Answer:
x = 0, y = 1
Step-by-step explanation:
2x + 6y = 6 → (1)
x - 3y = - 3 ( add 3y to both sides )
x = 3y - 3 → (2)
substitute x = 3y - 3 into (1)
2(3y - 3) + 6y = 6 ← distribute parenthesis and simplify left side
6y - 6 + 6y = 6
12y - 6 = 6 ( add 6 to both sides )
12y = 12 ( divide both sides by 12 )
y = 1
substitute y = 1 into (2)
x = 3(1) - 3 = 3 - 3 = 0
solution is x = 0 , y = 1
Write an equivalent expression by distributing the "-−" sign outside the parentheses: -(-8r-9.8s)+8.1
Answer: 8r + 9.8s + 8.1
Step-by-step explanation:
Given:
-(-8r-9.8s)+8.1
Distribute:
↳ A - times a - becomes a +, a -times a + stays a -
8r + 9.8s + 8.1
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The graph of the function f(x) = (x +2)(x + 6) is shown below.
On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0).
What is true about the domain and range of the function?
The domain is all real numbers, and the range is all real numbers greater than or equal to –4.
The domain is all real numbers greater than or equal to
–4, and the r
Answer: The domain is all real numbers, and the range is all real numbers greater than or equal to –4.
Step-by-step explanation:
The domain is the set of inputs, and the range is the set of outputs.
Answer: Option A
Step-by-step explanation
The domain is the set of allowed x inputs of a function.
We can replace x with any number we want to get some output for y = f(x)
This tells us the domain is the set of all real numbers.
-----------
The range is the set of numbers y such that
In other words, we can have y = -4 or y > -4
This is because y = -4 is the lowest output possible, as indicated by the vertex point.
What is the distance between the points (-8, -3) and (-2, -5)?
The distance between the points (-8, -3) and (-2, -5) is √40 units
How to find distance between two points?Using distance formula,
d = √(x₂ - x₁)² + (y₂ - y₁)²
Therefore, using (-8, -3) and (-2, -5).
x₁ = -8
x₂ = -2
y₁ = -3
y₂ = -5
d = √(-2 + 8)² + (-5 + 3)²
d = √(6)² + (-2)²
d = √36 + 4
d = √40
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Define the geometric sequence as a recursive function of the following five numbers.
The recursive definition of the geometric sequence is given as follows:
[tex]f(1) = \frac{1}{9}[/tex].f(n) = f(n-1) x 3.What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The recursive definition of the geometric sequence is given as follows:
[tex]f(1) = a_1[/tex].f(n) = q x f(n - 1).For this sequence, the first term and common ratio are given as follows:
[tex]a_1 = \frac{1}{9}, q = 3[/tex].
Then the recursive definition is:
[tex]f(1) = \frac{1}{9}[/tex].f(n) = f(n-1) x 3.More can be learned about geometric sequences at https://brainly.com/question/11847927
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15 Points please me I'm in a rush
Using proportions, it is found that out of the next 1500 pizzas, she should expect 420 pan style pizzas.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The proportion of pan style pizzas is given as follows:
294/(284 + 313 + 159 + 294) = 0.28.
Hence, out of 1500 pizzas, this amount is equivalent to:
0.28 x 1500 = 420
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waheda purchased 8 textbooks each costing rupees 12 and 4 story books each question rupees 9 find the ratio of amounts she spent on the two types of books .
Answer:
8/3 or 2(2/3) Textbooks to storybooks
Step-by-step explanation:
Textbooks: (8 books)*(12 rupees/book) = 96 rupees
Storybooks: (4 books)*(9 rupees/book) = 36 rupees
Total is 132 rupees
Ratio: Textbook/Storybook = 96/36
96/36 = 8/3 or 2(2/3) Textbooks to storybooks
Which expression is equivalent to 21/15 - 915?
A. 12
B. 30 15
c. 125
D. 12 15
[tex]\textbf{Heya !}[/tex]
the denominators are equal, so subtracting these two fractions is a piece of cake:-
[tex]\sf{\cfrac{21}{15}-\cfrac{9}{15}}[/tex]
[tex]\sf{\cfrac{21-9}{15}}[/tex]
[tex]\sf{\cfrac{12}{15}}[/tex]
`hope it's helpful to u ~
4. Alex is painting a house. He uses 1/3 of the
paint he bought on the dining room. He uses
twice as much on the living room as on the
kitchen, where he uses 1 ½ gallons. He has 12
gallons of paint left. How much paint did Alex
buy?
Alex bought 24.75 gallons of paint to use for the house painting.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the amount of paint bought by Alex, hence:
(1/3)x + 3/2 + 2(3/2) + 12 = x
X = 24.75 GALLONS
Alex bought 24.75 gallons of paint to use for the house painting.
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The diagram shows a hexagon inscribed in a circle.
Calculate the sum of the angles a, b and c.
Give a reason for your answer.
The sum of the angles, a, b and c is; 360° because, the sum measures 3 of all the equal angles in the regular hexagon.
What is the sum of all three angle Measures?It follows from the task content that the angle measures given in the task are a, b and c which are in a cyclic polygon (hexagon) in which case, the sum of all 6 angles in the hexagon is; 720.
Consequently, the sum of angle measures; a,b and c is; 720/2 = 360°.
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What is the domain and range of the following graph?
Using it's concepts, the domain and the range of the graph are given as follows:
Domain: all real values except x = -1.Range: All real values.What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input. In a graph, it is given by the values of x, which is the horizontal axis of the graph.The range of a function is the set that contains all the values of the output. In a graph, it is given by the values of y, which is the vertical axis of the graph.In this graph, have that the function is defined for all values of x except x = -1, and assumes all real values, hence the domain and the range of the graph are given as follows:
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Need help with this,30 points, please help very soon, thanks
A small airplane makes a 2400 kilometer trip in 7.30 hours and makes the returned trip in six hours. If the plane travels at a constant speed wind blows at a constant rate, find the airplanes airspeed and the speed of the wind.
The speed of the airplane is 360 km/h while the speed of the wind is 40 km/h.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let a represent the speed of the airplane and b represent the speed of the wind, hence:
(a + b)6 = 2400
a + b = 400 (1)
Also:
(a - b)7.5 = 2400
a - b = 320 (2)
From eqn 1 and 2:
a = 360 km/h, b = 40 km/h
The speed of the airplane is 360 km/h while the speed of the wind is 40 km/h.
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i need help again 100 pts
Answer:
1. Becky's rate of sales is 9 cups per hour
2. Mayisha's rate of sales is 10 cups per hour
3. Becky is selling 1 fewer cups per hour than Mayisha
4. Becky started with 2 fewer cups than Mayisha
Step-by-step explanation:
1. 30-12=18 18/2=9
2. 31-21=10 21-11=10
3. 10-9=1
4. 30+9=39 31+10=41 41-39=2
Answer:
Becky's rate of sales is [tex]\boxed{\sf 9}[/tex] cups per hour.
Mayisha's rate of sales is [tex]\boxed{\sf 10}[/tex] cups per hour.
Becky is selling [tex]\boxed{\sf 1\: fewer}[/tex] cup(s) per hour than Mayisha.
Becky started with [tex]\boxed{\sf 2}[/tex] fewer cups than Mayisha.
Step-by-step explanation:
Mayisha
[tex]\begin{array}{|c|c|c|c|}\cline{1-4} \sf Hours\:(x) & 1 & 2 & 3\\\cline{1-4} \sf Cups\: {left}\:(y) & 31 & 21 & 11\\\cline{1-4} \end{array}[/tex]
Becky
[tex]\begin{array}{|c|c|c|c|}\cline{1-4} \sf Hours\:(x) & 1 & 2 & 3\\\cline{1-4} \sf Cups\: {left}\:(y) & 30 & & 12\\\cline{1-4} \end{array}[/tex]
Selling at a steady rate.
To calculate the rate of sales, use the rate of change formula:
[tex]\sf Rate\:of\:change = \dfrac{change\:in\:y}{change\:in\:x}[/tex]
Therefore:
[tex]\textsf{Becky's rate of sales}=\dfrac{12-30}{3-1}=-9[/tex]
Therefore, as the number of cups reduces by 9 each hour, Becky's rate of sales is 9 cups per hour.
[tex]\textsf{Mayisha's rate of sales}=\dfrac{11-31}{3-1}=-10[/tex]
Therefore, as the number of cups reduces by 10 each hour, Mayisha's rate of sales is 10 cups per hour.
As 9 is one less than 10, Becky is selling 1 fewer cup(s) per hour than Mayisha.
As Becky had 30 cups left after 1 hour, and her rate of sales is 9 cups, then she started with 30 + 9 = 39 cups.
As Mayisha had 31 cups left after 1 hour, and her rate of sales is 10 cups, then she started with 31 + 10 = 41 cups.
As 39 is 2 less than 41, Becky started with 2 fewer cups than Mayisha.
Simplify (5√3 − 2√5) the whole square
Answer:
95 - 20[tex]\sqrt{15}[/tex]
Step-by-step explanation:
(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )²
= (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )
each term in the second factor is multiplied by each term in the first factor, that is
5[tex]\sqrt{3}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) - 2[tex]\sqrt{5}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) ← distribute parenthesis
= 75 - 10[tex]\sqrt{15}[/tex] - 10[tex]\sqrt{15}[/tex] + 20 ← collect like terms
= 95 - 20[tex]\sqrt{15}[/tex]
Answer:
95 - 20√15
Step-by-step explanation:
I assume the expression is (5√3 − 2√5)^2 (?).
(5√3 − 2√5)*(5√3 − 2√5)
25√3^2 - 20√15 + 4√5^2
25*3 - 20√15 +4*5
75 - 20√15 +20
95 - 20√15
Abe raises sheep. In his flock, there are 42 males and 56 females. What is the ratio of males to females in simplest form?
Answer:
3:4
Step-by-step explanation:
It's males to females. so we make 42:56 simplify that we get 3:4
URGENT WILL GIVE BRAINLIEST
Answer:
27.7 m²
Step-by-step explanation:
Area of equilateral triangle:In regular polygon, all the sides and angles are equal. The polygon in the picture is a equilateral triangle.
a = 8 m
√3 = 1.732
[tex]\sf \boxed{\bf Area \ of \ equilateral \ triangle= \dfrac{\sqrt{3}a^2}{4}}[/tex]
[tex]\sf =\dfrac{1.732 * 8 * 8 }{4}\\\\ = 1.732*2*8\\\\= 27.71\\\\= 27.7 \ m^2[/tex]
a) Three angles on a straight line at a point are in the ratio 3 : 2:5. Find the difference between the largest and the smallest angle.
Answer:
54°
Step-by-step explanation:
The ratio values can be used to find the angles, then the desired difference can be found. Alternatively, the desired difference can be figured in terms of the ratio units given.
Ratio of difference to wholeThe number of ratio units representing the largest angle is 5. The number of ratio units representing the smallest angle is 2. The difference of these is 5 -2 = 3.
The total number of ratio units is 3 +2 +5 = 10. This is the number of ratio units representing the straight angle, 180°.
The difference is 3 of those 10 ratio units:
3/10 × 180° = 54° . . . . . . largest - smallest difference
Find the angles
There are 10 ratio units in total (3+2+5=10), so each represents 180°/10 = 18°. Multiplying the given ratios by 18° gives the angle values:
3×18° : 2×18° : 5×18° = 54° : 36° : 90°
The difference between the largest and smallest is ...
90° -36° = 54° . . . . . . largest - smallest difference
Use this information to answer the questions.
You are helping plan your sister's wedding. You decide to help set up a night to prepare the decorations and gift bags, but worry it all won't get done and you will be stuck doing the rest by yourself. Use the information below to help you know how long it will take to get everything done.
1.
You plan to have 2 people work on each task. How would you pair them up to complete each task in the shortest amount of time? Explain using rational expressions.
2.
What is the shortest amount of time it would take to complete all the tasks? If you know people have to leave your house by 9pm, what time should they come over to get started? Explain using rational expressions.
The shortest possible time to perform the tasks is 30 minutes, these activities would be performed in this time by the couple made up of you and your aunt 1.
How to calculate the shortest time to perform the wedding tasks?To calculate the shortest time to complete the wedding tasks, we must carefully observe the information in the table and identify the time that each person takes to complete the tasks. Subsequently, we must identify the people who take the shortest time, in this case it is you and your aunt 1 as shown below:
You
2.5 + 5 + 1.5 = 9 hoursaunt 1
1.5 + 4 + 3 = 8.5 hours.Additionally, we must subtract the two values, to know how long it will take in total for both people to perform the three required activities.
9 - 8.5 = 0.5 hours = 30 minutesAccording to the above, the most efficient couple is your aunt 1 and you because you will take 30 minutes to complete the activities.
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To prove quadrilateral WXYZ is a parallelogram, Travis begins by proving △WZY ≅ △YXW by using the SAS congruency theorem.
Quadrilateral W X Y Z is shown. A diagonal is drawn from point W to point Y. Sides W Z and X Y are parallel and congruent.
Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.
∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.
WY ≅ WY by the reflexive property.
∠ZWY ≅ ∠XWY by the corresponding ∠s theorem.
WX ≅ ZY by definition of a parallelogram.
WZ ≅ XY by the given.
The reasons Travis can use to prove both triangles are congruent by the SAS congruency theorem are:
∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.WY ≅ WY by the reflexive property.WZ ≅ XY by the given.What is the SAS Congruency Theorem?The SAS congruency theorem states that two triangles are congruent when they both have two pairs of corresponding congruent sides and a pair of corresponding congruent included angles.
Given the image below, we have the following proof with the statement and reasons in bracket:
WZ ≅ XY [given]
WY ≅ WY [reflexive property]
∠ZWY ≅ ∠XYW [by the alternate interior ∠s theorem]
△WZY ≅ △YXW [by the SAS congruency theorem]
Therefore, the reasons Travis can use are:
∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.WY ≅ WY by the reflexive property.WZ ≅ XY by the given.Learn more about the SAS congruency theorem on:
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Answer:
A. ∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem;
B. WY ≅ WY by the reflexive property; & E. WZ ≅ XY by the given.
Step-by-step explanation: Trust Me! Answer is correct on Edge.
Good Luck! :)
Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.
A. ∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem B. WY ≅ WY by the reflexive property E. WZ ≅ XY by the given
Word Problem
Beau Thai has a rectangular mirror with a length of 6 inches and a width of 10 inches.
a) How much ribbon could Beau wrap around the outside of the mirror?
b) What is the area of Beau Thai's mirror?
10in
Beau can wrap 32 inches of ribbon outside the mirror.
Area of Beau Thai's mirror is 60 sq. inches.
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The word "area" refers to a free space. A shape's length and width are used to compute its area.
Given information:
Length of mirror = 6 inches
Width of mirror = 10 inches
To Find:
The amount of ribbon Beau could wrap around the outside of the mirror.
Perimeter of the mirror = 2(6+10)
= 2(16)
= 32 inches
The area of Beau Thai's mirror.
Area of the mirror = 6*10
= 60 sq. inches
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What is the point-slope form of a line with slope that contains the point
(-2, 1)?
Answer:
d; y - 1 = 4/5(x + 2)
Step-by-step explanation:
the equation for a point-slope form line is y - y1 = m(x - x1)
plug in the points and you will get your answer
y - 1 = 4/5(x + 2)
that is your answer
Which is the graph of the linear inequality 2x-3y < 12?
Answer:
First, transform the given equation into the slope-intercept form, y = mx + b.
2x - 3y < 12
3y > 2x - 12
y > [tex]\frac{2}{3}[/tex]x - 4
Since the equation is y > [tex]\frac{2}{3}[/tex]x - 4, first draw the graph of y = [tex]\frac{2}{3}[/tex]x - 4 with a dotted line (because it is >, not ≥) and shade the area above the dotted line.
PLEASE HELP VERY URGENT Let p represent "Two angles have the same measure," and let q represent "The angles are congruent."
Which symbolic statement represents the following conditional: "If two angles are not congruent,
then they have the same measure"?
answer choices:
~q->p
p->q
q->p
q->~p
The symbolic representation for the given statement " If two angles are not congruent, then they have the same measure" is ~q → p. So, option A is correct.
How a conditional statement is represented?The conditional statement consists of a hypothesis sentence and a conclusion statement. A conditional statement can be written as " If p then q" where p is called the hypothesis and q is called the conclusion.The statement "If p then q" - means q must be true whenever p is true.Calculation:It is given that,
p - "Two angles have the same measure"
q - "The angles are congruent"
Statement: " If two angles are not congruent, then they have the same measure"
So, symbolically it is written as,
The hypothesis "two angles are not congruent" is represented by ~q and the conclusion "they have the same measure" is represented by p.
That is,
The representation is "If ~q then p i.e., ~q → p. So, option A is correct".
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At a high school basketball game the lions and the eagles are playing. the lions attempted 16 free throws and made 13, attempted 51 two-point shots and made 22, and attempted 16 three-point shots and made 10. the eagles attempted 27 free throws and made 7, attempted 41 two-point shots and made 19, and attempted 16 three-point shots and made 7. (free throws are worth 1 point each, two-point shots worth 2 points each, and three-point shots worth 3 points each) what is the free throw percentage for the lions? number % (round the final percentage to one decimal place) what is the free throw percentage for the eagles? 025.9 % (round the final percentage to one decimal place) what is the field goal percentage (two-point and three-point shots combined) for the lions? number % (round the final percentage to one decimal place) what is the field goal percentage (two-point and three-point shots combined) for the eagles? number % (round the final percentage to one decimal place) how many points did the lions score? number how many points did the eagles score?
Answer:
a. The free throw percentage obtained by the Lions is of 81.25%.
b. The free throw percentage for the Eagles was of 37.04%.
c. The field goal percentage for the Lions was of 56.01%.
d. The field goal percentage for the Eagles was of 34.43%.
e. The Lions scored 96 points.
f. The Eagles scored 64 points.
Solution:
a. The lions attempted 16 free throws and made 13, which means lions scored 13 out of 16,
The free throw percentage obtained by the Lions = [tex]\frac{13}{16}[/tex] × 100 = 81.25%
The free throw percentage obtained by the Lions is 81.25%
b. The eagles attempted 27 free throws and made 7 which means 7 out of 27, so:
The free throw percentage obtained by the eagles = [tex]\frac{7}{27}[/tex] × 100 = 25.92 %
The free throw percentage obtained by the eagles is 25.92 %
c. The lions attempted 51 two-point shots and made 22, and attempted 16 three-point shots and made 10.
Total attempted = 51 + 16 = 67
Total shots made = 22 + 10 = 32
The field goal percentage (two-point and three-point shots combined) for the Lions = [tex]\frac{32}{67}[/tex] × 100 = 47.76 %
The field goal percentage for the Lions was of 47.76 %.
d. The eagles attempted 41 two-point shots and made 19, and attempted 16 three-point shots and made 7.
Total attempted = 41 + 19 = 60
Total shots made = 19 + 7 = 26
The field goal percentage (two-point and three-point shots combined) for the eagles= [tex]\frac{32}{67}[/tex] × 100 = 43.33 %
The field goal percentage for the eagles was of 43.33 %.
e. Total goals secured by lions 13 free throws, 22 two's and 10 three's. So
Total points = 10 × 1 + 22 × 2 + 10 × 3 = 84
The Lions scored 84 points.
f. Total goals secured by eagles 7 free throws, 19 two's and 7 three's. So
Total points = 7 × 1 + 19× 2 + 7 × 3 = 66
The eagles scored 66 points.
What is percentage?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
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Surface area=
Help me please thanks so much
The Surface Area of the sphere is 1017.16 unit^2.
what is the surface area of the sphere?
The surface area of the sphere is 4*pi*r^2.
where, r is the radius
Calculation :
given radius is 9 units
putting value in the formula of the sphere
S(area)=4*pi*r^2
=4*3.14*9^2
=4*3.14*81
=1017.16 UNIT^2
The Surface Area of the sphere is 1017.16 unit^2.
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The Surface Area of the sphere is 1017.16 unit^2.
The surface area of the sphere is 4*pi*r^2.
where, r is the radius
Calculation :
given radius is 9 units
putting value in the formula of the sphere
S(area)=4*pi*r^2
=4*3.14*9^2
=1017.16 UNIT^2
The Surface Area of the sphere is 1017.16 unit^2.
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Suppose the average commute time of your employees is unknown. The standard deviation of their commute time is estimated as 24.5 minutes. How many employees must be included in a sample to create a 90 percent confidence interval for the average commute time with a confidence interval width of no more than 13 minutes
The number of employees is 91.
According to the statement
Given that the standard deviation = 24.5
The width in the question = 13
We solve for the margin of error E.
E = width / 2
E= 13/2 = 6.5
At 90%
Alpha = 1-0.90
= 0.1
Alpha/2 = 0.1/2 = 0.05
Z 0.05 = 1.576
Now find the Sample size n
= ((1.576x24.5)/2)²
= 90.8
= 91
So, The number of employees is 91.
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Which of the following is the solution to the differential equation dy over dx equals 2 times x times y all over quantity x squared plus 1 end quantity comma with the initial condition y(1)
The solution of the differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex] is y=[tex]-x^{2} +1[/tex].
Given a differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex].
We are required to find the solution of the differential equation when y(0)=1.
dy/dx=[tex]2xy/(x^{2} -1)[/tex]
Taking y to left side and dx to right side.
1/y dy=2x/[tex](x^{2} -1)[/tex] dx
Integrating both sides.
[tex]\int\limits {1/y} \, dy[/tex]=[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]----------1
log y=[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]
Solving right side.
[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]
let [tex]x^{2} -1[/tex]=z
differentiating both sides with respect to x.
2x=dz/dx
2x dx=dz
Put 2x dx=dz in 1.
[tex]\int\limits {1/y} \, dy[/tex]=[tex]\int\limits {1/z } \, dz[/tex]
log y=log z+log c
Put z=[tex]x^{2} -1[/tex]
log y=log([tex]x^{2} -1[/tex])+log c
log y=log [{[tex]x^{2} -1[/tex])c]
y=([tex]x^{2} -1[/tex])c------------2
Put x=0 and y=1
1=(0-1)c
1=-c
c=-1
Put c=-1 in 2 to get the solution.
y=-1([tex]x^{2} -1[/tex])
y=[tex]-x^{2} +1[/tex]
Hence the solution of the differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex] is
y=[tex]-x^{2} +1[/tex].
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I NEED HELP ASAP PLEASEEEE
Answer:
[tex](f-g)(x)=x^2-6x+5[/tex] dom: (-∞,∞)
[tex](\frac{f}{g})(x)=x-7+\frac{7}{x+2}[/tex] dom: (–∞,–2)u(–2,∞)
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)=(x^2-5x+7)-(x+2)[/tex] *distribute the negative sign into (x+2)!
[tex]x^2-5x+7-x-2\\x^2-6x+5[/tex]
a parabola (anything that begins with [tex]x^2[/tex]) will have a domain of (-∞,∞) or all real numbers!!
[tex](\frac{f}{g} )(x)= \frac{x^2-5x+7}{x+2}[/tex] use synthetic division to divide (the attached picture)
domain: Because the graph is not continuous, you have to write the domains on both sides of the asymptote which is (-∞,-2)u(-2,∞)
synthetic division:
1. take the divisor (x+2) and solve for x. x= –2 this goes in the top left corner
2. write the numbers AND their signs on the top row. if there is no number and just the variable (like [tex]x^2[/tex] ) just write 1.
3. the first number gets pulled down
4. multiply -2 by 1 and subtract it from –5. (-5-2= -7)
multiply -2 by -7 and add that to the next number in the top row which is -7. (-7 + 14=7)
5. the first number in the bottom row of numbers is the first number in the answer but with one less exponent than the dividend. **write 1 as x**
6. the last number in the bottom row, if it is not 0, is a remainder. write it as that number over the divisor. in this case the remainder is 7. so write it as [tex]\frac{7}{x+2}[/tex]
Order the number from least to greatest square root of 1, 1/3,2.5,square root of 2
The required order of the number from least to greatest square root is
1/√3 < √1 < √2 < √2.5
Which number is greatest in value:
In the above numbers 1, 1/3 and 2.5 do not have square roots.
So, we will write 1, 1/3 and 2.5 inside the square root as shown below.
√1 = 1
√(1/3) = 1/√3 = 0.577350269
√2.5 = 1.58113883
√2 = 1.414
Arranging these numbers according to their value, we get the order as-
0.577350269 < 1 < 1.414 < 1.581138831
Hence, the required order of the number from least to greatest square root is 1/√3 < √1 < √2 < √2.5.
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Consider a standard deck of playing cards. If 5 cards are selected randomly without replacement from this deck then what is the probability that all of these are red
The probability that all of the cards drawn are red is 0.0253.
How can we find the probability?A standard deck of playing cards has 52 cards.
Of the 52 cards, 26 of the cards are red cards.
When we draw the first card, the probability of getting red is 26/52.
When we draw the second card, the probability of getting red is 25/51.
When we draw the third card, the probability of getting red is 24/50.
When we draw the fourth card, the probability of getting red is 23/49.
When we draw the fifth card, the probability of getting red is 22/48.
Therefore, the probability of drawing 5 red cards without replacement is
= [tex]\frac{26}{52}* \frac{25}{51}* \frac{24}{50} *\frac{23}{49}* \frac{22}{48}[/tex]
= 26*25*24*23*22/52*51*50*49*48
= 0.0253
Therefore, we have found that the probability that all cards drawn are red is 0.0253.
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Which function has the domain as y=2 square root of x
Using it's concept, any function with domain [tex]x \geq 0[/tex] has the same domain as [tex]y = 2\sqrt{x}[/tex].
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function.
Function [tex]y = 2\sqrt{x}[/tex] is defined for [tex]x \geq 0[/tex], hence any function with domain [tex]x \geq 0[/tex] has the same domain as [tex]y = 2\sqrt{x}[/tex].
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