If F(x,y,z)=(2x + y, x+z, y-z), G (x,y,z)=(x-z, y-z, x+2y) and the matrix of F o G in the canonical basis is *IMAGE*, then a+b+c+d+e is:
Answers
Solution
We are given
\(\begin{gathered} F(x,y,z)=(2x+y,x+z,y-z) \\ Writing\text{ out the associated matrix with respect to the canonical basis.} \\ Let\text{ the matrix be A} \\ \\ \\ A=\begin{bmatrix}{2} & {1} & {0} \\ {1} & {0} & {1} \\ {0} & {1} & {-1}\end{bmatrix} \end{gathered}\)The function
\(\begin{gathered} G(x,y,z)=(x-z,y-z,x+2y) \\ Writing\text{ the associated matrix for G} \\ Let\text{ the matrix be B} \\ \\ B=\begin{bmatrix}{1} & {0} & {-1} \\ {0} & {1} & {-1} \\ {1} & {2} & {0}\end{bmatrix} \end{gathered}\)Thus, to find F o G
\(\begin{gathered} FoG=AB \\ \\ FoG=\begin{bmatrix}{2} & {1} & {0} \\ {1} & {0} & {1} \\ {0} & {1} & {-1}\end{bmatrix}\begin{bmatrix}{1} & {0} & {-1} \\ {0} & {1} & {-1} \\ {1} & {2} & {0}\end{bmatrix} \\ \\ FoG=\begin{bmatrix}{2} & {1} & {-3} \\ {2} & {2} & {-1} \\ {-1} & {-1} & {-1}\end{bmatrix} \end{gathered}\)Comparing with M
It follows that
\(\begin{gathered} a=2 \\ b=2 \\ c=-1 \\ d=-1 \\ e=-1 \end{gathered}\)Therefore, the answer is
\(\begin{gathered} a+b+c+d+e=2+2-1-1-1 \\ \\ a+b+c+d+e=1 \end{gathered}\)
Related Questions
Mako runs 10 miles in 2 hours. If he continues at this rate, how many miles
will he run in 5 hours?
A. 50 miles
B. 10 miles
O C. 25 miles
O D. 30 miles
Answers
Answer:
Answer: 25 miles
Step-by-step explanation:
Explanation: He will run 5 hours= 5x5=25
Answer:
25 miles
Step-by-step explanation:
I'll create a set of proportions to figure out the answer (represented by x):
2:10 = 5:x
It looks like our proportion on the left, 2:10, can be simplified by dividing both sides by 2 to get 1:5.
1:5 = 5:x
You can multiply 1 by 5 to get 5, so we should be able to multiply 5 by 5 to get the value of x. 5 times 5 is 25, so the answer to the question is 25 miles.
If you have questions or need clarification on anything, let me know!
The irrigation design for a new backyard is shown with six sprinkler heads and two walkways. Which statement is true of this design? The area covered by each sprinkler head is approximately 113.10 ft2. The area covered by all the sprinkler heads together is approximately 169.64 ft2. Every square foot of the yard will be watered with this design. The sprinklers would cover more area if they were in a straight line.
Answers
Answer:B on edge
Step-by-step explanation:
Option third "The area covered by all the sprinkler heads together is approximately 169.64 ft2" is correct.
What is a circle?It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).
We have:
The distance between grid lines is 2 ft
As we can see from the figure each sprinkler head consists of 3 grid squares.
It means the diameter of each sprinkler head = 3×2 = 6 ft
The radius is half of the diameter = 6/2 ⇒ 3 ft
We know the area of the circle is given by:
\(\rm A = \pi r^2\)
The area of each sprinkler head:
\(\rm A = \pi \times 3^2\)
A = 9π square ft or
A = 28.2743 square ft
The total sprinkler head = 6
Now the total area covered by all the sprinkler heads together:
= 6×28.2743
= 169.64 square ft.
Thus, option third "The area covered by all the sprinkler heads together is approximately 169.64 ft2" is correct.
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3x + 4 - x = 2 (2x + 3) how many solutions'
Answers
Answer:This problem has one solution.
Step-by-step explanation:If you solve the equation you will get x=-1
Answer:
two solution
Step-by-step explanation:
On a 30 question test, Janice answered four-fifths of the questions correctly-
Which of the following is the number of questions she answered correctly?
A.26
B.24
C.38
D.25
Answers
The lengths of the sides of a triangle are 3 , 4 , 5 Classify the triangle as acute, right, or obtuse.
Answers
need to solve for Y by filling in the blanks
(y +44)°, 86, (3y)°
Answers
1.89
Solution:
We have -44x - 86 = -3
First, we move the non x terms to the RHS of the equation. To do this, we add 86 to both sides.
Note: if a = b, then a + c = b + c
Therefore, -44x - 86 + 86 = -3 + 86
or, -44x = 83
Next, divide both sides by -44, which is the coefficent of x
Note: if a = b, then a ÷ c = b ÷ c
-44x
-44
=
83
-44
or, x = -1.89
Explaination:
This is right I guess
If 18% of a $3,200.80 monthly net income is allotted for clothing, how much money is allotted for clothing in one year?
Answers
Answer:
Step-by-step explanation:
18% of $3200.80 = $576.144.
$576.144 is for one month. So, for a year is 12 * $576.144 = $6913.728.
answer all you get brainiest
Answers
Step-by-step explanation:
1. 44
2. 26 95
3. 294
4. 126
5. 36.04
6. 52.02
If 2x + 5 = 82, then 12x = ?
A 5
B
10
C 15
D 20
Answers
Answer:
2x= 38.5
Step-by-step explanation:
I'm not sure where u got 12x but 2 x = 38.5:
2x + 5 =82
subtract 5 for 82
2x = 77
77 divided by 2 is 38.5
x = 38.5
hope this helps :)
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with grams of a radioactive isotope, how much will be left after 4 half-lives?
Answers
After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.
The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:
Amount remaining = Initial amount × (1/2)^(number of half-lives)
In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.
So, the equation becomes:
Amount remaining = Initial amount × (1/2)^4
Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.
Simplifying the equation:
Amount remaining = Initial amount × (1/16)
Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.
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F(x) =∛2x g(x)=3x+1 Find (f/g) (x) Include any restrictions on the domain
Answers
Answer:
x ≠ -1/3
Step-by-step explanation:
(f/g)(x) = f(x)/g(x) = ∛2x/(3x+1)
since division by zero is undefined,
Answer:
Step-by-step explanation:
x = - 1/2
PLEASE HELP FAST !!!!!
The distribution of pitches thrown in the
80 at-bats in a baseball game is as follows.
Pitches 1 2 3 4 5
Frequency 12 16 32 12 8
Find the relative frequency that the pitcher
will throw exactly 4 pitches in an at-bat.
?
Relative Frequency =
Do NOT simplify your answer.
Answers
The relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:
3/20.
How to calculate a relative frequency?A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.
The total number of at bats in this problem is given as follows:
80.
In 12 of them, the pitcher threw exactly four pitches, hence the relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:
12/80 = 3/20.
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what is the present value of $400 invested each year for 12 years at a rate of 6%?
Answers
The present value is $804.84.
What is Present value?The term "present value" refers to the current value of an amount that will be charged with compound interest in the future. With the information provided, the present value can be estimated as follows:
PV= FV x 1/ \((1+r)^n\)
Given:
FV= $400
T= 12 years
r= 6
Now,
PV = 400 x 1/ \((1+0.06)^{12\)
PV = 400 x \(1.06^{12\)
PV = 400 x 2.0121
PV= 804.84
Hence, the present value is $804.84.
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what is the answer I need help
Answers
Answer:
Step-by-step explanation:
The vertex is at (-3, -1) and the leading coefficient is negative ( because the curve is inverted)
y = -a(x + 3)^2 - 1
One point on the curve is (-2, -3) so
-3 = -a(-2+3)^2 - 1
-3 = -a - 1
-a = -2
So we have
y = -2(x + 3)^2 - 1
y = -2(x^2 + 6x + 9) - 1
y = -2x^2 - 12x - 19.
Without solving, identify whether each of the following equations has a unique solution, no solution, or infinitely many solutions.
3.2 + 6 = -8
0 1 solution
O No Solution
O Infinite solutions
Answers
Answer:
No solution
Step-by-step explanation:
A certain disease has an incidence rate of 0.3%. If the false negative rate is 6% and the false positive rate is 4%, compute the probability that a person who tests positive actually has the disease.
Answers
The probability that a person who tests positive actually has the disease is 0.012%
How to determine the probability?From the question, we have the following parameters that can be used in our computation:
Incidence rate = 0.3%False negative rate = 6%False positive rate = 4%The probability that a person who tests positive actually has the disease is represented as
Probability = Incidence rate * False positive rate
Substitute the known values in the above equation, so, we have the following representation
Probability = 0.3% * 4%
Evaluate the products
Probability = 0.012%
Hence, the probability is 0.012%
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A painter leans an 18 foot ladder against the house so that the base of the ladder is 4 feet away from the wall. Approximately how far up the side of the house does the ladder reach?
Answers
Answer: 17.5ft
Step-by-step explanation:
Use Pythagorean theorem
A^2 + B^2 = c^2 where c is the hypotenuse
The ladder leaning against the wall is the hypotenuse.
4^2 + b^2 = 18^2
16 + b^2 = 324
324-16 = b^2
308 = b^2
B = 17.5ft
At a running race, the ratio of female runners to male runners is 3 to 2. There are 75 more female runners than male runners.
Determine which of the equations could be used to solve for the amount of male runners (m) in the race and which could not. Select True or False for each statement.
Answers
The equations that could be used to solve for the number of male runners (m) in the race are (m+75)/m = 3 / 2 and 150 + 2m = 3m. The correct options are A and B.
What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.
Given that at a running race, the ratio of female runners to male runners is 3 to 2. There are 75 more female runners than male runners.
The ratio is written as,
f/ m = 3 / 2
There are 75 more female runners than male runners.
f = m + 75
The equation can be written as,
f / m = 3 / 2
( m + 75 ) / m = 3 / 2
Or
150 + 2m = 3m
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Consider the function f whose graph is shown below
Answers
Answer:
domain - -9 <x < 7
range - -6 < y < 4
Step-by-step explanation:
Based only on the information given one the diagram which congruence theorems or postulates could be given as reasons why abc=uvw
Answers
Answer:
(B) and (D)
Step-by-step explanation:
It is given that there are two triangles ABC and UVH, then
From ΔABC and ΔUVH, we have
∠A=∠U(Each90°)
AC=UH (Given)
∠C=∠H (Given)
Thus, by ASA rule of congruency,
ΔABC≅ΔUVH
Also, From ΔABC and ΔUVH, we have
If the leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent, thus
AC=UH, then ΔABC≅ΔUVH (By LA rule)
therefore, option B and D are correct.
I hoped dis helped you stay safe!
Um what is the answer to this picture right here .
Answers
Answer: D
Step-by-step explanation:
the train travels 558 miles in 3 hours. At this rate, how far does the train travel?
b) per 2.5 hours?
Answers
Answer:
186 mph
Step-by-step explanation:
Miles per hour means miles divided by hour(s), so 558/3 is 186 miles per hour.
Answer:
186 mph in 3 hours, 232.2 in 2.5 hours.
Step-by-step explanation:
You divide the miles by hours, for example, 100 miles in 5 hours, said person would be going 20mph. Hopefully this helps, have a good day, good luck with whatever youre doing !!
DUE IN 30 MINS (6th grade) PLEASE PLEASE HELP ME ASAAP
The ages of people visiting a senior center one afternoon are recorded in the line plot.
A line plot titled Ages At Senior Center. The horizontal line is numbered in units of 5 from 40 to 95. There is one dot above 45 and 80. There are two dots above 70 and 85. There are three dots above 75.
Does the data contain an outlier? If so, explain its meaning in this situation.
No, there is no outlier. This means that the people were all the same age.
No, there is no outlier. This means that the people are all around the mean age.
Yes, there is an outlier of 45. This means that the average person at the center is 45 years old.
Yes, there is an outlier of 45. This means that one person's age was 45, which is 25 years younger than the next closest age
{Please follow the rules Dos and Don't}
Do :
Answer the question correctly
Leave a positive Comment
Make sure you have reviewed it before submitting
Don't
Answer incorrectly
Be Rude to the community
Spam/Send links to inappropriate Websites
Answers
Answer: Yes, there is an outlier of 45, This means that one person's age was 45, which is 25 years younger than the next closest age.
Hope this helps! :)
Step-by-step explanation:
Answer:
D
GIVE HIME BRAINLIEST
Step-by-step explanation:
Calculus hw, need help asap with steps.
Answers
Answers are in bold
S1 = 1
S2 = 0.5
S3 = 0.6667
S4 = 0.625
S5 = 0.6333
=========================================================
Explanation:
Let \(f(n) = \frac{(-1)^{n+1}}{n!}\)
The summation given to us represents the following
\(\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=\sum_{n=1}^{\infty} f(n)\\\\\\\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=f(1) + f(2)+f(3)+\ldots\\\\\)
There are infinitely many terms to be added.
-------------------
The partial sums only care about adding a finite amount of terms.
The partial sum \(S_1\) is the sum of the first term and nothing else. Technically it's not really a sum because it doesn't have any other thing to add to. So we simply say \(S_1 = f(1) = 1\)
I'm skipping the steps to compute f(1) since you already have done so.
-------------------
The second partial sum is when things get a bit more interesting.
We add the first two terms.
\(S_2 = f(1)+f(2)\\\\S_2 = 1+(-\frac{1}{2})\\\\S_2 = \frac{1}{2}\\\\S_2 = 0.5\\\\\\\)
The scratch work for computing f(2) is shown in the diagram below.
-------------------
We do the same type of steps for the third partial sum.
\(S_3 = f(1)+f(2)+f(3)\\\\S_3 = 1+(-\frac{1}{2})+\frac{1}{6}\\\\S_3 = \frac{2}{3}\\\\S_3 \approx 0.6667\\\\\\\)
The scratch work for computing f(3) is shown in the diagram below.
-------------------
Now add the first four terms to get the fourth partial sum.
\(S_4 = f(1)+f(2)+f(3)+f(4)\\\\S_4 = 1+(-\frac{1}{2})+\frac{1}{6}-\frac{1}{24}\\\\S_4 = \frac{5}{8}\\\\S_4 \approx 0.625\\\\\\\)
As before, the scratch work for f(4) is shown below.
I'm sure you can notice by now, but the partial sums are recursive. Each new partial sum builds upon what is already added up so far.
This means something like \(S_3 = S_2 + f(3)\) and \(S_4 = S_3 + f(4)\)
In general, \(S_{n+1} = S_{n} + f(n+1)\) so you don't have to add up all the first n terms. Simply add the last term to the previous partial sum.
-------------------
Let's use that recursive trick to find \(S_5\)
\(S_5 = [f(1)+f(2)+f(3)+f(4)]+f(5)\\\\S_5 = S_4 + f(5)\\\\S_5 = \frac{5}{8} + \frac{1}{120}\\\\S_5 = \frac{19}{30}\\\\S_5 \approx 0.6333\)
The scratch work for f(5) is shown below.
help i’m so confused on what’s the difference in rays and lines
Answers
Rays: BD, AC, CA, AB. Lines: AC
How to differentiate between a ray and a line?A line is a straight path of points that has no beginning or end
A ray is a portion of a line which has one endpoint and extends forever in one direction
Let's put the definitions:
Note: the arrow is an indication no endpoint
So we have ray BD (it starts from the dot at B and the arrow shows it extends forever in the direction of D)
We have ray AC (it starts from the dot at A and the arrow shows it extends forever in the direction of C)
We also have ray CA (it starts from the dot at C and the arrow shows it extends forever in the direction of A)
Then ray AB (it starts from the dot at A and the arrow shows it extends forever in the direction of B)
Then line AC (it's bounded by 2 arrows, so it has no endpoint)
Therefore, the rays are BD, AC, CA and AB, and the line is AC. So the 1st option is the answer
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The volume of a rectangular prism is 5,890.625cm3 . if the height is 14.5 cm and the length is 25 cm, with is the value of the width ?
A. 16.25 cm B. 16.5 cm C. 16.75cm D. 16.97cm
Answers
Answer:
Step-by-step explanation:
The answer is A. 16.25cm.
Explanation:-
We know,
The Volume of Prism =height*width*length;
Here, In the question Height and length is given.
So We have to do a simple calculation to find,width=
(Vol of Prism)/Heigth*length;=> 5890.625/(14.5*25)
=>16.25 cm .
We don't need to worry about dimensions because all are in the same cm dimensions.
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Answer:
A. 16.25 cm
Step-by-step explanation:
To solve for the volume of a rectangular prism, we would use the formula V = l·w·h, where:
"l" is the base length
"w" is the base width
"h" is the height of the prism
In this problem, we are given the volume, height, and length of the rectangular prism. That means we need to find the value of w, the base width. To do this, we plug our known values into the equation and solve for w.
5,890.625 = (14.5)(25)w
To get w by itself, we first divide each side of the equation by 14.5. Remember that when you divide a number by itself, they cancel out.
(5,890.625)/(14.5) = (14.5)(25)w/(14.5)
406.25 = (25)w
Next, we can divide each side of the equation by 25 to get our answer.
406.25/25 = (25)w/25
w = 16.25 cm
The number 2/5 is both an blank and an blank
Answers
The number 2/5 is both a ratio and a fraction.
How to describe the numberThe number 2/5 is both a ratio and a fraction. Fractions are meant to signify the numerator and denominator in an expression. in the above expression, we have the denominator as 5 and the numerator as 2.
The expression is also a ratio because it indicates the quantitative relationship between the figures.
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Manuel has brought 24 pounds of dog food. He feeds his dog 3/4 pounds for each meal. For how many meals will the food last ?
Answers
Answer:
32
Step-by-step explanation:
24/(3/4)
Answer:
32 meals
Step-by-step explanation:
24 / (3/4)
Multiply by reciprocal:
24 x (4/3) = 32
A circle has a diameter of 100 cm. which of these is closest to its area? show or explain your reasoning
a. 314 cm
b. 7,854 cm
c. 15,708 cm
d 31,400 cm
Answers
Answer:31r
Step-by-step explanation:
Formula=πd
22/7 × 100
3.14 × 100
314 cm square
Yesterday I went to buy some ice cream because it was on sale for $0.73. While I was there I also wanted to buy some sprinkles to put on top and they were only $0.15! What a bargain!!!! Since everything was so cheap, I also thought that I might want to buy a water bottle that was $2. When I went up to the cashier, they told me that I owed $9. EXCUSE ME?!? I said to them “I thought you all had a sale today, why am I paying $9?.”
how much you should’ve been charged
Answers
Given statement Sale Pricing Confusion solution is :- You should have been charged $2.88, not $9.
Let's break down the costs:
Ice Cream: $0.73
Sprinkles: $0.15
Water bottle: $2.00
The total cost of these three items would be:
$0.73 + $0.15 + $2.00 = $2.88
According to the prices you mentioned, you should have been charged $2.88, not $9. If the cashier told you that you owed $9, it's possible that there was an error in their calculations or that they included other items in your bill. It's best to clarify the discrepancy with the cashier and ask for an explanation or correction.
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