If A2 = I, where I is the identity matrix, which matrix correctly represents matrix A?
Answers
We know that [tex] \boldsymbol{A^2}=\boldsymbol{A\times A} [/tex]
We also know that [tex] \boldsymbol{I}=\begin{bmatrix}
1 &0 \\
0&1
\end{bmatrix} [/tex]
Now, it has been given to us that [tex] \boldsymbol{A^2}=\boldsymbol{I} [/tex]
Therefore, we will have to find the correct [tex] \boldsymbol{A} [/tex] from the given options and we find that when:
[tex] \boldsymbol{A}=\begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix} [/tex]
then [tex] \boldsymbol{A^2}=\boldsymbol{A\times A}=\begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix}\times \begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix}=\begin{bmatrix}
1 & 0\\
0 & 1
\end{bmatrix} [/tex]
Therefore, from the above given options, Option C is the correct option.
Therefore, [tex] \boldsymbol{A}=\begin{bmatrix}
3 & -2\\
4 & -3
\end{bmatrix} [/tex] is the correct answer.
Answer:
C. [3, -2]
[4, -3]
Step-by-step explanation:
PLATOOOO
Related Questions
Caitlin has 4 and 3/4 lb of place use 1 1/10 pound to make a cup and another 2 pounds to make a jar how many pounds are left
Answers
4 3/4---------> (4*4+3)/4----------> 19/4
1 1/10-----------> (10*1+1)/10----> 11/10
[pounds left]=[(19/4)-(11/10)-(2)]----> (10*19-4*11-40*2)/40
=(190-44-80)/40-------> 66/40---------> 1.65 pounds
1.65-----> 1 65/100--------> 1 13/20 pounds
the answer is 1.65 pounds (1 13/20 pounds)
A particularly long traffic light on your morning commute is green on 20% of the mornings. assume that each morning represents an independent trial. (a) what is the probability that the first morning that the light is green is the fourth morning?
Answers
p=0.2
independent Bernoulli trials (green=success)
Need to find: probability that first three trials are failures, and the fourth one is a success.
Method: The conditions given fit the requirements of the geometric distribution, where for k failures before the first sucess
P(k)=(1-p)^k*p
=(1-0.2)^3*0.2
=0.8^3*0.2
=0.1024
What is 15% of 40% of $180
Answers
PLZ HELP FOR BRAINLESS AND POINTS
Write a real-world problem that could be represented by the inequality. 2x + 5 > 23
Answers
Answer:
you have 2x oranges and you add 5 more but you still have 23 apples more than oranges
if Trigg spends 23.50 on gas, what is the total distance the boys could travel
Answers
To determine the total distance Trigg could travel with $23.50, you divide this amount by the cost per gallon of gas and then multiply by the car's MPG. Using an MPG of 27 and a gas price of $2.86 per gallon as example figures, Trigg could travel approximately 221.859 miles.
To calculate the total distance Trigg could travel with $23.50 spent on gas, we need to know the car's fuel efficiency (miles per gallon) and the current gas price per gallon. Since this information isn't provided directly in your question, let's use the example information provided. Assuming a car gets 27 miles per gallon and gas costs $2.86 per gallon, we first calculate how many gallons Trigg can buy with $23.50:
Divide $23.50 by the cost of a gallon of gas ($2.86) to find out how many gallons he can purchase:$23.50 / $2.86 = 8.217 gallons (approximately).Multiply the number of gallons by the fuel efficiency of the car to find out the total distance: 8.217 gallons x 27 miles per gallon = 221.859 miles (approximately).
Therefore, with $23.50 and the given fuel efficiency and gas price, Trigg could travel approximately 221.859 miles.
if slope =2;goes through(-1,4) y =
Answers
.. y = m(x -h) +k . . . . . for slope m through point (h, k)
.. y = 2(x +1) +4
This can be simplified to slope-intercept form.
.. y = 2x +6
PLEASE HELP 50 POINTS
Consider the following equation in chemical equilibrium. C2H4(g) + H2(g) mc009-1.jpg C2H6(g) + 137 kJ What happens to the amount of ethane (C2H6) when the temperature of the system is increased? The amount of ethane decreases. The amount of ethane increases initially and then decreases. The amount of ethane increases. The amount of ethane decreases initially and then increases.
Answers
A. The amount of ethane increases.
Create a 5th° polynomial with four terms in standard form
Answers
Tori Chang and her cousin, Sumi decide to open an accounting business. They will need a total of $60,000 to get the business started. Sumi has spent a lot of time getting the business set up, so Tori agrees to contribute $8,000 more than Sumi. How much money will Tori contribute?
Answers
_____
If you want to solve equations, let t and s represent Tori's and Sumi's contributions.
.. t + s = 60000
.. t - s = 8000
Add the two equations
.. 2t = 68000
.. t = 34000 . . . . . . divide by 2 to find t
The volume of a cylinder is 24(pi) ft3. What is the volume of a cone that has the same base and height?
Answers
now, if you notice there, for a cylinder with radius "r" and height "h", that is its volume.
and for a cone that has the same "h" and "r' as the cylinder's, that is its volume, however, notice, the cone's volume is one third of that of the cylinder's.
so if the cylinder has a volume of 24, well, you already know what is the cone's.
A recipe for lemon cranberry pound cake calls for 80 milliliters of lemon juice and 240 milliliters of plain yogurt. How many liters of lemon juice and yogurt are needed to make 11 cakes?
Answers
?ml lemon juice................................ 11 cakes
(80*11)/1=880 ml of lemon juice =0.88 liters
Answer: 3 liters 520 milliliters
Step-by-step explanation:
80 ml + 240ml = 320ml
total amount for 11 cakes 320ml x 11 3520ml
total amount for 11 cake conversion 3520ml divided by 1000 = 3 remainder 520
Answeer is 3 liters 520 mililiters
Add -4 + 2/3 . A) -52/3 B) -42/3 C) -32/3 D) -31/3
Answers
If D is supposed to be -3 1/3, that choice is the correct one.
___
As written, none of the answer choices are correct.
Which equation represents an inverse variation function that passes through the point (4,5) and (10,2)
Answers
https://brainly.com/question/5029365
Answer:
[tex]y*x=20[/tex] or [tex]y=20/x[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
so
Find the value of k
For [tex](4,5)[/tex]
[tex]y*x=k[/tex] -----> [tex]5*4=k[/tex] ----> [tex]k=20[/tex]
For [tex](10,2)[/tex]
[tex]y*x=k[/tex] -----> [tex]2*10=k[/tex] ----> [tex]k=20[/tex]
The equation that represent an inverse variation is equal to
[tex]y*x=20[/tex] or [tex]y=20/x[/tex]
collins cafeteria offers a selection of 5 meats,six vegetables and 8 deserts.in how many ways can you select a meal of 2 different meats,3 different vegetables and 2 different deserts
Answers
3 different vegetables are to be selected from 6 vegetables.
2 different deserts are to be selected from 8 deserts.
This is a combination problem.
Number of ways to select 2 meats from 5 meats = 5C2 = 10
Number of ways to select 3 vegetables from 6 vegetables = 6C3 = 20
Number of ways to select 2 deserts from 8 deserts = 8C2 = 28
Total number of ways to select a meal 2 different meats,3 different vegetables and 2 different deserts = 10 x 20 x 28 = 5600 ways.
This means the meal of 2 different meats,3 different vegetables and 2 different deserts can be selected in 5600 different ways.
What is the value of x when 3/x+6=6/8x-12
Answers
6(x+6) = 3(8x-12)
6x+36 = 24x-36
36+36= 24x-6x
72= 18x
4=x
X=4
Harry's fitness trainer recommends that Harry drink 8 fluid ounces of water 8 times a day. Harry has a water bottle that holds 1 1/4 pints of water when filled. Today he has filled the water bottle three times and drank all of the water each time. Harry claims that he drank the total amount of water recommended by his fitness trainer. Explain why hair is claim is not true
Answers
and
8 oz x 8=64 oz
60<64
therefore he was 4 oz short of the total recommended amount.
Amount of fluid recommended by Harry's fitness trainer =8 fluid ounces of water 8 times a day = 8x8=64 fluid ounces.
Amount of fluid Harry water bottle holds= [tex] 1\frac{1}{4}=1.25 pints [/tex]
Amount of fluid Harry drinks when he fills the bottle 3 times = 1.25x3=3.75 pints.
1 pint = 16 fluid ounce
3.75 pint =16x3.75 =60 fluid ounces.
Harry drank only 60 fluid ounce compared to 64 fluid ounce his trainer recommended.
Harry claims that he drank the total amount of water recommended by his fitness trainer is not true.
helen didvided her colored pencils evenly among herself and three freinds. write an expression to represent the number of pencils each person received
Answers
This would then signify that the expression would look like the following:
[tex]\boxed{p\div(4)}[/tex]
We really do not know how many pencils Helen had, so this is why p is in the equation.
The mathematical expression to represent the number of colored pencils each person received is [tex]\frac{P}{4}[/tex], where P represents the total number of pencils.
The question asks us to write an expression to represent the number of colored pencils each person received when Helen divided her pencils evenly among herself and three friends. To do so, we should first denote the total number of colored pencils Helen has as P. Since there are four people in total (Helen and her three friends), we need to divide the total number of pencils by four.
The expression to represent the number of colored pencils each person received is thus [tex]\frac{P}{4}[/tex]. This formula can be used to calculate how many pencils each person would get if you replace P with the actual number of pencils.
How do you write 331 in scientific notation?
Answers
331 = 3.31 x 10²
The answer is "3.31*10^2".
Reason:
331=331*10^3
If you need anymore help feel free to ask me!
Hope this helps!
~Nonportrit
Need help in geometry!!!
Answers
JKLM: J(8,4) ; K(4,10) ; L(12,12) ; M(14,10)
I'll just use the first vertex of every quadrilateral in comparison with J(8,4)
A(-8,-4) ; B(-4,-10) ; C(-12,-12) ; D(-14,-10) → a sequence of reflections across the x and y-axes, in any order. This is easy because each vertex has the same number but different signs.
E(11,2) ; F(7,8) ; G(15,10) ; H(17,8) → a translation of 3 units left and 2 units up. As you can envision with a graph, from 11 to 8, you need to move to the left of the x-axis. from 2 to 4, you need to move up of the y-axis.
O(6,7) ; P(2,13) ; Q(10,15) ; R(12,13) → a translation 2 units right and 3 units down. From 6 to 8 of the x-axis and from 7 to 4 of the y axis.
S(4,16) ; T(10,20) ; U(12,12) ; V(10,10) → This one has no pair but it seems as though this is rotated along the point U.
W(11,7) ; X(7,13) ; Y(15,15) ; Z(17,13) → a translation 3 units down and 3 units left.
solve the equation what is -12=3x+3
1.-5
2.-2
3.0
4.3
Answers
In this problem, you are tasked to find the value of x.
-12 = 3x + 3
This is the same as:
3x + 3 = -12
You have to transpose the 3 to the other side to solve the equation.
3x = -12 – 3
3x = -15
x = -5
-12-3=3x
-15=3x divide by 3
-5=x
choice 1
Jenny live 6 1/4 miles from school. Raymond lives 5 1/2 miles from school. How much farther from school does Jenny live then Raymond? Write an equation and solve it
Answers
6 1/4 - 5 2/4= 3/4
The answer is 3/4.
To find out how much farther Jenny lives from school than Raymond, we subtract Raymond's distance from Jenny's, converting both to improper fractions to subtract easily, resulting in Jenny living 3/4 of a mile farther than Raymond.
Explanation:The question asks how much farther from school Jenny lives compared to Raymond. Jenny lives 6 1/4 miles from school, and Raymond lives 5 1/2 miles from school. To find out how much farther Jenny lives from the school than Raymond, we can write an equation and solve it.
Let ‘d’ represent the difference in distance between how far Jenny lives from the school and how far Raymond lives from the school. The equation can be written as:
d = 6 1/4 miles - 5 1/2 miles
To solve this, we first convert the mixed numbers to improper fractions. Therefore, 6 1/4 miles becomes 25/4 miles, and 5 1/2 miles becomes 11/2 miles. Our equation now looks like this:
d = 25/4 miles - 11/2 miles
We need a common denominator to subtract these fractions, which is 4 in this case. So we convert 11/2 miles into 22/4 miles. The revised equation is:
d = 25/4 miles - 22/4 miles
When we subtract 22/4 from 25/4, we find d = 3/4 miles. Therefore, Jenny lives 3/4 of a mile farther from school than Raymond.
Two teams of interns are wrapping donated gifts at a hospital. if the teams work alone, team a can wrap all of the gifts in 7 hours, and team b can wrap all of the gifts in 5 hours. how many hours will it take the interns to wrap all of the gifts if both teams work together? round the answer to the nearest half hour.
Answers
Team A can wrap all gifts in 7 hours; thus they can wrap 1/7 of the gifts in 1 hour.
Team B can wrap all gifts in 5 hours; thus they can wrap 1/5 of the gifts in 1 hour.
1/7h + 1/5h = 1, where h is the number of hours; it equals 1 because it is 100% of the gifts;
Find a common denominator. 35 is the first thing 7 and 5 will both divide into. Convert the fractions:
5/35h + 7/35h = 1
12/35h = 1
Divide both sides by 12/35:
12/35h ÷ 12/35 = 1 ÷ 12/35
h = 1/1 ÷ 12/35
h = 1/1 × 35/12
h = 35/12
h = 2.9
h ≈ 3
Final answer:
When both teams work together, they can wrap the gifts with a combined rate of 12/35 of the work per hour. It would take them 35/12 hours, which is approximately 2.92 hours. Rounded to the nearest half-hour, both teams will take about 3 hours to wrap all of the gifts.
Explanation:
To determine the time it would take for both teams of interns to wrap the gifts when working together, we need to add their work rates. Team A can wrap the gifts in 7 hours, which means their rate is 1/7 of the work per hour. Team B can wrap the gifts in 5 hours, giving them a rate of 1/5 of the work per hour.
When combined, the rate at which they can wrap the gifts together is the sum of their individual rates:
Team A's rate: 1/7
Team B's rate: 1/5
Combined rate: 1/7 + 1/5 = 5/35 + 7/35 = 12/35 of the work per hour.
To find out how many hours it will take them to wrap all of the gifts together, we divide the entire job (1) by their combined rate (12/35):
1 / (12/35) = 35/12 hours = 2.9166... hours.
Rounded to the nearest half hour, they would take approximately 3 hours to wrap all of the gifts.
What are the roots of the polynomial equation x^3-10x=-3x^2+24? Use a graphing calculator and a system of equations.
a. -24, -3, 12
b. -12, 3, 24
c. -4, -2, 3
d. -3, 2, 4
Answers
simplifying the above we get
x^3+3x^2-10x-24=0
next we use the graphing tool to solve the expression above:
This will give us:
x=-4,x=-2, x=3
The answer is c] -4,-2,3
Answer : C
the roots of the polynomial equation x^3-10x=-3x^2+24
We use a graphing calculator
Graph the left hand side expression using graphing calculator
We graph [tex]y=x^3 - 10x[/tex]
Then we graph the right hand side expression using graphing calculator
[tex]y=-3x^2+24[/tex]
so we got two system of equations
The intersection of two graphs is our solution
The graph is attached below
We can see that the graph intersects at 3 points
(-4, -24) (-2,12) and (3,-3)
So the roots are -4, -2 , 3
What is the value of the expression shown below?
3 + (2 + 8)^2 ÷ 4 × 1 over 2 to the power of 4 (4 points)
4 and 1 over 32
4 and 9 over 16
6 and 1 over 8
6 and 1 over 32
Answers
Answer:
4 and 9 over 16
Step-by-step explanation:
The expression is 3 + (2 + 8)^2 ÷ 4 × 1 over 2 to the power of 4 . it can be represented mathematically as
3 + (2 + 8)^2 ÷ 4 × (1/2)^4
using PEMDAS
parenthesis come first
3 + 10^2 ÷ 4 × (1/2)^4
exponential comes next
3 + 100 ÷ 4 × 1/16
3 + 25 × 1/16
3 + 25/16
(48 + 25)/16
73/16
4 9/16
Answer:
I think the answer is B which is 4 9/16.
Step-by-step explanation:
All the answers to 6ft.12 in
Answers
7 ft
whats the slope of this graph??
Answers
By counting on the graph the slope is -1/2
By using the slope formula:
-2-0/4-0 = 4/-2 = 1/-2
Hence, the slope is same the both ways :)
A compact disc costs $17.97. The sales tax rate is 5%. How much will the total cost be for this compact disc?
Answers
$18.87
Why is 25 mg lighter than 25 cg
Answers
The denominator of a fraction is three more than twice the numerator. If both numerator and denominator are decreased by one, the simplified result is 7/16. Find the original fraction.
Answers
Numerator = n = x
denominator = d = 2n + 3
New Condition
(x - 1) /(2x + 3 - 1) = 7 / 16
(x - 1) / (2x + 2) = 7 / 16
Cross multiply and solve
16*(x - 1) = 7 * (2x + 2) Remove the brackets.
16x - 16 = 14x + 14 Add 16 to both sides.
16x = 14x + 30 Subtract 14x from both sides.
2x = 30 Divide by 2
x = 15
You really should check this.
Original fraction
15/33
Now subtract 1 from the top and bottom.
14/32 Divide both by 2
7 / 16 which checks out perfectly
Emma buys and sells truck parts. She bought two tires for $35.00 each and later sold them for $65.00 each. She bought three rims for $75.00 each and later sold them for $136.00 each. She bought five headlight covers for $4.00 each and later sold them for 15.00 each. What is Emma's total profit?
Answers
hope this helps:)
-Ashley
dont sue me if i get something wrong, im human @ other users
Answer:
Emma made a profit of $298.00
Step-by-step explanation:
Emma bought two tires = $35.00 each
Cost of two tires = 35 × 2 = $70.00
She bought three rims = $75.00 each
Cost of three rims = 75 × 3 = $225.00
She bought five headlight covers = $4.00 each
Cost of 5 headlight covers = 5 × 4 = $20.00
Total Cost price of the items = 70 + 225 + 20 = $315.00
She sold both tires = $65.00 each
= 65 × 2 = $130.00
She sold three rims = $136.00 each
= 136.00 × 3 = $408.00
She sold 5 headlight covers = $15.00 each
= 15 × 5 = $75.00
Selling price of all the items = 130 + 408 + 75 = $613.00
Profit = selling price - cost price
P = 613.00 - 315.00 = $298.00
Emma made a profit of $298.00