Given that
(2/x)+(3/y) = 13--------(1)
(5/x)-(4/y) = -2 -------(2)
Put 1/x = a and 1/y = b then
2a + 3b = 13 ----------(3)
On multiplying with 5 then
10a +15 b = 65 -------(4)
and
5a -4b= -2 ----------(5)
On multiplying with 2 then
10 a - 8b = -4 -------(6)
On Subtracting (6) from (4) then
10a + 15b = 65
10a - 8b = -4
(-)
_____________
0 + 23 b = 69
______________
⇛ 23b = 69
⇛ b = 69/23
⇛ b =3
On Substituting the value of b in (5)
5a -4b= -2
⇛ 5a -4(3) = -2
⇛ 5a -12 = -2
⇛ 5a = -2+12
⇛ 5a = 10
⇛ a = 10/5
⇛ a = 2
Now we have
a = 2
⇛1/x = 2
⇛ x = 1/2
and
b = 3
⇛1/y = 3
⇛ y = 1/3
Answer :-The solution for the given problem is (1/2,1/3)
Check: If x = 1/2 and y = 1/3 then
LHS = (2/x)+(3/y)
= 2/(1/2)+3/(1/3)
= (2×2)+(3×3)
= 4+9
= 13
= RHS
LHS=RHS is true
and
LHS=(5/x)-(4/y)
⇛ 5/(1/2)- 4/(1/3)
⇛(5×2)-(4×3)
⇛ 10-12
⇛ -2
⇛RHS
LHS = RHS is true
5. A bird is at 20 feet above sea level. A fish is 14 feet below sea level. What is the difference?
Answer:
it's either 6 or -6 because if uts Like negative and positive then it should be either one of those
Answer:
Step-by-step explanation:
34
Find the exact length of the third side.
82
18
Answer:
80
Step-by-step explanation:
Rewrite the following equation in slope-intercept form. Y + 5 = 1 7 ( x + 7 )
Answer: y = 17x + 114
Step-by-step explanation:
The equation for the slope-intercept form is y = mx + b.
Arrange the equation so that it resembles y = mx + b.
You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.
y + 5 = 17(x + 7)
y + 5 = 17x + 119
y + 5 - 5 = 17x + 119 - 5
y = 17x + 114
Answer:
Y = 17x + 114
Step-by-step explanation:
1. Y + 5 = 17 (x+7)
2. Y + 5 = 17x + 119 [Multiply the numbers in parenthesis by 17.]
3. Y = 17x + 114. [To keep the balance and move the 5 over, subtract it from 119.]
What is 6/14 + 1/5 equal to?
Answer:
22/35
Hope that helps!
It's a thing called photo math just download it and it will give you your answer
6
Select all the correct answers.
Which expressions are equivalent to the given expression?
780
04/10
085
45
160
Answer:
I can't understand hydggsdfffd
The chord joining the vertices of an ellipse is called the ______ ______, and its midpoint is the ______ of the ellipse.
The chord joining the vertices of an ellipse is called the major axis, and its midpoint is the center of the ellipse.
The major axis of an ellipse is the chord that passes through the two vertices of the ellipse. It is the longest chord and its length is equal to twice the length of the semi-major axis of the ellipse. The midpoint of the major axis is the point that divides the major axis into two equal segments, and it coincides with the center of the ellipse. The center of the ellipse is the point of intersection of the major and minor axes, and it is equidistant from all points on the ellipse.
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100%
The equation M = -20w + 300 shows the amount of money. M, in a savings account after w weeks.
How much does the amount of money in the account change each week?
Hey there! I'm happy to help!
We want to see what happens every week. In the equation, w is multiplied by -20. This means that for each value of w, we will subtract an additional 20. This means that the account will lose $20 a week.
Have a wonderful day! :D
Find each measure.
m∠ JLK
The measure of the major arc JLK will be 206°. Then the correct option is B.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
The measure of the minor arc JK will be 154°.
Then the sum of the major arc and minor arc in a circle is 360°.
Then the major arc JLK will be given as,
JLK + JK = 360°
JLK + 154° = 360°
JLK = 206°
The measure of the major arc JLK will be 206°. Then the correct option is B.
Your question was incomplete, but the complete question was attached below.
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Determine the
equation of a line
that has an
x-intercept of 3 and
a y-intercept of 4.
Answer:
Step-by-step explanation:
x intercept it means y=0 (3,0)
y intercept means x=0 (0,4)
find the slope : y2-y1/x2-x1
y2-y1= 4-0=4
x2-x1= 0-3=-3
m=4/-3
y=mx+b b=4 since x=0
y=-4/3 x+4
what is the eccentricity of an infinitely long ellipse?
Less than 1 is the eccentricity of an infinitely long ellipse.
The ratio of the focus's distance from the ellipse's centre and the ellipse's distance from one of its ends is called the eccentricity of an ellipse.
It is easy to understand how circular an ellipse is in relation to a circle when we assume its eccentricity. It also estimates the ovalness of the ellipse, and eccentricity close to 1 directs to the high degree of ovalness.
The eccentricity of an ellipse is always < 1, i.e. e < 1. The formula of the eccentricity of an ellipse is as follows:
Eccentricity = Distance from Focus/Distance from Directrix
Which can be written as
=> e = c/a.
Where
e = Eccentricity of the ellipse
c = Distance of the focus from the centre of the ellipse
a = Distance of the endpoint of an ellipse from its centre
As we know, the eccentricity of an ellipse is always less than 1, So we can conclude that the eccentricity of an infinitely long ellipse is less than 1.
Therefore, less than 1 is the eccentricity of an infinitely long ellipse.
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Please helpp!
Find the difference. Use a number line. Enter your answer as a simplified mixed number.
Answer:
2\(\frac{7}{9} \\\)
Step-by-step explanation:
-(2/9) + 3
= 27/9 - 2/9
= 25/9
= 2\(\frac{7}{9} \\\)
Sarah can shoe 12 horses in 3 hour. If she charges $50 per horse, how much money does she make per hour? (round answer to nearest whole number)
Answer:
200 per-hour
Step-by-step explanation:
12x50=600
600÷3
200
Answer:
1800
Step-by-step explanation:
I dont know what you mean by can shoe but if you meant to put can make this is the answer. 50 times 12 = 600 Dollars. 600 Dollars times 3 = 1800.
Fill in the blank. A polygon is _____ if there are "dents" or indentations in it (where the internal angle is greater than 180°)
A polygon is called non-convex if there are "dents" or indentations in it, where the internal angle is greater than 180 degrees.
In other words, a non-convex polygon is a polygon whose line segments intersect, creating an interior angle greater than 180 degrees. This is in contrast to a convex polygon, where all of the interior angles are less than 180 degrees and none of the line segments intersect.
Non-convex polygons can have a variety of shapes and sizes, and can be composed of any number of sides. However, they are generally more difficult to work with mathematically than convex polygons, and often require more advanced techniques to analyze and understand their properties.
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what is the area of the picture
Answer: 140
Step-by-step explanation:
Find the slope between the following two points: (3, 1), (5, 4).
Answer:
3/2
Step-by-step explanation:
Answer:
3/2
Step-by-step explanation:
Use a Venn diagram in which the event areas are proportional to their probabilities to illustrate three events A, B, and C that are independent.
A Venn diagram is a graphical representation of all possible logical relationships between a finite collection of sets. Venn diagrams are used to visualize how different sets overlap and the relationship between different groups of objects.
Venn diagrams are often used in statistics and probability to illustrate the relationship between different events.
In the context of probability, events A, B, and C are considered independent if the occurrence of one event does not affect the probability of the other events occurring. In other words, the probability of each event is independent of the other events.
To create a Venn diagram that illustrates three independent events A, B, and C, you would first draw three circles that are not overlapping.
Each circle represents one of the three events. Next, you would label each circle with the name of the corresponding event. In order to make the size of each circle proportional to the probability of the event occurring, you would adjust the size of each circle according to the probability of that event.
The larger the probability, the larger the circle. Finally, you would indicate the area of overlap between each pair of events. Because the events are independent, there should be no overlap between any of the circles. The Venn diagram would look something like this: In summary, to illustrate three independent events A, B, and C using a Venn diagram, you would draw three non-overlapping circles that represent each event and adjust their size to be proportional to the probability of that event.
There should be no overlap between any of the circles since the events are independent.
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Consider a death star under the command of Anakin Skywalker who wishes to target Obi-Wan's home planet that has a mass M and radius R. We are assuming both celestial bodies are spherical. The death star has a mass density as rho(r,θ,ϕ)=r 3 ϕ 2 and and radius r 1 . The distance between the death star and the planet is Z. (a) Find the mass of the death star. (b) The energy needed for a planet to form (or destroy) can be written as E=∫ 4/3 πrho 2r 3dV where the integration measure dV is just a infinitesimal volume in spherical polar coordinates. Using equation 9 find the total energy of Obi Wan's home planet.
a) Mass of the Death Star: To find the mass of the death star, the given density function will be integrated over the entire volume of the star. Mass of the death star=∫∫∫ρ(r,θ,ϕ)dV =4π/15×r15 .
where dV=r2sinθdrdθdϕ As we have ρ(r,θ,ϕ)=r3ϕ2, so the integral will be
Mass of the death star=∫∫∫r3ϕ2r2sinθdrdθdϕ
Here, the limits for the variables are given by r = 0 to r
= r1;
θ = 0 to π; ϕ
= 0 to 2π.
So, Mass of the death star is given by:
Mass of the death star=∫02π∫0π∫0r1r3ϕ2r2sinθdrdθdϕ
=1/20×(4π/3)ρ(r,θ,ϕ)r5|02π0π
=4π/15×r15
b) Total energy of Obi Wan's home planet:
Total energy of Obi Wan's home planet can be obtained using the relation
E=∫4/3πρr3dVUsing the same limits as in part (a),
we haveρ(r,θ,ϕ)
=Mr33/3V
=∫02π∫0π∫0RR3ϕ2r2sinθdrdθdϕV
=4π/15R5 So,
E=∫4/3πρr3dV=∫4/3π(4π/15R5)r3(4π/3)r2sinθdrdθdϕE
=16π2/45∫0π∫02π∫0Rr5sinθdϕdθdr
On evaluating the integral we get,
E=16π2/45×2π×R6/6=32π3/135×R6
a) Mass of the death star=4π/15×r15, b) Total energy of Obi Wan's home planet=32π3/135×R6
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Jonah drew two squares with the same dimensions. He then added 2 inches to the length of one square to make it a rectangle. He also added 2 inches to the width of the other square to make it a rectangle. Write an equation that compare the perimeters of the two rectangles.
Answer:
Perimeter of rectangle 1=4x+4
Perimeter of rectangle 2=4x+4
Step-by-step explanation:
Two squares with the same dimension
Square 1: let length=x
Square 2: let length=x
Since they have same dimensions
He added two inches to the length of square 1 to make it a rectangle
Rectangle 1: width=x, length=x+2
Perimeter=2(l+w)
=2{(x+2)+x}
=2(x+2+x)
=2(2x+2)
=4x+4
He added two inches to the width of square 2 to make it a rectangle
Rectangle 2: length=x, width=x+2
Perimeter=2(l+w)
=2{(x+(x+2)}
=2(x+x+2)
=2(2x+2)
=4x+4
The two rectangles have equal perimeter
what sequence is 3,5,8,12
Answer:
+3,+2+3+4+2
Step-by-step explantion
so nowd it be 14
What is the y-intercept of this line?
y = 6x – 9
b = [?]
Answer:
you have to find the slope it was hard for me too
Step-by-step explanation:
Answer:
-9
Step-by-step explanation:
y = mx + b
y = y
m = slope
x = x
b = y-intercept.
Note the placement of each variable. You are solving for the y-intercept (b). In this case, it is -9.
b = -9 is your answer.
~
f + 8 = b5q could you guys help me i don't understand at all
Answer:
Step-by-step explanation:
are there values for f or b or q? What are we trying to solve?
Newton's law of gravitation state that the force F of attraction between two bodies varies jointly as their masses M1 and M2 and inversely as the square of the distance between them. Two bodies whose centers are 500mi apart attract each other with a force of 15lb.What will be the force of attraction if their masses were tripled and the distance between their centers doubled?
Find two numbers if their ratio is 9:11 and their difference is 6.
Answer:
Step-by-step explanation:
27,33
9*3 is 27
11*3 is 33
33-27 is 6
i only have one, sorry!
Answer:
Step-by-step explanation:
Let the larger number = y
Let the smaller number = x
x/y = 9/11
y - x = 6
Add x to both sides of the second equation
y = 6 + x
Substitute into the first equation
x/(x + 6) = 9/11
Cross multiply
11x = 9(x + 6)
Remove the brackets
11x = 9x + 54
Subtract 9x from both sides.
2x = 54
x = 54/2
x = 27
y = 27 + 6
y = 33
(27,33)
The way I've done it, there isn't a second pair.
I suppose you could do it this way.
9/11 = -27/-33
-27 - - 33 = 6
So the second pair could be
(-27, - 33)
1. Solve the equation using square roots.
x² +10=9
Answer:
x=±√−1 (NO REAL SOLUTION)Step-by-step explanation:
x² + 1 = 0
1× x²+1=0
x=±√(−1×1)
x=±√−1 (NO REAL SOLUTION)
Circle any of the following that are isotopes of gallium-69. Explain your choices in 1-2 sentences.
Ga71
31
Ga69
30
Ga67
31
Ga66
32
The isotopes of gallium-69 are Ga71 and Ga67.
Ga71 is an isotope of gallium-69 because it has the same number of protons (31) but a different number of neutrons (40) compared to the standard isotope of gallium-69 (31 protons and 38 neutrons).
Ga67 is another isotope of gallium-69 because it also has 31 protons but a different number of neutrons (36) compared to the standard isotope of gallium-69.
These isotopes have different mass numbers due to the varying number of neutrons, while still retaining the same number of protons. Isotopes of an element have the same atomic number (number of protons) but different mass numbers.
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6 x 10^ is how many times as large as 3 x 10^3?
Answer: 1800000000
Step-by-step explanation:
Answer:
200 Times as large
Step-by-step explanation:
Solve for m.
D=(m− 3)
m=
(Simplify your answer. Use integers or fractions for any
numbers in the expression.)
m = D +3
What is algebra?The basics of algebra include numbers, variables, constants, equations, linear and equations. It also includes the basic arithmetic operations : addition, subtraction, multiplication, and division within the algebraic expressions. Algebra is the study of mathematical symbols and the rules for using these symbols in formulas .
The three most used laws are the Commutative, Associative, and Distributive Laws. The main rule of algebra is balancing. The equation has equals sign and both the sides should be equal.
Given, D = (m -3)
we can write,
m = D+3
if D is assumed to be 2 (integer) then,
m = 2+3= 5 (integer)
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0.6x = 31.2 ( it's multiplication)
Eleven students are competing in an art contest. In how many different ways can the students finish first second and third
The best way to solve this problem is to imagine the situation as follows: Suppose that each position (first, second and third) is a numbered box. (first is box number one, and so on).
Now, imagine that each student is a ball that is numbered from 1 up to 11.
The situation translates to calculate in how many different ways we can put a ball in each box, without putting 2 balls in each box. We have the following
To solve this, we will use the multiplication principle. This principle relays on multiplying the number of possibilites for each box. Consider the case in which we will fill the box number 1. We can choose any of the numbers, so we have 11 posibilites. Now, suppose that we chose one number for box 1, and now we want to fill box 2. Then, we will have 10 possibilites only, since we already picked one. In the same manner, to fill the third box we have 9 possibilities. So the total number of possibilites is the product of this three numbers. That is
\(11\cdot10\cdot9\text{ = 990}\)A point P lies in a plane and is a distance of r = 37 units from the origin of a Cartesian coordinate system. If the line joining the point and the origin makes an angle of = 350 degrees with respect to the x-axis, what are the (x, y) coordinates of the point P?
The (x, y) coordinates of point P are approximately (31.19, 20.67).
It is stated that the point P lies at a distance of r = 37 units from the origin and forms an angle of θ = 35° with respect to the x-axis, we can use trigonometry to find the x and y coordinates.
Using the trigonometric definitions, we have,
x = r * cos(θ) = 37 * cos(35°) ≈ 31.19
y = r * sin(θ) = 37 * sin(35°) ≈ 20.67
Therefore, the approximate (x, y) coordinates of point P are (31.19, 20.67). The coordinates (31.19, 20.67) represent the position of point P in the Cartesian coordinate system based on the given distance and angle measurements.
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Complete question - A point P lies in a plane and is a distance of r = 37 units from the origin of a Cartesian coordinate system. If the line joining the point and the origin makes an angle of = 35° degrees with respect to the x-axis, what are the (x, y) coordinates of the point P?