A: The differential equation can be expressed in the form f(x ,y) = g(x)h(y) = 0, indicating that it is homogeneous. Divide both sides of the equation by y to observe this, which results in dy/dx + sin^2(x) = cos^2(x)
B: Since there is just one function y and its derivative dy/dx involved in the equation, it is an ODE.
D: Because there is only one function y and its derivative dy/dx involved in the equation, first-order differential equations are what it is.
G: The formula for the equation is a(x)y' + b(x)y = c(x), where a(x)=1, b(x) = sin^2(x), c(x) = cos^2(x) . Given that x and the coefficients of y and dy/dx are constants, the equation is linear.
H: The equation may be written as dy / y = (cos^2(x))dx/(1+sin^2(x)),and it is a candidate for integrating factors because we can multiply both sides by (1+sin^2(x))dx .
I: The variables x and y can be separated by integrating both sides of the equation, which can be represented as (dy/y) = (cos^2(x))dx/(1+sin^2(x)) + (sin^2(x))dx .
J: The equation is self-sufficient; it is not dependent on any explicit function of t.
Therefore, the differential equation dy/dx+sin^2(x)y=cos^2(x)y .A candidate for integrating factors exists in the first-order linear, homogeneous, separable, and autonomous ODE known as y.
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Solve: 12 Superscript x squared + 5 x minus 4 Baseline = 12 Superscript 2 x + 6
x = 2
x = –5
x = 2, x = –5
no solution
The solutions to the exponential equation [tex]12^{x^2 + 5x - 4} = 12^{2x + 6}[/tex] are given as follows:
x = 2 and x = -5.
How to solve the exponential equation?The exponential equation for this problem is defined as follows:
[tex]12^{x^2 + 5x - 4} = 12^{2x + 6}[/tex]
The n^x function is an injective function, which means that if they are equal, and have the same base, than their exponents are equal.
Thus the equation can be simplified as follows:
x² + 5x - 4 = 2x + 6.
x² + 3x - 10 = 0.
The coefficients of the quadratic function are given as follows:
a = 1, b = 3, c = -10.
Hence the discriminant is given as follows:
D = 3² - 4(1)(-10)
D = 49.
The first solution is given as follows:
x = (-3 + 7)/2 = 2.
The second solution is given as follows:
x = (-3 - 7)/2 = -5.
Meaning that the third option is the correct option in the context of this problem.
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Answer:
c
Step-by-step explanation:
Kali’s school is selling tickets to a choral performance. On the first day of ticket sales the school sold 1 adult ticket and 8 student tickets for a total of $60. The school took in $48 on the second day by selling 5 adult tickets and 4 student tickets. What is the price each of one adult ticket and one student ticket?
Using simultaneous equations, the price of one adult ticket is $4 and one student ticket is $7.
What are simultaneous equations?Simultaneous equations are two or more equations solved concurrently.
Sales of Tickets:
Adult Student Sales Revenue
First day of ticket sales 1 8 $60
Second day of ticket sales 5 4 $48
Let the price per adult ticket = a and students ticket = s
Equations:Equation 1: a + 8s = 60
Equation 2: 5a + 4s = 48
Multiply equation 1 by 5:
Equation 3: 5a + 40s = 300
Subtract equation 2 from equation 3:
5a + 40s = 300
-
5a + 4s = 48
36s = 252
s = 7
= $7
In equation 1, substitute s = 7:
a + 8s = 60
a + 8(7) = 60
a + 56 = 60
a = 4
= $4
Thus, the price of one adult ticket is $4 while the price of one student ticket at Kali's school is $7.
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Find a formula for the
n
th term,
T
n
, of the following arithmetic sequence:
−
9
,
−
18
,
−
27
,
−
36
,
.
.
.
Answer:
x+9
Step-by-step explanation:
for example x is 18 , add 9 to it will become 18+9=27
HELP ME OUT PLEASE!!!!!!
The notation "f(x)" (f of x) is another way of representing y-values in a function
True
False
True, The notation "f(x)" (f of x) is another way of representing y-values in a function.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We know that;
When we write a function, then the notation "f(x)" (f of x) is another way of representing y-values in a function.
Hence, It is true, notation "f(x)" (f of x) is another way of representing y-values in a function.
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Suppose that the relation His defined as follows.
H={(−3, 1), (−4, −4), (1, −3), (0, 8)}
Give the domain and range of H.
Write your answers using set notation.
domain = []
range = 0
Domain of the relation will be {-3,-4,1,0} and
Range of the relation will be {1,-4,-3,8}.
What is range and domain of a function?
Domain
The set of all possible values which qualify as inputs to a function is known as the domain of the function, or it can also be defined as the entire set of values possible for independent variables. The domain can be found in – the denominator of the fraction is not equal to zero and the digit under the square root bracket is positive. (In the case of a function with fraction values).
Range
The set of all the outputs of a function is known as the range of the function or after substituting the domain, the entire set of all values possible as outcomes of the dependent variable.
Now,
As inputs in the given relation are {-3,-4,1,0}
and outputs are {1,-4,-3,8}.
Hence,
Domain of the relation will be {-3,-4,1,0} and
Range of the relation will be {1,-4,-3,8}
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Which function increases at a faster rate on 0 to infinity, f(x) = x2 or g(x) = 2x? Explain your reasoning.
The function that increases at a faster rate on 0 to infinity is g(x) = 2ˣ
What is an average rate?
An average rate measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
The functions are given as:
f(x) = x² --- quadratic
g(x) = 2ˣ --- exponential
The exponential function has the same base as the power of the quadratic function.
This means that the exponential function would increase faster from the point where f(x) = g(x)
This is illustrated using the following table
x 0 1 2 3 4 5
f(x) 0 1 4 9 16 25
g(x) 1 2 4 8 16 3
Hence, the function that increases at a faster rate on 0 to infinity is g(x) = 2ˣ
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Madison has a loyalty card good for a 15% discount at her local grocery store. What
number should she multiply the prices on the tags by to find the price she would have
to pay, before tax, in one step?
Madison should multiply the price on the tag by (1-0.15) = 0.85 to find the price she would have to pay
How may math issues involving discounts be solved?Discount Formulas can be used to solve Discount problems in mathematics. It aids in boosting sales. Where M.P. (Marked Price) denotes the item's full retail cost without any discounts. The selling price, or S.P., is what consumers pay for the item. A percentage of the marked price is the discount.
The loyalty card gives a 15% discount so Madison should multiply the price on the tag by (1-0.15) = 0.85 to find the price she would have to pay, before tax, in one step.
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Twenty percent of a town’s voters favor letting a major discount store move into their neighborhood, 63% are against it, and17% are indifferent. What is the probability that a randomly selected voter from this town will either be against it or be indifferent? Explain why this probability is not equal to 1.0.
The required probability is 0.8
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here: Twenty percent of a town’s voters favor letting a major discount store move into their neighborhood, 63% are against it, and 17% are indifferent.
Thus total percentage of voters that are either against or be indifferent is equal to P( against or indifferent)=80%
=0.8
The probability is not equal to one because there is also percentage of voters that are in favour which accounts for 20%
Hence, The required probability is 0.8
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How do I solve this?
general equation of the tangent line, expressed through the x-coordinate of the point, at which it touches the function.
How do you find the equation of a tangent line?The equation of the tangent line can be found using the formula y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate points of the line1) Find the first derivative of f(x). 2) Plug x value of the indicated point into f '(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent lineA tangent to a circle at point P with coordinates is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of the circle to the point P. As the tangent is a straight line, the equation of the tangent will be of the form y = m x + c
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I need help it’s timed and I’m fr struggling
Answer:
y = 3/4x + 1-----------------------------
Slope-intercept form:
y = mx + b, where m- slope, b - y-interceptUse two points on the line:
(0, 1) and (4, 4)The first point is the y-intercept:
b = 1Find the slope:
m = (4 - 1)/(4 - 0) = 3/4The line is:
y = 3/4x + 1HOW FAR FROM HOME PLATE
TO SECOND BASE?
The catcher at home plate often needs
to make a quick throw to second base.
According to the measurements shown on
the baseball diamond, the exact distance
is √16,200 feet. How far is that in decimal
form? (Round to the nearest hundredth.)(please hurry )
The catcher must throw the ball in a distance of 127.2 feet to force a runner out at second base.
What is the distance that the ball have to be throw?From the figure we understands that it is a right angled triangle.
A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a rectangled triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.The hypotenuse of a right triangle is formed by the line from home plate to second base. The triangle's two sides are each 90 feet.
We can calculate the length of the hypotenuse using the Pythagorean theorem:
90² + 90² = c²
= 8100 + 8100 = c²
= 16200 = c²
c = √16200
c = 127.2
c = 127 feet
As a result, the distance that the catcher must throw the ball to get a runner out at second base is 127 feet.
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Graph the following polygons and classify them.
2. (–3,8), (5,8), (–3,–5), (5,–5)
3. (4,3), (3,3), (2,2), (2,1), (3,0), (4,0), (5,1), (5,2)
The polygons with the specified vertices and their graphs are as follows;
2. The polygon is a rectangle
Please find attached the graph of polygon 2, a rectangle, created with MS Excel
3. The polygon is an irregular octagon
Please find attached the graph of the polygon, an octagon, created with MS Excel
What is a polygon?A polygon is a closed plane figure with three or more linear sides and interior angles.
2. The vertices of the polygon are; (-3, 8), (5, 8), (-3, -5), (5, -5)
The number of vertex points indicates that the polygon is a quadrilateral.
The vertices indicates that the vertical lines x = -5, and x = 8, are lines that form the sides of the quadrilateral
Similarly, the horizontal lines y = -3, and y = 5 are boundaries of the quadrilateral
The distance between the vertical lines = 8 - (-5) = 13
The distance between the horizontal lines = 5 - (-3) = 8
The quadrilateral is therefore a rectangle
The graph of the rectangle, created with MS Excel is attached
3. The vertices of the polygon are; (4, 3), (3, 3), (2, 2), (2, 1), (3, 0), (4, 0), (5, 1), and (5, 2)
The number of vertex points are 8 indicating that the polygon is an octagon.
The length of the sides are;
(4 - 3) = 1
√((3 - 2)² + (3 - 2)²) = √2
(2 - 1) = 1
√((3 - 2)² + (0 - 1)²) = √2
4 - 3 = 1
√((5 - 4)² + (1 - 0)²) = √2
2 - 1 = 1
The lengths of the sides of the octagon are alternating therefore, the figure is an irregular octagon.
Please find attached the graph of the octagon, created with MS Excel
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The first figure takes 5 matchstick squares to build, the second takes 9 to build, and the third takes 13 to build, as can be seen by clicking on the icon below.
(a) How many matchstick squares will it take to build the 10th figure?
(b) How many matchstick squares will it take to build the nth figure?
(c) How many matchsticks will it take to build the nth figure?
Click the icon to view the matchstick square figures.
(a) The 10th figure will take squares to build. (Simplify your answer.)
Answer:
5, 9, 13, 17, 21, 25, 29, 33, 37, 41
Step-by-step explanation:
every time you go up one number, there is a 4 matchstick difference
the ninth figure therefore would be using 37 matchstick squares (:
hope this helped have a good day!
Trisha says that since 4(3s + 2) and 5(7s + 3) both equal 20 when s=1, the expressions are equivalent. Is she correct? Explain.
Trisha is not correct in claiming that these mathematical expressions 4(3s + 2) and 5(7s + 3) both equal 20 when s = 1.
What are mathematical expressions?Mathematical expressions are the combinations of variables, numbers, and arithmetic operators without the equation symbol (=).
The basic mathematical or arithmetic operators are addition, subtraction, division, and multiplication.
Mathematical expressions are not the same as equations. Equations show that two or more mathematical expressions are equal or equivalent.
In this situation, the equality of the two expressions can be proved by substituting s with 1, as follows:
Let s = 1
4(3s + 2) = 4(3 + 2) = 4 x 5 = 20
5(7s + 3) = 5(7 + 3) = 4 x 10 = 40
We know that 20 ≠ 40.
Thus, Trisha is not correct in claiming that the two mathematical expressions are equal when s = 1.
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Kami needs to score at least an 83 on her quiz in order to make an A for the report card.Write the inequality.
The inequality for the expression is x≥83
What is inequality?inequality, In mathematics is a statement of an order relationship. The signs in inequality includes: greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
greater than( >)
less than (<)
less than or equal to ≤
greater than or equal to ≥
Kami needs to score at least 83 on her quiz, this means that kami need to score a mark greater than or equal to 83 in her quiz.
If we represent the score of kami by x, this means the expression can be represented as:
x ≥ 83
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Pentagon ABCDE is shown on the coordinate plane below:
Pentagon on coordinate plane with ordered pairs at A negative 2, 4, at B negative 6, 2, at C negative 5, negative 2, at D 1, negative 2, at E 2, 2.
If pentagon ABCDE is rotated 180° around the origin to create pentagon A′B′C′D′E′, what is the ordered pair of point A′?
If pentagon ABCDE is rotated 180° around the origin to create pentagon A′B′C′D′E′, the ordered pair of point A′ is equal to (2, -4).
What is a rotation?In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).
By applying a rotation of 180° to the ordered pair of point A in pentagon ABCDE, the coordinates of its image (pentagon A′B′C′D′E′) can be calculated as follows:
(x, y) → (-x, -y)
Ordered pair of points A = (-2, 4) → Ordered pair of points A' = (-(-2), -(4)) = (2, -4).
Therefore, the coordinates of points A' is equal to (2, -4).
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Answer:
The answer is A) (2, −4)
Step-by-step explanation:
The rotation rule for 180° is (x, y) → (−x, −y) so wll use this rule to find the ordered pair of A′.
A = (-2,4)
(x, y) → (−x, −y) → (−(-2), −(4)) Change the sign of both coordinates (2, −4)
so, the answer is (2, −4)
A rigid motion creates figures that are..
answer choices
A. congruent
B. different sizes
C. similar
D. larger
The final statement is: A rigid creates figure that are congruent.
What does a rigid motion create?A rigid motion is when an object is moved from one location to another and the size and shape of the object have not changed. Two figures are congruent if and only if there exists a rigid motion that sets up a correspondence of one figure as the image of the other.
Given here: A rigid motion
Rigid Motion and Congruence-Two figures are congruent if and only if there exists one, or more, rigid motions which will map one figure onto the other. (thus maintaining the conditions for the figures to be congruent)
Hence, The right option is A.Congruent.
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What are the features of the quadratic function graphed in the figure?
Vertex (3, -4) with x-intercepts (1, 0), (5, 0), and (0, 5) and an axis of symmetry of 3. As a result, choice B is the right response.
The characteristics of the quadratic function graphed in the figure must be identified.
f(x) = ax2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Vertex (3, -4) has an axis of symmetry of three and an x-intercepts of one, five, and five. Choice B is the appropriate response as a result.It is necessary to identify the traits of the quadratic function graphed in the figure.A parabola can have different "widths" or "steepnesses," as well as different opening directions, but they all have the same basic "U" shape.This is how the whole process occurs in the given featuresTo know more about quadratic functions here
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What is the answer to this
Answer:
[tex]\textrm {D. The derivative is }\dfrac{x^{3}\cdot(\boldsymbol{9x^{8}})-x^{9}\cdot(\boldsymbol{3x^{2}})}{x^{6}}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \dfrac{u(x)}{v(x)}[/tex]
the derivative of f(x) wrt x is
[tex]f'(x) = \dfrac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2}[/tex]
[tex]u(x) =x^9 \;so \; u'(x) = 9x^8[/tex]
[tex]v(x) = x^3 , v'(x) = 3x^2\\\\\[v(x)\]^2 = [x^3]^2 = x^6[/tex]
Putting all these together we get
[tex]f'(x)=y'=\dfrac{x^{3}\cdot(\boldsymbol{9x^{8}})-x^{9}\cdot(\boldsymbol{3x^{2}})}{x^{6}}[/tex]
Missing entries are in bold
Need help quick please.
y=2x²+4x+4 and y=3x²+6x+9 are two instances for the provided standard form, y=ax²+bx+c.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A condition on a variable (or variables) such that two expressions in the variable (variables) have equal value is referred to as an equation. • The solution or root of the equation is the value of the variable for which the equation is fulfilled.
Here,
given standard form,
y=ax²+bx+c
examples of this,
y=2x²+4x+4
y=3x²+6x+9
The 2 examples for given standard form, y=ax²+bx+c is y=2x²+4x+4 and y=3x²+6x+9.
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pls answer the first question
In a fruit punch drink, the 3 ingredients
are apple juice, orange juice and
cranberry juice. If 4 of the drink is apple
juice and % is orange juice then write
the ratio of cranberry juice to apple juice
to orange juice in its simplest form.
3: 4=6: 8 We discovered an analogous ratio by multiplying both terms by 2, as the ratio was already in lowest terms.
What is the simplest definition of ratio?The proportion between two or more items in terms of number, amount, or size. When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 40% are girls, and 14% are boys.
Comparing two numbers by dividing them is how ratios work. Your formula would be A/B if you were contrasting one data point (A) with another data point (B). By doing so, you are multiplying information A by information B.
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3a + 6 + 5a - 2; = 2, = 5, and =– 3
8 + 8 − 4 − 3; for = 2, = 5, and =– 3
5c - 4c + c - 3c; for = 2, = 5, and =– 3
The expression for each values of {a} and {c} are calculated below..
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the expressions as -
3a + 6 + 5a - 2
5c - 4c + c - 3
For the expression -
3a + 6 + 5a - 2
8a + 4
For {a} = 2, we can write -
8 x 2 + 4
20
for {a} = 5, we can write -
8 x 5 + 4
44
for {a} = -3, we can write -
8 x -3 + 4
-20
For the expression -
5c - 4c + c - 3c
- c
For {a} = 2, we can write -
- 2
for {a} = 5, we can write -
- 5
for {a} = -3, we can write -
3
Therefore, the expression for each values of {a} and {c} are calculated above.
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How much would a $75 video game be with 8.25% sales tax
Answer:
$81.19
Step-by-step explanation:
8.25% x 75 = 8.19
75 + 8.19 = $81.19
Suppose you found that the correlation between the life expectancy of citizens in a nation and the average number of TVs in households in that nation is r=0.89. Does that mean that watching TV helps you live longer?
Yes , watching TV helps you live longer by using correlation coefficient.
How to interpret a correlation coefficient?
The statistical measure of how well changes in the value of one variable predict changes in the value of another is called a correlation coefficient. The value rises or falls together when the variables are positively linked.
The r represents the correlation coefficient which has a value 0.89 for the given case.
we can say that there is a positive association between the life expectancy of citizen and the average number of TVs in households.
the r value is close to +1 which means that the association is close to linear relation .
so we put it like
R² = 0.89² = 0.7921
now 0.7921 signifies that almost 79% variation in life.
So we can say that watching TV helps you live longer.
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I really need help on this because I don't understand how to calculate this. (I need this answered now please!!)
Julia spins 2 spinners. One of the spinners is labeled 1, 2 and 3, and the other is labeled A, B and C. What is the probability that Julia will land on a 1 and an A?
A) 1/6
B)1/3
C)1/2
D)1/9
Based on the information provided, the probability that Julia will land on a 1 and an A is 1/6 or 0.166.
What is probability?The probability can be described as the likelihood of an event happening. In most cases, the probability depends on the ratio of the desired event and all possible outcomes. For example in a bag with a total of 6 red balls and 4 black balls the probability of getting a red ball is 6/10.
What is the probability in this case?To find out the total probability, we need to calculate the two probabilities involved and mutiply them.
Probability spinner 1 lands = 1/3 as there are three spinners
Probability A lands = 1/4 as there are 4 possible outcomes A, B, C, D
1/3 x 1/4 = 1/6This means the probability of this event happening is 1/6, which can be simplified as 0.166 or 16%.
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there are 25 spools each of blue , green , red , white ,and yellow thread in the sewing basket . without looking whats the probability of picking a spool of blue thread from the basket
The probability of randomly selecting a spool of blue thread from the basket is P = 1/5 = 0.2
How to find the probability of picking a spool of blue thread?We know that there are:
25 spools each of:
blue, green, red, white, and yellow thread in the basket.
So there are a total of:
25*5 = 125 spools in total.
If the probability is evenly distributed, then the probability of randomly selecting a spool of color blue is equal to the quotient between the number of blue spools and the total number of spools, we will get:
P = 25/125 = 1/5 = 0.2
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[tex]y = \frac{1}{3}x^{2} + 1\\y = 2x - 2[/tex] please help me
The value of x is equal to 3
What are quadratic equations?A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.
Given here
[tex]y=x^{2}/3+1 \\y=2x-2[/tex]
Solving these two equations we get
[tex]y=1x^{2} /3+1=2x-2\\1x^{2}/3-2x+3=0\\x^{2} -6x+9=0\\(x-3).(x-3)=0\\x=3,3[/tex]
Hence, the value of x is equal to 3
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2
3. Lewis says that the figure
below has an area of
4 square meters. Is he
correct? Explain.
=
1 square cm
Assessment
Practice
Answer:
The answer should be 7 [tex]cm^{2}[/tex]
Step-by-step explanation:
If I make a 4 by 4 rectangle around the figure, I will have a 4 by 4 square.
The area will be 16. Now subtract out the triangle on the bottom left and top right.
The triangles have a length and a height of 3.
a = 1/2 (lxh)
1/2(3x3) + 1/2(3x3) = 9
Subtract 9 from 16
16-9 = 7
sketch the region enclosed by the given curves. x = 7y2, x = 4 + 6y2
Find its area.
The enclosed area between the 2 equations, x = 7y² and x = 4 + 6y² is 32/3 sq units
Here equation 1 is x = 7y²
and equation 2 is x = 4 + 6y²
To find the area enclosed between the region, we need to first find the points where these two lines meet.
This implies,
eq 1 = eq 2
or, 7y² = 4 + 6y²
or, y² = 4
or, y = ±2
Now if we see the graph with respect to y, the area between the y-axis and eq 2 is greater than that of the y-axis and equation 1.
Now area is enclosed between 2 lines with respect to x. Hence it will be
= ∫eq 2 dy - ∫eq 1 dy with limts of 2 and -2
= ∫4 + 6y²dy - ∫7y²dy with limits 2 and -2
= [4y + 2y³ - 7/3 y³] with limits 2 and -2
= 8 + 16 - 56/3 + 8 + 16 - 56/3 sq. units
= 48 - 112/3
= 32/3 sq units
Hence the enclosed area is 32/3 sq units
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