Find the inverse of this 3x3 matrix. [1 5 2]
[ 1 1 7]
[0 -3 7]
Answers
M = [1 5 2 ]
[1 1 7 ]
[0 -3 7 ]
We apply the Gauss-Jordan elimination method (Procedure and result shown in the image below)
![Find The Inverse Of This 3x3 Matrix. [1 5 2] [ 1 1 7] [0 -3 7]](https://i5t5.c14.e2-1.dev/c-qa-images/answers/attachments/592RyznbduMvNQvfAKb0HrfPxNXdVF7e.jpeg)
Answer:
A
Step-by-step explanation:
⎡−25 26 −33⎤
⎥ 4 −4 5 ⎥
⎥ 3 −3 4 ⎦
Related Questions
if m/\a =150 and /\ a and /\b at supplementary, what is m/\ b
Answers
now, we know that ∡a = 150°, and we also know that
∡a + ∡b = 180
150 + ∡b = 180
∡b = 180 - 150.
This is a 5th grade Math Problem. Please help.
Answers
Li wants buy a jacket is originally Price at $65.00. Today the store is advertising the jacket for 40°/° off the original price.
Answers
65-26=39
$39 final price
Hope this helps :)
The new price is $39.00
Item 6 Find the amount of time. I=$30, P=$500, r=3% The amount of time is years.
Answers
.. I = Prt
.. 30 = 500*.03*t . . . . . substitute the given values
.. 30/15 = t = 2 . . . . . . . divide by the coefficient of t and evaluate
The time is 2 years.
what the circumstances of a circle with a diameter of 12ft
Answers
I have seen a circle about that size used for a labyrinth at a church.
Circumference is found by multiplying the diameter by pi.
(12 ft)*π ≈ 37.7 ft
this picture shows a magnified view of a tick on a penny. about how long is the tick
Answers
Write the equation in standard form for the circle passing through ( - 1,3) centered at the origin.
Answers
well, the radius is the distance from the center to any point on the circle, it just so happen that -1, 3 is on it, so then
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 0 &,& 0~) % (c,d) &&(~ -1 &,& 3~) \end{array}~~~ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ r=\sqrt{(-1-0)^2+(3-0)^2}\implies r=\sqrt{(-1)^2+3^2}\implies r=\sqrt{10}\\\\ -------------------------------[/tex]
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{0}{ h},\stackrel{0}{ k})\qquad \qquad radius=\stackrel{\sqrt{10}}{ r} \\\\\\ (x-0)^2+(y-0)^2=(\sqrt{10})^2\implies x^2+y^2=10[/tex]
Final answer:
The standard form equation of a circle centered at the origin and passing through (-1,3) is x² + y² = 10, where √10 is the radius of the circle calculated using the distance formula.
Explanation:
To write the equation of a circle in standard form that is centered at the origin and passes through the point (-1,3), you first need to calculate the radius using the distance formula. The distance formula is √((x2-x1)² + (y2-y1)²), where (x1, y1) is a point on the circle and (x2, y2) is the center of the circle. Since the circle is centered at the origin, (0,0), we can compute the radius as follows:
Radius = √((-1 - 0)² + (3 - 0)²) = √(1 + 9) = √10
The standard form of the equation for a circle centered at (h, k) with a radius r is:
(x - h)² + (y - k)² = r²
Since our circle is centered at the origin, h = 0 and k = 0, and the radius r = √10, the equation becomes:
x² + y² = 10
The standard form of the equation of a circle is (x−5)2+(y−6)2=1.
What is the general form of the equation?
x2+y2−10x−12y+60=0
x2+y2−10x−12y−62=0
x2+y2+10x+12y+62=0
x2+y2+10x+12y+60=0
Answers
Answer:
(A)[tex]x^2+y^2-10x-12y+60=0[/tex]
Step-by-step explanation:
The standard form of the equation of a circle is given as:
[tex](x-5)^2+(y-6)^2=1[/tex]
Simplifying the above given equation, we get
[tex]x^2+25-10x+y^2+36-12y=1[/tex]
[tex]x^2+y^2-10x-12y+36+25=1[/tex]
[tex]x^2+y^2-10x-12y+61=1[/tex]
[tex]x^2+y^2-10x-12y+60=0[/tex]
which is the required general form of the equation.
Hence, option A is correct.
vita wants to center a towel bar on her door that is 27 1/2 inches wide . she determines that the distance from each end of the towel bar to the end of the door is 9 inches. write and solve an equation to find the length of the towel bar
Answers
The length of the towel bar is 9.5 inches.
Explanation
Suppose, the length of the towel bar is [tex]x[/tex] inches.
The distance from each end of the towel bar to the end of the door is 9 inches. So, the total width of the door will be: [tex][x+(9*2)] = (x+18)inches[/tex]
Given that, the width of the door is [tex]27\frac{1}{2}[/tex] inches or 27.5 inches. So, the equation will be........
[tex]x+18=27.5\\ \\ x=27.5-18= 9.5[/tex]
Thus, the length of the towel bar will be 9.5 inches.
Final answer:
Vita can center the towel bar on her 27 1/2-inch wide door by ensuring it is 9.5 inches long. This is done by deducting the combined distances from the ends of the towel bar to the door edges (18 inches) from the total width of the door.
Explanation:
Vita wants to find the length of the towel bar that she wants to center on a door that is 27 1/2 inches wide, with the distance from each end of the towel bar to the end of the door being 9 inches. To solve for the length of the towel bar, we denote the length of the towel bar by x. Then, we can set up an equation where the sum of the distances from both ends of the towel bar to the door edges and the length of the towel bar itself equals the width of the door.
The equation will be:
9 inches + x + 9 inches = 27 1/2 inches
We combine the known distances to simplify the equation:
18 inches + x = 27 1/2 inches
To find x, we subtract 18 inches from both sides of the equation:
x = 27 1/2 inches - 18 inches
Converting 27 1/2 inches to a decimal, we have 27.5 inches. Thus:
x = 27.5 inches - 18 inches
x = 9.5 inches
Therefore, the length of Vita's towel bar should be 9.5 inches long to be centered on her 27 1/2-inch wide door.
Solve for x X^2+10+12=36
X=-12 or x=2
X
Answers
calculate the distance nathan rides his bike if he rides 9/12 mile each day for 3 days
Answers
Final answer:
Nathan rides a total distance of 2 1/4 miles when he rides 9/12 of a mile each day for 3 days. To calculate this, multiply the daily distance by the number of days and simplify the result.
Explanation:
To calculate the distance Nathan rides his bike if he rides 9/12 of a mile each day for 3 days, you need to multiply the distance he rides in a day by the number of days he rides.
Distance per day: 9/12 mileNumber of days: 3 daysSo, the total distance Nathan rides is:
9/12 mile/day × 3 days = 27/12 miles
To simplify the fraction:
Divide the numerator (27) and the denominator (12) by their greatest common divisor, which is 3.This gives us 9/4 miles.Convert 9/4 to a mixed number: 9 ÷ 4 = 2 with a remainder of 1, so it's 2 1/4 miles.Therefore, Nathan rides a total distance of 2 1/4 miles over the three days.
one inch equals to 2.54 cm. Write an equation for the length x, in inches, that equals to 15 cm
Answers
Final answer:
To convert 15 cm to inches, use the conversion factor 1 inch = 2.54 cm and set up a proportion. Solve for x to find that 15 cm is approximately equal to 5.91 inches.
Explanation:
To write an equation for the length x, in inches, that equals to 15 cm, we can use the conversion factor 1 inch = 2.54 cm. We can set up a proportion to solve for x:
1 inch/2.54 cm = x inch/15 cm
Cross multiplying, we get:
2.54x = 15
Dividing both sides by 2.54, we find that x = 5.91 inches.
Which tax bracket a person Falls into is determined by his or her ?
A. Salary
B. Taxable income
C. AGI
D.Gross income
Answers
Answer:
B. Taxable income
Step-by-step explanation:
Taxable income is the amount of money that a person earns in a period of time that can be taxated by the government, you could earn money that is not taxated, for example life insurances from deceased family members is not taxable, also upto a certain amount of money as a gift is not taxable. So the tax bracket a person falls into depends solely on the taxable income that they make in a year.
Final answer:
B: Taxable income
A person's tax bracket is determined by their taxable income, which is their adjusted gross income minus any deductions and exemptions.
Explanation:
The tax bracket into which a person falls is determined by his or her taxable income.
Taxable income is the amount of income that is subject to the official tax rates for each bracket.
This figure is the result of subtracting deductions and exemptions from your adjusted gross income (AGI). It's important to note that taxable income and AGI are not the same, as the latter is your income from various sources minus specific adjustments but before deductions and exemptions.
To calculate taxable income, the equation used is: taxable income = adjusted gross income - (deductions + exemptions).
Income Tax Brackets are the thresholds of income that are taxed at varying rates. As an individual’s taxable income increases, not only does the amount of tax paid increase, but typically so does the percentage of tax on additional income, as the tax rates in higher brackets are usually higher.
3 2/3 + 7 1/5 simplify if possible
Answers
[Change the denominator to be the same]
= 3 10/15 + 7 3/15
[Add them]
= 10 13/15
morgan cut exactly 35 strips of wood from a larger piece of wood.Each strip of wood was 2.45 centimeters long.How long was the larger piece of wood?
Answers
So, Morgan cut a large piece of wood into 35 smaller strips of wood. Each strip was 2.45 centimetres long. Mutliply:
35 × 2.45 = 85.75
ANSWER:
The larger piece of wood was 85.75 centimetres long.
The larger piece of wood was 85.75 centimeters long based on multiplying the number of strips by the length of each strip.
To find out how long the original piece of wood was, we need to multiply the number of strips by the length of each strip.
Given:
Number of strips: 35
Length of each strip: 2.45 centimeters
Step-by-Step Solution:
Multiply the number of strips by the length of each strip to get the total length: 35 strips * 2.45 cm = 85.75 cmTherefore, the larger piece of wood was 85.75 centimeters long.
Positive linear relationships are represented by values of the correlation, r, that are _____.
Answers
The pyramid shown has a square base that is 18 inches on each side. The slant height is 16 inches. What is the surface area of the pyramid?
Answers
.. S = s(s +2h)
Your pyramid will have area
.. S = (18 in)*(18 in +2*16 in)
.. S = (18 in)*(50 in)
.. S = 900 in²
Answer:
txt
Step-by-step explanation:
What is the volume of a sphere with a radius of 5 cm
Use 3.14 for pie
Answers
How many pennies are in $578
Answers
578 x 100 = 57,800
57,800 pennies
you have 3 bolts that are 3/8, 5/16 and 5/8 long. Which is the shortest?
Answers
Sandy is driving cross country. She has covered 200 miles from the east coast towards the west coast. She has driven this distance in 2 days.
If Sandy continues to drive at this rate, which equation represents the total number of miles , m, she would cover in d more days?
A
m=2d
B
m=100d+200
C
m=300d
D
m=200d+100
Answers
Hope this helps you
wade is 6 years older than Mariah in 8 years the sum of their ages will be 80 how old is Wade now
Answers
Wade:35
Mariah:29
(35+8)+(29+8)=80
35-29=6
What is 36j + j
please help and explain if you can!!! :)
Answers
Explanation.
You could translate this sum into a normal sebtence: I have 36 apples and add 1 apple more.
The sum will then be 36 apples + apple = 37 apples.
Replacing the word (in this explanation 'apple') by a letter learns us 36a + a = 37a
Hence 36j + j = 37j
write the computation in words for an expression that uses all four operations (addition, subtraction, multiplication, and division). Then write the expression for the words
Answers
Expression that has all the four basic mathematical operators can be written as [tex](\dfrac{a+b}{2}) \times [c-(a+b)][/tex].
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Let's take three numbers, a, b, and c.
Now, the expression in the word can be written as, The product of the addition of the first two numbers (a and b), divided by 2 and the sum subtracted from c.
If we try to write the above statement as an expression then we can write it as,
[tex](\dfrac{a+b}{2}) \times [c-(a+b)][/tex]
Hence, An expression that has all the four basic mathematical operators can be written as [tex](\dfrac{a+b}{2}) \times [c-(a+b)][/tex].
Learn more about Expression:
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Final answer:
The computation described involves multiplying six by three, adding eight, subtracting two, and then dividing the result by four. This results in the expression ((6 * 3) + 8 - 2) / 4, incorporating all four basic mathematical operations.
Explanation:
Writing the computation in words for an expression that uses all four operations - addition, subtraction, multiplication, and division - helps in understanding the application of these operations in a complex expression. Here's an example:
First, multiply six by three, then add eight to the product. From this sum, subtract two. Finally, divide the result by four. This sequence of operations involves all four basic mathematical operations.
The corresponding expression for the described computation is: ((6 * 3) + 8 - 2) / 4.
Breaking down the expression:
Multiplication: 6 * 3Addition: + 8Subtraction: - 2Division: / 4If a number is divisible by 2, then it is even. What is the inverse of this statementWhat is the inverse of this statement?
If a number is divisible by 2, then it is not even.
If a number is not divisible by 2, then it is not even.
If a number is not divisible by 2, then it is even.
If a number is even, then it is divisible by 2.
Answers
The inverse of the statement "If a number is divisible by 2, then it is even" is "If a number is not divisible by 2, then it is not even." According to logical operations in mathematics, an inverse involves both swapping and negating the components of the original statement.
Explanation:In the field of mathematics, the inverse of a statement swaps both the hypothesis and the conclusion, and applies a negation to them. The original statement given is, "If a number is divisible by 2, then it is even". The inverse of this statement switches and negates the components, resulting in: "If a number is not divisible by 2, then it is not even". Therefore, the second provided option is the correct one.
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The coordinates of the vertices of trapezoid EFGH are E(-8, 8), F(-4, 12), G(-4, 0), and H(-8, 4). The coordinates of the vertices of trapezoid E’F’G’H’ are E’(-8, 6), F’(-5, 9), G’(5, 0), and H’(-8, 3).
Which statement correctly describes the relationship between trapezoid EFGH and trapezoid E’F’G’H’?
a) Trapezoid EFGH is congruent to trapezoid E’F’G’H’ because you can map trapezoid EFGH to trapezoid E’F’G’H’ by reflecting it across the x-axis and then translating it up 14 units, which is a sequence of rigid motions.
b) Trapezoid EFGH is congruent to trapezoid E’F’G’H’ because you can map trapezoid EFGH to trapezoid E’F’G’H’ by translating it down 2 units and then reflecting it over the y-axis, which is a sequence of rigid motions
c) Trapezoid EFGH is congruent to trapezoid E’F’G’H’ because you can map trapezoid EFGH to trapezoid E’F’G’H’ by dilating it by a factor of 34 and then translating it 2 units left, which is a sequence of rigid motions
d) Trapezoid EFGH is not congruent to trapezoid E’F’G’H’ because there is no sequence of rigid motions that map trapezoid EFGH to trapezoid E’F’G’H’.Answers
Answer:
D
Step-by-step explanation:
1) We have and isosceles trapezoid DEFG and and another trapezoid D'E'F'G' dilated.
2) E'F'G'H' is not congruent to EFGH (due to its legs) Besides that, E'F'G'H has undergone not to rigid motions. Rigid motions are better known as translations and rotations and they preserve length and angles. That was not the case.
(Check graph 2)
3) So it's d, the only correct choice:
d) Trapezoid EFGH is not congruent to trapezoid E’F’G’H’ because there is no sequence of rigid motions that map trapezoid EFGH to trapezoid E’F’G’H’.
A 8920 note is signed for 160 days at a rate of 6.5% find the proceeds
Answers
If the note is dicounted, the proceeds will be 8920 less the interest due.
.. P(1 -rt)
.. = 8920*(1 -0.065*160/360) = 8662.31
The proceeds on a discounted note are $8662.31.
_____
If "exact" interest is used, then t=160/365 and the proceeds are 8665.84.
A woman borrows $6,000 at 9% compounded monthly, which is to be amortized over 3 years in equal monthly payments. for tax purposes, she needs to know the amount of interest paid during each year of the loan. find the interest paid during the first year, the second year, and the third year of the loan. [hint: find the unpaid balance after 12 payments and after 24 payments.
Answers
The first Earth Day was observed on April 22, 1970. Since then, the week of April 22 has been Earth Week, a time for showing support for environmental causes. Fans Cafe is offering a reduced refill rate for soft drinks during Earth Week for anyone purchasing a Fans mug. The mug costs $2.95 filled with 16 ounces of soft drink. The refill price is $0.50. A 16-ounce drink in a disposable cup costs $0.85. What is the approximate break-even point for buying the mug and refills in comparison to buying soft drinks in disposable cups? a. (5, 7.8) c. (4, 6.7) b. (8, 0.5) d. (7, 5.95)
Answers
Let x specify the number of 16 ounce serving
If you buy the mug you acquire the first serving including the mug.
So the price of x is:
295 + 50(x - 1)
the x - 1 here shows that the first serving with the mug.
And then count the whole thing in cents.
The fee of throwaway cups is 85x
So breakeven is computed by:
295 + 50(x - 1) = 85x
295 + 50x - 50 = 85x
245 = 35x
x = 245/35 = 7
Checking this will give us:
mug 2.95 + 50*6 = 5.95
disposable
8.5*7 = 5.95
So the answer is D.
The break-even point occurs after nine soft drink purchases(8,0.5). Hence, the correct option is b.
First, let's consider the cost of the mug with a soft drink:
Mug + Soft drink = $2.95
Next, the cost of each refill:
Refill = $0.50
Then, the cost of a soft drink in a disposable cup:
Disposable cup soft drink = $0.85
To find the break-even point, let's set up the equation. Let x be the number of refills (including the initial drink from the mug):
Cost of mug with initial drink + (Cost per refill × number of refills) = Cost of disposable cup × number of drinks
2.95 + 0.50x = 0.85x
Now we solve for x:
2.95 = 0.85x - 0.50x
2.95 = 0.35x
x = 2.95 / 0.35
x = 8.43
Since we cannot have a fraction of a refill, we will round up to the nearest whole number. Therefore, the break-even point is after 9 refills (including the initial drink from the mug).
The approximate break-even point is after purchasing nine 16-ounce drinks. Therefore, the correct answer is (8, 0.5).
Yul and Sarah's art class started at 11:25 A.M.The class lasted 30 minutes. Yulieft when the class was done. Sarah stayed an extra 5 minutes to talk with the teacher and then left. Write the time that each student left.Explain how you found each time.
Answers
We know that class lasts 30 minutes.
First of all, let's find the time class ends.
11:25 AM (class starts) + 00:30 (minutes) = 11:55 AM (class ends)
Let's start with Yul's time first.
We know that Yul left when class was done, the time was already calculated when we added the time the class started with the time the class lasted and we got (in the previous line) 11:55 AM was when class ended, therefore, Yul left at 11:55 AM.
Sarah stayed an extra 5 minutes.
Class ended 11:55 AM. Simply add 5 minutes (00:05) to 11:55 AM.
11:55 AM (time class ended) + 00:05 (extra time to talk with the teacher) = 12:00 PM. Therefore, Sarah left at 12:00 PM.
As stated in the beginning of this problem, each hour only lasts 60 minutes, not 100 minutes, so every time the minutes are at the 60 tick mark, a new hour starts (in this case, 12:00 PM).
Yul left at 11:55 AM.
Sarah left at 12:00 PM.
Yul left the class at 11:55 A.M. after it ended, having added 30 minutes to the start time. Sarah stayed for an extra 5 minutes, which implies she departed at 12:00 P.M.
Yul and Sarah's art class started at 11:25 A.M. and it lasted 30 minutes. To find out when Yul left, we simply add 30 minutes to the starting time. Starting at 11:25 A.M., after 30 minutes, it will be 11:55 A.M. That's when Yul left the class.
Sarah stayed an additional 5 minutes after the class to talk with the teacher. So, we add those 5 minutes to the time Yul left, which was 11:55 A.M. If we add 5 minutes to 11:55 A.M., it becomes 12:00 P.M. Therefore, Sarah left the class at noon.