.5 miles. If the executive spent the same amount of time in the car as he did the helicopter, how long did it take the executive to get to work?
Answer:
it took him 3 hours to get to work
Step-by-step explanation:
For the first part of the trip, the executive covered a distance "d" in time 't" at 35 mph, therefore we can write that the time it took to get to the helicopter was:
[tex]t-\frac{d}{35}[/tex]
which if the distance is in miles, will render the time in hours.
We can write something similar for the second part of the trip", using the same "t" since it took the same time as for the first one, and using for distance 169.5 - d (since it is the distance to complete the total traveled distance :
[tex]t=\frac{169.5-d}{78}[/tex]
Now we equal those two equations because the time "t" is the same, and solve for "d":
[tex]\frac{d}{35} =\frac{169.5-d}{78} \\78\,d=35\,(169.5-d)\\78\,d=5932.5-35\,d\\(78+35)\,d=5932.5\\d=\frac{5932.5}{113} \\d=52.5[/tex]
Now, knowing the distance covered in the first trip, we can find the time of that first trip:
[tex]t=\frac{52.5}{35} =1.5\,\,hours[/tex]
Therefore, the time it took for thye total trip is: 1.5 h + 1.5 h = 3 hours
How far would she have walked if she kept the same pace?
There are four points on a line: A, B, C and D, so that AB=1, BC=2, CD=4. Find all the possibilities of the length of segment AD.
Answer:
{1, 3, 5, 7}
Step-by-step explanation:
There are four possibilities:
AD = AB -BC -CD = 1 -2 -4 = -5
AD = AB +BC -CD = 1 +2 -4 = -1
AD = AB -BC +CD = 1 -2 +4 = 3
AD = AB +BC +CD = 1 +2 +4 = 7
Possible lengths of AD are 1, 3, 5, 7.
__
The negative sign means the segment is added toward the left instead of toward the right. A final negative value means D is left of A, instead of to the right.
In a survey, a soft drink company asks people to name as many brands of soft drinks as they can. Which measure gives the most frequently mentioned brand? a. median b. mode c.mean
The required measure for the given case is mode. The correct option is (b).
How to find the mean and median for a given sample of data?In order to find the mean, first sum all the values of the data and count the number of data then divide them.
In order to find the median, first check whether the number of data is even or odd. For even number, the median is n/2 th element of the sample and for odd number the median is (n + 1)/2 th element.
The given problem deals with a sample of data.
In order find the correct answer, each option is analysed one by one as follows,
(a) The mean of a sample of data represents a standard value for the whole sample such that the individual values of the data may be more or less than it. but, it does not tell about the number of times a value is repeated.
(b)The median of a given sample can tell the middle most value of data when arranged in ascending order.
(c) The mode of a sample is about the times of occurrence of a single value in the whole sample.
As per the given question, to tell about the most frequently brand mode can be used.
Hence, the statistical measure that measures gives the most frequently mentioned brand is mode.
To know more about Mean click on,
https://brainly.com/question/22871228
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can someone explain how to do this please
Answer:
2/5 [tex]cm^2[/tex]
Step-by-step explanation:
To find the area of a rectangle do A = bh
When you substitute 4/6 for base and 3/5 for height it will be A = 4/6 x 3/5
This means the area is 2/5
Answer:
2/5 cm^2
Step-by-step explanation:
The area of a rectangle is found by
A = l*w
A = 4/6 * 3/5
Rewriting
=4/5 * 3/6
= 4/5 *1/2
= 2/5 cm^2
Can you find x for me?
Answer:
x = 120 degrees
Step-by-step explanation:
Since the angle given is 30 and the four lengths given are equal corresponding the angles opposite to their given sides for the top left triangle and bottom right triangle, the corresponding angles are equal and also 30 degrees. Since x is where the top left triangle is, we need an equation to relate x. The sum of all the angles in the top left triangle is 180. So, x + 30 + 30 = 180.
Therefore,
x = 180-30-30 = 120
Answer:
Step-by-step explanation:
There are two equal Angels in the triangle so!
X=180°- (30+30)°
=180-60
=120°
help me plz can somewon help me i am bad at math mostly
Answer:
Definitely the bottom left
Step-by-step explanation:
5 Sandeep bought 30 punnets of strawberries for £20. 1/6 of the punnets were rotten so he threw them away. He sold the remaining punnets for £1.50 each. Work out Sandeep's profit.
Answer:
£17.50
Step-by-step explanation:
30 punnets / £20
= 30 / 20
= 1.5
1 punnet costs £1.5
30 strawberries * (1/6 punnets)
= 30 * (1/6)
= 30/6
= 5
5 punnets were rotten.
5 rotten punnets * £1.5
= 5 * 1.5
= 7.5
Sandeep lost £7.5 in profits.
6/6 punnets - 1/6 rotten punnets
= 6/6 - 1/6
= 5/6
5/6 punnets are good
30 punnets * 5/6 good punnets
= 30 * 5/6
= 150/6
= 25
Sandeep has 25 punnets left to sell
25 punnets to sell * £1.50
= 25 * 1.5
= 37.50
Sandeep will get £37.50 from selling the punnets. However, you must take into account that he lost £20 when he bought the strawberies. THat money while be added back with some extra money left over:
£37.50 - £20
= 37.50 - 20
= 17.50
Put all into 1 equation:
{[30 * (5/6)] * 1.50} - 20
= {(150/6) * 1.50} - 20
= {25 * 1.50} - 20
= 37.50 -20
= 17.50
Overall, Sandeep's actual profits are equal to 17.50
I hope this is correct! Please tell me if the answer or info I gave was wrong!
Plz answer I’ll mark brainliest
Answer: B
Step-by-step explanation:
Any inscribed quadrilateral (quadrilateral in a circle) has opposite angles that add up to 180 degrees.
So looking at he picture we can see that, (x+16) + (6x-4) = 180.
So your answer is B.
Answer:
Hey There!! The answer to this is B: angle P + angle R = 180
angle O + angle Q = 180
Here, they are only interested in R, therefore the first equation will be enough to solve for R.
angle P + angle R = 180
y + (3y + 8) = 180
We need to solve for y, so put that y value in (3y + 8) to find angle R.
y + (3y + 8) = 180
y + 3y + 8 = 180
We add the y terms: 4y + 8 = 180
Subtract 8 from both sides: 4y = 180-8 = 172
Divide both sides by 4
y = 172/4 = 43
Angle R = 3y + 8
Put y = 43 and calculate R.
R = 3(43) + 8
R = 137
Therefore, the measure of angle R is B:
Hope It Helped!~ ♡
ItsNobody~ ☆
Find the interquartile range for a data set having the five-number summary: 3.5, 12, 19.1, 25.8, 31.8 A. 28.3 B. 13.8 C. 15.6 D. 12.7
Answer:
B. 13.8
Step-by-step explanation:
The five-number summary consists of five items which is usually displayed on a box plot, and can be represented in ascending order.
The five-number summary given: 3.5, 12, 19.1, 25.8, 31.8, represents the following in ascending order:
1. The minimum value = 3.5
2. First quartile (Q1) = 12
3. The median = 19.1
4. Third quartile (Q3) = 25.8
5. The maximum value = 31.8
The interquartile range = Q3 - Q1
Therefore, the interquartile range of the data = 25.8 - 12 = 13.8
Solve the system of equations 2x - y = 11 and x + 3y = -5
Answer:
x = 4, y = -3
Step-by-step explanation:
{2x - y = 11
{x + 3y = -5
You can use the substitution method by solving for x in the second equation:
x + 3y = -5
Subtract 3y from both sides:
x = -3y - 5
Now, substitute this value for x into the first equation:
2x - y = 11
2(-3y - 5) - y = 11
Distribute:
-6y - 10 - y = 11
Add 10 to both sides:
-6y - y = 21
Combine like terms:
-7y = 21
Divide both sides by -7:
y = -3
Next, substitute this value for x into the second equation:
x + 3y = -5
x + 3(-3) = -5
Multiply:
x - 9 = -5
Add 9 to both sides:
x = 4
Answer:
(7, 3)
Step-by-step explanation:
2x - y =11 2x-y =11
-2(x+3y)= (-5)-2 -2x-6y= 10
Then you will cross out the x, and add.
-7y =21 divide 7
y=-21/7 or y=3
Then you plug in the y where the y is and solve
2x-(3) = 11
2x = 14
x=7
