The required elementary matrix E such that EA = B is
[tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex].
Any matrix obtained by performing a single elementary row operation on the identity matrix is called an elementary matrix.
The elementary operations are as follows:
1. Interchange the two rows of a matrix
2. Multiply a row of a matrix by the non-zero scalar k.
3. Add k-times of a row into another row of the matrix.
Each type of elementary operation may be performed by matrix multiplication, using square matrices called elementary operators.To perform an elementary row operation on A, an n×m matrix, take the following steps:
1. To find E, the elementary row operator, apply the operation to an n×n identity matrix.
2. To carry out the elementary row operation, premultiply A by E.
We want to interchange the first and second rows of A, a 3×3 matrix to get B. To create the elementary row operator E, we interchange the first and second rows of the identity matrix I3:
[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex] is changed to [tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex].
So, [tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex][tex]\left[\begin{array}{ccc}2&1&3\\-2&4&5\\3&1&4\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}2&1&3\\3&1&4\\-2&4&5\end{array}\right][/tex]
Thus, the required elementary matrix E such that EA = B is
[tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex]
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what is another name for a chord that passes through the center of the circle? A) Diameter B) Circumference C) center D) radius
Answer:
A
Step-by-step explanation:
diameter
The another name for the chord that passes through the center of the circle is the diameter.
The correct option is (A).
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.
As per the given data:
We have to find out the alternate name for a chord that passes through the center of a circle out of the given options.
Diameter:
It's a chord that passes through the center and touches the ends of the circumference of the circle.
Hence, this is correct.
Circumference:
It's the length of the boundary of a circle, hence this cannot be a chord.
This is incorrect.
Center:
It's a point and a chord is a line, hence this cannot be true.
Radius:
A radius is not a chord, as it does not touch the endpoints on the circumference of the circle.
The another name for the chord that passes through the center of the circle is the diameter.
Hence, The another name for the chord that passes through the center of the circle is the diameter.
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The width of a rectangle is the length minus 3 units. The area of the rectangle is 28
units. What is the length, in units, of the rectangle?
Which of the following pairs of equations has exactly the same solution?(1 point)
−3.2x=0.64 and x/4 =−0.05
⅜ x=1 and ⅓ x=⅛
x/3.2 =1.8 and 1.8x=3.2
− 3/4 x=5/2 and 5/2 x=− 3/4
Answer: The first pair of equations, i.e., −3.2x=0.64 and x/4 =−0.05, have exactly the same solution. In both of these equations, the value of x comes out as -0.2.
Step-by-step explanation: Simplifying the first set of equations, we get:[tex]-3.2x=0.64[/tex]
[tex]x=0.64/-3.2[/tex]
x=-0.2
[tex]x/4=-0.05[/tex]
[tex]x=-0.05*4[/tex]
x=-0.2
Simplifying the second set of equations, we get:
[tex]3/8x=1[/tex]
[tex]x=8/3[/tex]
x=2.66
[tex]1/3x=1/8[/tex]
[tex]x=1/8*3[/tex]
x=0.375
Simplifying the third set of equations, we get:
[tex]x/3.2=1.8[/tex]
[tex]x=1.8*3.2[/tex]
x=5.76
[tex]1.8x=3.2[/tex]
[tex]x=3.2/1.8[/tex]
x=1.77
Simplifying the fourth set of equations, we get:
[tex]-3/4x=5/2[/tex]
[tex]x=5/2*-4/3[/tex]
x=-3.33
[tex]5/2x=-3/4[/tex]
[tex]x=-3/4*2/5[/tex]
x=-0.3
Therefore, the first pair of equations, i.e., −3.2x=0.64 and x/4 =−0.05 have exactly the same solution.
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What is the best unit to measure the capacity of a washing machine.
A) milliliter
B) liter
Answer:
Liter
Step-by-step explanation:
Milliliters are used for much smaller amounts of liquid.
Question 11
Erica recorded the number of sales she made during each of the first 4 months when she began her new career. Erica plotted the data on a coordinate grid, and she noted that the data correlate to an exponential equation, as shown What is the domain of the function shown in the graph?
The domain of the graph is {1, 2, 3, 4}
What is Domain?"All the values" that are input into a function are referred to as the domain of a function. The set of all potential inputs for a function is its domain.
Given:
As, we know domain of a function is the set of all possible inputs for the function.
from the Graph, we can find the coordinates ( 1, 10), (2, 20), (3, 40) and ( 4, 80)
So, the domain of the graph is {1, 2, 3, 4}
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Consider the graph of the line y = 1//2x – 4 and the point (−4, 2). The slope of a line parallel to the given line is . A point on the line parallel to the given line, passing through (−4, 2), is . The slope of a line perpendicular to the given line is . A point on the line perpendicular to the given line, passing through (−4, 2), is ✔ (–2, –2) .
For the given line y = 1/2x - 4,
The slope of the line parallel to the given line is m = 0.The point on the line parallel to the given line, passing through (-4, 2) is (0, 4) and its equation is x - 2y + 8 = 0.The slope of the line perpendicular to the given line is m = -2.The point on the line perpendicular to the given line, passes through (-4, 2) is (-2, -2) and its equation is y = -2x - 6.How to calculate the slopes and equations of parallel and perpendicular lines of a line?Consider a line with the equation ax+by+c=0
The slope of the line is m = -b/a.The slope of the line parallel to the given line is m = 0.The slope of the line perpendicular to the given line is m = a/b or the product of their slopes equal to -1.The equation of the line parallel to the given line and passing through the point (x1, y1) is a(x - x1) + b(y - y1) = 0.The equation of the line perpendicular to the given line and passing through the point (x1, y1) is b(x - x1) - a(y - y1) = 0.Calculation:It is given that, the equation of a line is given as y = 1/2x - 4.
The slope of the given line is m = 1/2; (since it is in the form of y=mx+c)
Then, the slope of the line parallel to the given line is m = 0.
And the equation of the parallel line passing through the point (-4, 2) is
a(x - x1) + b(y - y1) = 0; where a = 1; b = -2 (y = 1/2x-4 ⇒ 2y = x - 8)
⇒ 1(x + 4) - 2(y - 2) = 0
⇒ x + 4 -2y + 4 = 0
⇒ x - 2y +8 = 0
So, the point on the parallel line is (0, 4).
The slope of the line perpendicular to the given line is m = -1/1/2 = -2.
And the equation of the perpendicular line passing through the point (-4, 2) is
b(x - x1) - a(y - y1) = 0; where a = 1; b = -2;
⇒ -2(x + 4) - 1(y - 2) = 0
⇒ -2x - 8 - y +2 = 0
⇒ y = -2x - 6
So, the point on the perpendicular line is (-2, -2).
All of these are shown in the graph below:
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bill and julio each thought of a whole number between 1 and 20.Bill"s number was 15 and Julio's number was 6.What percent of Julio's number was Bill"s number?
60% of Julio's number was Bill"s number
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
bill and julio each thought of a whole number between 1 and 20.
Bill"s number was 15
Julio's number was 6
We need to find what percent of Julio's number was Bill"s number
Original number minus new number by original number
(15-61)/15
9/15
0.6
Now we have multiply with 100 as it is a hundredth part.
0.6×100=60
Hence, 60% of Julio's number was Bill"s number
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How do you write 3/4 as a percent?
Answer:
0.75 or 75%
Step-by-step explanation:
I know that 2/4 is 0.5 or 50% and 1/4 is 0.25 or 25% so it goes by 25. One more than 2/4 is 3/4, which is what you are trying to find, so it would be 0.75, or 75%.
How do you write 0.85 as a percent?
Answer: 85%
Step-by-step explanation:
Since percentages are numbers/ratios expressed as a fraction of 100, 85/100 becomes 85%
Solve the equation for a. K = 4a + 9ab a = K(4 + 9b) a = 4(K + ...
The equation K = 4a + 9ab solved for a is a = K /(4 + 9b). (Option D)
In mathematics, an equation refers to a formula that expresses the equality of two mathematical expressions by connecting them with the equals sign =.
The given equation is K = 4a + 9ab.
In order to solve for a, the a variable must be isolated at one side of the equation and the other variables must be collected on the other sides.
On the right-hand side, as both terms contain the variable a, hence factoring it,
K = a(4 + 9b)
Dividing both sides by (4 + 9b) to isolate a,
a = K /(4 + 9b)
Note: The question is incomplete. The complete question probably is: Solve the equation for a in K = 4a + 9ab. A) a = K(4 + 9b) B) a = 4(K + 9b) C) a = (4 + 9b)/K D) K /(4 + 9b)
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Complete the coordinate proof of the theorem.
Given: ABCD is a square.
Prove: The diagonals of ABCD are perpendicular.
The coordinates of the square be
A (0, 0)
B (a, 0)
C (a, a)
D (0, a)
slope of line AC = 1
How to find the slope of ACSlope is the rate of change of the line AC this is solved by taking the ratio of change in y to change in x
A (0, 0) and C (a, a)
= (0 - a) / (0 - a)
= -a / -a
= 1
Slope of line BD = -1
the product of the slopes
= 1 * -1
= -1
therefore the diagonals of the ABCD are perpendicular since the product of the slope is -1
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pq²(p² - 3pq - 4q²) answer fast pls
(GEOMETRY) PLEASE HELP ME WRITE A TWO COLUMN PROOF FOR THIS PROBLEM!!!!
If right triangle ABC with right angle ACB and altitude CD then
ΔABC ~ ΔACD
ΔABC ~ ΔCBD
ΔACD ~ ΔCBD
What is Angle-Angle Similarity (AA~) Theorem?
If two angles of one triangle and two corresponding angles of another triangle are congruent, then the triangles are similar.
According to the given question:
A right triangle is given with its altitude drawn from the right angle to its hypotenuse.
Consider the triangled ABC and ACD
By the reflexive property of angle congruence, it follows that:
∠A ≅ ∠A
Since the angles B and D are right angles, from the right angles congruence theorem, it also follows that:
∠C ≅ ∠D
Hence, by the Angle-Angle Similarity (AA~) Theorem, it follows that triangles ABC and ACD are similar. Similarly triangle ABC is similar to triangle CBD
Consider triangles ACD and CBD:
Triangles ABC and ACD are similar. Also triangle ABC is similar to triangle CBD
Therefore, Triangle CBD is similar to triangle ACD as both of them are similar to triangle ABC.
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Addison has x dimes and y nickels, having a minimum of 20 coins worth at most $1.60 combined. No less than 4 of the coins are dimes. Solve this system of inequalities graphically and determine one possible solution.
The required graph of the inequality has been shown and the solution is; 8 Nickels and 12 dimes.
How to solve a system of inequalities?
Inequality can be defined as the relation of the equation possessing the symbol of ( ≤, ≥, <, >).
Let the number of nickels be x and let the number of dimes be y,
We are told that Addison has x dimes and y nickels, having a minimum of 20 coins worth at most $1.60 combined. Thus, we can generate the equations as;
x + y = 20
x = 20 - y - - - - (1)
0.05x + 0.10y ≤ 1.60 - - - -(2)
We are also told that no less than 4 of the coins are dimes. Thus;
x ≥ 4
From the graph, one solution is given as 8 Nickels and 12 dimes.
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HELPPPP ASAPPPP PLEASEE!!!
Answer:
step 4 ,step 2, step 1 , step 3 , step 5
Which parent functions have a domain of all real values of x? Select all that
apply.
A. Reciprocal
B. Cubic
C. Quadratic
D. Cube root
E. Linear
F. Absolute value
Answer:
A D F
Step-by-step explanation:
The parent functions with a domain of all real values of x are the linear function, the absolute value function, the square root function, and the cube root function.
The linear function is defined by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. The domain of this function is all real values of x.
The absolute value function is defined by the equation y = |x|, where |x| is the absolute value of x. The domain of this function is all real values of x.
The square root function is defined by the equation y = √x, where √x is the square root of x. The domain of this function is all nonnegative real values of x.
The cube root function is defined by the equation y = ∛x, where ∛x is the cube root of x. The domain of this function is all nonnegative real values of x.
Therefore, the correct answers are A, D, and F. The reciprocal function, the cubic function, and the quadratic function do not have a domain of all real values of x.
a new vaccination is being used in a laboratory experiment to investigate whether it is effective. there are 273 subjects in the study. is there sufficient evidence to determine if vaccination and disease status are related?vaccination statusdiseasednot diseasedtotalvaccinated5762119not vaccinated8371154total140133273step 2 of 8: find the expected value for the number of subjects who are vaccinated and are diseased. round your answer to one decimal place.
The expected value for the number of subjects who are vaccinated and are diseased is 56.7
Since we are given the information that a new vaccination is being used in a laboratory experiment to investigate whether it is effective. there are 273 subjects in the study. We can calculate this by taking the total number of subjects who are vaccinated (119) and multiplying it by the proportion of subjects who are diseased
(47/273). 119 x (47/273) = 56.7
which is the expected value for the number of subjects who are vaccinated and are diseased
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50 POINTS! Please Help!
what is the value of tan a?
The value of tanA is always less than 1.
What is a number's tan of?
Tangent is the ratio of the side opposite the angle we know or want to know over the side next to that angle, and is sometimes abbreviated as T-A-N.
Describe tan angle A.
The trigonometric ratio between the opposite and adjacent sides of a right triangle that contains an angle is its tangent.
Tangent is the mathematical term for the length of the leg that faces the angle and is often abbreviated as "tan." For instance, in the triangle above, tan(A) = 68 or 34 and tan(B) = 86 or 43.
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8010005 in international number system
Answer:
8,010,005
Step-by-step explanation:
eight million ten thousand and five
hope this helps
Jerry bulit a table with a square top. the perimeter of the tabletop is 18 feet. He knows that the side lentgh of the table is 3, 3 1/4 4 or 4 1/2 use the equation 18 = 4s where s is the side length of the table to determine the side length explain how you found your answer
Answer:
4 1/2 ft
Step-by-step explanation:
18 = 4s
Divide both sides by 4.
18/4 = 4s/4
9/2 = s
4 1/2 = s
The side of the table is 4 1/2 ft.
if you select a random sample of full-time college students, there is an hance that the sample mean is less than how many hours per week?
The sample mean is less than 26.92 hours per week .
What is standard deviation?
Your dataset's average level of variability is represented by the standard deviation. In general, it reveals how far away from the mean each value is.
A low standard deviation denotes that values are grouped closely to the mean, while a high standard deviation denotes that values are typically spread widely from the mean.
Let X~ Normal (26, 4/√16) distribution ie Normal (26, 1) distribution
We want,
P(X<a) = 0.82
Using standard normal approximation,
P(z< (a-26)/1) = 0.82
Using standard normal distribution tables, we get
(a-26)/1 = 0.915
(Since P(z<0.915) = 0.82)
So, a= 26+0.915= 26.915
So the required value is 26.92 (rounded to two decimals)
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Fill in the blank there is a correspondence between In a probability histogram, there is a correspondence between volume and probability area and volume variation and area. area and probability
In a probability histogram, there is a correspondence between area and probability. Hence, option D is the right answer.
An histogram shows the variation in a variable over time. There are a certain number of samples in each category: this is called the frequency distribution. The number of children born according to their birth gender, such as males or females.
Probability histogram
A probability histogram is a histogram with probabilities on the y-axis and all the possible values on the x-axis. They represent chance. The area above a class interval represents the chance of that class interval.
A probability distribution shows the probabilities related to all possible outcomes of an event.
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The complete question is-
Fill in the blank.
In a probability histogram, there is a correspondence between--------------
A. volume and probability
B. area and volume
C. variation and area
D. area and probability
Claudia spends $2.00 a day for lunch. Her cafeteria lunch account has a balance of $48.00. How many days, d, can Claudia eat without adding money to her lunch account?
Answer:
24 days
Step-by-step explanation:
you have to divide the balance by the spending money, so £48.00, divided by £2.00 will equal 24 meaning, Claudia can last 24 days without adding money to her account
Which of the following pair of linear equations is inconsistent?
A. x - 2y = 6; 2x + 3y = 4
B. 9x - 8y = 17; 18x -16y = 34
C. 2x + 3y = 7; 4x + 6y = 5
D. 5x - 3y =11; 7x + 2y =13
Draw the net diagram of the the 3-object below and determine the total surface area
Answer:
see below for the netarea: 168 cm²Step-by-step explanation:
You want the net and total surface area for the triangular prism shown.
NetThe net diagram is attached. It consists of three rectangles with triangles attached to the ends of the widest rectangle. Of course, these parts can be arranged in any order you find convenient, as long as the common edges match the original prism.
AreaThe net shows the area can be computed as the sum of a rectangle 9 cm high and 5+6+5 = 16 cm wide, together with two triangles of base 6 cm and height 4 cm.
A = (9 cm)(16 cm) +2(1/2)(6 cm)(4 cm)
= 144 cm² +24 cm²
= 168 cm²
The total surface area of the prism is 168 cm².
__
Additional comment
The formulas for the area of a rectangle and triangle are ...
A = LW . . . . . area of a rectangle of length L and width W
A = 1/2bh . . . . area of a triangle of base b and height h
In 1846 the depth of the river was 5 feet deep. In 1847 it dropped to 3.5 feet. This year, 1848, it rose to 5.3 feet.
What is the percentage change
Answer:
From 1846 to 1847 there was a 30% decrease and from 1847 to 1848 it increased by 51.4%
Step-by-step explanation:
How it decreased by 30%
V2-V1/V1x100
V2=3.5 V1=5
=(3.5−5)|5|×100
=−1.55×100
=−0.3×100
=−30%change
=30%decrease
How it increased by 51.4%
V2-V1/V1x100
V2=5.3 V1=3.5
=(5.3−3.5)|3.5|×100
=1.83.5×100
=0.514286×100
=51.4286%change
=51.4%increase
Condense the logarithm
log d +8log q
The value of the condensed logarithm is, log(dq^8).
What is logarithm?
The opposite of exponentiation in mathematics is the logarithm. The exponent to which b must be raised in order to produce a number x is therefore the logarithm of a number x to the base b. For instance, since 1000 = 10^3, log10 of 1000 is 3, or [tex]log_1_0[/tex] = 3.
Given: log d + 8 log q.
We have to condense the given logarithm
Frist to simplify 8 log q by moving 8 inside the logarithm.
⇒ log(q)^8
⇒ log d + log(q^8)
Applying the product rule of logarithm
log(a) + log(b) = log(ab)
⇒ log d + log (q^8) = log(dq^8)
Hence, the condensed logarithm form of the given logarithm is, log(dq^8).
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write the equation of the line in slope-int form that is perpendicular to y=-x - 18 and passes through (-6,11)
Answer:
y = x + 17
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - x - 18 ← is in slope- intercept form
with slope m = - 1
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1 , then
y = x + c ← is the partial equation of the perpendicular line
to find c substitute (- 6, 11 ) into the partial equation
11 = - 6 + c ⇒ c = 11 + 6 = 17
y = x + 17 ← equation of perpendicular line
aspurpinion has 17 teeth and a diametral pitch of 8 teeth/in. it runs at 1120 rpm and drives a gear at 544 rpm. find the number of teeth on the gear and the distance between the centers of the pinion and gear
Theoretical centre-to-centre distance (C)=3.25 which is the distance between the centers of the pinion and gear
Given data:
No. of teeth on the pinion(TP)=17.
Diametral pitch(pd)=8 teeth/in.
The rotational speed of the pinion(NP)=1120 rev/min or 1120 rpm.
The rotational speed of the gear(NG)=544 rev/min or 544 rpm.
To calculate:
No. of teeth on gear(TG) & theoretical centre-to-centre distance(C).
We know that;
Diametral pitch(pd)=No. of teeth in the gear/Diameter of the gear
For pinion,
pd=TP/DP
Pittiong the values in above eq.
8 teeth/in =17/DP =>DP=17/8 in.
or DP=2.125 in.
Gear ratio(G)=(NP/NG)=(TG/TP)=(DG/DP)
(NP/NG)=(TG/TP)
1120/544 =TG/17 =>TG=35
therefore No. of teeth the gear(TG)=35 {Ans}
Also from gear ratio formula,
(NP/NG)=(DG/DP)
1120/544=DG/2.125
DG=4.375 in.
In figure I have drawn a rough diagram of the pinion and gear arrangement which will help you to understand how to calculate the centre-to-centre distance(C)
From fig.,
centre to centre distance,C=rP+rG {Where rP and rG are the radii of pinion and gear respectively}
C=(DP+DG)/2 {\large \because Diameter =2*radius}
C=(2.125+4.375)/2 in. =3.25 in.
therefore Theoretical centre to centre distance (C)=3.25
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