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:
Please solve these! Read the instructions too!
If the probability that a person will die in the next year is 771/100,000
what is the probability that the person will not die in the next year?
A. 0.771%
B. 99.229%
C. 0.229%
D. 99.771%
Answer:
(B) 99.229%
Step-by-step explanation:
If the probability of someone dying next year is [tex]\frac{771}{100000}[/tex], that means the probability of someone NOT dying next year is [tex]\frac{100000-771}{100000} = \frac{99229}{100000}[/tex].
To find the percent value of this fraction, we divide 99229 by 100000 and multiply by 100.
[tex]\frac{99229}{100000} = 0.99229\cdot100=99.229[/tex]
So, the answer is B, 99.229%.
Hope this helped!
Help pls will give brainliest
Answer:
The surface area of the rectangular prism is 292 cm²
can anyone answer this pls. will mark u as brainliest.
Answer:
6
Step-by-step explanation:
We first want to rewrite it and make the square roots into power of 1/2 as its is easier in most cases to work with.
We will first solve for a^2 because it appears twice
3+2×2^1/2
3+2.828=5.828427
Now we will solve 1/a^2
1/5.828427=.171572
.171572+5.828427
now you add them and it equals 6.
On a map the scale showing is 1 inch by 5 mi if a park is 75 square miles what is the area of the park on the map. The parks area is _____ square inches on the map
Answer: 15 square Inches
Step-by-step explanation: I believe you should divide 75 and 5(75mi÷5mi=15in) to get 15in.
Answer: 3 square inches.
If the park is 25 square miles, it could be 5×5 miles. If the scale is 1 inch = 5 miles, that would be 1×1 inch or 1 square inch on the map. Since 75 is 3×25, it will be 3×1 square inches on the map.
Step-by-step explanation: Remember that the scale represents linear measurements. For area, you must square the linear "sides" to get the number of actual square units represented by a square unit on the map.
Step 2 Using Proportional Relationships
Answer:
a ( 567 miles to unit)
b( looks like 2 units so i would say 1134 miles
Answ: the scale is
Step-bstep explanatio
For the equation, determine whether the equation is true for all, some, or no values of x.
Explain how you know.
Answer:
You can check if an equation is true for all some or no values of x by simply to try and solve the equation if you get something like x = x, then the equation is true for all, if you get a specific answer like x=3, then it is true to some values, in simple terms. Try and solve the equation there is no other way to check unless you solve, I don't know if there is another way but this is just my intution.
Step-by-step explanation:
Answer:
111
Step-by-step explanation:
111
Write an equation to find the nth term. Then find ₐ₂₄
-1, -4, -7, -10,...
The equation to find the nth term is:
an = a+(n-1)d
Where a is the first term in the sequence, which is -1 and d is the difference, which in this sequence the next term is found by subtracting 3 from the previous term, so d = -3 and n is the term you want to find.
The equation becomes:
an = -1 +(n-1)(-3)
a24 = -1 + (24-1)(-3) = -1 + (23(-3)) = -1-69 = -70
PLS HELP ME WITH THIS I NEED IT QUICK!!!!!!!!!!!
Answer:
Below in bold.
Step-by-step explanation:
-6x + 3y = -7
The x intercepts occur when y = 0, so
-6x + 3(o) = -7
x = -7/-6
x = 7/6
So the x-intercept = (7/6, 0).
The y intercept:
-6(0) + 3y = -7
y = -7/3.
So the y-intercept = (0, -7/3.t).
Factorize. (i) 2mn +m^2-6n - 3m (ii) 4y^2 -81 (iii) t^2 - 6t+8
Answer:
(i) (m-3)(2n+m) (ii) (2y+9)(2y-9) (iii) (t-4)(t-2)
Step-by-step explanation:
2mn+m^2-6n-3m
m(2n+m)-3(2n+m)
(m-3)(2n+m)
Answer: (m-3)(2n+m)
------------------------------
4y^2-81
(2y+9)(2y-9)
Answer: (2y+9)(2y-9)
-------------------------------
t^2-6t+8
(t-4)(t-2)
Factors of the given equations are
(i) (2n +m)(m - 3)
(ii) (2y-9)(2y + 9)
(iii) (t -4) (t - 2)
What is factorization?" Factorization is the process of breaking down large number or quantity into a smaller number or quantity."
Formula used
(a² - b²) = (a -b) (a +b)
According to the question,
(i) 2mn + m² -6n -3m
= m (2n +m) - 3 (2n +m)
= (2n + m) (m - 3)
(ii) 4y² - 81
= (2y)² - (9)²
= (2y - 9) (2y + 9)
(iii) t² - 6t +8
= t² - 4t - 2t + 8
= t (t - 4) -2 (t - 4)
= (t -4) (t -2)
Hence, Factors of the given equations are
(i) (2n +m)(m - 3)
(ii) (2y-9)(2y + 9)
(iii) (t -4) (t - 2)
Learn more about factorization here
https://brainly.com/question/14067703
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Complete the statement. The line x = −2 is _______.
Answer:
see explanation
Step-by-step explanation:
The line x = - 2
Is a vertical line parallel to the y- axis
It passes through all points with an x- coordinate of - 2
Four letters are selected at random with replacement from the word MATHCOUNTS. What is the probability that the letters in the order they are selected will form the word MATH?
So "MATHCOUNTS" has 10 letters.
And "MATH" has 4 letters.
So the probability of you getting the letters "M" "A" "T" "H" is 4/10 or 2/5.
But it has to be in order...
There are 32 ways you can arrange the 4 letters. There is only 1 way you can write "MATH"
So 1/32 probability of 2/5 is 2/160 or 1/80
The probability of getting the word MATH is 1/80
What is Probability ?The study of likeliness of an event to happen is probability .
It is given that
Total letters in MATHCOUNTS : 10 letters.
Total chances of getting letter M , A , T , H is 4
Probability of getting the letters M , A , T , H is 4/10
= 2 /5
The probability of getting the word MATH is 1
And the total number of ways the letters can be arranged is 2⁴
= 32
The probability of getting the word MATH is
= 1 /32 * 2 /5
=1/80
Therefore , The probability of getting the word MATH is 1/80
To know more about Probability
https://brainly.com/question/11234923
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In the triangles, TR = GE and SR = FE.
Triangles S T R and F G E are shown. Angle S R T is 56 degrees. Angle F E G is 42 degrees. Sides T R and G E are congruent. Sides S R and F E are congruent.
if Line segment G F = 3.2 ft, which is a possible measure of Line segment T S?
Answer:
3.2 ft
Step-by-step explanation:
the only thing you need to know is that congruent means that all the side and the same and the shape can be flipped and still look the same so the measure of the line segment is 3.2ft
Answer:
3.2 ft
Step-by-step explanation:
The answer above is correct.
can someone turn this into slope intercept form please ?? thank you .
Answer:
1) -1 - 0 fraction on top of -4 -3
Step-by-step explanation:
(x1,y1) and the second (x2,y2)
and the formula is x2- minus x1 over as ina fraction over y2- minus y1,,,, apply this to the other questions
Answer:
Hi there!!!
just use double point formula for the equation of st.line.
(i.e (y-y1 )= y2-y1/x2-x1 times (y-y1)
I hope the answers in the pictures will help you....
14+12= -15x+2x need help thanks
Answer:
x = -2
Step-by-step explanation:
Collect terms:
26 = -13x
Divide both sides of the equation by the coefficient of x:
26/-13 = x = -2
The solution is x = -2.
Answer:
-2
Step-by-step explanation:
14+12=-15x+2x
26=-13x
x=26/-13
x=-2
Are the ratios 5:4 and 8:2 equivalent? yes or no
Answer:
no
Step-by-step explanation:
no its no
Answer:
I believe no
Step-by-step explanation:
I believe it is no but I could be wrong...if I am wrong I am very sorry and hope you can forgive me
Solve the equation using the square root method. Select all solutions that apply. x^2 = 36 A.-8 B.6 C.-6 D.8
Answer:
x = ± 6
Step-by-step explanation:
x^2 = 36
Take the square root of each side
sqrt(x^2) = sqrt(36)
x = ± 6
Answer:
[tex]\large \boxed{\boxed{x=\pm 6}}[/tex]
Step-by-step explanation:
[tex]x^2 =36[/tex]
Take the square root on both sides.
[tex]\sqrt{x^2} =\pm \sqrt{36}[/tex]
Simplify.
[tex]x=\pm 6[/tex]
Sasha deposited $1,400 in an account that pays 1.5% simple interest. She created a graph of her
account balance equation (A = Prt + P) with a slope of 21.
true or false?
Answer:
The answer is False.
Guys pls help me in this coz im very confused in this
Answer:
Step-by-step explanation:
1. Copy the diagram using ruler for parallel lines * ensure they (the parallel lines) each have the same distance each point to one another before drawing or adding the transversal line L(3)
The transversal doesn't have to be exact to the diagram but the parallel lines do have to be correct to prove that angle 1 + 5 are identical and fit into each other.
2. They only become corresponding because of being on transversal to add to 180 degree. As you will see when you draw angle 1 on colored paper near the first blue/green circle and match with 5 below in the second blue/green circle.
3. The reason they want tracing paper afterwards of the same shape is so you can use alternatively to cover angle 5 in your book.
You will see they do cover each other.
Additional
''When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles. ''
Should you enter search for the above statement it will show you an interactive tool you can use for regarding maths transversal.
Here you can compare parallel lines like l(1) and l(2) as even if they were not parallel they would still be corresponding angles. As you will see.
Determine whether each equation is an identity or whether it has no solution.-3(2x+1)=2(-3x-1) help is this a no solution or infinite
Answer:
No solution.
Step-by-step explanation:
Distribute.
-3(2x + 1) = 2(-3x - 1)
-6x - 3 = -6x - 2
Combine like terms.
-6x - 3 = -6x - 2 add 3 to both sides
-6x = -6x + 1 add 6x to both sides
0 = 1 this is false.
Because we ended up with a false equation, there is no solution to this equation.
Answer:
no solution
Step-by-step explanation:
Perform the indicated multiplication, using the distributive property.
-3(2x+1)=2(-3x-1) becomes -6x - 3 = -6x - 2
This has no solution because -3 is never equal to -2.
Kevin has a rectangular farm mapped on a coordinate plane. He wants to make a fence along one of the longer sides of the farm. What would be the length of the fence? A. 6 B. 10 C. 12 D. 8
Answer:
10
Step-by-step explanation
Answer:
10
Step-by-step explanation:
What is the surface area of this rectangular pyramid?
I got 288 but that could be wrong. graduated a while ago. hope it helps though.
(08.01) Two lines, A and B, are represented by the following equations: Line A: y = x − 1 Line B: y = −3x + 11 Which of the following options shows the solution to the system of equations and explains why? (3, 2), because the point does not lie on any axis (3, 2), because one of the lines passes through this point (3, 2), because the point lies between the two axes (3, 2), because both lines pass through this point
Answer:
the answer is D
Step-by-step explanation:
y=x-1
2=3-1
2=2
y=-3x+11
2=-3(3)+11
2=-9+11
2=2
Answer:
Step-by-step explanation:
If both lines pass through the point (3, 2), we automatically know that (3, 2) is the soution of the system of linear equations given here, AND that (3, 2) is a solution of equation A and equation B both.
Select all decimals that are equivalent to (9 x 100) + (2 x 10) + (3x ) + (5 x it).
A. 92.35
B. 920.350
C. 902.35
D. 92.350
D E 920.35
F. 920.035
Answer:
the answer to the question is letter E I believe
Two birds start from the same nest and head off in opposite directions. The speed of the first bird is 15mph more than the speed of the second.After 6 hours the two birds are 402 miles apart. Find the speed of each bird?
Answer:
41 mph26 mphStep-by-step explanation:
The rate at which distance is increasing between the birds is ...
r = d/t = (402 mi)/(6 h) = 67 mi/h
This is the sum of the speeds of the two birds, so is 15 mph more than double the speed of the slower bird. That bird's speed is then ...
(67 -15)/2 = 26 . . . miles per hour
The faster bird is 15 mph faster so is 26+15 = 41 mph.
The slower bird's speed is 26 mph; the faster bird's speed is 41 mph.
A state highway department uses a salt storage enclosure that is in the shape of a cone, as shown above. If the volume of the storage enclosure is 48π m3, then what is the diameter of the base of the cone, in meters?
Answer:
Diameter of the base of the cone = 8 meters
Step-by-step explanation:
State highway department uses a salt storage enclosure which is in the shape of a cone.
Height of the storage in conical shape = 9 meters
Volume of the storage = 48π m³
Let the radius of this conical storage = r meters
Formula to get the volume of a cone = [tex]\frac{1}{3}\pi r^{2}h[/tex]
Here 'r' is the radius of the base of the cone and 'h' is the height of the cone.
Therefore, Volume = [tex]\frac{1}{3}(\pi ) r^{2}(9)[/tex]
[tex]48\pi=3\pi r^{2}[/tex]
r² = [tex]\frac{48\pi }{3\pi }[/tex]
r = [tex]\sqrt{16}[/tex]
r = 4 meters
Since, diameter = 2r
= 2(4)
= 8 meters
Therefore, diameter of the base of the cone = 8 metres
Kaitlin compared the statistics from her team's baseball season. She determined that having fewer hits did not imply that a player caught more or fewer balls. What should she conclude? a. There is no correlation between the number of hits and the number of balls caught. b. There is a correlation between the number of hits and the number of balls caught. There may or may not be causation. Further studies would have to be done to determine this. c.There is a correlation between number of hits and number of balls caught. However, there is no causation. This is because there is probably a decrease in the number of balls caught with a decrease in the number of hits.
Answer: c.There is a correlation between number of hits and number of balls caught. However, there is no causation. This is because there is probably a decrease in the number of balls caught with a decrease in the number of hits.
Step-by-step explanation:
Correlation is a term used to define a relationship between two variables.Causation is a term used to define the effect of one variable on other.Given, Kaitlin compared the statistics from her team's baseball season. She determined that having fewer hits did not imply that a player caught more or fewer balls.
There is a correlation between number of hits and number of balls caught. However, there is no causation as " fewer hits did not imply that a player caught more or fewer balls.".
This is because there is probably a decrease in the number of balls caught with a decrease in the number of hits.
Hence, the correct option is "c".
Function f(x) =ax +b where a and b are integers and a<0 has a domain 1
Answer:
sorry i read the question wrong and put a wrong answer im not sure how to delete
Step-by-step explanation:
If a person earned $32,000 a year and received $800 raise, what was the percent increase in her salary?
Answer:
Hey there!
This would be a 2.5% increase in salary.
Using the percent increase formula we find the answer to be a 2.5% increase.
Let me know if this helps :)
Answer:
2.5%
Step-by-step explanation:
((new - original) / original) * 100
328-320 = 8/320 = 0.025
0.025 * 100 = 2.5
Richard bought a car for $2,500. The value of the car depreciates by 5% each year,
What is the average rate of change in the value of the car during the first 3 years?
Round your answer to the nearest dollar.
-$232
- $116
-$119
- $357
Step-by-step explanation:
Hello, there!!!
The answer is option D.
I have given solution on the picture.
Hope it helps.....