The eigenvalues of A are 5 and 10.
What is eigenvalues ?
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.
The eigenvalues of the 2 x 2 matrix are described by the following characteristic polynomial:
[tex]$$t^2-{tr}(A) \cdot t+{det}(A)=0$$[/tex]
The roots of the characteristic polynomial are deflned by the quadratic formula:
[tex]t=\frac{{tr}(A) \pm \sqrt{[{tr}(A)]^2-4-{det}(A)}}{2} \text { (2) }$$[/tex]
If we know that [tex]${tr}(A)=15$[/tex]and [tex]${det}(A)=50$[/tex], then the elgenvalues of A are:
[tex]$$\begin{aligned}& t=\frac{15 \pm \sqrt{15^2-4 \cdot(50)}}{2} \\& t_1=10 \vee t_2=5\end{aligned}$$[/tex]
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solve for x
7/x =10
Give your answer as a fraction in its simplest form
Answer:
Step-by-step explanation:
Answer:
x = 7/10
Step-by-step explanation:
You multiply both sides by "x", to get 7 = 10x. Then divide both sides by 10 to get 7/10 = x, or 0.7 = x.
Brainliest please!
Ava made 5% of her free throws over the season. If she shot 120 free throws,
how many did she make?
The free throws she made by an accuracy of 5% in 120 is a total of 6
How to determine how many of the free throws she make?The given parametes from the question are
Free throw made = 5%
Total number of free throws = 120
The above means that we multiply the percentage of free throws made by the total number of free throws to determine the count of free throws made
Having mentioned that, we have
Free throw made = 5% * Total number of free throws
So, we have
Free throw made = 5% * 120
Evaluate
Free throw made = 6
Hence, she made 6 of 120 free throws
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Write the equation of the line in slope-intercept form (y=mx+b) for each of the following.
ill brainlist
The equation of the line in slope intercept form of y is -2x + 19
How to calculate the equation slope intercept ?When you know the slope of the line to be examined and the given point is also the y intercept, you can use the slope intercept formula, y = mx + b. The y value of the y intercept point is denoted by the symbol b in the formula.
Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.
To find this, we can use the point and the slope in point-slope form. The we solve for y.
y - y1 = m(x - x1)
y - 7 = -2(x - 6)
y - 7 = -2x + 12
y = -2x + 19
The equation would be y = -2x + 19
The complete question is : Write an equation in slope- intercept form y=mx=b of the line through point p(6,7) with slope -2
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Write an equivalent expression by using the distributive property.
a. 2(3x+5)
b. 7(7a+6)
c. Sa(4a+8b)
d. 2y(4x-3y)
e. 3z(9-10z)
f. 6(3x+4+2y)
g. 11c(2c+7a)
h. 8b(5+2s+3b²)
i. 7a(a²-3a+6)
j. 9(4p²+3p-5)
The equivalent expression of each expression given, using the distributive property, are:
a. 6x + 10
b. 49a + 42
c. 20a² + 40ab
d. 8xy - 6y²
e. 27z - 30z²
f. 18x + 24 + 12y
g. 22c² + 77ac
h. 40b + 16bs + 24b³
i. 7a³ - 21a² + 42a
j. 36p² + 27p - 45
What is the Distributive Property?If we have an expression given as a(b + c), according to the distributive property, we can write an equivalent expression by using the term "a" to multiply each of the terms within the bracket, which will give us: a(b + c) = ab + ac.
a. 2(3x + 5), applying the distributive property, multiply each of the terms within the parentheses by 2:
2(3x) + 2(5)
6x + 10
Therefore, the equivalent expression of 2(3x + 5) is 6x + 10.
b. 7(7a+6)
7(7a) + 7(6)
= 49a + 42
c. 5a(4a+8b)
= 5a(4a) + 5a(8b)
= 20a² + 40ab
d. 2y(4x-3y)
= 8xy - 6y²
e. 3z(9 - 10z)
= 27z - 30z²
f. 6(3x + 4 + 2y)
18x + 24 + 12y
g. 11c(2c + 7a)
22c² + 77ac
h. 8b(5 + 2s + 3b²)
40b + 16bs + 24b³
i. 7a(a² - 3a + 6)
7a³ - 21a² + 42a
j. 9(4p² + 3p - 5)
36p² + 27p - 45
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many states run lotteries, giving away millions of dollars if you match a certain set of winning numbers. how are those numbers determined? do you think this method guarantees randomness? explain.
The method to determine the numbers is random only if the balls generate numbers in equal frequencies.
The entire process is random and is not generated by a computer or humans.
One of the most important requirements for a random number is independence, as this aids in the establishment of no correlations between successive numbers. It must be ensured that the frequency of occurrence of these random numbers is roughly the same. As a result, it is theoretically difficult to generate a long random number.
The frequency of a repeating event is the number of occurrences per unit of time. It is distinct from angular frequency and is sometimes referred to as temporal frequency. The frequency is expressed in hertz (Hz), which equals one event per second. Because the period is the time interval between events, it is the reciprocal of the frequency.
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Kate wants to post three parcels Each parcels cost £1.20 how much changed should she get from £10 note
Answer: 6.40
Step-by-step explanation:
1.20 times 3 = 3.60
10 - 3.60 = 6.40
(GEOMETRY) PLEASE HELP ME WRITE A TWO COLUMN PROOF FOR THIS PROBLEM!!!!
If right triangle ABC with right angle ACB and altitude CD then
ΔABC ~ ΔACD
ΔABC ~ ΔCBD
ΔACD ~ ΔCBD
What is Angle-Angle Similarity (AA~) Theorem?
If two angles of one triangle and two corresponding angles of another triangle are congruent, then the triangles are similar.
According to the given question:
A right triangle is given with its altitude drawn from the right angle to its hypotenuse.
Consider the triangled ABC and ACD
By the reflexive property of angle congruence, it follows that:
∠A ≅ ∠A
Since the angles B and D are right angles, from the right angles congruence theorem, it also follows that:
∠C ≅ ∠D
Hence, by the Angle-Angle Similarity (AA~) Theorem, it follows that triangles ABC and ACD are similar. Similarly triangle ABC is similar to triangle CBD
Consider triangles ACD and CBD:
Triangles ABC and ACD are similar. Also triangle ABC is similar to triangle CBD
Therefore, Triangle CBD is similar to triangle ACD as both of them are similar to triangle ABC.
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How do you convert 0.26 into a percent and fraction?
Answer: 26% and 26/100
Step-by-step explanation:
Use 0.26 as a fraction; 26/100, and use that 26/100 to convert it as a percentage using 26% out of 100% giving you 26%
Write a linear function with the given values : f(0)=3, f(1)=5
The linear function that has f(0) = 3 and f(1) = 5 will be f(x) = 5x.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The function is a linear function which is given as,
f(x) = mx + c
The value of the function at x = 0 is 3, then we have
f(0) = m × 0 + c
3 = c
Then the equation is given as,
g(x) = mx
The value of the function at x = 1 is 5, then we have
f(1) = m × 1
5 = m
The linear function that has f(0) = 3 and f(1) = 5 will be f(x) = 5x.
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Alex tracked the number of cups of coffee he drank each day for the following month and
created a new probability distribution.
Number of Cups of Coffee, X 0
1 2 3 4
Relative Frequency, P(X) 0.035 0.579 0.286 0.080 0.020
According this new data, Alex is expected to drink 1.471 cups per day.
4. Calculate s(X) of Alex's new probability distribution. (1 point)
0.599
0.775
1.471
4.223
S(x) of Alex's new probability distribution will be 0.599.
What is Probability distribution ?
A mathematical function called a probability distribution explains how likely it is that a variable will take on several possible values. Utilizing graphs or probability tables, probability distributions are frequently represented.
Given, The no. of cups of coffee he drank with the probability.
If he drinks 1.471 cups per day, So the S(X) will be calculated in the following manner:
Step 1 : calculate the deviation of X from N.( here N = 1.471 )
Step 2 : find the square of (X- N).
Step 3 : multiply it with the given P(X).
Step 4 : find the sum of the (X-N)^2* P(X).
Hence, By following the given steps, we get S(X) as 0.599.
(Refer to the table given in Excel file).
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AABC has vertices A(2, 1) B(4, 4) and C(4,1) . ADEF has corresponding vertices D(7, 3)
E(9, 6) and F(9, 3) Which of the following describes a translation that would produce ADEF from the pre-image of triangle ABC ?
To the right five units, and up two units To the left five units, and down two units
To the left five units, and up two units
To the right five units, and down two units
A statement which describes a translation that would produce ΔDEF from the pre-image of triangle ΔABC include the following: A. To the right five units, and up two units.
What is a translation?
In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.
Next, we would determine the translation rule as follows;
ΔABC → ΔDEF = (2 + 5, 1 + 2) = D (7, 3)
ΔABC → ΔDEF = (4 + 5, 4 + 2) = E (9, 6)
ΔABC → ΔDEF = (4 + 5, 1 + 2) = F (9, 3)
Therefore, the translation rule is given by this mathematical expression ΔABC → ΔDEF = (x + 5, y + 2). This ultimately implies that, triangle ABC (ΔABC) was translated by five units to the right and up two units in order to produce triangle DEF (ΔDEF).
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How do you simplify the fraction 10/20?
Answer:
by dividing
Step-by-step explanation:
by dividing them by a same factor that they both have like 2.
a tank contains 1,000 l of brine with 16 kg of dissolved salt. pure water enters the tank at a rate of 10 l/min. the solution is kept thoroughly mixed and drains from the tank at the same rate. (a) how much salt is in the tank after t minutes?
The salt that is left after t minutes is y = 16e^[-t/100]
We have to mix problems we use:
dy / dt = (rate in) - (rate out)
The water entering the tank at a speed of 10 L / min but it has no salt, therefore
rate in = 0
The tank has 1000 liters of brine with 16 kg of salt initially, therefore the concentration of salt at time "t" is:
y (t) / 1000
then rate out would be:
rate out = y (t) / 1000 * 10 = y (t) / 100
The difference equation would then be:
dy / dt = 0 - y (t) / 100
1 / y (t) * dy = 1/100 * dt
We integrate from both sides and we have:
ln y = - (1/100) * t + C1
y = e ^ [- (1/100) * t + C1]
y = e ^ [- (1/100) * t] * e ^ [C1]
We assume that C = e ^ [C1]
Thus:
y = C * e ^ [- (1/100) * t]
now y = 16 to t = 0, replacing:
16 = C * e ^ [- (1/100) * 0]
16 = C, therefore we would have:
y = 16*e ^ [- t / 100]
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Luke has blue and red ballsEvery day he wins 2 blue balls and loses 3 red onesAfter 5 days he has the same amount of blue and red ballsAfter 9 days, he has twice as many red balls as blue ballsHow many red balls did he have at the beginning?
The number of red balls Luke has at the start is 47.
blue ball per day = 2
red ball per day = -3 ('-' ve sign as he is loosing them)
let the number of red balls be represented by r
let the number of blue balls be represented by b
after 5 days
b+ 10 = r -15 -(i)
After 9 days
b + 18 =2(r-27)-(ii)
subtracting (i) from (ii)
b + 18 - b - 10 = 2r - r - 54 +15
8 = r - 39
r = 39 + 8
r = 47
The number of red balls Luke has at the start is 47
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How do you write 82 in scientific notation?
The way is...
m x 10n
What is the approximate total length of iron edging needed to create the square frame and the two diagonals?
43.5 inches
50.9 inches
54.0 inches
61.5 inches
The approximate total length of iron edging needed to create the square frame and the two diagonals is 43.5 inches. So, option A is correct.
What is a diagonal?When two vertices of a polygon or polyhedron are not on the same edge, a diagonal in geometry is a line segment that connects them. The term "diagonal" is a colloquial term for any sloping line.
The elements on the line connecting the top left corner and bottom right corner of a square matrix make up the diagonal of a matrix in matrix algebra.
Given, The diagonal of a square is 9 inches.
The side of the square be x as we have assumed.
We have to apply Pythagoras theorem for Δ ABC
AB²+BC²=AC²
x²+x²=9²
x=9/√2
We know that the diagonals in the square bisect each other.
OA = 4.5 inches=OC
OD = 4.5 inches=OB
Therefore, the total length of iron edge that is required for the window is:
=4×Length of square+2 diagonals
= 4×6.36+2×9=43.46 inches
The approximate total length of iron edging needed to create the square frame and the two diagonals is 43.5 inches.
Hence, option A is correct.
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Look carefully at the diagram.
The value of y is ___ °
The value of y in the triangle is 20°
How to find the value of y in the triangle?Consider the labeling on the image I attached
Since vertically opposite angles are equal. Thus:
x = 50°
Since the sum of angles on a straight line is 180°. Thus:
t + 70° = 180°
t = 180°-70°
t = 110°
Since the sum of angles in a triangle is 180°. Thus:
x + t + y = 180°
50 + 110 + y = 180°
160 + y = 180
y = 180 - 160
y = 20°
Therefore, the value of y is 20°
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the system below shows a periodic function and an absolute value function. how many solutions does the system have?
The system that contains periodic function and an absolute value function has two solution
In the given system there are two function, those are periodic function and absolute value function
The function is defined as the statement that shows the relationship between one dependent variable and other independent variables. The function consist of different types of variables numbers and the mathematical operators
The periodic function is a function that repeats its value at a regular interval of time
The absolute value function is a function that contains the mathematical expression with absolute value symbols
The system contains periodic and absolute value function and it will contains two solution
Therefore, the system has two solution
I have solved the question in general, as the given question is incomplete
The complete question is:
The system below shows a periodic function and an absolute value function. how many solutions does the system have?
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what is the probability of drawing a yellow? leave your answer as a fraction/ratio. what are the odds in favor of drawing a yellow? leave your answer as a fraction/ratio. explain how you could have obtained the answer for number 2 by only looking at the answer from number 1. (i.e. how are probability and odds related?) reply to others' posts.
The correct answers are -
1. Probability of drawing a yellow is 12/99
2. Odds in favour of drawing are 12/87
3. Probability and odds are related through favourable and unfavourable outcomes.
Firstly calculating the total number of candies.
Total number of candies = 115 + 75 + 95 + 60 + 45 + 50 + 55
Performing addition on Right Hand Side of the equation
Total number of candies = 495
Now, the probability of drawing a yellow = number of yellow candies ÷ total number of candies
Probability of drawing a yellow = 60 ÷ 495
Performing division on Right Hand Side of the equation
Probability of drawing a yellow = 0.12
Now, for calculation of second part and answer of third part, relating the probability and odds.
Odds = favourable outcomes ÷ non favourable outcomes
Simplifying the probability in fractional form = 12/99
Favourable outcomes = 12
Non favourable outcomes = 99 - 12
Non favourable outcomes = 87
Odds = 12/87
Thus, probability is 0.12 and odds are 12/87.
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The complete question is attached in the figure.
given forecast errors of -1, 4, 8, and -3, what is the mean absolute deviation? group of answer choices 2 16 3 8 4
Answer:
4
Step-by-step explanation:
What is the value of (8.59 × 10^4) - (3.2 × 10^3)? Select all that apply.
a. 5.39 * 10^1
b. 2.7488 × 10^7
c. 8.27 * 10^4
d. 82,700
Answer: D. 82,700
Step-by-step explanation:
Locate points A and B in the coordinate plane below. Use the Pythagorean Theorem to find the straight-line distance from each point to the origin.
Which point is close to the origin and by how much?
the options for the first one is "A" or "B" and the options for the second one is " more than" or "less than". (please ignore my chosen answer, I was just guessing.)
The coordinates of points A and B are (-4, 5) and (2, 6) respectively. Point B is close to the origin by 0.1 unit
How to locate points A and B in the coordinate plane?The positions or coordinates of points A and B are (-4, 5) and (2, 6) respectively
In order to use the Pythagorean Theorem to find the straight-line distance from each point to the origin (Consider the attached image):
Distance for point A
d = √((-4)²+5²)
d = √41 = 6.40 units
Distance for point A
d = √(2²+6²)
d = √40 = 6.32 units
To find which point is close to the origin and by how much:
The distance of B is less, so point B is close to the origin
Difference of distance = 6.40 - 6.32 = 0.08 ≈ 0.1 unit
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Claudia spends $2.00 a day for lunch. Her cafeteria lunch account has a balance of $48.00. How many days, d, can Claudia eat without adding money to her lunch account?
Answer:
24 days
Step-by-step explanation:
you have to divide the balance by the spending money, so £48.00, divided by £2.00 will equal 24 meaning, Claudia can last 24 days without adding money to her account
given: line segment wz bisects line segment xy. line segment xy bisects line segment wz. to prove: triangles wax and zay are congruent. statements reasons 1. segment wz bisects xy. 1. given 2. segments xa and ya are congruent. 2. when a segment is bisected the resulting segments are congruent. 3. segment xy bisects wz. 3. given 4. 4. when a segment is bisected the resulting segments are congruent. 5. angles wax and zay are congruent. 5. vertical angles of intersecting lines are congruent. 6. triangles wax and zay are congruent. 6. triangles with two sides and an included angle equal are congruent. what should be in statement 4 to complete the proof? a angles xwa and yza are congruent. b segments wa and az are congruent. c segments wx and yz are congruent. d angles wxa and zya are congruent.
This takes into account the fact that each of the angles has an opposite ray on its other side in addition to the common side they share.
What are angles?When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.
When two lines meet at a point, an angle is created.
An "angle" is the measurement of the "pening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.
Angles are a common occurrence in daily life.
Angles are used by engineers and architects to create highways, structures, and sports venues.
Hence, This takes into account the fact that each of the angles has an opposite ray on its other side in addition to the common side they share.
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Evaluate 1/2 (x ÷ 4) +y
Answer:
35
Step-by-step explanation:
What is the slope of the line with equation y-3- - } (x-2)?
-2
We can rewrite the linear equation as:
y = -x + 3
There we can see that the slope is -1.
What is the slope of the linear equation?A linear equation written in the slope-intercept form is:
y = a*x + b
Where a is the slope.
Here the linear equation is written kinda weird, I guess that the line is:
y - 3 = -(x - 2) - 2
Let's isolate y and simpify the equation, we will get:
y - 3 = -(x - 2) - 2
y = -(x - 2) - 2 + 3
y = -(x - 2) + 1
Now we can apply the rule of signs in the right side:
y = -x + 2 + 1
y = -x + 3
y = -1*x + 3
So the slope of the linear equation is -1.
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Rewrite the following equation in slope-intercept form.
13x − 3y = 18
Answer: y=(13/3)*x-6
Step-by-step explanation: -3y=18-13x -y=6-13/3 x
y= (13/3)x-6
! for all values of x, x² + 2x +4 = (x + 2)² + a( x + 2) + b where a and b are constants. what is the value of a ?
The value of a in the quadratic equation x² + 2x +4 = (x + 2)² + a( x + 2) + b is equal to -2.
How to solve the constant "a" in the quadratic equation.We shall first expand the right hand side and express it in form of the left hand side of the quadratic equation, and then compare their coefficients to derive the value of the constant as follows;
Left hand side; {open brackets}
(x + 2)² + a( x + 2) + b = x² + 4x + 4 + ax + 2a + b
(x + 2)² + a( x + 2) + b = x² + 4x + ax + 4 + b {group like terms}
(x + 2)² + a( x + 2) + b = x² + (4 + a)x + 4 + b
such that :
x² + 2x +4 = (x + 2)² + a( x + 2) + b, then;
x² + 2x +4 = x² + (4 + a)x + 4 + b
by comparing coefficients, we have that;
4 + a = 2
a = 2 - 4 {subtract 4 from both sides}
a = -2
Therefore, for all values of x, the constant a = -2 for the quadratic equation x² + 2x +4 = (x + 2)² + a( x + 2) + b.
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Is 9 hundredths greater than 6/10
Step-by-step explanation:
9 hundredths = 9/100
is 9/100 > 6/10 ?
let's bring both to 1/100
9/100 > 6×10/100
9/100 > 60/100
no, this is wrong. 9/100 is not greater than 60/100 (or 6/10).
9/100 would be greater than 6/100. but not greater than 6/10.
What is the solution to the equation1 over the square root of 8 = 4(m + 3)? (1 point)
m = − 15 over 4
m = − 11 over 4
m = 5 over 4
m = 9 over 4
Answer:
A) m = − 15 over 4-------------------------------------------------
The equation should read:
[tex]1/\sqrt{8}=4^{m+3}[/tex]Solve it in below steps:
[tex]1/\sqrt{2^3}=(2^2)^{m+3}[/tex][tex]1/2^{3/2}=2^{2(m+3)}[/tex][tex]2^{-3/2}=2^{2m+6}[/tex][tex]-3/2=2m+6[/tex][tex]-3=4m+12[/tex][tex]4m=-15[/tex][tex]m=-15/4[/tex]Correct choice is A.
