The values of the constant λ that will make y = e^(λx) a solution of the differential equation y′′ −3y′ + 2y = 0 are λ = 1 and λ = 2.
To find the value(s) of the constant λ that will make y = e^(λx) a solution of the differential equation y′′ −3y′ + 2y = 0, we can substitute y = e^(λx) into the differential equation and solve for λ.
First, we need to find the first and second derivatives of y = e^(λx):
y′ = λe^(λx)
y′′ = λ^2e^(λx)
Now, we can substitute these derivatives into the differential equation:
λ^2e^(λx) − 3λe^(λx) + 2e^(λx) = 0
e^(λx)(λ^2 − 3λ + 2) = 0
Since e^(λx) cannot equal 0, we can set the expression in parentheses equal to 0 and solve for λ:
λ^2 − 3λ + 2 = 0
(λ − 1)(λ − 2) = 0
λ = 1 or λ = 2
Therefore, the values of the constant λ that will make y = e^(λx) a solution of the differential equation y′′ −3y′ + 2y = 0 are λ = 1 and λ = 2.
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Fill in the blank. (a) For a line, the ratio of the change in y to the change in x is called the _________ of the line. (b) The point-slope form of the equation of a line with slope m passing through (x1, y1) is _________
(a) For a line, the ratio of the change in y to the change in x is called the slope of the line.
(b) The point-slope form of the equation of a line with slope m passing through (x1, y1) is y - y1 = m(x - x1).
The slope of a line is a measure of its steepness and is calculated by finding the ratio of the change in y (the rise) to the change in x (the run) between two points on the line.
The point-slope form of the equation of a line is a way to write the equation of a line when you know its slope and one point on the line. It is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is the point on the line.
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Dan and Jenny are selling pies for a school fundraiser. Customers can buy apple pies and lemon meringue pies. Dan sold 14 apple pies and 9 lemon meringue pies for a total of $147. Jenny sold 8 apple pies and 12 lemon meringue pies for a total of $132.
Find the cost each of one apple pie and one lemon meringue pie.
From the system of equations one apple pie costs $6 and one lemon meringue pie costs $7.
What exactly is an equation system?A group of equations that need to be solved concurrently is referred to as a system of equations. The values of the variables that satisfy each and every one of the system's equations are the solutions to the corresponding equations. Systems of equations can be solved using a variety of techniques, such as substitution, elimination, and graphing. Systems of equations can be used to simulate situations in business, science, and engineering when there are several variables at play. Systems of differential equations, linear equations, and quadratic equations are a few examples of systems of equations.
Let us suppose the cost of the apple pie = x.
Let us suppose the cost of the meringue pie = y.
Given that, Dan sold 14 apple pies and 9 lemon meringue pies for a total of $147.
14x + 9y = 147
For Jenny:
8x + 12y = 132
Using the elimination method we have:
Multiplying Dan's equation by 4 gives:
56x + 36y = 588
Multiplying Jenny's equation by 3 gives:
24x + 36y = 396
Subtracting the second equation from the first:
32x = 192
x = 6
Substitute the value of x in equation:
14(6) + 9y = 147
84 + 9y = 147
9y = 63
y = 7
Hence, from the system of equations one apple pie costs $6 and one lemon meringue pie costs $7.
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You will be marked as brainlest
i need correct ans now please
and extra points will be given
please
Answer:
3m-4
Step-by-step explanation:
marcie's age be x
her father age is four less than three times
the equation tht describes her father age is 3m-4=40
a
b
C
d
The boxplot shows the cost of 40 sandwiches.
18
28
11
22
If you had $18 how many of the sandwiches could you
afford?
40
20
10
25
46
Answer:
C. 10 sandwiches
Step-by-step explanation:
Each section of a box plot makes up 25% of it. Since Q1 is marked by $18, that means 25% of 40 sandwiches can be bought with it. So, [tex]\frac{40}{4}[/tex] = 10.
The question involves a basic division operation in Mathematics. Without the cost of a sandwich, it's impossible to answer. If provided, just divide the total money by the price of a sandwich to find the number that can be purchased.
Explanation:The student's question involves simple division, which is a topic under the subject of Mathematics. To determine how many sandwiches one can afford with $18, it is necessary to have the cost of one sandwich. Unfortunately, without the given price of a single sandwich as indicated in the boxplot, we cannot compute the answer.
But if we are provided the cost of a single sandwich, we would simply divide the total amount of money ($18) by the cost of a single sandwich. This would give us the total number of sandwiches affordable with the given amount of money.
Assuming a sandwich costs $2, here is how the computation would be: $18 ÷ $2 = 9 sandwiches. So, with $18, we could afford 9 sandwiches at $2 each.
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Consider the matrix that transforms a vector (x1, x2, x3) into (x2, x3, x1) in 3D:
1-Show that this is a rotation matrix.
2-Find the axis of rotation.
3-Find the angle of rotation
1- This is a rotation matrix because the determinant is 1 and the transpose is equal to the inverse. 2- The line passing through the origin and the point (1, 1, 1) is the axis of rotation. 3- 120° is the angle of rotation.
1. To show that this is a rotation matrix, we need to check that the matrix satisfies the following properties:
- The determinant of the matrix is 1.
- The transpose of the matrix is equal to its inverse.
The matrix that transforms a vector (x1, x2, x3) into (x2, x3, x1) is:
| 0 1 0 |
| 0 0 1 |
| 1 0 0 |
The determinant of this matrix is:
det = 0×0×0 + 1×1×1 + 0×0×0 - 0×0×1 - 1×0×0 - 0×1×0 = 1
The transpose of this matrix is:
| 0 0 1 |
| 1 0 0 |
| 0 1 0 |
The inverse of this matrix is:
| 0 0 1 |
| 1 0 0 |
| 0 1 0 |
Since the determinant is 1 and the transpose is equal to the inverse, this is a rotation matrix.
2. To find the axis of rotation, we need to find the eigenvector of the matrix corresponding to the eigenvalue of 1. The characteristic equation of the matrix is:
| -λ 1 0 |
| 0 -λ 1 |
| 1 0 -λ | = 0
Expanding the determinant, we get:
-λ × (-λ × (-λ)) - 1 × 1 x 1 = 0
λ = 1
The eigenvector corresponding to the eigenvalue of 1 is:
| -1 1 0 | | x1 | = | 0 |
| 0 -1 1 | | x2 | | 0 |
| 1 0 -1 | | x3 | | 0 |
Solving this system of equations, we get:
x1 = x2 = x3
So the eigenvector is:
| 1 |
| 1 |
| 1 |
This means that the axis of rotation is the line passing through the origin and the point (1, 1, 1).
3. To find the angle of rotation, we can use the formula:
cosθ = (trA - 1)/2
Where trA is the trace of the matrix A. The trace of the matrix is:
trA = 0 + 0 + 0 = 0
So the angle of rotation is:
cosθ = (0 - 1)/2 = -1/2
θ = 120°
Therefore, the angle of rotation is 120°.
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6 times a number plus 3
Answer:
6x + 3
Step-by-step explanation:
Answer:
6x + 3
Step-by-step explanation:
x = a number
6 times a number (x) can also be written as 6x.
Plus 3 is simply adding 3, therefore, it is written as 6x+3
The minimum payment is 15% of the new balance or $25 which is greater the new balance is 158
The minimum payment would be $23.70 if we only used the 15% rule.
What is minimum payment ?Minimum payment refers to the smallest amount of money that a borrower or a credit card holder must pay towards their outstanding balance each billing cycle in order to avoid late fees. This minimum payment is usually a percentage of the total balance due or a fixed dollar amount whichever is greater.
The minimum payment is either 15% of the new balance or $25, whichever is greater.
If the new balance is $158, we can first find 15% of the new balance:
15% of $158 = 0.15 * $158 = $23.70
So, the minimum payment would be $23.70 if we only used the 15% rule.
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Question
What is the value of p in this proportion?
6/p=15/3.5
Enter your answer as a decimal in the box.
Answer:
1.4
Step-by-step explanation:
If 6/p =15/3.5
You can cross multiply the equation
6x3.5 =15P
21=15P
Divide both sides by 15
21/15 = P
1.4 =P
PKEASE HELPPP 15 POINTSSSSSSSSSSss
Answer: you can see herhere
Step-by-step explanation:
try times like x=1 and find the answer true
target sells 12 bottles of water for $2 and 24 bottles of water for $3. which is the better buy and by how much
example: how much per bottle
Answer:
1/ 24 bottle of water for $3 is a better buy
2/ $0.045
Step-by-step explanation:
12 bottles of water for $2
2 / 12 =$0.17
So, it costs $0.17 for each bottle of water.
24 bottles of water for $3
3 / 24 = $0.125
So, it costs $0.125 for each bottle of water.
0.17 - 0.125 = $0.045
So, 24 bottles of water for $3 is a better buy by $0.045
Observa la siguiente pirámide, en la cual cada casilla tiene un número que se forma sumando las dos casillas inferiores.
¿Cuál es el número que ocupa la casilla de color rojo?
A.
167√
B.
197√
C.
217√
D.
247√
Doy 5 estrellas y corona por favor
The value in the red box would be 19√7.
What is algebraic expressions?An algebraic expression is a made up of terms both constants and variables. For example, we can write -
2x + 3y + z
5x + y
x + 8y
Given is a pyramid as shown in the image.
We can write -
b{4} = 2√7 - 4√7 = - 2√7
b{4} = - 2√7
- 4√7 + b{9} = 3√28
b{9} = 3√28 + 4√7
b{9} = 6√7 + 4√7
b{9} = 10√7
b{6} = 10√7 - √7
b{6} = 9√7
b{2} = - 2√7 + 6√7
b{2} = 4√7
b{3} = 3√28 + 9√7
b{3} = 6√7 + 9√7
b{3} = 15√7
b{1} = 4√7 + 15√7
b{1} = 19√7
Therefore, the value in the red box would be 19√7.
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{QUESTION IN ENGLISH -
Look at the following pyramid, in which each box has a number that is formed by adding the two bottom boxes.
What is the number that occupies the red box?}
I need help with these pls!
5. 24 hours over 7 days (Because 1 day = 4 hrs)
6. 16 limes over 2 bags (1 bag = 8 limes)
7. 54 cups over 9 boxes (6 cups = 1 box)
8. 27 meters (or minutes) over 3 seconds (9 meters over 1 second)
9. 36 lbs over $24 ($1 = 1.5lbs)
find from the first principle, the derivative with respect to x of the function.y=2x^2-x+3
Answer:
[tex]\dfrac{\text{d}y}{\text{d}x}=4x-1[/tex]
Step-by-step explanation:
Differentiating from First Principles is a technique to find an algebraic expression for the gradient at a particular point on the curve.
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\\\end{minipage}}[/tex]
The point (x + h, f(x + h)) is a small distance along the curve from (x, f(x)).
As h gets smaller, the distance between the two points gets smaller.
The closer the points, the closer the line joining them will be to the tangent line.
To differentiate y = 2x² - x + 3 using first principles, substitute f(x + h) and f(x) into the formula:
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{2(x+h)^2-(x+h)+3-(2x^2-x+3)}{(x+h)-x}\right][/tex]
Simplify the numerator:
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{2x^2+4xh+2h^2-x-h+3-2x^2+x-3)}{x+h-x}\right][/tex]
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{2x^2-2x^2+x-x+3-3+4xh+2h^2-h)}{h}\right][/tex]
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{4xh+2h^2-h)}{h}\right][/tex]
Separate into three fractions:
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{4xh}{h}+\dfrac{2h^2}{h}-\dfrac{h}{h}\right][/tex]
Cancel the common factor, h:
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[4x+2h-1\right][/tex]
As h → 0, the second term → 0:
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=4x-1[/tex]
6. Show thatT:R2→R2defined byT([xy])=[xy0]is not a linear transformation. 7. Assume thatAis a square matrix that satisfiesA3−3A+2I=0. Use this equation to conclude thatAis invertible and write downA−1in terms ofA.
A-1 = (A - 2I)-1(A2 + 2A + 4I)-1.
6. To show that T:R2→R2 defined by T([x y]) = [x y 0] is not a linear transformation, consider T(u+v) = T([u1 + v1, u2 + v2]) = [u1 + v1, u2 + v2, 0]. Since T(u+v) is not equal to T(u) + T(v), which is [u1, u2, 0] + [v1, v2, 0] = [u1 + v1, u2 + v2, 0], then T is not a linear transformation.
7. Assume A is a square matrix that satisfies A3 - 3A + 2I = 0. This equation can be written as (A - 2I)(A2 + 2A + 4I) = 0. Since A - 2I is non-zero and A2 + 2A + 4I is non-zero, then A - 2I and A2 + 2A + 4I are both invertible and therefore A is invertible. Since A is invertible, A-1 = (A - 2I)-1(A2 + 2A + 4I)-1.
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Tammy wants to run at least 10 miles per week.
So far this week, she ran 4.5 miles.
Write and solve an inequality to determine how many more miles tammy must run this week to reach her goal.
Answer:
Let x be the number of additional miles Tammy needs to run this week to reach her goal of at least 10 miles per week.
To determine the inequality, we can start with the given information and use the inequality symbol for "greater than or equal to" (≥):
4.5 + x ≥ 10
This inequality states that the sum of the distance Tammy has already run this week (4.5 miles) and the additional distance she still needs to run (x miles) must be greater than or equal to 10 miles in total for her to reach her goal.
To solve for x, we can start by subtracting 4.5 from both sides of the inequality:
x ≥ 10 - 4.5
Simplifying, we get:
x ≥ 5.5
Therefore, Tammy must run at least 5.5 more miles this week to reach her goal of at least 10 miles per week.
Step-by-step explanation:
wag na mag delete pls lng ang bob0 nyo namn pag na delete nyo toh mga admin
I NEED HELP ON THIS ASAP!
Answer:
its nissa
Step-by-step explanation:
Ez
5. Find the equation of the line through the points (-3,7) and (2, 17). Write the answer in slope-intercept form, y=mx+b.
The equation of the line through the points (-3,7) and (2, 17) is y = 2x + 13.
To find the equation of the line through the points (-3,7) and (2, 17), we need to first find the slope of the line and then find the y-intercept.
Step 1: Find the slope of the line
The slope of a line is given by the formula:
m = (y2 - y1)/(x2 - x1)
Where (x1, y1) and (x2, y2) are the two points on the line.
Plugging in the given points, we get:
m = (17 - 7)/(2 - (-3))
m = 10/5
m = 2
Step 2: Find the y-intercept
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We can plug in one of the given points and the slope we found to solve for b.
Using the point (-3,7), we get:
7 = 2(-3) + b
7 = -6 + b
b = 13
Step 3: Write the equation in slope-intercept form
Now that we have the slope and y-intercept, we can write the equation of the line in slope-intercept form:
y = 2x + 13
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In your opinion, which is the best and simplest way to factor polynomials (including quadratics)? Explain why you chose this method compared to other methods. Are there some exceptions to this, maybe a polynomial that might factor better with another method?
2x^2 + 7x + 3 factors into (2x + 1)(x + 3).
What is factoring?
The factoring approach can be used if the quadratic polynomial can be divided into two linear factors:
Look for two numbers that add up to b and multiply to c.
With these numbers, rewrite the quadratic polynomial as the sum of two terms.
Choose the term that has the most in common with each group of terms.
Remove the common binomial factor between the two groups.
Take the quadratic polynomial 2x2 + 7x + 3, for instance. We must choose two values that sum up to seven and multiply by three in order to factor this polynomial. These are the numbers 3 and 1. The quadratic can then be rewritten as follows:
2x² + 3x + 4x + 3
Then, for each collection of terms, we factor out the term with the highest common factor:
x(2x + 3) + 1(4x + 3)
Lastly, we remove the common binomial factor between the two groups:
(2x + 1)(x + 3)
As a result, 2x2 + 7x + 3 equals (2x + 1)(x + 3).
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A submarine is descending to examine the seafloor 2100 feet below the surface. It takes a submarine two hours to make this decision. What’s an equation to represent the relationship between submarines elevation time
Elevation = 0 - 1050 × Time or Elevation = -1050t, where Elevation is in feet and Time is in hours, is the expression that describes the connection between the submarine's elevation and time.
What is a mathematical measure of time?Seconds, mins max, minutes, days, periods, months, and years are the fundamental elements of time. To determine the time of day, we use secs, minutes, as well as hours; to determine the date, we use times, months, and years. The lesser measures of time are seconds, minutes, and hours, while the larger ones are days, months, and years.
Assuming that the submarine is descending at a constant rate, we can use the equation:
Elevation = Initial Elevation - Rate × Time
where Initial Elevation is the starting elevation (in this case, the surface), Rate is the rate of descent, Time is the time elapsed, and Elevation is the current elevation.
In this case, the Initial Elevation is 0 feet (the surface), the Rate is -1050 feet per hour (since the submarine is descending at a rate of 1050 feet per hour), and Time is the elapsed time in hours.
Therefore, the equation that represents the relationship between the submarine's elevation and time is:
Elevation = 0 - 1050 × Time
or
Elevation = -1050t
where Elevation is in feet and Time is in hours.
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Which function grows at the fastest rate for increasing values of x?
Responses
h(x)=6x2+1
h open parentheses x close parentheses equals 6 x squared plus 1
g(x)=4x
g open parentheses x close parentheses equals 4 to the power of x end power
f(x)=9x+14
This is due tο the fact that as x grοws, the quadratic cοmpοnent in g(x) and f(x), respectively, predοminates οver the cοnstant term and the linear term.
what is functiοn?A functiοn is a mathematical fοrmula that relates every element in οne set, knοwn as the dοmain, tο a single element in anοther set, knοwn as the range. The relatiοnship between input and οutput, the relatiοnship between a variable and its rate οf change, and many οther real-wοrld phenοmena are all examples οf this basic mathematical idea. Algebraic expressiοns, graphs, tables, and even wοrds can be used tο describe functiοns. They are a crucial instrument in many disciplines, including cοmputer science, statistics, and calculus.
given:
Fοr rising values οf x, the fοllοwing functiοn exhibits the fastest grοwth:
h(x) = 6x² + 1.
This is due tο the fact that as x grοws, the quadratic cοmpοnent in g(x) and f(x), respectively, predοminates οver the cοnstant term and the linear term. As a result, οf the functiοns listed, h(x) grοws at the fastest pace.
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Determine whether the experiment is a binomial experiment. If it is a binomial experiment, identify p and n. If it is not a binomial experiment, explain why it is not.
A jar contains nine red marble, six blue marble, five green marbles, and four white marbles. Assume success is determine by probability of a red ball drawn. Three marbles are randomly selected from the jar without replacement.
A 10-gallon jar full of pennies contain 1% steel pennies minted in 1943. One penny is selected and is repeated 100 times.
The first experiment is not a binomial experiment because it does not meet the criteria of a binomial experiment. The criteria of a binomial experiment are:
1. The experiment consists of a fixed number of trials, n.
2. Each trial has only two possible outcomes: success or failure.
3. The trials are independent of each other.
4. The probability of success, p, remains constant for each trial.
In the first experiment, the trials are not independent of each other because the marbles are selected without replacement. This means that the probability of success changes with each trial. Therefore, it is not a binomial experiment.
The second experiment is a binomial experiment because it meets the criteria. There are a fixed number of trials (100), each trial has only two possible outcomes (steel penny or not steel penny), the trials are independent of each other (one penny is selected and then replaced), and the probability of success remains constant (1% for each trial). Therefore, p = 0.01 and n = 100.
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URGENT! Please give the correct answer.
The product that results in an irrational number is given as follows:
[tex]\sqrt{84} \times 21[/tex]
What are rational and irrational numbers?Rational numbers are numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.Irrational numbers are numbers that cannot be represented by fractions, being non-terminating and non-repeating decimals, such as non-exact square roots.21 is a rational number, hence for the product to be irrational, we need an irrational number, which is the non-exact square root of 84.
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A study of 4393 adults from country a, 3074 think mainstream media is more interested in making money than in telling the truth
The point estimate for p(cap) and q(cap) as per defined condition of mainstream media is equal to 0.700 and 0.300 respectively.
Total number of adults in the country = 4393
Number of adults think mainstream media is more interested in making money = 3074
The point estimate for p, denoted as p(cap),
p(cap) represents proportion of individuals in the sample.
Individual who think mainstream media is more interested in making money than in telling the truth.
This implies,
p(cap)
= 3074/4393
≈ 0.700
The point estimate for q, denoted as q(cap), is the proportion of individuals in the sample.
Individuals who do not think mainstream media is more interested in making money than in telling the truth.
This implies,
q(cap)
= 1 - p(cap)
= 1 - 0.700
≈ 0.300
Therefore, the point estimate for p(cap) is approximately 0.700 and the point estimate for q(cap) is approximately 0.300.
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The above question is incomplete, the complete question is:
Let p be the population proportion for the following condition. Find the point estimates for p and q.
A study of 4393 adults from country A, 3074 think mainstream media is more interested in making money than in telling the truth.
The point estimate for p, p(cap), is (Round to three decimal places as needed.)
The point estimate for q, q(cap), is (Round to three decimal places as needed.)
The equation px²+16x+4=0 is certified by x=-2/3. Find the value of p and x
P therefοre has a value οf 45/2 and x = -0.4.
What is equatiοn?A mathematical assertiοn that twο expressiοns are equivalent is knοwn as an equatiοn. It frequently includes οne οr mοre variables, which are unknοwable things with a wide range οf pοssible values. Finding the value οr values οf the variable that make the equatiοn true is the aim οf equatiοn sοlving. Mοst equatiοns take the fοrm: expressiοn is alsο expressiοn. Fοr instance, the fοrmula x + 2 = 5 states that the prοduct οf x and 2 is 5.
given
If the answer tο the equatiοn px² + 16x + 4 = 0 is x=-2/3, we can be cοnfident that we will οbtain an equivalence if we replace x = -2/3 in the fοrmula.
Adding x=-2/3 tο the sοlutiοn results in:
p(-2/3)² + 16(-2/3) + 4 = 0
Simplifying the phrase:
(4/9)p - (32/3) + 4 = 0
(4/9)p = (32/3) - 4
(4/9)p = (20/3)
By adding (9/4) tο bοth ends, we get:
p = (20/3) * (9/4)
p = 15
P therefοre has a value οf 45/2.
For x,
15x² + 16x + 4 = 0
3x(5x + 2) + 2(5x + 2)
(3x + 2)(5x + 2)
x = -2/3 and x = -0.4
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A teacher collected data from her students on the amount of homework that each student completed over the week. She used a scale of integers from 0 to 10 where 0 meant none of the
homework was completed and 10 meant that all of the homework was completed.
a) Would the data be discrete or continuous? Explain.(3)
b) Would the data be ordinal data or nominal data? Explain.(3)
Answer:
a) The data would be discrete because it can only take on a finite number of values.
The teacher used a scale of integers from 0 to 10, which means that the data can only take on one of those 11 values. Continuous data, on the other hand, can take on an infinite number of values within a given range.
b) The data would be ordinal data because it can be ordered or ranked.
The scale of integers from 0 to 10 represents a ranking of how much homework was completed, with 0 being the lowest and 10 being the highest. Nominal data, on the other hand, cannot be ordered or ranked and is used to classify or categorize things.
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1) Which of the following are the coordinates of point B’ , the image of point B after a translation of (x-4, y-3)
A- B’(-1,2)
B- B’(-4,-3)
C- B’(1,5)
D- B’(1,-2)
2) The two figures are congruent. Describe the isometry that maps the original figure onto the new figure.
A- Translation (x-3,y-1)
B- Reflection over the line x = 1
C- 90 Degree Rotation
D- 270 Degree Rotation
3) The smaller figure is a dilation of the original figure. Which two statements below are true?
A- The dilation is an enlargement.
B- The dilation is a reduction.
C- The dilation has a scale factor of 1/2
D- The dilation had a scale factor of 2
E- The dilation has a scale factor of 1/4
4) Complete a glide translation (x-2,y) and then reflect over x axis. What would be the new ordered pairs for P’ and S’?
A- P’(1,-2) S’(2,5)
B- P’(5,-2) S’(6,-5)
C- P’(1,2) S’(2,5)
D- P’(3,2) S’(4,5)
5) Complete a dilation with scale factor of 1/2 around the origin and then reflect over the y-axis. What are the new ordered pair of A’?
A- A’(-4,-10)
B- A’(-1,-2.5)
C- A’(2,5)
D- A’(1,2.5)
The transformation of the points and shapes after being transformed are calculated below
The coordinates of B' after the translationThe coordinates of B in the figure is
B = (5, 1)
A translation of (x-4, y-3) means
B' = (5 - 4, 1 - 3)
B' = (1, -2)
The isometry transformationHere, we have the following corresponding points
Pre = (2, 1)
Image = (-1, 2)
This represents
(x, y) = (-y, x)
This represents (d) 270° clockwise rotation
The statements of the dilationGiven that the smaller figure is gotten from a bigger figure
Then the dilation is a reduction and the scale factor could be 1/2 or 1/4
The glide transformatonWe have
P = (3, -2) and S = (4, -5)
For the first transformation, we have
(x - 2, y)
P' = (1, -2) and S' = (2, -5)
For the second, we have
P'' = (1, 2) and S'' = (2, 5)
The new ordered pair of point AHere, we have
A = (-2, -5)
This means that the new ordered pair of point A is
A' = (-2, -5) * 1/2
A' = (-1, -2.5)
Hence, the new ordered pair of point A is (-1, -2.5)
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let f(x)=-2x+4 and g(x)=-6x-7
find f(x) g(x)
find f(g(4))
please help and show work
Given,
f(x) = -2x + 4
g(x) = -6x - 7
To find,
The value of f(x) - g(x)
Solution,
The value of f(x) - g(x) is 4x + 11.
We can simply solve the given mathematical problem by the following process.
We know that,
f(x) = -2x + 4
g(x) = -6x - 7
Now,
f(x) - g(x) = (-2x+4) - (-6x-7)
= -2x - 4 + 6x + 7
= 4x + 11
Thus, the value of f(x) - g(x) is 4x+11.
Step-by-step explanation:
in the part a take the f(x) as the normal equation but in the place of x put the equation of g , its as g is now x .
in part b its the exact same only that instead of the x in equation of g(x) the gave you a number to plug into the x
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answer:
[tex]27\pi[/tex]
Step-by-step explanation:
The area of a circle is given by the formula [tex]A = \pi r^2[/tex].
We are given the radius of this circle, so we can plug in.
[tex]A = \pi r^2\\A=6^2\pi \\A=36\pi[/tex]
Seeing that there is [tex]\frac{3}{4}[/tex] of the circle left, multiply [tex]36\pi[/tex] by [tex]\frac{3}{4}[/tex].
[tex]36\pi(\frac{3}{4})\\ 9\pi (3)\\27\pi[/tex]
PLS HELP! I WILL GIVE YOU BRAINLIEST IF YOU HELP! PLEASE HURRY AND PLEASE SHOW WORK! IT IS IN THE PHOTO!
Answer:
Below
Step-by-step explanation:
12 000 * r = 9600
r = 9600 / 12000 = .8
So multiply each term by .8 to get the next term:
year 1 12 000
year 2 12 000 * .8
year 3 12 000 * .8 * .8
Year 4 12 000 * .8 * .8 * .8 = 12 000 * .8^3
.
.
year 7 12 000 * (.8)^6 = $ 3145.73
an = a1 r^(n-1)
an = 12 000 (.8)^n-1
Two angles in a triangle measure 102 and 54. What measure of the third angle?
Answer:
24
Step-by-step explanation:
The sum of the three angles in a triangle is always 180 degrees.
Let x be the measure of the third angle.
Then we have:
102 + 54 + x = 180
Simplifying the left side:
156 + x = 180
Subtracting 156 from both sides:
x = 180 - 156
x = 24
Therefore, the measure of the third angle is 24 degrees.