The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
Answers
The solution of the system of equations is:
x = 5t - 4
y = -5t + 1
z = t
Option B is the correct answer.
What is a matrix?A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.
We have,
From the row-echelon form of the augmented matrix of a system of equations, we get,
x + 0y -5z = -4
x - 5z = -4
x = 5z - 4
0x + y + 5z = 1
y + 5z = 1
y = -5z + 1
0x + 0y + 0z = 0
Now,
Put z = t (any real number)
We get,
x = 5t - 4
y = -5t + 1
Thus,
The solutions are:
x = 5t - 4
y = -5t + 1
z = t
Learn more about matrix here:
https://brainly.com/question/28180105
#SPJ1
Related Questions
you do mot have to exsplain the answer i just wat the correct answer
no links please
Answers
Answer:
144
Step-by-step explanation:
if you shift the linear parent function, f(x)=x, left 14 units, what is the equation of the new function
Answers
Answer: This is a horizontal translation so, the equation is f(x) = (x + 5). Whenever you translate to the right it is negative
Step-by-step explanation:
Find the probability that a point chosen at random in the figure will be shaded region. Write your answer as a percentage rounding to yhe nearwst hundreth in percent
Answers
Bess and Carolina and their 14 classmates write their names on cards. The teacher, Miss Scott, picks two cards without replacing the first card. What is the probability that Bess is chosen first and Carolina is chosen second?
Answers
Hs. shhsbsnsjajwjkwjwkwjsnsnnsnenenen
I need help with this ASAP! Its about budgeting.
Answers
Answer:
Step-by-step explanation:
I gave you all of the information to fill out the first page
i also answered some of the questions on the 2nd page. They are written sideways on the page. The other questions I didn’t answer yneed calculations after you add all of the expenses together.
put the amounts from each category I listed in the image and put them into the respective category and get the total for each category. Use those totals to fill out page two. If you get stuck I don’t mind helping but I thought this is the best way to get you started.
HELP ASAP PLS 50!!!!
Identify or mark the missing side or angle that would make triangle ABC a congruent to triangle PDF by SAS
Answers
Answer:
AC = PF
Step-by-step explanation:
3. In the figure, c || d. What are the measures
of 1 and 2
Answers
Answer:
1: 105 degrees
2: 75 degrees
Step-by-step explanation:
2 is a corresponding angle with 75.
1 is supplementary so x+75 = 180
x=105
Which expressions are equivalent to 6x - 18 ?
Answers
c.) 3(2x-6)
Reason:-
3(2x-6) = 6x-18
Answer:
C, D, and E are your answers
3 x 2x = 6x, 3 x 6 = 18
6x - 18
x + 5x = 6x
6x - 18
2 x 3x = 6x
2 x 9 = 18
6x - 18
Please I need help on this problem
Answers
Answer:
148
Step-by-step explanation:
180 is the whole thing and if the inner of one is 16 then the other one is also 16 so u add this and subtract 180-32=148
(16+16=32)
Answer:
C. x=42
Step-by-step explanation:
First find the measurement of missing angles. 126+16=142
180-142=38
Now, 16, 3x and 38 should add up to 180 because it is a line.
16+38+3x=180
54+3x=180
Solve for x.
3x=126
3 = 3
x=42. Hope this helps.
Write a quadratic equation in standard form
Answers
Answer:
s
[tex]4x {}^{2} + 3x - 11 = 0[/tex]
Step-by-step explanation:
Hope it helps :)
You are standing 10 feet away from a tree. There is a cat up in the tree. Your eyes make
a 48 degree angle to look up at the cat. How high is the cat?
Answers
Answer:
11.1 feet
Step-by-step explanation:
person = B cat = C
C
/ |
/ | x
B /_48]________ ______|
|____10ft____|
since we know the adjacent side but want the opposite side, we can use tan(angle)=opp/adj to solve. (make sure to be in degrees lol)
tangent ( 48) = x/10
10 * tan(48) = x
11.1 = x
The cat is 11.1 feet high.
Answer this please I need help.
Answers
Answer:
im not sure about this, but ithink i know how to solve it!
Step-by-step explanation:
you have to take the 10and multiply its self by 70 (10 x 10 x 10 x 10 x10 x 10 x10)
and then take what you got by multiplying that, and multipy by 4.457. then you do they same for the other two, then add them all together :)
I need help on this question. I dont understand it.
Answers
a. The system of equations is given as follows:
35x = 15 + 32x.
The solution is given as follows:
x = 5.
b. The meaning of the solution is that the cost to purchase 5 jackets in each company is the same.
c. Gabriela should choose Anastasia's Monogram, as the function has a lower numeric value when x = 10.
How to model the situation?The cost per jacket for each company is constant, hence a linear function is used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the cost paid per each jacket.b is the y-intercept, representing the design fee, which is a one-time payment.Hence the functions for each company are given as follows:
Anastasias's Monograms: y = 15 + 32x.Monograms Unlimited: y = 35x.The system of equations is used to find when both will have the same cost, as follows:
35x = 32x + 15
3x = 15
x = 5 jackets.
For 10 jackets, the costs are given as follows:
Anastasias's Monograms: y = 15 + 32(10) = $335 -> lower cost.Monograms Unlimited: y = 35(10) = $350.More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
HELPPPPPP PLEASEeeeeeeeeeeeeee
Answers
Answer:
x > 3
Step-by-step explanation:
6x - 2 - 3x + 9 > 16
3x + 7 > 16
3x > 9
x > 3
find the volume of the sphere. r = 3 cm. V= cm^3
Answers
Answer:
113.1 is the volume of the sphere.
Answer:
[tex]volume = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \times 3.14 \times {(3)}^{3} \\ = 113.04 \: {cm}^{3} [/tex]
You have $9 to spend on lip balm and hand sanitizer. The equation $1.5x+2.5y=9$ represents this situation, where x is tubes of lip balm and y is bottles of hand sanitizer. How many tubes of lip balm can you buy when you do not buy any bottles of hand sanitizer?
Answers
Answer:
6 tubes of lip balm
Step-by-step explanation:
We can start solving this problem by isolating the variable x.
Given the equation 1.5x + 2.5y = 9, and we know that y = 0 (because we're not buying any bottles of hand sanitizer), we can substitute this into the equation:
1.5x + 2.5(0) = 9
Simplifying this, we get:
1.5x = 9
To solve for x, we can divide both sides of the equation by 1.5:
x = 9/1.5
x = 6
So we can buy 6 tubes of lip balm if we do not buy any bottles of hand sanitizer
If the simple interest on a sum of a money invested at 3. 5% per annum for 44 years is birr 420, find the principal
Answers
As per the given simple interest, the principal amount is $165.35.
The term simple interest in math is defined as the interest charge on borrowing that's calculated using an original principal amount only and an interest rate that never changes.
Here we have given that If the simple interest on a sum of a money invested at 3. 5% per annum for 44 years is birr 420.
Therefore, through the given question we have identified the value of
interest rate = 3.5%
time period = 44
sum amount = 420.
Then the principal amount is calculated by using the formula of simple interest as,
P = A / (1 + rt)
Here first we have to convert R percent to r a decimal, then we get
r = R/100 = 3.5%/100 = 0.035 per year.
Now, we have to apply the values on the equation and then we have to solve our equation, then we get
P = 420 / ( 1 + (0.035 × 44)) = 165.35433070866
P = $165.35
Therefore, the principal investment required to get a total amount, principal plus interest, of $420.00 from simple interest at a rate of 3.5% per year for 44 years is $165.35.
To know more about simple interest here.
https://brainly.com/question/22621039
#SPJ4
Which of the statements best describe the origin on the coordinate system?
1. The X and y-axes intersect at the origin.
Il. The origin is the distance from right to left.
III. The point, (0.0). is the ordered pair at the origin.
IV. The origin is the distance from top to bottom
Answers
Answer:
The point, (0.0). is the ordered pair at the origin.
Step-by-step explanation:
Sara is building a garden box to plant flowers. For which measurement would she need to find the area?
Answers
Answer:
A
Step-by-step explanation:
Answer: B: the length of the wooden sides of the garden box
Step-by-step explanation:
because if she is going to plant flowers she will need to know how big the box she would need for her plants
You lose 0.3 point for stepping out of bounds during a gymnastics floor routine. Your final score is 9.124. Write and solve an equation to find your score $x$ without the penalty.
Answers
Your score without the penalty is 9.424.
To find your score without the penalty, we need to add 0.3 points back to your final score of 9.124. We can use the linear equation:
x = 9.124 + 0.3
This equation represents the original score, represented by x, plus the penalty of 0.3. To solve for x, we need to add 0.3 to 9.124:
x = 9.124 + 0.3
x = 9.424
So your score without the penalty is 9.424.
In this equation, x is being used to represent the original score, before the 0.3-point penalty was applied. The equation x = 9.124 + 0.3 represents that the original score was 9.124 and 0.3 points were taken off due to stepping out of bounds. By solving the equation, we are able to find the original score without the penalty which is 9.424
To learn more about linear equations, visit:
brainly.com/question/11897796
#SPJ4
How to graph 4x-6y=36
What’s the x intercept
What’s the y intercept
Answers
Therefore . the solution of the given problem of equation comes out to be x-intercept(s): (9,0) and y-intercept(s): (0,−6).
Clarify the equationA depiction of two equal variables, one on either side of a "equals" sign, is what constitutes an equation in mathematics. To solve common issues, one can use equations. We frequently look for help with pre algebra to overcome obstacles in real life. Basic mathematical concepts are covered in pre-algebra lessons.
Here,
the x-intercepts,
In order to determine the x-intercept(s), put in for y and calculate 4x6y=36.
Make the equation work.
x=9 point form x-intercepts.
x-intercept(s): \s(9,0) (9,0)
the y-intercepts, please.
In order to determine the y-intercept(s), replace with and solve for y=.4(0-)6y=36.
Make the equation work.
To continue, tap.
Point shape y=6 y-intercept(s).
The y-intercept is (0, 6).
Write down the junctions.
x-intercept(s): (9,0)
The y-intercept is (0, 6).
Therefore . the solution of the given problem of equation comes out to be x-intercept(s): (9,0) and y-intercept(s): (0,−6).
To know more about equation visit:
brainly.com/question/649785
#SPJ1
Jon invested $5,000 dollars into an account with an interest rate of 15% compounded continuously. Approximately how long will it take the investment to triple? A=P(1±rn)nt Group of answer choices
Answers
2 = (1.15)^x
logbase(1.15) of 2 = x
x = ~4.96
The time for it take the investment to triple will be 8 years.
What is Simple interest?
A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
The principal amount = $5,000
The interest rate = 15%
The total amount after x years = 3 x $5,000
= $15,000
Now,
We know that, the formulate for total amount is,
⇒ [tex]A = P (1 + r)^x[/tex]
Substitute all the values we get;
⇒ [tex]A = P (1 + r)^x[/tex]
⇒ 15,000 = 5,000 (1 + 0.15)ˣ
⇒ 3 = (1.15)ˣ
Take log,
⇒ log 3 = x log 1.15
⇒ 0.47 = x × 0.06
⇒ x = 8 years
Thus, The time for it take the investment to triple will be 8 years.
Learn more about the simple interest visit:
https://brainly.com/question/20690803
#SPJ5
Find the area. Simplify your answer.
Answers
2x *3x
First you multiply the numbers
2*3=6
Then you multiply the variable
x*x=x^2
Area =6x^2
Amy operates a coffee kiosk and is blending her special house coffee. She is mixing Kenya beans that cost $9. 00 per pound with Colombia
beans that cost $7. 50 per pound to create a 30 pound blend that sells for $8. 50 per pound. How many pounds of Kenya beans and how many
pounds of Colombia beans does Amy need to use to create her blend?
Answers
So Amy needs to use 2 pounds of Colombia beans and 32 pounds of Kenya beans to create her blend.
Define Unitary Method.The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
What is direct and indirect variation in the unitary method?We are aware that an inverse variation or indirect variation occurs when two values are coupled in a way that a rise in one generates a corresponding reduction in the other, and vice versa.
Let x be the number of pounds of Kenya beans and y be the number of pounds of Colombia beans. We know that:
x + y = 30 (since the blend is 30 pounds)
We also know that the blend sells for $8.50 per pound, so the total cost of the blend is:
8.50(x + y) = 8.50(30) = $255
We know that the cost of the Kenya beans is $9.00 per pound and the cost of the Colombia beans is $7.50 per pound, so the total cost of the Kenya beans is:
9.00x and the total cost of the Colombia beans is 7.50y
We can set up the following equation:
9x + 7.5y = 255
We have 2 equations and 2 variables, we can solve this system of equation by different methods, one of them is substitution:
x + y = 30
9x + 7.5y = 255
We can substitute the first equation into the second equation
9(x + y) + 7.5y = 255
9(30) + 7.5y = 255
270 + 7.5y = 255
7.5y = -15
y = -2
So Amy needs to use 2 pounds of Colombia beans. We can substitute that value into the first equation to find the amount of Kenya beans:
x + (-2) = 30
x = 32
So Amy needs to use 32 pounds of Kenya beans.
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ4
The age of people waiting in line for a movie are given. Use the data to make a frequency table with intervals.
12, 27, 15, 31, 6, 45, 65, 55, 10, 49, 6, 8
Answers
The frequency table for the given data is shown above.
What is is frequency table?A table drawn up to show the distribution of the frequency of occurrence of a given characteristic according to some specified set of class intervals.
Given is the age of people waiting in line for a movie as -
12, 27, 15, 31, 6, 45, 65, 55, 10, 49, 6, 8
Arrange the data in ascending order -
6, 6, 8, 10, 12, 15, 27, 31, 45, 49, 55, 65
INTERVALS FREQUENCY
0 - 10 4
11 - 20 2
21 - 30 1
31 - 40 1
41 - 50 2
51 - 60 1
61 - 70 1
Therefore, the frequency table for the given data is shown above.
To solve more questions on frequency table, visit the link below -
https://brainly.com/question/28931302
#SPJ1
seven pounds of fertilizer can cover 1400 square feet.canbe covered by 2 pounds of fertilizer
Answers
The area for 2 pounds of fertilizer is 400 square feet
How to determine the amount of fertilizer for 2 pounds?
From the question, we have the following parameters that can be used in our computation:
seven pounds of fertilizer can cover 1400 square feet
This means that
7 pounds of fertilizer = 1400 square feet
Divide both sides of the equation by 7
So, we have the following representation
1 pounds of fertilizer = 200 square feet
Multiply both sides of the equation by 2
So, we have the following representation
2 pounds of fertilizer = 400 square feet
Hence, the area is 400 square feet
Read more about unit rates at
https://brainly.com/question/19493296
#SPJ1
The shapes below are mathematically similar
Not drawn
to scale
8 cm
9 cm
12 cm
Calculate the length of side x.
Answers
Answer:
I think it is 9 cm
Step-by-step explanation:
PLEASE HELPPP
WILL GIVE BRAINLIEST
Answers
Answer:
1 3/16
Step-by-step explanation:
1/8 = 2/16
Answer:
1 3/16
Step-by-step explanation:
I need help.
The truth is, I don't know why the Brainly appears in English, if I needed it in Spanish. So, homework is in Spanish. I really need the help because I'm very behind in math. Thanks. And sorry for the horrible traduction. I'm so bad at english.
Answers
Answer:
Hey you can login in Spain Server if you find difficulty here
Find the area of the regular pentagon below
Answers
Answer:
247.75
Step-by-step explanation: