Answer:
K = -7
Step-by-step explanation:
If A=[1 0 -1 7] find K such that A^2-8A-ki-KI=0
Given the 2×2 matrices
A = [tex]\left[\begin{array}{ccc}1&0\\-1&7\\\end{array}\right][/tex]
We are to find K if =0
A² = [tex]\left[\begin{array}{ccc}1&0\\-1&7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}1&0\\-1&7\\\end{array}\right][/tex]
A² = [tex]\left[\begin{array}{ccc}1&0\\-8&49\\\end{array}\right][/tex]
8A = 8[tex]\left[\begin{array}{ccc}1&0\\-1&7\\\end{array}\right][/tex]
8A = [tex]\left[\begin{array}{ccc}8&0\\-8&56\\\end{array}\right][/tex]
Since [tex]I = \left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right] \\[/tex]
[tex]KI = \left[\begin{array}{ccc}K&0\\0&K\\\end{array}\right][/tex]
Substitute the resulting matrices into the expression above:
A^2-8A-KI = [tex]\left[\begin{array}{ccc}1&0\\-8&49\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}8&0\\-8&56\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}K&0\\0&K\\\end{array}\right][/tex] =[tex]\left[\begin{array}{ccc}0&0\\0&0\\\end{array}\right][/tex]
From the expression, we have the equations;
1 - 8 - k = 0
-7 - k = 0
-7 = k
k = -7
Hence the value of K is -7
Please help me with question 5
Answer:
Third choice, 3/20
Step-by-step explanation:
Add all the numbers on the right side of the chart together:
16 + 12 + 22 + 15 + 26 + 9 = 100
So they're rolled the dice 100 times, and of that, they got a 4 fifteen times. So it's 15/100, simplify that equation and it's 3/20
Simplifying an equation means making an equation have smaller numbers if possible. For this question 15 and 100 can both be divided by 5, it is also the biggest number they can both be divided by, so u divide both by 5 and it's 3 and 20, making it 3/20
Is 16 greater than 16.2 ?
Answer:
No :)
Step-by-step explanation:
the .2 is added to 16 so it's.2 bigger
Answer:
No.
Step-by-step explanation:
Because 16 is 16.00, while 16.2 is 16.02.
16.2 is .02 more than 16.
Write an equation of the line that passes through (-2,3) and (0,8).
Answer: y = 5/2 x + 8
Step-by-step explanation:
Find m using two points (-2,3) and (0,8) = 8-(3) / 0- (-2) = 5/2
y = 5/2 x + b
8 = 5/2 (0) + b
8 = b
y = 5/2 x + 8
What is a secure line of credit?
A)A line of credit offered only to individuals with excellent credit ratings.
B)A line of credit offered to a business or corporation.
C)A line of credit backed by the government.
D)A line of credit backed by collateral.
Answer:
It's D. A line of credit backed by collateral.
Step-by-step explanation:
Just took the test and got it right.
the secure line of credit is:
D)A line of credit backed by collateral.
What is Collateral?Collateral is an item of value pledged to secure a loan. Collateral reduces the risk for lenders. If a borrower defaults on the loan, the lender can seize the collateral and sell it to recoup its losses. Mortgages and car loans are two types of collateralized loans.
A revolving loan that can be utilized for any purpose is known as a line of credit (LOC). Up to a maximum amount determined by the lender, the borrower may draw from the line of credit at any moment, pay it back, and then borrow again.
There are substantial variations between secured and unsecured lines of credit, including the interest rate that the borrower must pay.
Collateral, such as a house, serves as the guarantee for a secured line of credit.One example of an unsecured line of credit is a credit card, which is not backed by any assets.Because it is riskier for lenders, unsecured credit always has a higher interest rate.Therefore, the secure line of credit is:
D)A line of credit backed by collateral.
Learn more about collateral here:
https://brainly.com/question/6779619
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Which equation matches the graph of the greatest integer function given
below?
Answer:
[tex]y = x + 2[/tex]
Step-by-step explanation:
Given
The attached graph
Required
Determine the equation
First, pick any 2 corresponding coordinates
[tex](x_1,y_1) = (0,2)[/tex]
[tex](x_2,y_2) = (6,8)[/tex]
Next, calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{8-2}{6-0}[/tex]
[tex]m = \frac{6}{6}[/tex]
[tex]m =1[/tex]
The equation is calculated as:
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
[tex](x_1,y_1) = (0,2)[/tex] and [tex]m =1[/tex]
[tex]y - 2 = 1(x - 0)[/tex]
[tex]y - 2 = (x - 0)[/tex]
[tex]y - 2 = x[/tex]
Make y the subject
[tex]y = x + 2[/tex]
PLEASE ANSWER
Type SSs, SAS, ASA, SAA, or HL
to justify why the two larger triangles are
congruent.
Answer:
hope my answer is helpful to you
plz mark me as brainlist and also follow me
thank you
Answer: The answer is ASA
I hope this helps!
What is the slope of the line?
slope-2
slope 1
slope1
Answer:
-1
Step-by-step explanation:
Answer:
Slope = difference in y / difference in x
slope = 0 - 2 / 2 -0
slope = -2 / 2
slope -1
Step-by-step explanation:
A card is drawn from a
standard, well-shuffled
deck of 52 cards.
What is the probability that
it is a face card (J, Q, or K)?
I dont understand this can someone plz explain.
the answer is A but how is it A?
Answer:
Step-by-step explanation:
here is what I think logically is going on.. and does this happen to be some kind of computer sciency class question? b/c this seems like a primer for Boolean logic.. ask your teacher that question :D .. see if he knows :P anyway.. soooo by subtracting 4 reds.....
R R B B B our starting chips ( the letters represents the the chips below)
OOOOO subtracting one red changes the next black to a red.. I think
R R R B B (-1)
OOOOO subtract one more red changes the next black to a red
R R R R B (-2)
OOOOO subtract one more red
R R R R R (-3)
OOOOO subtract one more and they all fip ..
B B B B B (-4)
OOOOO
This is a bit like a binary counter.. :/ why are you learning this :D
Help immediately!!!!! Question: select all the intervals where g is increasing.
Answer:
It is said that g is increasing when the slope is positive.
We see a positive increase or a positive concavity at -inf to -3Thats not an answer choice so the answer is None of the aboveEn el parque infantil hay una zona de aprendizaje de conducción que tiene miniautos y triciclos. Si en total hay 18 vehículos y 64 llantas, ¿cuántos miniautos y cuántos triciclos hay?
Answer:
There are 6 mini cars and 12 tricycles.
Step-by-step explanation:
In the playground, there is a driving learning area that has mini cars and tricycles. If there are 18 vehicles and 64 tires in all, how many miniature cars and how many tricycles are there?
Given that there are a total of 18 vehicles in the driving learning area.
Let there are x number of the mini car,
so, the number of tricycles = 18-x
As one car has 4 tires, so the total number of car tires = 4x
As one tricycle has 3 tires, so the total number of tricycle tires = 3(18-x)
Given that the total number of tires is 60, so
4x+3(18-x) =60
4x+54-3x=60A
x=60-54=6
So, the total number of mini cars= 6
and the total number of tricycles = 18-6=12
Hence, there are 6 mini cars and 12 tricycles.
Is (3,4) a solution to the system of
equations.
X + y = 7
x - 2y = - 5
Answer: Yes, the point (3,4) is a solution to the system.
===================================================
Proof of this:
Replace x with 3 and y with 4 in the first equation
x+y = 7
3+4 = 7
7 = 7
This confirms the first equation. Repeat for the second equation
x-2y = -5
3-2(4) = -5
3 - 8 = -5
-5 = -5
We get true equations for both when we plug in (x,y) = (3,4). This confirms it is a valid solution to the system of equations. It turns out it's the only solution to this system of equations. Visually, the two lines cross at the single location (3,4).
A. −1≤x<0
B. 1≤x≤2
C. 0
D. −1≤x≤5
Answer: C
Step-by-step explanation:
please can someone help me with this?
Point A is at (0,0). This is the origin.
To move to A'(5,2), we will do two things:
shift 5 units to the rightshift 2 units upThis will have (0,0) move to (5,2).
Points B,C, and D follow the same steps to get what the diagram shows. This is why the entire figure moves 5 units to the right and 2 units up. Everything is in lock-step with each other. This keeps the same shape and size.
If you want to use symbols, then you can describe the translation rule as [tex](x,y) \to (x+5, y+2)[/tex]. We add 5 to the x coordinate to shift 5 units to the right, and we add 2 to the y coordinate to shift 2 units up.
Aria borrowed some money from her friend in order to help buy a new video game
system. Aria agreed to pay the friend back some amount every week until her loan
was paid off. An equation representing the amount Aria owes her friend after t weeks
is L = -25t + 100. What is the x-intercept of the equation and what is its
interpretation in the context of the problem?
Answer:
t is the x-intercept
and it represents the weeks
Step-by-step explanation:
Answer: 4 is the x intercept for the number of weeks until loan is paid off
Step-by-step explanation:
1/4 of the total bird population in your town is 200 birds. How many birds are there in your town?
Answer:
800 birds
Step-by-step explanation:
1/4 of the birds = 200
200 x 4 = 800
Answer:
800
Step-by-step explanation:
1/4 of 800 is 200
you can solve this by multiplying 200 by 4. to under stand this concept just multiply the population by the reciprocal
72 = 5x + 22 X = can some one answer this plz
Answer:
x = 10
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
72 = 5x + 22
Step 2: Solve for x
Subtract 22 on both sides: 50 = 5xDivide 5 on both sides: 10 = xRewrite: x = 10Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 72 = 5(10) + 22Multiply: 72 = 50 + 22Add: 72 = 72Here we see that 72 does indeed equal 72.
∴ x = 10 is the solution to the equation.
Quinten ordered dinner from Domino’s. The cost was $27.45. He wants to give the driver a 15% tip. What is the total that Quinten will spend?
Answer:
The correct answer would be 4.11
Please help!!! 15 pts The black graph is the graph of y=f(x). Choose the equation for the red graph
Answer:
Option C is the correct answer.
Step-by-step explanation:
Let's take 1 point from each graph and make sure that they have the same "x" coordinate. We are going to notice that it does not matter what 2 points with he same "x" coordinate we are going to choose the "y" value of the the point located on the red graph will always be greater by 1. That means that if black graph has the equation (y = f(x)), the red graph is going to have and equation that looks like (y = f(x) + 1). Now we get the following......
y = f(x) + 1
y - 1 = f(x) + 1 - 1
y - 1 = f(x)
So the answer is the option c.
Denis is looking to buy a new car. He can take a loan out for $12,000 with an interest rate of 4% for 5 years. How much would his loan cost in total, including interest?
work out the input for this function machine
Answer:
Answer is 12 isnt it
Step-by-step explanation:
12×4=48
48+9=57
8h + (-6.9d) -18 + 5d -3.4h help
Answer:
−1.9d + 4.6h − 18
Explanation:
8h − 6.9d − 18 + 5d − 3.4h
= 8h + −6.9d + −18 + 5d + −3.4h
[ Combine Like Terms ]
= 8h + −6.9d + −18 + 5d + −3.4h
= (−6.9d + 5d) + (8h + −3.4h) + (−18)
= −1.9d + 4.6h + −18
- PNW
Im supposed to solve this equation using logarithms but I don't know how.
Given:
[tex]3(4^x)=5^(x+1)[/tex]
To find:
The solution of the given equation.
Solution:
We have,
[tex]3(4^x)=5^(x+1)[/tex]
It can be written as
[tex]3((2^2)^x)=5^(x+1)[/tex]
[tex]3((2^{2x})=5^(x+1)[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
Taking log on both sides.
[tex]\log [3((2^{2x})]=\log 5^(x+1)[/tex]
[tex]\log 3+ \log ((2^{2x})=\log 5^(x+1)[/tex] [tex][\because \log (ab)=\log a+\log b][/tex]
[tex]\log 3+ 2x\log 2=(x+1)\log 5[/tex] [tex][\because \log x^n=n\log x][/tex]
Putting values of logarithms, we get
[tex]0.477+ 2x(0.301)=(x+1)0.699[/tex] [tex][\because \log 2 =0.301, \log 3=0.477, \log 5=0.699][/tex]
[tex]0.477+ 0.602x=0.699x+0.699[/tex]
[tex]0.602x-0.699x=0.699-0.477[/tex]
[tex]-0.097x=0.222[/tex]
Divide both sides by -0.097.
[tex]x=\dfrac{0.222}{-0.097}[/tex]
[tex]x=-2.288656[/tex]
[tex]x\approx -2.289[/tex]
Therefore, the value of x is -2.289.
DOES ANYONE KNOW THIS??
Answer:
49-9i²
Step-by-step explanation:
(7+3i)(7-3i)
expand the brackets
49-21i +21i -9i²
49-9i²
If 945 kg of wheat is packed in 9 bags how much in each bag
Answer:
105 kg per bag
Step-by-step explanation:
...... ....................
The distance AB rounded to the nearest tenth = [ ? ]
Answer:
4.5 units
Step-by-step explanation:
To get the distance we need the coordinates of the points
A is ( 3,1)
B is (-1,-1)
Let A be (x1,y1) and B be (x2,y2)
So applying the formula, we have the distance as;
D = √(-1-3)^2 + (-1-1)^2
D = √(16 + 4)
D = √20
D = 4.5 units
The city plans to extend the Wildflower Tral to make it 2 ½ times its current length in the next 5 years. How long will the Wildflower Trail be at the end of 5 years?
Answer: 5¹⁵/₁₆
Step-by-step explanation:
The Wildflower Trail is currently 2³/₈ miles long.
If the city will extend it by 2¹/₂ in 5 years, the length in five years will be;
= 2³/₈ * 2¹/₂
= 19/8 * 5/2
= 95/16
= 5¹⁵/₁₆
Which equation represents the line that passes through points B and C on the graph
PROBLEM SOLVING The profit P (in millions of dollars) for a shoe manufacturer can be modeled by P= -21x3 + 46x where x
is the number (in millions) of shoes produced. The company now produces 1 million shoes and makes a profit of $25 million, but it
would like to cut back production. What lesser number of shoes could the company produce and still make the same profit?
Answer:
Step-by-step explanation:
at 700,200 shoes there is also a 25 million dollar profit
I bought a used,beat up car for $2000.i rebuilt it.
I sold the car for 75% more the what I bought it for. What was my profit
Please help me I need this answer by the end of the day.
Answer:
The answer is 3500
Step-by-step explanation:
All you have to do is get 175% of 2000. This is 3,500.