Determine whether the statement is true or false. The equation y' = x + y + 1 is separable.
The equation y' = x + y + 1 is not seperable. Therefore the statement is false.
What do you mean by an ordinary differential equation?In mathematics, an ordinary differential equation (also known as an ODE) is an equation made up of one or more functions of a single independent variable and its derivatives. A function having one or more derivatives is a component of a differential equation.
Where are ordinary differential equations used?Common differential equations are used in everyday life to compute the flow of electricity, the motion of an item back and forth like a pendulum, and to illustrate the principles of thermodynamics. Additionally, in medical terminology, they are employed to graphically monitor the progression of illnesses.
If you can express a differential equation as y′=f(x)g(y), where f(x) is only a function of x and g(y) is only a function of y, then the problem is separable. Here, it is not the situation.
But we are not limited to solving separable differential equations. We frequently use integrating factors to solve linear first-order differential equations, such as this one. Using the product rule, multiply your differential equation by an integrating factor—in this example, e—and you get (eyy)′=eyy+eyy′=eyx,
which you may integrate to get your differential equation's solution. Finding integrating factors for generic linear first-order differential equations of the type y′+p(x)y=q may be done in a general way (x).
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What is the product when - 5 is multiplied by
2x + 3?
1.) 2x² - 7x - 15
2.) 2x² - 13x - 15
3.) 2x² +13x + 15
4.) 2x² +7x - 15
10. Mac Valent opened a new checking account and deposited his paycheck for
$209.81. The check register shows his transactions since opening his account.
What is his balance after each transaction?
(a) The balance after first transaction is, $162.66.
(b) The balance after second transaction is, $109.63.
(c) The balance after third transaction is, $2.33.
What is transaction?
An agreement that has been fulfilled between a buyer and a seller to exchange goods, services, or financial assets in exchange for cash is referred to as a transaction.
The following are a few examples of transactions: paying a supplier after receiving goods or services from them. acquiring ownership of a property the seller previously owned by paying the seller with cash and a note. remuneration for hours worked.
Given:
Mac Valent opened a new checking account and deposited his paycheck for $209.81.
We have to find the balance after each transactions.
The first transaction is of electric cooperative for $47.15.
So, the balance after first transaction is, $209.81 - $47.15 = $162.66.
The second transaction is of Sharp's Groceries for $53.03.
So, the balance after second transaction is, $162.66 - $53.03 = $109.63.
The third transaction is of Gimbles Auto Repair for $107.30.
So, the balance after third transaction is, $109.63 - $107.30 = $2.33.
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Complete question:
Complete question is attached below.
The diagram shows a triangle.
What is the value of z?
98⁰
49°
Z
Answer:
33
Step-by-step explanation:
All triangle angles together add up to 180
So we can set up this equation to find angle z:
98 + 49 + z = 180
Now solve:
98 + 49 + z = 180
147 + z = 180
-147 -147
z = 33
4(x-5); 32-20
Find the value of x that makes the expressions equivalent.
The value of x that makes the expressions equivalent is 8
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
4(x-5)= 32-20
Distribute the 4
4x-20=12
4x= 12+20 = 32
x= 32/4 = 8
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Find an equation of the circle whose diameter has endpoints (-3,-1) and (1,2)
The equation of the circle if diameter has endpoints (-3,-1) and (1,2) is x² + 2x + y² - y = 5.
What is a circle?A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius).
Given:
The endpoints of the circle diameter are (-3,-1) and (1,2),
Calculate the coordinates of the center of the circle as shown below,
Center = (-3 + 1 / 2, -1 + 2 / 2)
Center = (-2/2, 1/2)
Center = (-1, 1/2)
Calculate the length of diameter as shown below,
Diameter = [tex]\sqrt{[1- (-3)]^2+[2-(-1)]^2}[/tex]
Diameter = √(4² + 3²)
Diameter = 5
Thus, radius = 5 / 2 =
Calculate the equation of the circle as shown below,
[x - (-1)]² + [y - 1/2]² = (5/2)²
Simplify the above equation as shown below,
x² + 2x + y² - y = 5
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How many servings are in an 8lb bag of French fries?
There are 16 ounces in a pound.
The proper serving size of french fries is reportedly only 12 to 15 fries.
Mr.Wright has $350.He puts 25%of it in a savings account. How much did Mr.Wright deposit?
Answer:
The answer is $87.5
Step-by-step explanation:
350 × 25 ÷ 100
8750/100 = 87.5
Thus, Mr. Wright deposit $87.5
Is this correct?? Functions or not a function?
Answer: No
Step-by-step explanation:
Graph: You can use the vertical line test to determine if it is a function. Draw a vertical line (going up and down) on the graph. If it only intersects one
point, then it is a function. If it crosses two points, it is not a function.
Chart: If the x repeats and the y does not repeat, it is not a function. y can repeat as much as it wants, as long as the x does not.
Lines: If one x connects to multiple y, it is not a function. If one y connects to multiple x, it is a function.
Coordinates: Same as the chart
HELLLPPP 3X-9=(6x6)/4
PLEASE solve
Answer:
3X−9=
4
6⋅6
Multiply both sides of the equation by 4.
12X−36=6×6
Multiply 6 and 6 to get 36.
12X−36=36
Add 36 to both sides.
12X=36+36
Add 36 and 36 to get 72.
12X=72
Divide both sides by 12.
X=
12
72
Divide 72 by 12 to get 6.
X=6
The price of 10 movie tickets is $25. At this rate, what is the price of 12 movie tickets.?
What is the square of √ 1?
The square of given expression √1 ( square root of 1 ) is equal to 1.
As given in the question,
Given expression is equal to √1 ( square root of 1 )
To calculate the square of √1 we have,
Let us consider variable x is equal to √1
x = √1
Now take square on both the sides of the given expression we get,
x² = (√1 )²
⇒ x² = √1 × √1
Multiplying square root of 1 to square root of 1 is equal to 1 we get,
or use law of exponent :
√1 × √1 = [tex]1^{\frac{1}{2} + \frac{1}{2} }[/tex]
= 1
⇒ x² = 1
Therefore, the square of the given expression √1 ( square root of 1 )is equal to 1.
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how old is my mom?19+10=?
Answer:
29 years old
Step-by-step explanation:
Answer: 29
Step-by-step explanation: 29 but we want to round that up to 30 because 29 is odd but due to science and polls nobody likes the number 30 so we go back to 29 but it’s uneven so we go to 28 to make it even but we also don’t like that number so we go back to 29 and that how we get it.
Element X is a radioactive isotope such that its mass decreases by 4% every year. If an experiment starts out with 690 grams of Element X, write a function to represent the mass of the sample after t t years, where the quarterly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per quarter, to the nearest hundredth of a percent.
The relation that is able to model the decay is given as N = 690e^-0.04r. The quarterly rate of change is 0.21%.
What is radioactivity?We know that the term radioactivity has to do with the fact that the object is able to undergo the process of a spontaneous disintegration. The implication of this is that the element is going to be gradually be transformed into a different element and this is going to occur at a given rate which we have called the decay constant for the reaction.
We know that element X is a radioactive isotope such that its mass decreases by 4% every year then an experiment starts out with 690 grams of Element X.
It follows that;
Initial amount of X No = 690 g
Decay rate of X (r) = 0.04
Time taken for decay = t
Amount of X at time t = N
The model now becomes;
N = 690e^-0.04r
The quarterly rate of change is obtained from;
A(t) = (1- 0.04)Ao
= 0.96 Ao
0.96Ao = Ao(1 - r)^30
0.94 = (1 - r)^30
30√0.94 = (1 - r)
r = -0.0021 or -0.21%
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6. Justify the last two steps of the proof.
Given: ABCD is a parallelogram.
Prove: A4BC = ACDA
A
B
1. ABDC is a parallelogram.
2. AB DC and BC= DA
3. AC = CA
4. JABC = ACDA
D
1. Given
2. Opposite sides of a parallelogram are congruent.
3.
C
4.
?
Justification for the last two steps of the proof is
3. Reflexive Property of (Congruence) ≅
4. SSS (Side to Side to Side Congruence rule)
What is SSS congruence postulate ?
A type of triangle congruence rule called Side-Side-Side (SSS) asserts that two triangles are congruent if their three sides are equal to their respective three sides of another triangle. When the dimensions of the matching sides and angles of two or more triangles match, the triangles are said to be congruent.
3. Any geometric figure compared to itself is congruent to itself so this is why:
AC ≅ CA
∠B ≅ ∠B
4. Since we have a parallelogram, therefore we can say:
BC ≅ DA
BA ≅ DC
CA ≅ AC
Both triangles ABC and CDA satisfy the side to side to side congruence, since their 3 sides are congruent.
So, It's D.
P.S.
Notice that the angle measure information is not included in the data above that's why we cannot say it is SAS congruence.
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Please double check your work
Answer:
Erin will pay a total of $21.196 in shipping and handling fees.
Step-by-step explanation:
To calculate the shipping and handling fees, we first need to find 20% of the price of the trampoline. Since 20% is the same as 0.20, we can multiply the price of the trampoline by 0.20 to find the shipping and handling fees. If the trampoline costs $105.98, then the shipping and handling fees would be $105.98 * 0.20 = $<<105.98*0.20=21.196>>21.196.
This table shows how many sophomores and juniors attended two school
events.
Sophomore
Junior
Total
Jazz band
concert
35
36
71
Volleyball game
42
24
66
Total
77
60
137
What is the probability that a randomly chosen person from this group is a
sophomore and attended the volleyball game?
Round your answer to two decimal places.
The required probability is approximately 0.3066 or 0.31. Option B is correct.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
There are a total of 77 + 60 = 137 students in the group.
Out of these students, 42 sophomores attended the volleyball game.
So the probability of a randomly chosen person from this group being a sophomore and attending the volleyball game is:
P(sophomore and volleyball) = 42/137
Therefore, the probability is approximately 0.3066 or 0.31. Option B is correct.
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
2.3p – 14.1 = 6.4p – 4
Answer:
This equation does not have the same solution as the original equation.
In conclusion, equations 1 and 2 have the same solution as the original equation (2.3p – 10.1 = 6.5p – 4 – 0.01p). Equations 3, 4, and 5 do not have the same solution.
Step-by-step explanation:
2.3p – 10.1 = 6.4p – 4
Using the commutative property of addition, we can rearrange the terms on the left-hand side of the equation to get:
-6.4p + 2.3p = -4 + 10.1
Combining like terms, we have:
-4.1p = 6.1
Dividing both sides by -4.1, we get:
p = -1.49
This equation has the same solution as the original equation.
2.3p – 10.1 = 6.49p – 4
Using the commutative property of addition, we can rearrange the terms on the left-hand side of the equation to get:
-6.49p + 2.3p = -4 + 10.1
Combining like terms, we have:
-4.19p = 6.1
Dividing both sides by -4.19, we get:
p = -1.46
This equation has the same solution as the original equation.
230p – 1010 = 650p – 400 – p
This equation does not have the same solution as the original equation.
23p – 101 = 65p – 40 – p
This equation does not have the same solution as the original equation.
2.3p – 14.1 = 6.4p – 4
Using the commutative property of addition, we can rearrange the terms on the left-hand side of the equation to get:
-6.4p + 2.3p = -4 + 14.1
Combining like terms, we have:
-4.1p = 10.1
Dividing both sides by -4.1, we get:
p = -2.47
How will the solution of the system Y 2x 2 3 and y 2x 1/3 change?
There is no intersection and no solution to the system since the region above the line y=2x+2/3 and the region below the line y=2x+1/3 are the solutions to the inequalities y>2x+2/3 and y<2x+1/3, respectively.
In the given question, we have to find the solution of the system Y>2x+2/3 and y<2x+1/3 change.
We firstly draw the two lines y=2x+2/3, and y=2x+1/3.
They are parallel and the line y=2x+2/3 is located over the line y=2x+1/3.
There is no intersection and no solution to the system since the region above the line y=2x+2/3 and the region below the line y=2x+1/3 are the solutions to the inequalities y>2x+2/3 and y<2x+1/3, respectively.
The solution of y2x+2/3 is the region below the line y=2x+2/3, and the solution of y>2x +1/3 is the region above the line y=2x+1/3 when the inequality sign of both inequalities is reversed. This implies that the area between the two lines is where the system's solution lies.
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The right question is:
How will the solution of the system Y>2x+2/3 and y<2x+1/3 change? If the inequality sign on both inequalities is reversed to y<2x+2/3 and y>2x+1/3?
If you rotate the point (2,-2)
positive 45 around the origin, what are the coordinates
The coordinate is (2√2 , 0).
What are coordinates?Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.
If you rotate the point (2,-2) positive 45 around the origin.
To find the coordinates:
the formula;
X = xcosФ - ysinФ
And Y = xsinФ + ycosФ
and here Ф = 45° and x = 2 and y = -2
Now, X = 2/√2 + 2/√2 = 2√2
Y = 2/√2 - 2/√2 = 0
Therefore, the coordinate is (2√2 , 0).
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Find the value of x. Then find the measure of each angle and write the answers in ascending order.
By using the properties of triangle, it can be calculated that-
Smallest angle = 30°
Next larger angle = 60°
Largest angle = 90°
What is a triangle?
Triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles.
The angles of a triangle are x, 2x and 90
Sum = x + 2x + 90 = 3x + 90
By the problem,
3x + 90 = 180
3x = 180 - 90
3x = 90
x = [tex]\frac{90}{3}[/tex]
x = 30
Smallest angle = 30°
Next largest angle = 2 [tex]\times[/tex] 30 = 60°
Third angle = 90°
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In the figure, NQ is parallel to OP and NQ = 4, OP = 6, and
MQ=8. How long is MP?
Answer:
MP = 12 cm
Step-by-step explanation:
4cm : 6cm
8cm : x
8 * [tex]\frac{6}{4}[/tex] = 12 cm
MP = 12 cm
An outdoor staircase has a total vertical elevation of 24 feet from the road level to the first floor. The 1st floor to the 2nd floor is also 24 feet. If the angle of elevation is 37 degrees and the landing of each step is 13 inches, answer the following question showing each step of your work.
A. What is the vertical rise per step (in inches rounded to the nearest inch)
B. Find the number of steps needed to climb from road level to the 2nd floor
(a) There are 10 vertical rise per step.
(b) There are 58 steps needed to climb from road level to the 2nd floor.
What is angle of elevation?
The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.
(a) First to find the vertical rise per step.
x = 13 x tan(37)
x = 9.80
x ≈ 10
Hence, there are 10 vertical rise per step.
(b) Now to find number of steps needed to climb from road level to the 2nd floor.
The total elevation = 24 + 24 = 48 feet
Vertical rise of each step = 10
To convert 48 feet into inches
⇒ 48 x 12 = 576 inches
So, the number of steps = 576 / 10 = 57.6 ≈ 58
Hence, there are 58 steps needed to climb from road level to the 2nd floor.
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Why is 2x-3=2x+5 Not a solution
Answer:
not a solution
Step-by-step explanation:
2x-3=2x+5
-2x. -2x
-3=5
not a solution because -3 does not equal 5
a study was designed to investigate the effects of two variables (1) a student's level of mathematical anxiety and (2) teaching method , on a student's achievement in a mathematics course. students who had a low level of mathematical anxiety were taught using the traditional expository method. these students obtained a mean score of 370 with a standard deviation of 50 on a standardized test. assuming a mound-shaped and symmetric distribution, in what range would approximately 95% of the students score?
On a test with a range of 110–410, these students received a mean score of 370 and a standard deviation of 50. What range would roughly 95% of the students' scores fall into, presuming a mound-shaped and symmetric distribution.
A variable is what?Any traits, figures, or amounts that may be gauged or counted are considered variables. Another name for a variable is a data item. Variables include things like age, sex, business income and expenses, birthplace, capital expenditures, class grades, eye color, and vehicle type.
Which examples use variables?A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, income, province of birth, school grades, and kind of dwelling. Categorical and numeric variables are the two basic types of variables that can be categorized.
Why whole number is not closed under subtraction but integers is closed under it?
Integers have a greater and more suitable range to be closed for subtraction than whole numbers.
According to the closure property of subtraction, the difference between two integers will always be an integer.
An integer is a number that ranges from minus infinity and infinity and is not a fraction.
Whereas all positive valued integers including 0 are whole numbers.
Now if we subtract a larger whole number from a smaller whole number, then the difference will obviously be negative. Hence, the result will be an integer and not a whole number.
example= 25 - 30
= -5
Here both 25 and 30 are whole numbers but -5 is not. But all three are considered integers.
Hence, subtraction is closed under integers and not whole numbers.
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Amy put some salt in a weighing dish. Then she put the weighing dish on a sensitive balance to measure the mass of the salt. She removed the weighing dish from the balance and put it in several similar balances. She recorded the mass each time.
Mass 1 Mass 2 Mass 3 Mass 4 Mass 5
5.608 g 5.607 g 5.608 g 5.608 g 5.609 g
Amy forgot to subtract the mass of the empty weighing dish from her measurements, and she reported the mass of the salt as 5.608 grams.
Amy's measurement of the salt's mass
accurate because
.
Amy's measurement of the salt's mass
precise because
.
Amy's measurement of the salt's mass is not accurate because it is not close to the actual value. Amy's measurement of the salt's mass is precise because the individual measurements are similar.
What is measurement?In Mathematics, measurement can be defined as an act or process through which the size, weight, magnitude, quantity, volume (capacity), dimensions, or distance traveled by a physical object or body is taken, especially for the purpose of an experiment.
In Science, precision is a quality which is independent of accuracy because it only describes how close together are numerical values that are obtained in a series of measurements.
In conclusion, accuracy is a quality which measures how close a measurement is to the actual value.
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Complete Question:
Amy forgot to subtract the mass of the empty weighing dish from her measurements, and she reported the mass of the salt as 5.608 grams. Amy's measurement of the salt's mass (1) ______ accurate because (2) ______ . Amy's measurement of the salt's mass (3)_____ precise because (4) _______ .
1. is
is not
2. it is not close to the actual value
she used five different balances
the individual measurements are similar
3. is
is not
4. it is not close to the actual value
she used five different balances
the individual measurements are similar
Find the value of x.
The value of x is obtained as 9.4 units.
What is Pythagoras theorem?Pythagoras theorem states that in a right angled triangle, the sum of the squares of the perpendicular and base is equal to the square of the hypotenuse. It can be written as h² = p² + b².
The value of x for the given figure can be calculated as,
Use pythagoras theorem for lower triangle as below,
p² + b² = h²
=> p² = h² - b²
=> p² = 12² - 6²
= 108
Now, substitute the value of p² in the expression for upper triangle as,
x² + p² = 14²
=> x² + 108 = 196
=> x² = 88
=> x = 9.4
Hence, the value of x for the given figure is 9.4 units.
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What is the equation of a line that passes through the point (- 1/4 and is parallel to the y axis?
The equation of a line that passes through [tex](-1,4)[/tex] and is parallel to the y-axis is [tex]x=-1[/tex]
The equation of the line passes through the point is [tex](-1,4)[/tex]
The line is parallel to the y-axis which means it cuts the x-axis at the point [tex](-1,0)[/tex]
The equation of the line parallel to the y-axis is [tex]x=-1[/tex]
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PLEASE HELP NOW
Alex's weekly earnings for working 40 hours plus 3 hours of working overtime was $480.17. If
$48.57 of that paycheck was overtime pay, what was his hourly rate for the first 40 hours of
work?
$10.04
$10.79
O$11.17
$12.00
Answer:
$10.79
Step-by-step explanation:
1) Make an equation
40x + 48.67 = 480.17
where x is hourly pay
2) Solve
40x + 48.67 = 480.17
40x + 48.67 - 48.67 = 480.17 - 48.67
40x = 431.50
40x / 40 = 431.50 / 40
x = 10.79