9.1 The eigenvalues of matrix A are 2 and 2.
9.2 The bases for the eigenspaces of A are {(1, 0)} and {(0, 1)}.
9.3 A is not diagonalizable because it does not have a complete set of linearly independent eigenvectors.
9.4 The matrix P is {{1, 0}, {0, 1}} and the diagonal matrix D is {{2, 0}, {0, 2}}.
9.5 The value of 423 is not provided.
9.6 The given system of differential equations can be solved using the eigenvalues and eigenvectors of matrix A.
9.1 To find the eigenvalues of matrix A, we need to find the values of λ for which the equation (A - λI)x = 0 has non-trivial solutions. By solving this equation, we find that the eigenvalues of A are 2 and 2.
9.2 The eigenspace corresponding to the eigenvalue 2 is the null space of the matrix (A - 2I). By solving (A - 2I)x = 0, we find that the basis for this eigenspace is {(1, 0)}. Similarly, for the eigenvalue 2, the basis for the corresponding eigenspace is {(0, 1)}.
9.3 A matrix is diagonalizable if it has a complete set of linearly independent eigenvectors. Since matrix A only has two distinct eigenvalues (both equal to 2) and the eigenvectors corresponding to these eigenvalues are not linearly independent, A is not diagonalizable.
9.4 To find the matrix P and diagonal matrix D such that P⁻¹AP = D, we need to construct P using the eigenvectors of A. In this case, the matrix P is the identity matrix {{1, 0}, {0, 1}} and the diagonal matrix D is {{2, 0}, {0, 2}}.
9.5 The value of 423 is not provided in the question.
9.6 To solve the system of differential equations using the given matrix A, we can express it in matrix form as dX/dt = AX, where X = (x₁, x₂) and A is the given matrix. By substituting the eigenvalues and eigenvectors of A, we can find the solution to the system of differential equations.
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Question 7 of 10
What is the value of n?
1131-
160"
A. 690
B. 29°
C. 20°
D. 49°
Calculate the distance between the points =G−9, 6 and =Q−2, 1 in the coordinate plane.
The distance between the points G(-9, 6) and Q(-2, 1) in the coordinate plane is approximately 8.6.
To calculate the distance between two points in a coordinate plane, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and can be stated as follows:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the given points are G(-9, 6) and Q(-2, 1).
Step 1: Identify the coordinates of the two points.
G has coordinates (-9, 6) and Q has coordinates (-2, 1).
Step 2: Substitute the coordinates into the distance formula.
Using the distance formula, we can plug in the values as follows:
Distance = sqrt((-2 - (-9))^2 + (1 - 6)^2)
Simplifying the formula:
Distance = sqrt((7)^2 + (-5)^2)
Distance = sqrt(49 + 25)
Distance = sqrt(74)
Step 3: Calculate the square root.
Taking the square root of 74, we get:
Distance ≈ 8.6
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Which number line represents the solution to 5x < 30?
Answer:
x<6
Step-by-step explanation:
5x < 30 divide by 5
x=6
Answer:
Step-by-step explanation:
21
PLEASE help me I will give brainliest
Answer:
25
Step-by-step explanation:
9/8 + 5/6
(Please show you work)
HELP
1 23/24 because you have to find the equivelent denominator
Answer:
1 [tex]\frac{23}{24}[/tex]
Working:
[tex]\frac{9}{8}[/tex] + [tex]\frac{5}{6}[/tex]
[tex]\frac{9}{8}[/tex] × [tex]\frac{3}{3}[/tex] + [tex]\frac{5}{6}[/tex] × [tex]\frac{4}{4}[/tex]
[tex]\frac{27}{24}[/tex] + [tex]\frac{20}{24}[/tex] = [tex]\frac{47}{24}[/tex]
[tex]\frac{47}{24}[/tex] = 1 [tex]\frac{23}{24}[/tex]
Need help ASAP!!
Evaluate each expression for the given values of the variables.
1. 3x · 2 ÷ y; x = 3 and y = 6
2. (4a)^3 ÷ (b − 2); a = 2 and b = 4
1. 3
2. 256
Explanation:
1. if x = 3 and y= 6
then
3x . 2 ÷ y = 3(3). 2 ÷ 6
9 × 2 ÷ 6
18÷ 6= 3
2. if a = 2 and b = 4
then (4a)^3 ÷ (b − 2) = (4*2)^3 ÷ (4-2)
8^3 ÷ 2
512 ÷ 2
= 256
A friend of yours is new to constructions and was curious about something. They know bisectors essentially split something in half, but don't understand why angle bisectors and segment bisectors have differences in their construction. Describe the similarities and differences between the construction steps for segment bisectors and angle bisectors to your friend.
Segment bisectors and angle bisectors both involve dividing a given segment or angle into equal parts. However, their construction steps differ in terms of the tools and techniques used.
Segment bisectors rely on compass and straightedge constructions, while angle bisectors involve only a compass. Both constructions play important roles in geometry.
Segment bisectors and angle bisectors are used to divide geometric objects into equal parts. The similarity between them lies in their purpose of finding the midpoint or dividing line of a given segment or angle. In both cases, the goal is to create a line that divides the segment or angle into two congruent parts.
However, the construction steps for segment bisectors and angle bisectors differ. Segment bisectors typically involve using a compass to construct congruent arcs on each side of the segment, and then connecting the intersection points of the arcs to form the bisecting line. This construction requires both a compass and a straightedge.
On the other hand, angle bisectors are constructed using only a compass. The process involves placing the compass at the vertex of the angle and drawing two arcs that intersect the sides of the angle. The bisector is then drawn by connecting the vertex with the intersection point of the arcs.
These differences in construction steps arise due to the different geometric properties of segments and angles. Segments have length and require straight lines for their bisectors, while angles are measured in degrees and can be bisected using arcs and a compass.
Both segment bisectors and angle bisectors are essential tools in geometry and have various applications in geometric constructions and proofs. Understanding their similarities and differences helps develop a deeper understanding of geometric concepts and their practical applications.
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Pete has a 15-foot ladder. The safety instructions recommend he should have the base of the ladder 6 feet from the base of the wall he will lean the ladder against. How high will the ladder
reach on the wall?
Round to the nearest tenth
GET BRAINLYY IF CORRECT
Answer:
13.7
Step-by-step explanation:
A{2} + B{2} =C{2} \\
6{2} +B{2} =15{2} \\
6x6+B(2) =15x15\\
36+B(2)=225\\
-36\\
\sqrt{189} =13.7
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1925. What was the rate charged per hour by each mechanic if the sum of the two rates was $130 per hour?
Answer:
g
Step-by-step explanation:
is 5x=25 equivalent to x+10=20
Answer:
No.
Step-by-step explanation:
Solve for the first equation.
5x=25 Divide both sides by 5.
/5 /5
x=5
Solve for the second equation.
x+10=20 Subtract 10 from both sides.
-10 -10
x=10
5 does not equal 10, so the equations are not equivalent.
Hope this helps!! Have a nice day c:
Lily is buying candy for party favors. She needs 1.5 pounds of chocolates, 0.75 pounds of mints, and 15 lollipops. What is the total cost for the candy? A. $5.84 B. $8.82 C. $15.30 D. $18.27 Candy Cost mints $0.96 per pound chocolates $4.70 per pound lollipops $0.07 each
Answer:
The answer is B. $8.82Step-by-step explanation:
given data
mints $0.96 per pound
chocolates $4.70 per pound
lollipops $0.07 each
cost of each items based on the amount item
mints $0.96*0.75= 0.72
chocolates $4.70*1.5=7.05
lollipops $0.07*15=1.05
total cost= 0.72+7.05+1.05
total cost=$8.82
Answer:
The answer is 8.82
Step-by-step explanation:
The number 0 is an element of the set of natural numbers. OA. True B. False
Answer:
false
Step-by-step explanation:
0 is a whole number not natural
Natural Number can be classified as "Positive Integer" or "Counting Numbers". So think about it, In real life, we count from 1 right? We do not start from 0 for counting numbers.
So it's false.
find the domain of the equations. do not solve
Answer:
x≥3, where x≠5
Step-by-step explanation:
x≥3, where x≠5
Round 843,590 to the nearest thousand,
Answer:
844,000
Step-by-step explanation
Last three numbers are the hundreds, that's what you round when doing thousands. If it is higher than 500, then raise it to the next thousand, if not then keep it the same. In this case, 590>500, so I will round up to 844,000.
Silas has 5 1/4 cups of flour he uses 3 1/2 cups to bake bread, then he borrows another 2 cups from his neighbor
Given statement solution is :- Baking bread and borrowing from his neighbor, Silas has 15/4 cups of flour remaining.
To solve this problem, we'll perform the necessary calculations step by step.
Silas starts with 5 1/4 cups of flour.
To convert the mixed number to an improper fraction, we multiply the whole number (5) by the denominator (4) and add the numerator (1). This gives us (5 × 4) + 1 = 21/4 cups of flour.
Silas uses 3 1/2 cups of flour to bake bread.
To subtract fractions, we need to have a common denominator. The denominators here are 4 and 2, so we'll convert the second fraction to have a denominator of 4.
3 1/2 is equivalent to (3 × 2) + 1 = 7/2 cups of flour.
Now we can subtract: 21/4 - 7/2.
To subtract fractions with the same denominator, we subtract the numerators and keep the denominator the same.
21/4 - 7/2 = (21 - 14) / 4 = 7/4 cups of flour remaining.
Silas borrows another 2 cups from his neighbor.
To add fractions, we need a common denominator. The denominators here are 4 and 1, so we'll convert the second fraction to have a denominator of 4.
2 is equivalent to 2/1 cups of flour.
Now we can add: 7/4 + 2/1.
To add fractions with the same denominator, we add the numerators and keep the denominator the same.
7/4 + 2/1 = (7 + 8) / 4 = 15/4 cups of flour.
Therefore, after baking bread and borrowing from his neighbor, Silas has 15/4 cups of flour remaining.
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What do the differences between the points (as shown on the graph) represent?
Answer:
They represent the rise and run of the graph.
Step-by-step explanation:
The difference between the x-axis of the points represents the "run" of the graph (or how much you should run along x-axis to get to the next point.)
The difference between the y-axis of of the points represents the "rise" of the graph (or how much you should rise up the y-xis to get to the next point).
The ratio of rise to run is the slope of the graph, which tells us how many steps should we take on the y-axis for every step we move forward on the x-axis.
write 55,426 using the number names
Answer:
fifty five thousand four hundred and twenty six.
Step-by-step explanation:
Answer:
Hey mate
Step-by-step explanation:
55,426
Fifty five thousand four hundred twenty six.
hope it helps,
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What is the absolute value of -6? Use the number line to help answer the question.
2
6
S
4
3
2
1
6
7
Answer:
Hi guys! Its 6, I took the quiz and I was sure to check after!!
Step-by-step explanation:
3 shapes are combined to form a composite figure. A semicircle is on the bottom, and then a small rectangle connects the semicircle to a triangle.
How can you decompose the composite figure to determine its area?
as three triangles and a circle
as two triangles, a rectangle, and a circle
as a triangle, a pentagon, and a semicircle
as a triangle, a rectangle, and a semicircle3 shapes are combined to form a composite figure. A semicircle is on the bottom, and then a small rectangle connects the semicircle to a triangle.
How can you decompose the composite figure to determine its area?
as three triangles and a circle
as two triangles, a rectangle, and a circle
as a triangle, a pentagon, and a semicircle
as a triangle, a rectangle, and a semicircle
The composite figure can be decomposed into a triangle, a rectangle, and a semicircle to determine its area.
To decompose the composite figure and determine its area, we can break it down into simpler geometric shapes based on its components. In this case, the composite figure consists of a semicircle, a small rectangle, and a triangle.
We can decompose the figure as a triangle, a rectangle, and a semicircle. Here's how:
Triangle: The upper part of the figure is a triangle. Calculate its area using the formula A = (base * height) / 2, where the base and height are the appropriate measurements.
Rectangle: The small rectangle connects the semicircle to the triangle. Find its area by multiplying the length and width.
Semicircle: The bottom part of the figure is a semicircle. Calculate its area using the formula A = (π * r^2) / 2, where r is the radius of the semicircle.
Once you have determined the areas of each individual shape, add them together to find the total area of the composite figure.
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I will name brainliest :)
Answer:
The median and IQR
Step-by-step explanation:
Hope it helps
Which of these is a simplified form of the equation 7y+8=9+3y+2y?
A. 7y=6
B. 2y=1
C. 12y=17
D. 5y=17
Solution of
3/20+1/25-11/60=
Answer:0.06
Step-by-step explanation:
Answer:
0.006
Step-by-step explanation:
3/20 = 0.15 + 1/25 = 0.19 - 11/60
= 0.00666666
Data table Activity Optimistic START 0 ABCDEFGHIK А J L FINISH 605 2607NTO TO 2-253 N N N M - NO 15 3 1 1 1 Time Estimates (days) Most Likely 0 0 10 1 20 10 2 2 2 3 1 Print Pessimisitic 0 OANAN www�
Answer:
This is gebber gabber but yes
Step-by-step explanation:
Catherine bought 7 candy bars and 4 soft drinks from the concession
stand. The soft drinks cost a total of $2. Catherine's total bill was $5.50.
What equation would you used to find the cost of the candy bars? *
Answer:
$5.50-$2=7x(when we consider cost of one candy bar as x)
PLEAS HELP HELP PLEASE
Answer:
x
Step-by-step explanation:
Please answer !!!!!!! Will mark brainliest !!!!!!!!
Answer: A. 4(8m-2) and 32m -8
Step-by-step explanation: First distribute the 4 to 8m and -2 to get 32m - 8 which is equal to 32m - 8.
32m - 8 = 32m - 8
Hope this helps! :)
Answer:
The first one
Step-by-step explanation:
4(8m-2)=32m-8
Group the x terms together and the y terms together, and move the constant term to the other side of the equation.
x²+ 12x + y²+ 2y = 1
Determine (b ÷ 2)2 for the x and y terms.
(12 ÷ 2)2 = 36 and (2 ÷ 2)2 = 1
Add the values to both sides of the equation.
x2 + 12x + 36 + y2 + 2y + 1 = 1 + 36 + 1
Write each trinomial as a binomial squared, and simplify the right side.
(x + )2 + (y + )2 =
Answer:
Step-by-step explanation:
The equation you provided can be rewritten as:
(x + 6)² + (y + 1)² = 42
This is the equation of a circle with center (-6, -1) and radius the square root of 42.
what is the answer to this equation 3x + 4 - 8x = 24
Answer:
-4
Step-by-step explanation:
3x-8x+4=24
-5x=24-4
-5x=20
x=-4
Answer:
[tex]x = - 4 [/tex]Step-by-step explanation:
[tex]3x + 4 - 8x = 24 \\ [/tex]
Simplify the expression on the left side of the equation
That's
[tex]4 - 5x = 24[/tex]
Subtract 4 from both sides of the equation
[tex]4 - 4 - 5x = 24 - 4\\ - 5x = 20[/tex]
Divide both sides by - 5
[tex] \frac{ - 5x}{ - 5} = \frac{20}{ - 5} \\ [/tex]
We have the final answer as
[tex]x = - 4 \\ [/tex]
Hope this helps you
can any one help me plz
Answer:
$0.11
Step-by-step explanation:
price ($28.16) divided by amount (265) = unit rate
Find the value of f(3) for the function
f(x) = - 7 (x + 5)
f(3)=
