5/2 and 3 are the solutions to the equation 2x² - 10x + 15 = x.
What is equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows 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 mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.
Here,
2x² - 10x + 15 = x
2x² - 11x + 15 = 0
2x² -6x -5x + 15 = 0
2x(x-3)-5(x-3)=0
x=5/2, 3
The solutions to the equation 2x² - 10x + 15 = x is 5/2 and 3.
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if matrix a is symmetric show that any two eigenvectors of a correspond to different eigenvalues are orthogonal
A symmetric matrix is a square matrix that is equal to transpose of itself. If A is a symmetric matrix, then it satisfies the condition: A = AT. (AT is the inverse of A )
A square matrix with real numbers or elements is said to be an orthogonal matrix if its transpose is equal to its inverse matrix. Or we can say when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix.
Suppose λ and μ are 2 distinct values of matrix A.
For the matrix to be Symmetric,
( Ax,y)=(x,Ay)
condition needs to be satisfied.
Here, ( x,y) is dot product between vectors x and y
λ (u,v) = (λu,v)
where u,v are eigen vectors for eigen values λ and μ
λ(u,v) = (Au,v)
λ(u,v) = (u,Av)
λ(u,v) = μ(u,v)
λ(u,v) = μ(u,v)
but λ≠μ
∴ (u,v) = 0.
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The complete question is :
If a matrix is symmetric then show that any two eigenvectors of that matrix corresponding to different eigenvalues are orthogonal. Assume square matrix.
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
Three polynomials are factored below, but some coefficients and constants are missing. All of the missing values of a, b, c, and
d are integers.
1. x² - 8x + 15 = (ax + b)(cx + d)
2. 2x³ - 8x² - 24x = 2x(ax + b)(cx + d)
3.6x² + 14x + 4 = (ax + b)(cx + d)
Fill in the table with the missing values of a, b, c, and d.
b
a
1. 1
2. 1
3.
Submit
Pass
-5
1
C
1
2
d
Question ID: 504360
-6
Save an
150
The values of variables a to d are
a = 1 and c = 1, b = -3 and d = -5a = 1 and c = 1, b = 2 and d = -6a = 1, b = 2. c = 6 and d = 2How to determine the values of the variablesPolynomial 1
This is given as
x² - 8x + 15 = (ax + b)(cx + d)
The factors of 15 that add up to -8 are
-3 and -5
This means that
b = -3 and d = -5
Because the coefficient of x² is 1, then
a = 1 and c = 1
Polynomial 2
This is given as
2x³ - 8x² - 24x = 2x(ax + b)(cx + d)
Divide through by 2x
x² - 4x - 12 = (ax + b)(cx + d)
The factors of -12 that add up to -4 are
2 and -6
This means that
b = 2 and d = -6
Because the coefficient of x² is 1, then
a = 1 and c = 1
Polynomial 3
This is given as
6x² + 14x + 4 = (ax + b)(cx + d)
Factorize
(x + 2)(6x + 2) = (ax + b)(cx + d)
By comparison, we have
a = 1, b = 2. c = 6 and d = 2
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For each value below, enter the number to four decimal places Suppose an arrow is shot upward on the moon with a velocity of 60m / s then its height in meters after seconds is given by h(t) = 60t - 0.83t ^ 2 Find the average velocity over the given time intervals [4, 4, 5]; (4,4,1) 2; [4,4,01]:; [4,4,001]:
Average speed is determined by dividing the total distance you traveled by the total time,
How fast is it moving on average?In order to calculate average velocity, divide the change in position or displacement (x) by the time intervals (t) during which the displacement takes place. Depending on the displacement's sign, the average velocity can either be positive or negative. The SI unit for average speed is meters per second (m/s or ms-1).
Average speed is determined by dividing the total distance you traveled by the total time, whereas average velocity is determined by dividing your displacement, which is a vector pointing from your initial location to your end position, by the whole time.
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really confused please help
The given relationship is such that 1 / z⁴ = z ⁻⁴.
What is the relationship ?When given 1 / z⁴, this can be rewritten in such a way that it becomes z ⁻⁴.
This is because when a denominator is raised to a exponent , it can be transformed to a numerator if the sign on the power is changed to the negative.
This means that when the fraction was 1 / z⁴, it can become the value of z ⁻⁴ because the negative in front of the 4 shows that it is a fraction.
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Find E(X) and Var(X) for a continuous random variable X with a pdf f(x) = 4x³,0 < x < 1.
Simply multiply each value of the discrete random variable by the probability associated with that value to obtain the expected value, E(X), or mean. E(X)=xP is the formula's notation (x).
How do you find ex and Var X?It is common to refer to the long-term average or mean (symbolized as ) as the expected value of a discrete random variable X, denoted by the symbol E(X). Thus, if you conducted an experiment again throughout time, you could anticipate this average result. If you toss three fair coins, for instance, let X be the number of heads you receive. The expected value of X is the average number of heads you would anticipate receiving after three fair coin tosses if you were to perform this experiment a significant number of times.f(x) = 4x³,0 < x < 1
Domain of f(x) = 4x³,0 < x < 1 : Solution : 0 < x < 1
Interval notation : (0,1)
Range of 4x³ ,0 < x < 1;
Solution : 0 < f(x) < 4
Interval Notation : (0,4)
Axis interception points of 4x³,0 <x <1.
Asymptotes of 4x³. 0 < x < 1;
Extreme Points of 4x³ . 0<x < 1:
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Simplify each expression by combining like terms
-9y-10y -2z
By Simplify expression -9y-10y -2z this we get - 19y - 2z.
What is the Simplify expression ?Expression simplification is a crucial skill to master if you want to comprehend algebra. We can convert a complicated expression into one that is more condensed and straightforward by simplifying it.When constants and variables are merged with the help of the operation symbols (+, -, x, and ), the result is an algebraic expression.The process of solving a math problem is simply known as simplifying an expression. An expression is simplified when it is written in the most straightforward way feasible. There should be no more multiplying, dividing, adding, or subtracting to be done once everything is done.Examples :
-9y-10y -2z
Simplify
-9y - 10y - 2z : -19y - 2z
-9y - 10y - 2z
= - 19y - 2z.
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Solve the initial value problem 2yy' + 3 = y^2 + 3x with y(0) = 9. 1. To solve this, we should use the substitution u = _____ With this substitution, y = _____
y' = _____
Enter derivatives using prime notation (e.g., you would enter y' for dy/dx). 2. After the substitution from the previous part, we obtain the following linear differential equation in x, u, u'. 3. The solution to the original initial value problem is described by the following equation in x, y.
The given initial value problem y(0)=8, solution is [tex]y=\sqrt{64e^x-3x}[/tex]
Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation. Assuming that a function's rate of change with regard to x is inversely proportional to y, we may write it down as dy/dx = k/y. An equation involving the derivative (derivatives) of the dependent variable with respect to the independent variable is referred to as a differential equation in calculus (variables). The differential equation assists us in presenting a relationship between the changing quantity with respect to the change in another variable. The derivative represents nothing more than a rate of change. If y is a dependent variable, f is an unknown function, and x is an independent variable, then y=f(x) is a function.
The given differential equation is,
[tex]2yy'+3=y^2+3x\\\\2y\frac{dy}{dx}=y^2+3x-3\\\\(3-y^2-3x)dx+2ydy=0\\\\compare, Mdx+Ndy=0\\\\M=3-y^2-3x\\\\N=2y[/tex]
The given equation is not exact but if we multiplied by [tex]e^{-x}[/tex]
[tex]The D.E.\\(3-y^2-3x)e^{-x}dx+2ye^{-x}dy=0\\\\then M_y=-2ye^{-x}=N_x\\The G.S,=y^2e^{-x}+3xe^{-x}=c\\\\y(0)=8\\c=64\\hence,\\y=\sqrt{64e^x-3x}[/tex]
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xplain in words and write mathematically how the fundamental theorem of calculus is used to evaluate definite integrals.
a freshly poured cup of coffee from mcdonald’s is measured to be 185 degrees fahrenheit. if left alone in a cup, the temperature of the coffee decreases by about 3.2% each minute. what would be the temperature if left alone in the cup for 20 minutes? round to the nearest degree
The temperature of the cup if it is left alone for 20 minutes, can be found to be 97 degrees Fahrenheit
How to find the temperature of the cup ?To find the tempertature of the cup, the formula would be:
= Beginning temperature x ( 1 - rate of decrease per minute ) ^ number of minutes
Beginning temperature = 185 degrees fahrenheit
rate of decrease per minute = 3.2% each minute
number of minutes = 20 minutes
The temperature is:
= 185 x ( 1 - 3 .2 %) ²⁰
= 97 degrees Fahrenheit
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Suppose that X and Y are integer valued random variables with joint probability mass function given by pX, Y(a, b) = {1/4a, for 1 > b > a > 4, otherwise. a. Show that this is indeed a joint probability mass function. b. Find the marginal probability mass function of X and Y. c. Find P(X = Y + 1).
The joint probability mass function given by PX, Y(a, b) = {1/4a, for 1≤ b≤a≤4, otherwise is indeed a joint probability mass function because the sum of all the joint probabilities is equal to 1.
To find the marginal probability mass function of X, we need to sum the joint probabilities over all possible values of Y:
PX(a) = ∑ PX, Y(a,b) = ∑ (1/4a) = 1/4
To find the marginal probability mass function of Y, we need to sum the joint probabilities over all possible values of X:
PY(b) = ∑ PX, Y(a,b) = ∑ (1/4a) = 1/4
To find P(X = Y + 1), we need to find the joint probability of X = a and Y = a-1, where a = 2,3.
P(X = Y + 1) = PX, Y(2,1) + PX, Y(3,2) = (1/42) + (1/43) = 1/4 + 3/12 = 5/12
So the probability that X is one more than Y is 5/12.
It's important to note that the given joint probability mass function is valid as it satisfies the non-negativity and the condition of summing to 1.
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Question 4 of 10
The lines shown below are perpendicular. If the green line has a slope of
what is the slope of the red line?
ch
10
KO
1
-10
+0
6
10
16
OA
OB./
OC
OD
Answer:
B
Step-by-step explanation:
Trust
Solve this system of linear equations. Separate
the x- and y-values with a comma.
2x + 2y = -8
-13x + 7y = -48
Enter the correct answer.
Answer:
x = 1, y = - 5
Step-by-step explanation:
2x + 2y = - 8 → (1)
- 13x + 7y = - 48 → (2)
multiplying (1) by 7 and (2) by - 2 and adding will eliminate y
14x + 14y = - 56 → (3)
26x - 14y = 96 → (4)
add (3) and (4) term by term to eliminate y
40x + 0 = 40
40x = 40 ( divide both sides by 40 )
x = 1
substitute x = 1 into either of the 2 equations and solve for y
substituting into (1)
2(1) + 2y = - 8
2 + 2y = - 8 ( subtract 2 from both sides )
2y = - 10 ( divide both sides by 2 )
y = - 5
then solution is x = 1, y = - 5
Trapezoid PQRS has vertices P(0, 0), Q(0, 4), R(6, 4), and S(12, 0).
What is the length of the midsegment?
please help me its the last question on this test and i only have 20 mins left of this class
Trapezoid PQRS having vertices P(0, 0), Q(0, 4), R(6, 4), and S(12, 0),
has the length of the midsegment as 11.07 units.
What is a trapezoid?
A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.
The length of the mid segment of trapezoid is half the sum of the lengths of the two parallel sides, PQ and RS.
The points for vertices are given as - P(0, 0), Q(0, 4), R(6, 4), and S(12, 0).
Length of sides PQ and RS is given as -
The line segment PQ = √(x2 - x1)² + (y2 - y1)²
PQ = √(0 - 0)² + (4 - 0)²
PQ = √0² + (4)²
PQ = √0 + 16
PQ = √16
PQ = 4 units
The line segment RS = √(x2 - x1)² + (y2 - y1)²
RS = √(12 - 6)² + (0 - 4)²
RS = √(6)² + (-4)²
RS = √36 + 16
RS = √50
RS = 5√2 units
To find the mid segment add the length of PQ and RS.
So, the equation will be -
Midsegment = PQ + RS
Midsegment = 4 + 5√2
Midsegment = 11.07 units
Therefore, the length of midsegment is 11.07 units.
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Answer: 9
Step-by-step explanation: (6+12) / 2 = 9
Need help with question attached below in an image.
Average rate of change for the first 10 minutes after the soup was placed in the bowl is 200 .
How can I determine the graph's average rate of change?To get the slope of a graphed function, use the average rate of change formula. Divide the y-value change by the x-value change to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.Measure the temperature change every hour and compute the average rate of change. In order to achieve that, we calculate the temperature difference between 220 and 180 and divide it by the number of hours in that period.220 +180/2 = 200
average rate of change for the first 10 minutes after the soup was placed in the bowl 200.
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When lisa was born, her parents put 8000 into a college fund account
The initial deposit was $8000 and after 18 years the simple interest earned is $12960. So, the total amount for Melissa in college account is $20,960.
What is Simple Interest?
Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
The amount that was put in college fund for Melissa, P = $8000
The rate at which interest was earned is, R = 9%
The time period after which the account was checked, T = 18 years
The formula for Simple Interest is -
S.I. = (P R T)/100
Substitute the values into the equation -
S.I. = (P R T)/100
S.I. = (8000 × 9 × 18)/100
S.I. = 1296000/100
S.I. = 12960
The amount of interest earned in 18 years is $12960.
The total amount after 18 years will be -
Total Amount = Initial deposit + Interest earned
Total Amount = $8000 + $12960
Total Amount = $20960
Therefore, the total amount after 18 years is $ 20,960.
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When Melissa was born, her parents put $8,000 into a college fund account that earned 9% simple interest. After 18 years, she had $20,960 in the account. How did this happen?
You are single and your gross pay for this week is $710. Using the
percentage method of withholding, what amount will you pay in federal
income tax if you claim 3 allowances. Each weekly allowance is $80.80.
(Use percentage method.)
The amount that you would have to pay in federal income tax if you claim 3 allowances would be: $65.46
How to solve for the claimable amountTo calculate the amount you will pay in federal income tax using the percentage method of withholding, you will need to know the withholding percentage for your gross pay and the number of allowances you are claiming.
If you claim 3 allowances, each allowance is $80.80, and you gross pay for the week is $710, your taxable income is:
$710 - 3*$80.8 = $710 - $242.4 = $467.6
To find the amount of federal income tax you will pay, you will need to use the withholding percentage for your taxable income. You can find this information by consulting the IRS Circular E (Employer's Tax Guide) or by using an online withholding calculator.
If we use the IRS Circular E, we can find that if you are single and claim 3 allowances, the withholding percentage for a taxable income of $467.6 is 14%.
So the amount you will pay in federal income tax is:
$467.6 * 14% = $65.46
Therefore, you will pay $65.46 in federal income tax if you claim 3 allowances, and your gross pay for the week is $710.
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The probability of picking two black marbles from a box at random without replacement is 10/91 . The probability of drawing a black marble first is 5/14 . What is the probability of picking a second black marble, given that the first marble picked was black?
The probability of picking a second black marble is 4/13
What is probability?Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability helps us know the chance an event has to occur. The closer it gets to zero(0) the less chance it has to occur. The closer it gets to one(1) the more chance it has to occur.
Therefore, The probability of picking a second black marble is 4/13
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The option are :
4/13
85/182
25/637
45/182
a meter is about 1 1/10 yards about how many meters long is an automobile
The number of yards of the automobile of length 'x' meters will be 1.10x yeads.
What is conversion?Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
It is the measure of distance between the two points and is known as length. The length is measured in meters generally.
A meter is about 1 ¹/₁₀ yards.
Convert the mixed fraction number to a decimal number. Then we have
1 meter = 1 ¹/₁₀ yards
1 meter = 1 + ¹/₁₀ yards
1 meter = 11 / 10 yards
1 meter = 1.10 yards
Let the length of the automobile be 'x' meters. Then the number of yards in 'x' meters is given as,
⇒ x × (1.10)
⇒ 1.10x yards
The number of yards of the automobile of length 'x' meters will be 1.10x yeads.
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24 of the students in a Biology class passed a Biology test. If these students are 80% of
all the students in the class, how many students are in this Biology class? Round your
answer to the nearest whole number if necessary.
Anything would be great!
The glide reflection that maps triangle ABC into triangle A'B'C' is given as follows:
C) Translation (x,y) -> (x + 7, y), and reflection over the x-axis.
What is a glide reflection?The glide reflection is a combination of a reflection with a translation.
The vertices of the original triangle are given as follows:
A(-3,-2), B(-6,-5) and C(-1,-4).
The vertices of the reflected triangle are given as follows:
A'(4,2), B'(1,5) and C'(6,4).
The composite rule for these two transformations is given as follows:
(x,y) -> (x + 7, -y).
The transformation y -> -y is a reflection over the x-axis, hence the correct option is given by option C.
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Write an explicit formula for the sequence generated by a1 = 10, an = an − 1 + 7 where n = 2, 3, 4, ….
Group of answer choices
an = n + 7 where n = 1, 2, 3, …
an = 3n + 4 where n = 1, 2, 3, …
an = 7n − 10 where n = 1, 2, 3, …
an = 7n + 3 where n = 1, 2, 3, …
Answer:
= 7n − 3 emde n = 1, 2, 3, ...
Which does not represent a way to show 3+3+3+3+3 with multiplication
The ways to represent 3+3+3+3+3 with multiplication are:
3 * 55*3What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, an expression 3+3+3+3+3
To represent this in multiplication terms,
We need to figure out what the expression tells us. So, there are 5 terms all terms have a value of 3.
Thus,
represent a way to show 3+3+3+3+3 with multiplication is either 3*5 or 5*3.
Therefore, The correct ways of representing the expression 3+3+3+3+3 are:
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Please help me, I really need this so bad.
Answer:
slope = 1/2
Step-by-step explanation:
rise = 3
run = 6
rise/run
3/6 = 1/2
Answer:
The slope is 1/2
Step-by-step explanation:
The slope is rise over run, from point 1 to point 2 the line rises 3.
The run from point 1 to point 2 is 6.
That means that rise over run is 3/6
Simplify this so that it is in the simplest form to get 1/2.
The image shows the rise and the run.
I hope this helps you out :D
W तल दिइएका तथ्याङ्कको मध्यिका पत्ता लगाउनुहोस् । Find the median of the following data: 16, 15, 14, 18, 17, 20, 25 .00 16
Answer:
arrange in ascending order
14,15,16,17,18,20,25
there are odd number of terms so
median = (n+1/2) th observation
here n = 7 which is odd
therefore, 7+1/2 th observation
which is 4th observation
ans) 17
what is the value of 8 divided by 3
Answer:
there's ur answer ...........
What represents the expression below simplified?
[tex](4x-1) + (-6x+3)[/tex]
whats the solution to the equations
Answer:
A solution of an equation is any value of the variable that satisfies the equality, that is, it makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation the same value. To solve an equation is to find the solution(s) for that equation.
Step-by-step explanation:
help for brainliested
Answer:
Jade will be farther by 0.6 or .6 miles in 3 hours
Step-by-step explanation:
Jade walks at a speed of 3 miles per hour so 3×3=9 miles per hour
Elena walks at a speed of 2.8 miles per hour so 2.8×3=8.4 miles per hour
Next,the question is how much farther will Jade walk after 3 hours so that means 9-8.4 which is 0.6 or .6 in decimals and we read it as six tenths
hope it helps you
(12 - 31) + (7 + 31)
given values of median, mean, mode, first and third quartiles for the observations of a numeric feature, what insights can we gain into the statistical distribution of its observations? you may use an example to further illustrate your points. (word limit: 100-150). you must post first before being able to read the responses of others. it is recommended that you respond to your classmates' responses, but not required.
The terms mean median, mode, and range describe properties of statistical distributions.
The statistical distributions' characteristics are described by the terms mean, median, mode, and range. The set of all potential values for terms that indicate predetermined events is known as a distribution in statistics. A term's value stated as a variable is referred to as a random variable.
The two main categories of statistical distributions are as follows. There are discrete random variables in the first category. This indicates that each phrase has a distinct, precise numerical value. A continuous random variable is present in the distribution of the second major kind. An unlimited number of possible values can be represented by a continuous random variable. A term is said to have a probability density function when any value can be assigned to it within an uninterrupted interval or span.
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