Answer: a. The rate of change in this situation represents the average number of pages read per minute. From the table, it can be seen that the rate of change is constant, as the ratio of the change in y (pages) to the change in x (minutes) is always the same.
For example, when x increases from 0 to 5, y increases from 0 to 25, so the rate of change is 25/5 = 5 pages per minute.
b. To represent the total number of pages as it relates to the number of minutes read, a linear equation can be used. The slope of the line represents the rate of change, and the y-intercept represents the number of pages read when x is equal to 0 (minutes).
Using the rate of change from the above example (5 pages per minute), the equation can be written as y = 5x + 0, where x represents the number of minutes and y represents the total number of pages read.
Step-by-step explanation:
PLEASE HELP I DONT UNDERSTAND!
Write the following polynomial in descending powers of the variable and with no missing powers
3x^3 -70
3x^3 -70=?
If we are to write the following polynomial in descending powers of the variable and with no missing powers 3x^3 -70, it would be 3x^3 - 70 + 0x^2 + 0x + 0
What is a Polynomial?A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.
Hence, it can be seen that descending order is basically when the power of a term decreases for each succeeding term. For example, x3 + x2 + x or 2 x4 + 3 x2 + 7 x are arranged in descending order. Descending order is more commonly used.
The polynomial in descending powers of the variable with no missing powers is:
3x^3 - 70 = 3x^3 - 70 + 0x^2 + 0x^1 + 0x^0
= 3x^3 - 70 + 0x^2 + 0x + 0
Note: The polynomial can also be written as 3x^3 - 70x^0.
Read more about polynomials here:
https://brainly.com/question/24662212
#SPJ1
Can anyone help me? Find m
Answer:
m∠Y = 60°WY = 7 inStep-by-step explanation:
Given triangle WXY with sides WX = 7 in and XY = 7 in and angle X = 60°, you want the measure of angle Y and the length of side WY.
Isosceles triangleThe equal given side measures tell you that their opposite angles (W and Y) have equal values. Those values will be such that the total of all angles is 180°:
W +Y +X = 180°
Y +Y +60° = 180° . . . . . . . . . . . use given values; substitute Y for W
Y = (180° -60°)/2 = 60° . . . . . . . subtract 60°, divide by 2
All of the angles in this triangle have the same measure, so it is an equilateral triangle. All of the sides have the same measure, too.
angle Y = 60°
WY = 7 inches
__
Additional comment
It is helpful to recognize that an isosceles triangle with a vertex angle of 60° is an equilateral triangle. That recognition lets you write down the answer with no further work.
carry out the following matrix multiplications. for each problem, say what the function represented by each matrix does to the standard basis vectors and what the product of the two matrices would do to these vectors.
The row in the original matrix and the column in the primary matrix must match. Hence, the matrix product has the first matrix's number of rows and the second matrix's number of columns.
A matrix is exactly what?Read an overview of this subject. a collection of numbers lined up in rows or columns to form a flat array is called a matrix. The atoms, or units, of the matrix are the integers.
The matrix theory is what?The study of squares is the main focus of the mathematical field known as matrix theory. It started out as a branch of linear algebra but quickly expanded to cover topics in graph theory, algebra, combinatorics, and statistics.
To know more about integers visits:
https://brainly.com/question/1768255
#SPJ1
Consider the line 5x-8y=-6.
Find the equation of the line that is parallel to this line and passes through the point (4,-4).
Find the equation of the line that is perpendicular to this line and passes through the point (4, -4).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Equation of parallel line:
Equation of perpendicular line: []
8x 12
5
The equation of the line that is perpendicular to 5x-8y=-6 and passes through (4,-4) is y = (-8/5)x + 16/5.
What are Parallel lines?Parallel lines are two or more lines in a coordinate plane that are equidistant from each other at all coordinates.
The given line can be rewritten in slope-intercept form as y=(5/8)x+(3/4), where the slope is 5/8. So, any parallel line will also have a slope of 5/8.
Using the point-slope form of a line, we can write the equation of the line as:
y - (-4) = (5/8)(x - 4)
Simplifying, we get:
y = (5/8)x - 23/8
Therefore, the equation of the line that is parallel to 5x-8y=-6 and passes through (4,-4) is y = (5/8)x - 23/8.
The slope of the given line is 5/8, so the slope of any line perpendicular to it will be -8/5.
y - (-4) = (-8/5)(x - 4)
Simplifying, we get:
y = (-8/5)x + 16/5
Therefore, the equation of the line that is perpendicular to 5x-8y=-6 and passes through (4,-4) is y = (-8/5)x + 16/5.
Learn more about the equation of line here:
https://brainly.com/question/29278800
#SPJ9
Jimena finances a $4,200 furniture purchase. The store offers 3%
simple interest, and Jimena will pay off the balance in 6 months.
How much simple interest will Jimena pay the store?
Answer: To calculate the simple interest, you can use the formula:
I = Prt
where I is the interest, P is the principal (the amount borrowed), r is the interest rate as a decimal, and t is the time in years.
In this case, P = $4,200, r = 0.03, and t = 6/12 = 0.5 (since the interest is paid over 6 months, which is half of a year). Plugging these values into the formula, we get:
I = Prt = 4,200 * 0.03 * 0.5 = $63
So, Jimena will pay the store $63 in simple interest.
Step-by-step explanation:
A rectangular field is 0.4 m longer than it is wide. If its length is 6m find its Perimeter.. When the breadth of the rectangle is reduced by 0.5m. the length is increased such that the perimeter is increased by 1/4 of its Original What is the Change in the length of the rectangle ?
Juan's mother gave him a recipe for trail mix. What is the order of the ingredients from least to greatest?3/4 cup raisins1/3 cup almonds2/3 cup peanuts1/2 cup cereal
The answer to question of trail mix in ascending order would be, 1/2 cup cereal, 3/4 cup raisins, 1/3 cup almonds, 2/3 cup peanuts.
The order of ingredients from least to greatest for Juan's trail mix recipe is: 1/2 cup cereal, 3/4 cup raisins, 1/3 cup almonds, and 2/3 cup peanuts. Juan's mother provided the recipe which consists of a combination of dried fruits, nuts, and cereal. The recipe calls for 1/2 cup of cereal, which is the least amount of any of the ingredients. The next ingredient is 3/4 cup of raisins, followed by 1/3 cup of almonds, and finally 2/3 cup of peanuts, which is the greatest amount of any of the ingredients. These ingredients can be combined and enjoyed as a snack.
Hence the answer is, 1/2 cup cereal, 3/4 cup raisins, 1/3 cup almonds, 2/3 cup peanuts.
Click here to learn about ascending order:
brainly.com/question/20681445
#SPJ4
Is it possible to draw an acute isosceles triangle with side lengths of 6 cm, 9 cm, and 12 cm and angles of 30°, 50°, and 100° ?
Use the given sides and angles to explain why or why not.
Answer:
No
Step-by-step explanation:
An isosceles triangle has two sides of equal length.
All interior angles in an isosceles acute triangle are less than 90°.
Therefore, it is not possible to draw an acute isosceles triangle with side lengths of 6 cm, 9 cm, and 12 cm and angles of 30°, 50°, and 100° as two sides are not of equal length and 100° > 90°.
The fact that 1 liter = 1.057 quarts can be written as the conversion factor
The conversion factor of litre to quarts is 1 litre = 1.057 quarts and its meaning is discussed below.
What is a conversion factor?
A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. The correct conversion factor to convert minutes to hours is 60 minutes = 1 hour.
The metric unit of a volume known as the litre is mostly used to measure liquids.
An English measurement of volume equal to the one-quarter gallon is the quart. There are now three different types of quarts in use: the liquid quart, dry quart, and imperial quart of the British imperial system.
The standard value of converting liquid to quarts is 1 litre = 1.057 quarts.
This means that volume of 1 litre of a substance is equivalent to the volume of 1.057 quarts of the same substance.
Therefore the conversion factor of litre to quarts is 1 litre = 1.057 quarts.
To learn more about conversion factors, follow the link.
https://brainly.com/question/97386
#SPJ4
When two numbers are added together, the sum is at least 100. One of the numbers is 77. Question 1 PART A Which of these numbers could be the other number? Select all the correct answers. response - correct Responses 15 15 20 20 9 9 41 41 50 50 23 23 25 25 Question 2 PART B Write an inequality to represent the possible values of the other number n . Enter the correct answer in the box.
Answer:
Part A: 23
Part B: n < 77
Step-by-step explanation:
A linear function is shown on the graph.
a linear function beginning with closed circle at 2 comma 0 and ending with a closed circle at 9 comma 7
What is the domain of the function?
{x | 2 < x < 9}
{x | 2 ≤ x ≤ 9}
{y | 0 < y < 7}
{y | 0 ≤ y ≤ 7}
The domain of the linear function shown in the graph is given as follows:
{x | 2 ≤ x ≤ 9}.
How to obtain the domain of the function?The domain of a function is composed by the set containing all the possible input values for the function, hence it is composed by all the values of x assumed by the function.
The bounds of the domain in this problem are given as follows:
Lower bound: closed at x = 2.Upper bound: closed at x = 9.Hence the correct option regarding the domain of the function is given by the second option.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
8-642
A
O
B
B
6
#2
E
2465
C4
2
D
B
6 8
Mr. Paulsen challenges Olivia and Angelica to move figure ABCDE onto figure
A'B'C'DE" using a series of two different transformations. They give two different
answers.
Answer the questions to investigate ways to transform ABCDE.
1. Olivia finds a combination of two different transformations that moves ABCDE
onto A'B'C'DE". What is one way she might have done this? (3 points)
Olivia could have used a translation and a rotation to move ABCDE onto A'B'C'DE".
What is distance?Distance in numerical measurement of how far apart to 16 places in point are in space age is often measured in unit like came miles with as for free system also can be conceptualized in the term of time as Indian distance between two points in the time.
A translation would involve shifting the figure ABCDE along some axis by a certain distance, while a rotation would involve rotating the figure ABCDE around a fixed point. By combining the two transformations, Olivia could move ABCDE onto A'B'C'DE".
To know more about distance click-
https://brainly.com/question/26550516
#SPJ1
vector a has a magnitude 5.00 and points in a direction 60.0degrees clockwise from the negative y axis. what are the x and y components of vector a.
A is directed along negative X and Y axes respectively having magnitudes 3.214 and 3.83 units respectively.
A vector is an object that, as we all know, possesses both magnitude and direction. We must determine a vector's length in order to determine its magnitude. Vector quantities include things like velocity, displacement, force, momentum, etc. However, scalar quantities like as speed, mass, distance, volume, temperature, etc. exist. In contrast to vectors, which
have both magnitude and direction, scalars only have magnitude.
Magnitude of vector A = |A| = 5 units
We know, the negative Y-axis is an angle of 270° counterclockwise with a positive X-axis.
θ = Angle of vector A with positive X-axis = (270° - 40°) = 230°
So, x component of vector A = Ax = |A| * cos 230° = |A| * cos (180° + 50°) = |A| * (- cos 50°) = 5 * (-0.6428) = -3.214
And, y component of vector A = Ay = |A| * sin 230° = |A| * sin (180° + 50°) = |A| * (- sin 50°) = 5 * (-0.766) = -3.83
Since Ax and Ay both are negative relative to positive X and Y axes respectively; so, the x and y components of vector A are directed along negative X and Y axes respectively having magnitudes 3.214 and 3.83 units respectively.
the complete question is -
Vector img has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis.What are the x and y components of vector img .
A)Ax = 3.83 and Ay = 3.21
B)Ax = 3.83 and Ay = -3.21
C)Ax = -3.21 and Ay = -3.83
D)Ax = -3.21 and Ay = 3.83
E)Ax = 4.29 and Ay = 2.16
learn more about magnitudes,
https://brainly.com/question/14452091
#SPJ4
What are the constants in this expression?
2 y
x−3+²7 - 12/2
X-3+
O1 and -3
O-3 and
O-3 and
2/3
y
2
2
1
3 and 2
Answer: The constants in the expression are -3 and 2.
In the expression:
2 y
x−3+²7 - 12/2
X-3+
The term -3 is a constant and does not change its value regardless of the values of any variables. The term 2/2 can also be simplified to 1, which is another constant. Hence, the constants in the expression are -3 and 2.
Step-by-step explanation:
Use Empirical Rule………
Approximately 99.7% of the vehicles travel between 53 miles per hour and 77 miles per hour.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.The mean and the standard deviation for this problem are given as follows:
Mean of 65.Standard deviation of 4.Hence:
65 - 3 x 4 = 53.65 + 3 x 4 = 77.Meaning that the approximate percentage is of 99.7%.
More can be learned about the Empirical Rule at https://brainly.com/question/10093236
#SPJ1
What equation represents the proportional relationship displayed in the table?
-picture-
Enter your answer by filling in the box to complete the equation.
y = (answer)x
Answer:
y = 5x
Step-by-step explanation:
It can be observed that as ‘x’ increases, ‘y’ also increases.
It can also be observed that
[tex]\frac{y}{x}[/tex] = the same constant for all four sets of values
k =[tex]\frac{10}{2} = \frac{20}{4} = \frac{30}{6} =\frac{40}{8}[/tex]=5
It can concluded that y is directly proportional to x:
y = kx Where k = constant of proportionality
For these four sets of values:
y = 5x
Points X, Y, and Z are on the sides QR , PR, and PQ respectively, of right triangle PQR such that PZXY is a square. If PQ=1 and PR=1, then what is the side length of the square?
Answer:
Step-by-step explanation:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Triangles PQR and ZQX are similar!
Square side => a
XZ / (PQ - PZ) = PR / PQ
a / (12 - a) = 8 / 12
a = 4.8
The side length of the square PZXY is sqrt(2).
What is a square?A square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given as side².
We have,
Since triangle PQR is a right triangle, we can use the Pythagorean theorem to find the length of QR:
QR² = PQ² + PR²
QR² = 1² + 1²
QR² = 2
QR = √2
Since PZXY is a square, its sides are equal in length.
Let's denote the length of one side of the square as s.
Then, we can write:
PR = PX + RX
1 = s + QY
Since QY = PZ = s and PX = QX = QR - QY = sqrt(2) - s,
we can substitute these values into the equation for PR to get:
1 = s + (√2 - s)
1 = √2
Therefore,
The side length of the square PZXY is √2.
Learn more about squares here:
https://brainly.com/question/22964077
#SPJ2
What is the quotient of 2 3/4 divided by 4 1/2
The quotient of 2 3/4 divided by 4 1/2 is approximately 0.622222222.
What do you mean by Quotient?The outcome of dividing two numbers is referred to mathematically as the quotient. It is the amount produced when a numerator is divided by a denominator.
For example, consider the expression "10 ÷ 2". 10 is the numerator, and 2 is the denominator. The quotient of this expression is 5. This has the following notation in mathematics:
10 ÷ 2 = 5
The quotient can also be a fraction, in which case it represents a ratio of two numbers. For instance, the fraction representation of the equation "5 2" is as follows:
5 ÷ 2 = 5/2
In this case, the quotient represents the ratio of 5 to 2.
The quotient is an important concept in mathematics, as it is used in many areas, including arithmetic, algebra, and calculus. It is used to solve problems involving division and ratios, and it is a basic building block for more advanced mathematical concepts.
To know more about algebra visit:
https://brainly.com/question/13106618
#SPJ1
Four classes are on a field trip. There are 6 tour guides. of studentsCan each tour guide have an equal number
The solution is, each tour guide have an equal number of 8 students.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
there are 12 students in each class.
Four classes are on a field trip.
There are 6 tour guides.
total students = 12*4
= 48
so, each guide have = 48/6
= 8
Hence, The solution is, each tour guide have an equal number of 8 students.
To learn more on multiplication click:
brainly.com/question/5992872
#SPJ1
Solve the following system of equations:
-2x + 5y = −11
4x - 3y = 15
Answer: (x,y)=(3,-1)
Step-by-step explanation:
Let f(x)=6x2+18x. Answer the following questions. 1. Find the x intercepts of the parabola. Intercepts (separate with commas): x=2. Find the vertex of the parabola. Write the vertex as a point (a,b) where a and b are numbers.
The x-intercept is -3 and the vertex of the parabola is (-1.5, -13.5).
What is vertex?The intersection of two lines, two line segments, or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location is known as an angle's vertex.
The x coordinate of the vertex is given as:
x = -b/2a= -18/ 2(6)= - 1.5
The y coordinate of the vertex is given as:
y = f(- 1.5)
f(- 1.5) = 6(- 1.5)² + 18(- 1.5) = 13.5 - 27= -13.5
Hence, the vertex of the parabola is (-1.5, -13.5).
The x intercept is found by substituting the value of y = 0 in the function:
0 = 6x² + 18x
0 = 6x (x + 3)
x + 3 = 0
x = -3
Hence, the x-intercept is -3 and the vertex of the parabola is (-1.5, -13.5).
Learn more about vertex here:
https://brainly.com/question/29030495
#SPJ4
Suppose that a particle moving along the x-axis encounters a resisting force that results in an acceleration of a =-=-0.10 V v. Given that x = 0 cm and v = 36 cm/s at time t = 0, find the velocity v and position x as a function of t for t 2 0. v= 2 cm/s Edit C x= 2 cm
The velocity of the particle v as a function of time t is given by v(t) = 36 - 0.10 * t^2 cm/s and the position x as a function of time t is given by x(t) = 36 * t - 0.05 * t^3 cm.
The problem states that at time t = 0, the particle has an initial velocity of v = 36 cm/s and is located at x = 0 cm. The particle is accelerating with a=-0.10 V v. This means that the velocity of the particle is changing by -0.10 V v each second. This can be expressed in terms of the time t as v(t) = 36 - 0.10 * t^2 cm/s. The position of the particle at any time t can be expressed as x(t) = x0 + v0 * t + 1/2 * a * t^2, where x0 is the initial position and v0 is the initial velocity. In this case, x0 = 0 and v0 = 36, so the position of the particle at any time t can be expressed as x(t) = 36 * t - 0.05 * t^3 cm. This means that the particle will move away from the origin (x=0) and its velocity will decrease each second.
Learn more about velocity here
https://brainly.com/question/14534415
#SPJ4
What is the quotient when the dividend is 40 and the divisor is 2.5?
Answer:
16.00
Step-by-step explanation:
400 divided by 25 is also 16, so divide that and it should be the same as 40 divided by 2.5
QUOTIENT-
The answer to a division problem
40/2.5 =
16
Write the first five terms of the arithmetic sequence with the first term a1=7 and the common difference d=4
Answer:
7, 11, 15, 19, 23
Step-by-step explanation:
Since the common difference is 4 each successive term is 4 more than the previous term
If we let aₙ be the nth term,
a₁ = 7
a₂ = 7 + 4 = 11
a₃ = 11 + 4 = 15
a₄ = 15 + 4 = 19
a₅ = 19 + 4 =23
The first five terms are: 7, 11, 15, 19, 23
We can also use the generalized formula for the nth term:
aₙ = a₁ + d(n - 1)
where a₁ = first term
d = common difference
Plugging in the known values we get
aₙ = 7 + 4(n- 1)
aₙ = 7 + 4n - 4
aₙ = 3 + 4n
Substituting n = 1, 2, 3, 4, 5 into the above equation will yield the same values
Maybe your teacher prefers one of the above approach.
whats the liner expression for 2h - 1 and 3h + 4
The linear expression for 2h - 1 and 3h + 4 is 5h + 3. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
According to mathematicians, the four fundamental operations, also referred to as "arithmetic operations," can be used to describe all real numbers. Division, multiplication, addition, and subtraction are the four mathematical operations that result in the terms quotient, product, sum, and difference, respectively.
We are given two expressions as 2h - 1 and 3h + 4.
On adding both, we get
2h - 1 + 3h + 4 = 5h + 3
Hence, the linear expression for 2h - 1 and 3h + 4 is 5h + 3.
Learn more about arithmetic operations from the given link
https://brainly.com/question/30283549
#SPJ1
1. What is the approximate volume of the sugar container? Show your work. (2 points)
2. What is the approximate height of the rice container? Show your work. (2 points)
3. Compare the heights of the sugar container and the rice container. Next, compare their volumes. How many times as large is the volume of the rice container compared to the volume of the sugar container? Explain your answer. (2 points)
4. In the formula V = Bh, B is the area of the base. Use this formula to calculate the volume of the flour container. (2 points)
5. Compare the volumes of the containers. Which container has the greatest volume? Which has the smallest volume? (2 points)
PLS HELP I WILL GIVE BRAINLIST
The greatest volume and smallest volume container is of rice and flour.
What is the volume of a right circular cylinder?Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
Given;
Sugar container radius and height is 2.5in and 8.5inch
Rice container radius and volume is 2.5in and 235.3inch^3
Sugar container area of base and height is 12.26in and 4inch
Now,
1. volume= pi*r*r*h
=3.14*2.5*2.5*8.5
=166.8125
2. volume= pi*r*r*h
235.3=3.14*2.5*2.5*h
h=11.98in
3. volume= base*h
=12.26*4
=49.04in^3
Therefore, the volume of flour container is 49.04in^3.
Learn more about volume of cylinder here:
https://brainly.com/question/12763699
#SPJ1
Which expression represents the phrase shown? "3 added to the quotient of a number divided by 6"
The required expression is n/6 +3
What is an Algebraic Expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
Given here: The statement " 3 added to the quotient of a number divided by 6
Let the number be n
Dividing the number by 6 we get the quotient as n/6
Again adding 3 to the quotient we get
3+n/6
Hence, The required expression is n/6 + 3
Learn more about expressions here:
brainly.com/question/29159730
#SPJ1
Choice A: $0.10 on January 1, $0.20 on January 2, $0.40 on January 3, $0.80 on January 4, doubling the amount each day, or
Choice B: $5.00 on the first day, $10.00 on the second day, $15.00 on the third day, getting $5.00 more each day.
Which of the choices can be defined using an exponential function? explain
Step-by-step explanation:
Choice A.
Choice A is exponentially because the amount is double each day. In other words each day the amount gets larger. One day it increased by 10 cents, the next day 20 cents, the next day 40 cents and so on... eventually it'll be a day where it increases by a million cents.
Choice B is not exponentially, it is linearly because each day the amount increase stays the same. One day is $5.00 more, the next day it's $5.00 more, the next day it's $5.00 more... and so on.
Because of that, we can get rid of those two choice B options.
Both Choice A's look the same. The only difference is that one has a 2 and the other doesn't. That 2 indicates that we're doubling. Makes sense because that's what we associate with doubling.
Making the second Choice A the correct formula.
Given A= {{4,1,6},{-7,5,3},{9,-3,3}}
Observe that the first column plus twice the second column equal the third column. Find a nontrivial solution Ax=0
The nontrivial solution to the equation Ax = 0 is x = [1, 1, 1]^T.
What is the nontrivial solution?
To find a nontrivial solution to the equation Ax = 0, where A is the given matrix, we need to find a vector x that satisfies the equation and is not the trivial solution x = 0.
We can start by using the observation that the first column plus twice the second column equal the third column:
4x1 - 7x2 + 9x3 = 0
x1 + 2x2 - 3x3 = 0
6x1 + 3x2 + 3x3 = 0
Applying row reduction to the matrix A, we find:
{{4,1,6},{-7,5,3},{9,-3,3}}
{{1,1/2,-3/2},{-7,5,3},{9,-3,3}}
{{1,1/2,-3/2},{0,11/2,15/2},{0,11/2,15/2}}
The rank of the matrix A is 2, which is less than the rank of the matrix of the system of linear equations, which is 3. This means there is a nontrivial solution to the equation Ax = 0.
One such nontrivial solution can be found by setting x3 = 1 and solving for x1 and x2:
x1 + 2x2 - 3(1) = 0
x1 + 2x2 = 3
x1 = 3 - 2x2
Setting x2 = 1, we find:
x1 = 3 - 2(1) = 1
x2 = 1
x3 = 1
Hence, a nontrivial solution to the equation Ax = 0 is x = [1, 1, 1]^T.
To learn more about nontrivial solution, Visit
https://brainly.com/question/30508372
#SPJ4
PLS HELP EMERGENCY I NEED U
Answer:
1. sin∠EDA is equal to sin∠EBC
2. sin∠CEB is not equal to sin∠EBC
3. cos∠BEC is equal to sin∠EBC
4. cos∠ADE is not equal to sin∠EBC
5. sin(90 - m∠EBC) is not equal to sin∠EBC
6. cos(90 - m∠EDA) is equal to sin∠EBC
Step-by-step explanation:
From inspection of the given diagram, ∠EAD = ∠ECB = 90°.
According to the vertical angles theorem, ∠BEC = ∠DEA.
According to AA similarity theorem, ΔADE ~ ΔCBE
Therefore, ∠EDA = ∠EBC.
This means that:
sin∠EDA is equal to sin∠EBCsin∠CEB is not equal to sin∠EBC[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
Since cos∠BEC = CE/BE and sin∠EBC = CE/BE then:
cos∠BEC is equal to sin∠EBC.As ∠BEC ≠ ∠ADE then:
cos∠ADE is not equal to sin∠EBC.As sin(90° - x) = cos(x) then sin(90 - m∠EBC) = cos∠EBC.
As cos∠EBC ≠ sin∠EBC then:
sin(90 - m∠EBC) is not equal to sin∠EBCAs cos(90° - x) = sin(x) then cos(90 - m∠EDA) = sin∠EDA.
As sin∠EDA = sin∠EBC then cos(90 - m∠EDA) = sin∠EBC.
Hence:
cos(90 - m∠EDA) is equal to sin∠EBC.