Answers
The row echelon form of the matrix is presented as follows;
[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}[/tex]
What is the row echelon form of a matrix?The row echelon form of a matrix has the rows consisting entirely of zeros at the bottom, and the first entry of a row that is not entirely zero is a one.
The given matrix is presented as follows;
[tex]\begin{bmatrix}-3 &6 &15 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}[/tex]
The conditions of a matrix in the row echelon form are as follows;
There are row having nonzero entries above the zero rows.The first nonzero entry in a nonzero row is a one.The location of the leading one in a nonzero row is to the left of the leading one in the next lower rows.Dividing Row 1 by -3 gives:
[tex]\begin{bmatrix}1 &-2 &-5 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}[/tex]
Multiplying Row 1 by 2 and subtracting the result from Row 2 gives;
[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 1&0 &-1 \\\end{bmatrix}[/tex]
Subtracting Row 1 from Row 3 gives;
[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&2 &4 \\\end{bmatrix}[/tex]
Adding Row 2 to Row 3 gives;
[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&0 &18 \\\end{bmatrix}[/tex]
Dividing Row 2 by -2, and Row 3 by 18 gives;
[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}[/tex]
The above matrix is in the row echelon form
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Related Questions
7. Which expression is equivalent to the distance between -2 and -15 on a number line? Select all that apply. OT-15 - (-2)] O 1-15-2 O 1-15+ (-2) 1-2 + (-15) 1-2-(15)
Answers
A straight line l1 with equation 5x - 7 = 0 cuts the x axis at point A. Straight line l2 is perpendicular to straight line l1 and passes through point A. What is the coordinates of point A and the equation of the straight line l2?
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The coordinates of point A are (7/5, 0), and the perpendicular line that also passes through that point is:
y = 0.
How to get the perpendicular line?Here we want to get a line perpendicular to:
5x - 7 = 0
Solving this for x, we get:
5x = 7
x = 7/5.
This is a vertical line, so the perpendicular line will be a horizontal line, which is of the form:
y = a.
We know that the line:
x = 7/5.
Cuts the x-axis at point A.
Remember that the x-axis as coordinates (x, 0).
So the coordinates of point A are (7/5, 0).
Now, the perpendicular line:
y = a
Needs to pass through the point (7/5, 0), so the value of a must be zero, then the line is:
y = 0.
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write an equation and solvefour times the complement of an angle is 40° lessthan twice the angles supplement. Find the angle,its complement, and its supplement
Answers
Let the angle be 'x' degrees.
The complement (C) of the corresponding angle will be,
[tex]C=90-x[/tex]And the supplement (S) of the corresponding angle will be,
[tex]S=180-x[/tex]According to the condition given in the problem,
[tex]4C=2S-40^{}[/tex]Substitute the values,
[tex]\begin{gathered} 4(90-x)=2(180-x)-40 \\ 360-4x=360-2x-40 \\ -4x=-2x-40 \\ 4x-2x=40 \end{gathered}[/tex]Simplify the expression further,
[tex]\begin{gathered} 2x=40 \\ x=\frac{40}{2} \\ x=20 \end{gathered}[/tex]Substitute this value of 'x' to obtain the complement and supplement angles as follows,
[tex]\begin{gathered} C=90-20=70 \\ S=180-20=160 \end{gathered}[/tex]Thus, the angle measures 20 degrees, its complement measures 70 degrees, while its supplement measures 160 degrees.
Solve for x in the equation below:3(x - 5) = 5x - (3 - x)
Answers
Step 1: We have the following equation:
3(x - 5) = 5x - (3 - x)
Step 2: Solve the parentheses
3x - 15 = 5x - 3 + x
Step 3: Like terms
3x - 5x -x = - 3 + 15
-3x = 12
Step 4: Dividing by -3 at both sides
-3x/-3 = 12/-3
x = -4
Step 5: Let's prove the answer is correct
3 (-4 - 5) = 5 * -4 - (3 - -4)
3 (-9) = -20 -3 - 4
-27 = - 27
The solution is correct
for #5 solve for x. then find the missing piece(s) of parallelogram.
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Answer:
Given that,
From the parallelogram, the opposite sides of the parallelogram are -2+4x and 3x+3
Explanation:
From the properties of parallelogram, we have that
Opposite sides of a parallelogram are equal
We get,
[tex]-2+4x=3x+3[/tex]Solving we get,
[tex]4x-3x=3+2[/tex][tex]x=5[/tex]Answer is :x=5
Solve the system of equations by adding or subtracting.S3x + y = 412x + y = 0The solution of the system is
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Step 1:
Choose either Substitution or elimination method to solve system of equation.
Step 2:
If you choose substitution,
firstly, name the equation
3x + y = 4 .............................1
2x + y = 0 ..............................2
secondly, choose one of the equation and make one of the varable subject of the relation
2x + y = 0 .......................1
y = -2x
Step3
substitute y in equation 2
3x + (-2x) = 4
3x - 2x = 4
x = 4
Step 4:
find y from y = -2x
y = -2(4)
y = -8
( 4 ), ( -8 )
Answer:
x = 4
y = - 8
Step-by-step explanation:
3x + y = 4
2x + y = 0
(3x + y ) (-1 ) = 4 ( - 1 )
2x + y = 0
- ( 3x + y ) = - 4
2x + y = 0
What polynomial identity should be used to prove that 40 = 49 − 9?
a
Difference of Cubes
b
Difference of Squares
c
Square of a Binomial
d
Sum of Cubes
Answers
A polynomial identity that should be used to prove that 40 = 49 − 9 is: B. Difference of Squares.
What is a polynomial function?A polynomial function is a mathematical expression which comprises variables (intermediates), constants, and whole number exponents with different numerical value, that are typically combined by using the following mathematical operations:
AdditionMultiplication (product)SubtractionIn Mathematics, the standard form for a difference of two (2) squares is modeled or represented by this mathematical expression:
a² - b² = (a + b)(a - b).
Where:
a and b are numerical values (numbers or numerals).
Given the following equation:
40 = 49 − 9
40 = 7² - 3³
40 = (7 + 3)(7 - 3).
40 = (10)(4)
40 = 40 (proven).
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timmy stated that the product of 3/3 and 12 is greater than the product of 3/2 and 12. is timmy correct?
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Hence the product of 3/3 and 12 is not greater than the product of 3/2 and 12.
So timmy is not correct
A random sample of CGCC students found that 19% say math is their favorite subject with a margin of error of 2.5 percentage points.a) What is the confidence interval? % to %b) What does the confidence interval mean?
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If 19% say that math is their favorite subject, with a margin of error of 2.5%, then the confidence of interval is:
[tex]\begin{gathered} Confidence\text{ of interval= 19\% math }\pm\text{ 2.5\% margin of error} \\ Confidence\text{ of interval= 16.5\% to 21.5\%} \end{gathered}[/tex]b) The confidence of interval is the range of values in which you think the study or the values are going to fall between if anyone redo the study, it doesn't contain the margin of error because this percentage means the probability that the values aren't going to fall between the confidence of interval.
Simplify to create an equivalent expression. 2(3r + 7) - (2 +r) Over Choose 1 answer: Intro INCORRECT (SELECTED 4r + 12 You might have confused terms. Sub B 5r + 13 809 C 5r + 12
Answers
The frist step in simplifying the expression is expanding the term on the left. This gives
[tex]2(3r+7)=6r+14[/tex]therefore, the expression becomes
[tex]2(3r+7)-(2+r)=6r+14-(2+r)[/tex]and since
[tex]-(2+r)=-2-r[/tex]the above becomes
[tex]6r+14-2-r[/tex]Adding/subtracting the like terms gives
[tex]6r-r+14-2[/tex][tex]5r+12[/tex]which is our answer!
This question is from a MATH extra credit assignment, so unless I accidentally clicked on a subject other than maths... This question is also not from a test. Please help me if you can. Thank you if you do :)
Answers
Answer
$6,314
Step-by-step explanation
Compound interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
• A: final amount, in dollars
,• P: principal, in dollars
,• r: interest rate, as a decimal
,• n: number of times interest is applied per year
,• t: time in years
In this case, the investment is compounded annually, that is, once per year (n = 1). Substituting P = $4,625, r = 0.0352 (=3.52/100), n = 1, and t = 9 years, we get:
[tex]\begin{gathered} A=4,625(1+\frac{0.0352}{1})^{1\cdot9} \\ A=4,625(1.0352)^9 \\ A=\text{ \$}6,314 \end{gathered}[/tex]Find the volume of cylinder with r=25.5 ft and height=45ft use 3.14 for pi. Round the answer to the nearest hundredth
Answers
The Volume of a Cylinder
Given a cylinder of base radius r and height h, its volume is calculated as follows:
[tex]V=\pi r^2h[/tex]We have a cylinder with dimensions r = 25.5 ft and h = 45 ft. Substituting the values in the formula:
[tex]V=\pi\cdot25.5^2\cdot45[/tex]Using π = 3.14:
[tex]\begin{gathered} V=3.14\cdot650.25ft^2\cdot45ft \\ V=91,880.325ft^3 \end{gathered}[/tex]Rounding to the nearest hundredth:
V = 91,880.33 cubic ft
2. A bag contains 50 marbles, 28 red ones and 22 blue ones. A marble is picked at random from the bag. What is the probability of picking: a red marble first? a blue marble?
Answers
Answer:
28/50
Step-by-step explanation:
If there is 50 marbles and you have 22 blue and 28 red and they want you to find what the chance of picking a red marble out of the bag your chances would be 28/50 hope this helps!
what would the annual rate of interest have to be? round to two decimal places.
Answers
To find:
The rate of interest.
Solution:
It is known that the rate of interest is given by:
[tex]r=n[(\frac{A}{P})^{\frac{1}{nt}}-1][/tex]Here. P = 60000, A = 61200, t = 2.5 and n = 12.
[tex]\begin{gathered} r=12[(\frac{61200}{60000})^{\frac{1}{12(2.5)}}-1] \\ r=0.00792366 \end{gathered}[/tex]Change into the percentage by multiplying by 100:
[tex]\begin{gathered} r=0.00792366 \\ r=0.79\% \end{gathered}[/tex]Thus, the answer is 0.79% per year.
From question: Montell is practicing his violin. He is able to play six songs for every nine minutes he practices.*Picture has the table and other questions*
Answers
Answer:
The complete table:
6 18 2 42
9 27 3 63
Explanation:
We know that for every 9 minutes Montell practices he is able to play 6 songs. This means that the ratio between the number of minutes practices to the number of songs played is
[tex]\frac{\min}{\text{song}}=\frac{9}{6}[/tex]Therefore, if we want to solve for minutes plated, we just multiply both sides by 'song' to get
[tex]song\times\frac{\min}{\text{song}}=\frac{9}{6}\times\text{song}[/tex]which gives
[tex]min=\frac{9}{6}\times\text{song}[/tex]This means the number of minutes practised is 9/6 of the number of songs played.
Now 9/ 6 can be simplfied by dividing both the numerator and the denominator by 3 to get
[tex]\frac{9\div3}{6\div3}=\frac{3}{2}[/tex]therefore, we have
[tex]min=\frac{3}{2}\times\text{song}[/tex]Now we are ready to fill the table.
If Montell plays 18 songs then we have
[tex]\min =\frac{3}{2}\times18[/tex][tex]\min =27[/tex]the minutes practised is 27 for 18 songs.
If Montell practices for 3 minutes then we have
[tex]3=\frac{3}{2}\times\text{song}[/tex]then the value of song must be song = 2, since
[tex]\begin{gathered} 3=\frac{3}{2}\times2 \\ 3=3 \end{gathered}[/tex]Hence, for 3 minutes of practice, Montell sings 2 songs.
Now for 42 songs, the number of minutes played would be
[tex]\min =\frac{3}{2}\times42[/tex]which simplifies to give
[tex]\min =63[/tex]Hence, for 42 songs played, the practice time is 63 minutes.
To summerise, the complete table would be
songs 6 18 2 42
minutes 9 27 3 63
Using the order of operations, which operation should you perform last to evaluate the expression below?(7*4)+(10 ÷ 2)*(14.7 - 9)A.multiplicationB.divisionC.additionD.subtractionHELP! A.P.S
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Explanation
Given (7*4)+(10 ÷ 2)*(14.7 - 9), we can see that only two operations occur outside of the parenthesis which is multiplication and addition.
In the order of evaluation of expressions, the parenthesis comes first before multiplication and then addition. Therefore,
Answer: Option C (Addition)
Maxim has been offered positions by two car companies. The first company pays a salary of $12000 plus a commission of $800 for each car sold. The second pays a salary of $15600 plus a commission of $600 for each car sold. How many cars would need to be sold to make the total pay the same?
Answers
To make the total pay the same, 18 cars would need to be sold
Explanation:Let the number of cars sold be x
The first company pays a salary of $12000 plus a commission of $800 for each car sold
Total pay for the first company = 12000 + 800x
The second pays a salary of $15600 plus a commission of $600 for each car sold
Total pay for the second company = 15600 + 600x
If the total pay is the same:
12000 + 800x = 15600 + 600x
800x - 600x = 15600 - 12000
200x = 3600
x = 3600/200
x = 18
To make the total pay the same, 18 cars would need to be sold
What is the probability of drawing a jack from a standard deck of cards, replacing it,shuffling, then drawing an ace?
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- We have 52 cards in a deck of cards.
- We have 4 cards of the same number (4 jack, 4 aces...).
Probability of drawing a jack = 4/52
Probability of drawing a jack followed by an ace =(4/52)*(4/52)=0.00592
Find the surface area of the prism. 8 cm. 3 cm. 3 cm. 3 cm.) - 3 cm. Surface Area cm2
Answers
Surface area of a rectangular prism:
[tex]\begin{gathered} SA=2(l\cdot h+w\cdot h+l\cdot w) \\ l=\text{lenght} \\ w=\text{width} \\ h=\text{height} \end{gathered}[/tex]For the given prims:
l=8cm
w=3cm
h=3cm
[tex]\begin{gathered} SA=2(8\operatorname{cm}\cdot3\operatorname{cm}+3\operatorname{cm}\cdot3\operatorname{cm}+8\operatorname{cm}\cdot3\operatorname{cm}) \\ SA=2(24cm^2+9cm^2+24cm^2) \\ SA=2(57cm^2) \\ SA=114cm^2 \end{gathered}[/tex]Then, the surface area is 114 square centimeters
4. A pool measuring 24 feet by 16 feet is
surrounded by a uniform path of width x feet.
The total enclosed area is 768 ft².
Find x, the width of the path.
Answers
The width of the path, x, is 48 feet
How to determine the parametersThe formula for determining the area of a rectangle is expressed as;
Area = lw
Where;
l is the length of the given rectanglew is the width of the given rectangleFrom the image shown and the information given, we can see that;
The width is given as = x
The area of the rectangle = 768 ft²
The length of the rectangle = 16
Now, substitute the values, we have;
768 = 16x
Make 'x' the subject of formula by dividing both sides by its coefficient, we have;
768/16 = 16x/16
Find the quotient
x = 48 feet
But, we have;
Width = x = 48 feet
Hence, the value is 48 feet
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The number of chaperones on a field trip must include 1 teacher for every 4 students, plus 2 parents total. The function describing the number of chaperones for a trip of x students is f(x) = 1/4x + 2.
a. How will the graph change if the number of parents is reduced to 0?
b. How will the graph change if the number of teachers is raised to 1 for every 3 students?
Answers
Number of chaperones for a trip defined by function f(x) = (1/4)x+2 then,
a. If the parents is reduced to 0 then the graph passes through origin (0,0).
b. If the number of teachers is raised to 1 for every 3 students then line cut x-axis at (-6,0) .
As given in the question,
Given conditions:
Field trip must include 1 teacher for every 4 students and add 2 parents in total.
Number of chaperones for a trip defined by function f(x) = (1/4)x+2
a. If the parents is reduced to 0 then the changes seen in the graph are as follow:
f(x) = (1/4)x+2 passes through the point (0,2)
when parents changes to 0 then graph passes through (0,0).
b. If the number of teachers is raised to 1 for every 3 students then the changes seen in the graph are as follow:
For f(x) = (1/4)x+2 the graph cut axis at (-8,0)
When for every 1 teacher there are 3 students then graph cut x-axis at (-6,0).
Therefore, number of chaperones for a trip defined by function f(x) = (1/4)x+2 then,
a. If the parents is reduced to 0 then the graph passes through origin (0,0).
b. If the number of teachers is raised to 1 for every 3 students then line cut x-axis at (-6,0) .
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A card is drawn from a deck of 52 cards. What is the probability that it is a numbered card (2-10) or a heart?
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we know that
Total cards=52
Total numbered card (2-10)=36
Total heart=13
numbered card and heart=9
therefore
The probability is equal to
P=(36+13-9)/52
P=40/52
P=20/26=10/13
The answer is 10/13Can you tell me if im right or wrong
Answers
I will begin typing in the answer tab. It will take me approximately _
Find the reference angle of [tex] \frac{ - 13\pi}{6} [/tex]
Answers
Reference angle
The reference angle of a given angle A is the acute angle that A forms with the x-axis
We need to calculate the reference angle of
[tex]\frac{ - 13\pi}{6}[/tex]This angle is greater than any angle of a single turn on the trigonometric circle.
Let's convert the improper fraction to a mixed fraction:
[tex]-\frac{13\pi}{6}=-2\pi-\frac{\pi}{6}[/tex]-2π corresponds to a complete turn around the circle, so we can discard that part and take only the -π/6
Since it's a negative angle, it runs clockwise and is located at the IV quadrant. The reference angle is π/6 because it's the angle it forms with the x-axis.
We'll include an image of the angle below
Question 9 (1 point) Jennifer is a car saleswoman. She is paid a salary of $2200 per month plus $300 for each car that she sells. Write a linear function that describes the relationship between the number of cars sold x and the monthly salary y. Then, graph the function to show the relationship.
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A company orders business cards for their employees. The company pays $9.00 per 100 cards ordered. The company orders2,000 business cards for Karen and 2,500 business cards for Lamar. How much more do the business cards for Lamar cost than thebusiness cards for Karen?$9$45$450d $500
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Take into account what the company pays per 100 cards ordered, which is $9.00.
To determine the cost of the cards for Karen and Lamar
Refer to the rectangle ABCD, shown below, where m(<4)=10degrees. Need help.
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From the statement of the problem, we know that:
[tex]m(\angle4)=18^{\circ}\text{.}[/tex]From the diagram, we see that:
1) ∠1 and ∠4 are complementary angles, so they sum up 90°:
[tex]\begin{gathered} m\mleft(\angle1\mright)+m\mleft(\angle4\mright)=90\degree \\ m\mleft(\angle1\mright)=90\degree-m\mleft(\angle4\mright), \\ m(\angle1)=90\degree-18^{\circ}=72^{\circ}\text{.} \end{gathered}[/tex]2) ∠4, ∠3 and a right angle are inner angles of a triangle, so they must sump up 180°:
[tex]\begin{gathered} m(\angle4)+m(\angle3)+90^{\circ}=180^{\circ}\text{.} \\ m(\angle3)=180^{\circ}-90^{\circ}-m(\angle4), \\ m(\angle3)=180^{\circ}-90^{\circ}-18^{\circ}=72^{\circ}\text{.} \end{gathered}[/tex]3) ∠3 and ∠2 are complementary angles, so they sum up 90°:
[tex]\begin{gathered} m(\angle3)+m(\angle2)=90^{\circ}, \\ m(\angle2)=90^{\circ}-m(\angle3), \\ m(\angle2)=90^{\circ}-72^{\circ}=18^{\circ}\text{.} \end{gathered}[/tex]Answer
c. m(∠1) = 72°, m(∠2) = 18°, m(∠3) = 72°.
A baseball stadium has 50,100 seats. Each ticket for a seat costs $30. Tara created a function to model this situation and drew the graph of the function, where y represents profit from ticket sales, in dollars, given the number of tickets sold, x.
Is the graph function correct? why or why not?
Answers
The graph as shown in the image is the correct graph of the function.
What is the correct graph of the function?A function shows a mathematical relationship. We would need to look at the graph very closely so as to know weather or not the graph as it has been shown is the correct graph that is befitting of the function must be a straight line graph.
Clearly, the slope of the graph would be positive and beginning from the origin because the number of tickets that is sold is increasing just and the amount of the tickets is increasing. Thus the graph follows the general equation of a straight line; y = mx + c
All these goes to show that what we have befits the function.
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can you please find the slope and the y intersept of the graph of the linear equation y= 4x-5
Answers
the slope of the linear equation is 4 and the y intercept is -5
Explantion:we apply the equation of line to find the slope and intercept
Equation of line is in the form: y = mx + c
where m = slope and c = y - intercept
comparing the given equation with the equation of line:
linear equation y= 4x-5
y = y
4x - 5 = mx + c
This means m = 4
4x = mx
m = 4
-5 = c
Hence, the slope of the linear equation is 4 and the y intercept is -5
Teachers' Salaries The average annual salary for all U.S. teachers is $47,750. Assume that the distribution is normal and the standard deviation is $5680Find the probabilities.P (X>45,500)