Jerry was using matrices to solve the system of three equations. He has shown all his steps. Did he make a mistake if so in what step.
Answers
Answer:
Step 3
Step-by-step explanation:
There are several ways to solve a system of equation; one of these ways is the use of matrix.
Jerry made a mistake at step 2
From the attachment, the step 1 is represented as:
\(\mathbf{\frac 12R_1 \left[\begin{array}{cccc}1&1&1&0\\5&3&-2&-4\\3&2&1&1\end{array}\right] }\)
The equation in step 2 is given as:
\(\mathbf{R_2 = 5R_1 - R_2}\)
This means that:
We subtract the elements of row 2 from the elements of row 1, multiplied by 5
So, we have:
\(\mathbf{R_2 = 5\left[\begin{array}{cccc}1&1&1&0\end{array}\right] } - \left[\begin{array}{cccc}5&3&-2&-4\end{array}\right] }\)
Expand
\(\mathbf{R_2 = \left[\begin{array}{cccc}5&5&5&0\end{array}\right] } - \left[\begin{array}{cccc}5&3&-2&-4\end{array}\right] }\)
Subtract corresponding cells
\(\mathbf{R_2 = \left[\begin{array}{cccc}0&2&7&4\end{array}\right] }\)
So, the new row 2 elements should be:
\(\mathbf{ \left[\begin{array}{cccc}0&2&7&4\end{array}\right] }\)
However, the row 2 elements of Jerry's steps are:
\(\mathbf{R_2 = \left[\begin{array}{cccc}0&-2&-7&-4\end{array}\right] }\)
This means that:
Jerry made a mistake; and the mistake is at step 2
Read more about matrix at:
https://brainly.com/question/21848291
Related Questions
Match each expression with A, B, C or D.
A=a^3
B=6a
C=12a
D=3a^2
i)3a x 4
ii)a^2xa
iii) 6 1/2 a^2
Answers
The matching expressions are:
\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)
i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.
ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.
iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.
To understand the matching expressions, let's break down each one:
i) 3a x 4:
This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).
ii) a^2 x a:
This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).
iii) 6 × 1/2 a^2:
This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).
Therefore, the matching expressions are:
i) 3a x 4 = C (12a)
ii) a^2 x a = A (a^3)
iii) 6 × 1/2 a^2 = D (3a^2)
for such more question on matching expressions
https://brainly.com/question/12270624
#SPJ8
What are the foci of the graph x^2/40-y^2/81=1
Answers
Answer:
Step-by-step explanation:
(y^2)/1600-(x^2)/81=1. y21600−x281=1 y 2 1600 - x 2
Answer: y21600x281=1 y 2 1600 - x 2
Step-by-step explanation: for sure chfjjgffjfj ;)
In the pattern shown below Day 1 has 4 night eyes,
followed by Day 2 with 8 night eyes, and Day 3 with 16
night eyes, how many eyes will there be on Day 25?
Explain using words or numbers a pattern that you see in
the picture below and write it in complete sentences.
Answers
Answer:
The pattern that we know is:
D₁ = 4 night eyes
D₂ = 8 night eyes
D₃ = 16 night eyes
Ok, with these 3 elements we can see that this seems like a geometric sequence.
How we test it? well, the quotient between any pair of consecutive terms must be constant.
D₂/D₁ = 8/4 = 2
D₃/D₂ = 16/8 = 2
Then we can write the n-th term as:
Dₙ = D₁*2^(n-1) = 4*2^(n-1)
Then in day 25, we have n = 25.
Then the term is:
D₂₅ = 4*2^(24) = 67,108,864 night eyes
Please help me! I'm really stuck on this question!
Answers
i think the answerd is a
(3, 4, 5, ...} is finite or infinite
Answers
The given set is (3, 4, 5, ...} is infinite set.
A set with an infinite number of elements is one that cannot be numbered. A set that has no last element is said to be endless. A set that can be put into a one-to-one correspondence with a suitable subset of itself is said to be infinite. No issue with the in-class assignment.
The stars in the clear night sky, water droplets, and the billions of cells in the human body are just a few examples of endless sets of objects that surround us. A set of natural numbers, however, serves as the best illustration of an infinite set in mathematics. There is no limit to the amount of natural numbers.
Learn more about infinite here
https://brainly.com/question/3928632
#SPJ9
Emilio is pickling tomatillos with his grandfather. The tomatillos are approximately
spheres with a diameter of 6 cm. The pickling jar they are using has a diameter of
8 cm and a height of 21 cm. The jar can hold 3 tomatillos.
Answers
The jar can hold a total of three tomatoes at a time.
What is volume?
Volume is the amount of space occupied by a three dimensional shape or object.
The tomatoes is spherical with a diameter of 6 cm (radius = 6/2 = 3cm), hence:
Volume of tomatoes = (4/3) * π * radius³ = (4/3) * π * 4³ = 268 cm³
The jar is cylinder with diameter of 8 cm (radius = 8/2 = 4) and a height of 21 cm, hence:
Volume of jar = π * radius² * height = π * 4² * 21 = 1055.6 cm³
Amount of tomatoes that can be contained in jar = 1055.6 cm³ / 268 cm³ = 3.9
The jar can hold a total of three tomatoes at a time.
Find out more on volume at: https://brainly.com/question/12410983
Answer:
228\pi
Step-by-step explanation:
1 and two-thirds minus 2 and one-third
Answers
Answer:
The answer is -2/3.
Hope this helps and if you could mark as brainliest. Thanks!
write an equation of a line that is perpendicular to y-4=2(x-6) and passes through the point (-3,-5)
Answers
Anempt 1012
Find the mean for the given set of data.
-4,-3,-1,-1, 0,1
Answers
Answer:
-1 1/3
Step-by-step explanation:
To find the mean, add up all the numbers
(-4+-3+-1+-1+0+1) =
-8
Then divide by the number of terms
-8/6
-4/3
-1 1/3
Answer A is your answer
Step-by-step explanation:
I want to double-check my answer. I think it may be wrong. I need this ASAP. Have a great day.
Answers
This is not the correct answer.
1. 2.30 is not even close to the point given in the number line.
2. My guess for the correct answer would be 0.23 because in between 0.2 and 0.3 is 0.25, so the best answer would be 0.23.
10.8.8 Check Your Understanding
Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to
park her car. Each night, the hotel charged d dollars and $17.20 for parking. Which equation represents the total
amount, in dollars, Allison paid for the three nights?
A) d+3(17.20) = 782.07
(B) 3d+17.20 = 782.07
C) 3(d-17.20) = 782.07
D) 3(d+17.20) = 782.07
Answers
We can see that the correct equation that can depict the problem is 3(d+17.20) = 782.07. Option D
Which equation shows the total charge?We have to look at the problem that we have here. In the case of the question that we have been asked, we can see that for the problem that has been given here, it is clear that; Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to park her car.
If it is known that Each night, the hotel charged d dollars and $17.20 for parking. We can say that let the amount that is charged for the lodging be d and we have the equation as; 3(d+17.20) = 782.07.
Learn more about equation:https://brainly.com/question/29657983
#SPJ1
which expressions are equivalent to 3^4/9/3^2/9? select all that apply
Answers
Answer:
first and third expressions
Step-by-step explanation:
using the rule of exponents
\(\frac{a^{m} }{a^{n} }\) = \(a^{m-n}\)
then
\(\frac{3^{\frac{4}{9} } }{3^{\frac{2}{9} } }\)
= \(3^{\frac{4}{9}-\frac{2}{9} }\) ← first expression
= \(3^{\frac{2}{9} }\) ← third expression
Work out m and c for the line: 3 y + 2 x = − 1
Answers
Answer:
Step-by-step explanation:
graphing in the image
Answers
Answer:
It would be C because it moves to the negative side and but still stays at 0 so it would be (-4,0)
Answer:
C
Step-by-step explanation:
The answer is c bcs dot J is moving to 4 units left when we go to the left or down below of the 0 is negative
hi how do i integrate this?
Answers
The expression gotten from integrating the trigonometry function ∫sec²(2x)tan²(2x) dx is tan³(2x)/6 + C
How to integrate the trigonometry functionFrom the question, we have the following trigonometry function that can be used in our computation:
∫ sec^2(2x)tan^2(2x) dx
Express properly
So, we have
∫sec²(2x)tan²(2x) dx
When integrated using a graphing tool, we have
∫sec²(2x)tan²(2x) dx = tan³(2x)/6 + C
Where C is a constant value
Hence, integrating the trigonometry function ∫sec²(2x)tan²(2x) dx gives tan³(2x)/6 + C
Read more about derivatives at
https://brainly.com/question/5313449
#SPJ1
The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with electronic trades handled by discount brokers. As part of die survey, members were asked to rate members were asked to rate their satisfaction with the trade price and the speed of execution, as well as provide an overall satisfaction rating. Possible responses (scores) were no opinion (0), unsatisfied (1), somewhat satisfied (2), satisfied (3), and very-satisfied (4). For each broker, summary scores were computed by computing a weighted average of die scores provided by each respondent. A portion the survey results follow (AAII Web site. February 7, 2012). Develop an estimated regression equation using trade price and speed of execution to predict overall satisfaction with the broker. Interpret die coefficient of determination. Use the F test to determine die overall significance of the relationship. What is your conclusion at the 0.05 level of significance? Use the t test to determine the significance of each independent variable? What are your conclusions at the 0.05 level of significance? Interpret the estimated regression parameters. Are die relationships indicated by these estimates what you would expect? Finger Lakes Investments has developed a new electronic trading system and would like to predict overall customer satisfaction assuming they can provide satisfactory service levels (3) for both trade price and speed of execution. Use the estimated repression equation developed in part a to predict overall satisfaction level for Finger Lakes Investments if they can achieve these performance levels. What concerns (if any) do you have with regard to die possible responses the respondents could select on the survey.
Previous question
Answers
The estimated regression equation developed in part (a) was found to be an effective predictor of overall customer satisfaction, as indicated by the significant F and t test results.
The estimated regression equation developed in part (a) to predict overall customer satisfaction is given by:
Overall Satisfaction = 0.3151*Trade Price + 0.3132*Speed of Execution + 1.5026
The coefficient of determination (R2) is a measure of how well the equation fits the data and is calculated as the proportion of the variation in overall satisfaction that is explained by the model. In this case, the R2 = 0.39, which means that 39% of the variation in overall satisfaction can be explained by the trade price and speed of execution variables.
To determine the overall significance of the relationship, the F test was used. The F statistic was calculated to be 17.874, which was significant at the 0.05 level (p-value = 0.000), indicating that the model was an effective predictor of overall customer satisfaction.
The t tests were then used to determine the significance of each independent variable. The t statistic for Trade Price was 2.639 (p-value = 0.009), indicating that the variable was significant at the 0.05 level, while the t statistic for Speed of Execution was 2.565 (p-value = 0.012), indicating that the
The estimated regression equation developed in part (a) was found to be an effective predictor of overall customer satisfaction, as indicated by the significant F and t test results.
Learn more about regression equation here:
https://brainly.com/question/30738733
#SPJ4
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Your local gas stations are having a price war. During the past 7 days they have lowered the price of regular gas by $.02 each day. Define a variable. Then write and solve an equation to find the total change in gas price. Show your work.
Answers
Enter your answer and show all the steps that you use to solve this problem in the space provided. Your local gas stations are having a price war. During the past 7 days they have lowered the price of regular gas by $.02 each day. Define a variable. Then write and solve an equation to find the total change in gas price. Show your work.
step 1
define the variables
x -----> number of days
y ----> the total charge
P ---> intial price before the 7 days
the linear equation in slope intercept form is equal to
y=mx+b
In this problem we have
m=-0.02 ( is teh slope or unit rate)
b=P ( is the y-intercept or initial value)
substitute
y=-0.02x+P
For x=7 days
y=-0.02*(7)+P
y=-0.14+P ----> this is the equation for the price after 7 daysthe total change in 7 days is -$0.14Determine the values of x in the equation x2 = 64.
Answers
Explain= When a variable(the letter next to the number in this case the “x”) is placed next two a coefficient(the number next to a variable, in this case “2”), that means the variable is being multiplied by that number. To solve for x, we must divide the sum of x2 (64) by the coefficient. The number will equal x.
x2=64? X = 32!
1. Global warming creates local problems. Projections forecast that even a moderate air temperature increase of only 1.8 °F could cause brook trout distributions to decrease dramatically. For example, such a temperature increase would take Washburn county's 19 ponds that support brook trout down to 10 ponds. What would be the percent decrease in the number of ponds that support brook trout?
Answers
The percent decrease in the number of ponds that support brook trout would be approximately 47.37%.
To calculate the percent decrease in the number of ponds that support brook trout, we need to determine the difference between the initial number of ponds and the final number of ponds, and then express that difference as a percentage of the initial number of ponds.
Initial number of ponds: 19
Final number of ponds: 10
To calculate the percent decrease, we can use the following formula:
Percent Decrease = (Difference / Initial Value) * 100
Let's apply this formula to the given data:
Difference = Initial number of ponds - Final number of ponds
Difference = 19 - 10
Difference = 9
Percent Decrease = (9 / 19) * 100
Now, let's calculate the percent decrease:
Percent Decrease = (9 / 19) * 100
Percent Decrease ≈ 47.37%
For such more question on number:
https://brainly.com/question/30752681
#SPJ8
Plz help BRAINLIEST
Which situation most likely cannot be represented by a linear function?
Anna gets paid $10 per hour.
Briar gets paid $100 for the day.
Constance gets paid whatever her Dad feels like giving her for that day, and this is partially based on how long she works.
Danica gets paid $20 for the day, plus $7 per hour.
Answers
i need help, no links please
Answers
Answer:
a
Step-by-step explanation:
Which inequality is the solution to 20+2 <
Ž -8?
Answers
Answer:
the 20 +2
Step-by-step explanation:
what is the surface area for this figure
Answers
The surface area of the triangular prism is 313.47 cm².
Given is a triangular prism, we need to find the surface area,
A triangular prism is a 3D shape with two identical faces in the shape of a triangle connected by three rectangular faces. The rectangular faces are referred to as the lateral faces, while the triangular faces are called bases. The bases are also called the top and the bottom (faces) of the prism.
Triangular Prism Meaning: A triangular prism is a 3D polyhedron with three rectangular faces and two triangular faces. The 2 triangular faces are congruent to each other, and the 3 lateral faces which are in the shape of rectangles are also congruent to each other. Thus, a triangular prism has 5 faces, 9 edges, and 6 vertices. Observe the following image of a triangular prism in which l represents the length of the prism, h represents the height of the base triangle, and b represents the bottom edge of the base triangle.
so, the surface area of a triangular prism =
perimeter × length + 2 × base area
So,
SA = (4.5+7.2+9) × 8.1 + 2 × 8.1 × 9
= 167.67 + 145.8
= 313.47
Hence the surface area of the triangular prism is 313.47 cm².
Learn more about surface area click;
https://brainly.com/question/29298005
#SPJ1
una persona cobra 7/4 de una cantidad, gasta 1/4 y presta 1/8 ¿Que fraccion de la cantidad cobrada le quedo?
Answers
Answer: (11/8)
Step-by-step explanation:
I will answer this in English.
a person collects 7/4 of an amount, spends 1/4 and lends 1/8. What fraction of the amount collected is left?
If the amount is A, then he collects:
C = (7/4)*A
Now, he spends 1/4 and lends 1/8 of the amount A, so the fraction left is:
Left = (7/4)*A - (1/4)*A - (1/8)*A
now i will write 7/4 as 14/8 and 1/4 as 2/8.
left = (14/8)*A - (2/8)*A - (1/8)*A = ((14 - 2 - 1)/8)*A = (11/8)*A
Determine if the number is a negative or positive integer. Dived 28 ft below sea level. *
Answers
Answer:
Its BELOW sea level
Step-by-step explanation:
KHAN ACADEMY LESSON HELP ME : Two-step inequality word problems
Answers
Answer: d> 5 1/2
Step-by-step explanation:
34 + (12 × d) > 100
34 + 12d > 100
12d > 100 - 34
12d > 66
d > 66 / 12
d > 5 1/2 days
Therefore, the number of days, (d), it will take Katie to collect over 100 seashells is 5 1/2 days.
I need this solved for x. Just the quick answer I’m checking myself!
Answers
Answer:
126+93=219 180-219=-39
Step-by-step explanation:
or the other way around
Answer:
X = 147
Step-by-step explanation:
Triangle = 180
180 - 126 = 54
93 + 54 = 147
180 - 147 = 33
180 - 33 = 147
X = 147
Given parallelogram ABCD,
find m ZADB.
A
В'
m/DAB = 138°
m/CDB = 23°
mZADB = [?]°
D
![Given parallelogram ABCD,find m ZADB.A'm/DAB = 138m/CDB = 23mZADB = [?]D](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/TuexyP3zJ8AhHfImywK3FpYuvoBhu7ME.png)
Answers
The value of angle ADB in the parallelogram given is 19°
Using the parallelogram laws :
Consecutive angles in a parallelogram are supplementarySupplementary angles adds up to 180°, Hence we can use that to find CDA :
∠ CDA = 180° - ∠ DAB = 180° - 138° = 42°The sum of angles ∠ ADB + ∠ CDB should add up to 42°
∠ ADB + ∠ CDB = 42°
∠ ADB + 23° = 42°
∠ ADB = 19°
Hence, ADB is 19°
Learn more on parallelogram: https://brainly.com/question/31277047
#SPJ1
The coordinates of C are ( 4 , 4 ) , and the midpoint of CD ¯ is at M ( - 2 , - 6 ) . What are the coordinates of point D
Answers
Answer:
D (-8, -16)
Step-by-step explanation:
(4+x)/2 = -2
4+ x = -2 · 2
4 + x = -4
x = -4 - 4
x = -8
(4 + y)/2 = -6
4 + y = -6 · 2
4 + y = -12
y = -12 - 4
y = -16
You borrow $1400 from a friend and promise to pay back
$2000 in two years. What simple interest rate, to the nearest
tenth of a percent, will you pay?
Answers
Answer:
21.4%
Step-by-step explanation:
You would pay back a 21.4%
The simple interest rate on the loan of $1400 is approximately 21.4% per year.
What is the simple interest rate of the loan?The simple interest can be expressed as:
A = P( 1 + rt )
Where A is accrued amount, P is the principal, r is the interest rate and t is time.
Given the parameter:
Principal P = $1400
Accrued amount A = $2000
Time t = 2 years
Interest rate r =?
Plug these values into the above formula and solve for the interest rate.
A = P( 1 + rt )
\(r = \frac{1}{t} * ( \frac{A}{P} - 1 ) \\\\r = \frac{1}{2} * ( \frac{2000}{1400} - 1 ) \\\\r = \frac{1}{2} * ( \frac{2000}{1400} - 1 ) \\\\r = 0.21428\)
Convert r decimal to R a percentage
R = 0.214 × 100
R = 21.4% per year
Therefore, the rate is approximately 21.4% per year.
Learn more about simple interest here: brainly.com/question/25845758
#SPJ2