let a be a 3x2 matrix. suppose we know that 3 -5 and -1 1 satisfy the equations and . find a solution to .
The solution matrix x is [-15 15].
Without any additional information, matrix representations of linear mappings allow for explicit computations in linear algebra.
We can use the properties of matrices and vectors to simplify the equation.
First, we know that Au = a and Av = b, so we can substitute these equations into our original equation:
Ax = -5Au + 5Av
Now we can substitute in the values of u and v that we know:
Ax = -5[3 -3] + 5[-5 3]
Which simplifies to:
Ax = [-15 15]
So x = [-15 15] is a solution to the equation Ax = -5a + 5b.
Correct question :
Let A be a 3x2 matrix. Suppose we know that u = [3 -3] and v = [-5 3] satisfy the equations Au = a and Av = b. Find a solution matrix x to Ax = -5 a + 5 b.
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Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.
The congruence theorems used in this problem are given as follows:
9. AAS.
10. SAS.
11. Not similar.
12. SSS.
What are the congruence theorems used?For item 9, the AAS theorem is used, as the two angles, the 72º and the vertical angle, are congruent, along with the another side.
For the item 10, we have that the SAS theorem is used, as we have that the sides between the same angle are proportional.
For item 11, the triangles are not similar, as the side lengths are not proportional.
For item 12, the SSS theorem is used, as the three angles of the similar triangles have the same measure.
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Help please
The mathematician Girolamo Cardano is credited with the first use of negative square roots in solving the now-famous problem, "Find two numbers whose sum is 10 and whose product is 40. Show that the complex numbers 5 + iv15 and
5 - i~15 satisfy the conditions of the problem.
View image
Girolamo Cardan or Cardano was an Italian doctor and mathematician who is famed for his work Ars Magna which was the first Latin treatise devoted solely to algebra.
What is Cardano's formula?For which the relation =p/3 holds (such a value of p exists always), the Cardano formula for the roots of (1) has the form: x=3q2+q24+p327+3q2q24+p327.
P and Q are arbitrary complex numbers in the Cardano formula. By substituting y = x + b/3a, the square term is eliminated. Rewrite the aforementioned equation to u3 + v3 + (u+v)(3uv + p) + q = 0 if x = u+v. The equation above is changed to u3 + v3 = -q by setting 3uv + p = 0. We achieve the system in this manner.
With regards to scalability, interoperability, and sustainability issues on cryptocurrency platforms, Cardano is specifically designed to address these. The first issue is the sluggishness of networks and excessive costs brought on by an increase in transaction volume.
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is 5 a quartly number
Answer:
Step-by-step explanation:
Quarter implies 4. If there were 20 items, and you broke them into quarters, each quarter would have 5 items.
The sum of the measures of angle S and angle T is 120°
*The measure of angle S is (8x + 5).
The measure of angle Tis 35°
What is the value of a ?
A) x=20
B) x=10
C) x=40
D) x=80
The value of x in the angles is 10.
How to find the measure of angles ?The sum of the measures of angle S and angle T is 120 degrees. Therefore, the measure of the angles are as follows:
The measure of angle S is (8x + 5) degreesThe measure of angle T is 35 degreesTherefore, the value of a can be found as follows;
∠S + ∠T = 120
∠S = 8x + 5 degrees
∠T = 35 degrees
Therefore,
8x + 5 + 35 = 120
8x + 40 = 120
8x = 120 - 40
8x = 80
divide both sides by 8
x = 80 / 8
x = 10
Therefore,
x = 10
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create an equivalent boolean algebra expression for a circuit with 2 inputs a and b, whose output q is true when less than two inputs are true.
An equivalent boolean algebra expression for a circuit with 2 inputs a and b is q = (a XOR b)
One way to represent this circuit using Boolean algebra is to use the logical operators AND, OR, and NOT.
The output of the circuit, q, is true when less than two inputs, a, and b, are true. This can be represented as:
q = (NOT(a) AND NOT(b)) OR (NOT(a) AND b) OR (a AND NOT(b))
This can also be represented using the XOR operator (Exclusive OR) which output is true if one and only one input is true:
q = (a XOR b)
Another equivalent representation can be achieved by using the NOR operator which gives true only when none of the inputs is true:
q = NOT( a NOR b)
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a boeing 747 has a wingspan of 195.7 feet and a 6.95 aspect ratio. it cruises at 500 mph at a weight of 550,000 pounds at 35,000 feet (density of 0.000737 slug/ft3). assume that the reynolds number can be approximated using: re
1)Therefore the wing area is determined as 5511 ft2 2) The elliptic chord length is 35.87 f t 3) The Reynolds number for the given elliptical wing is 1.672 X 10^8 4) So, the speed of the plane is 733.33 f t/s.
1) Wing Area
Wing Area determined by using the wingspan and aspect ratio of the Boeing. Where the Aspect ratio of the wing written as,
AR=S^ 2/A
Here s is the wingspan, A is the Wing area and AR is the Aspect ratio.
A=S^ 2/AR=195.7^ 2/6.5=5510.57 FT^ 2
Therefore the wing area is determined as 5511 ft2
2) Average Elliptical chord
Elliptic chord of the Boeing wing determined by the elliptical wing Aspect
ratio,
AR=4xspan/π x chord
chord=4x span/π x AR
chord=4x 195.7/πx6.95=35.87f t
Therefore, the elliptic chord length is determined as35.87 f t
3) Reynolds Number
Reynolds number for the given wing is determined by the average speed and the average chord length
Re=9324xVxc
Here V is the average speed and c is the chord length using the determined values we can find the Reynolds number as,
Re=9324x500x35.87=1.67225x10^ 8
Therefore, the Reynolds number for the given elliptical wing is 1.672 X 10^8
4) Cruise Speed
Where the Speed of the cruise is given as 500 mph to convert the speed mph into the f t/s,
Speed=500x5280/3600=733.33 f t/s
Here 1 mile = 5280 f t and 1 hour = 3600 seconds
So, the speed of the plane is determined in the f t/s as 733.33 f t/s.
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What type of transformation is shown?
Answer:
the third one.
Step-by-step explanation:
clockwise rotation of 90*
Answer:
clockwise rotation of 90 degrees
Step-by-step explanation:
Please put me as brainliest answer :)
The table shows the number of smartphones sold at an electronics store each day. A 2-column table with 5 rows. Column 1 is labeled Day with entries Monday, Tuesday, Wednesday, Thursday, Friday. Column 2 is labeled Smartphones sold with entries 8, 13, 12, 10, 15. To the nearest tenth, what is the standard deviation of the data? Use this formula: s = StartRoot StartFraction Sigma-summation (x Subscript I Baseline minus x Overbar) squared Over n minus 1 EndFraction EndRoot 1.5 smartphones 1.9 smartphones 2.1 smartphones 2.7 smartphones
The standard deviation of the data is 2.41 smartphones.
What are the types of representing data?Data refers to the elements that make up persons, things, events, and ideas. It could be an integer, a title, or anycast. Data must be tabulated after collection in order to study their prominent characteristics. The presentation of data is the name given to such a configuration.
Bar Chart, Histogram, Line Graph, Pie Chart, Frequency Distribution Table.
Given, The number of smartphones sold at an electronic store each day
is represented by the table with two columns and 5 rows.
The mean of the data set is,
= (8 + 13 + 12 + 10 + 15)/5.
= 11.6.
We know the formula for the standard deviation of a data set is,
= [tex]\frac{1}{\sqrt{n}}\sqrt{\sum_{i =1}^{n} (x_i - \overline{x}{}})^2[/tex].
= (1/√5)×√[(-3.6)² + (-1.4)² + (-0.4)² + (-1.6)² +(-3.4)²].
= (1/√5)×[√29.2].
= 2.41.
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Answer:
2.7 Smartphones
Step-by-step explanation: Just did it
Calculate the percent change. Then, describe
the change as an increase or decrease.
20 to 14
The percentage change from 20 to 14 is 30% decrease
How to determine the percentage changeFrom the question, we have the following parameters that can be used in our computation:
20 to 14
The final value (14) is less than the initial value (20)
So, the change is a percentage decrease
The change is then calculated as
Change = (Final value - Initial value)/Initial value * 100%
Substitute the known values in the above equation, so, we have the following representation
Change = (14 - 20)/20 * 100%
Evaluate
Change = -30%
Hence, the percentage decrease is 30%
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The graph of h is a translation 4 units right and 1 unit down of the graph of f(x) = x^2. Write function h in vertex form
After translation of the graph 4 unit right and 1 unit down the graph of the function h(x) = (x +4)² -1
What is translation?The translation is defined as the displacement of the geometrical shape as per the given condition in the coordinate plane.
According to the question, The graph of h is a translation of 4 units right and 1 unit down of the graph of f(x) = x^2.
Given function,
f(x) = x^2.
As per the given condition,
Graph of h is a translation of 4 units right and 1 unit down of the graph of f(x).
x translated by 4 unit right = (x +4)²
f(x) translated 1 unit down = f(x) -1
Vertex form of function h(x) = (x +4)² -1
Therefore, h(x) = (x +4)² -1 is the function After translation of the graph 4 unit right and 1 unit down
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what 20903 x 8748 because i do not understand and keep getting mixed up
Answer:
182859444
Step-by-step explanation:
You just have to times them together
Write an equation for a line perpendicular to y= -5x-1 and passing through the point of (10,3)
Answer: The slope of a line perpendicular to y = -5x - 1 is 5, as the slopes are negative reciprocals of each other. To find the equation of a line passing through the point (10, 3), we can use the point-slope form of a line, which is:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through, m is the slope of the line, and y and x are the variables representing the coordinates of a point on the line.
Plugging in the given values:
y - 3 = 5(x - 10)
Simplifying, we get:
y = 5x - 25 + 3
y = 5x - 22
So the equation of the line is y = 5x - 22
Step-by-step explanation:
3
Module One - The 2 R's of Infection
Select the one (1) correct answer. Which of these statements is
correct?
There is no need for infection control risk assessments
The infection control risk assessments are not important
There is a need for infection control risk assessment
There is a need for infection control risk assessment is correct statements.
What does risk assessment in infection control accomplish?To evaluate infection hazards and risks and to make sure that they are, if feasible, eliminated, minimised, confined, and managed effectively, an infection control risk assessment must be conducted.Tools called Infection Control Assessment and Response (ICAR) are used to systematically evaluate infection prevention and control (IPC) procedures in healthcare facilities and direct quality-improving initiatives (e.g., by addressing identified gaps).hand cleanliness Personal protective equipment usage (e.g., gloves, masks, eyewear). Coughing manners and respiratory hygiene. Sharps security (engineering and work practise controls).There is a need for infection control risk assessment is correct statements.To learn more about risk assessment refer to:
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Given this equation for converting temperature from Fahrenheit (f) to Celsius (c) is C = [5(f – 32)]/9, what is the Celsius temp when Fahrenheit is 104 degrees?
Answer:
40
Step-by-step explanation:
c= 5*(104-32)/9 =40
Solve.
Morgan's school is 10 miles from his house on the same
street. If he walks down the street directly from his school
to his house he passes a park and a snack shack. The park
is 2.55 miles from the school to the and the snack shack is
3.45 miles from the park. How many miles is it from the
park to Morgan's house?
2021 Gifted on the Go
The distance between Morgan's house and the park is 7 miles.
How many miles is it from the park to Morgan's house?We know that the Morgan's house, the park, the snach shack, and the high school are on the same street.
We know that the distance between Morgan's house and the school is 10 miles.
The distance between the park and the high school is 2.55mi, the the distance between Morgan's house and the park is:
10 mi - 2.55mi = 7.45mi
And the snack shack is at 3.45 miles from the park, then we will get that the distance between Morgan's house and the snack shack is:
7.45mi - 3.45mi = 4mi
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Lian's dog eats
of a bag of dog food each week. Lian currently has of a bag remaining.
How many weeks will it take Lian's dog to finish this remaining food?
weeks
Stuck?
The period that it would take the Dog to finish the remaining food would be a period of 12.5 weeks
How to solve for the period that it would take to finish the foodThe amount that the dog eats weekly is given as 1 / 20 of the food.
The amount that Lian has left in the bag is given as 5 / 8
To get the number of weeks that it would take to finish the food, we would divide 1 / 20 by 5 / 8
1 / 20 ÷ 5 / 8
20 / 1 * 5 / 8
= 100 / 8
= 12.5
Hence it would take 12.5 weeks for the dog to finish the remaining food here.
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'Lian's dog eats 1/20 of a bag of dog food each week. Lian currently has 5/8 of a bag remaining.How many weeks will it take Lian's dog to finish this remaining food?weeksStuck?
The compound figure shown is composed of a
semicircle and a rectangle.
Which best represents the area of the composite
figure
A) 88ft2
B) 108 ft2
C) 75 ft2
D) 100ft2
Answer:
A
Step-by-step explanation:
this is a college level question ? oh my ...
to get the total area we need to add the area of the rectangle and the area of the half-circle.
the area of the rectangle is
length × width = 15 × 5 = 75 ft²
the area of the half-circle is
pi×r² / 2
how do we get r (radius) ?
we know, both lengths of the rectangle must be equally long. so, 15 ft.
we see that the remaining length after the half-circle is 9 ft.
so, the diameter of the half-circle is 15 - 9 = 6 ft.
the radius is half the diameter, so r = 6/2 = 3 ft.
the area is therefore
pi×3² / 2 = 9pi /2 = 14.13716694... ft²
in total that makes
75 + 14.13716694... = 89.13716694... ft²
the closest of your answer options is A : 88 ft²
Find measure angle ACB
Answer:
87 degrees
ADE ~ ACB (AB is twice the length of AE, AC is twice of AD, CAB and DAE common angle)
So AED and ABC should be equal
11x-2=6x+13
5x=15
x=3
Angle ABC will equal:
6(3)+13= 31 degrees
ACB = 180-31-62
ACB = 87 degrees
18. Subtract:
8.50
- 4.75
19. Multiply:
X
0.625
5
20. Divide: 0.04)26.4
Answer:
18.
3.25
19.
3.125
20.
-26.36
Step-by-step explanation:
What number gives a result of −4
when 8
is subtracted from the quotient of the number and 4
?
The number that gives a result of −4 when 8 is subtracted from the quotient of the number and 4 is: 16.
What is the Quotient of Two Numbers?The quotient of two numbers is the result obtained when one number is divided by the other. It is the number of times one number can be divided into the other. For example, if you divide 20 by 4, the quotient is 5, meaning that 4 can be divided into 20 five times. It is represented mathematically as: quotient = numerator/denominator.
Let x represent the number. Therefore, you can find this number by solving the equation:
(x/4) - 8 = -4
(x/4) = -4 + 8
x/4 = 4
x = 4 * 4 = 16
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simplfy : -3 1/2- (-12 1/4)
Answer: 35/4 or 8.75 or 8 3/4
Step-by-step explanation:
First, you start by multiplying the minus sign by the parenthesis.
you multiply a negative sign by a negative sign so it cancels out into a positive one.
Then it will be -3 1/2 + 12 1/4. Change the denominator to do both 4, so we can solve the equation.
-3 2/4 + 12 1/4. That will equal 8 3/4 or 35/4.
The answer is 8 3/4 or 35/4.
what is 15 ones dividend by eight and seven fifty eight thousandths
15 divided by eight and seven fifty eight thousandths will give a quotient of one and seven hundred and three thousandths
What is division operation?One of the four fundamental operations, along with addition, subtraction, and multiplication, is division. A number is split using the straightforward method of division.
The division (/) operator creates the product of its operands, where the dividend is the left operand and the divisor is the right operand.
In the problem written the words the division is done by writing in figure as below
15 ÷ 8.758
Using calculator the quotient is 1.7127 = 1.713 to the nearest thousandth
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Which expression is equivalent to 3 times 5 times 5 times 5 times 5 times 5 times 5?
the si (metric) unit of length, the meter, is defined as the distance between two marks on a standard metal bar
The SI unit of length is meter and it defines the length between two end points.
The term length in math is defined as the measurement or extent of something from end to end.
Here we need to find the SI unit of length.
As we all know that the SI unit of length is The meter ad the symbol m and it is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m s⁻¹ where the second is defined in terms of ΔνCs.
Here the value of length is required to be measured ad it can convert a meter into various units like milliliters (mm), kilometer (km), centimeter (cm).
Complete Question:
What is the SI unit of length and elaborate the details about it.
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In a garden,
5
6
6
5
start fraction, 5, divided by, 6, end fraction of the area is filled with native plants. The native plants take up
107
4
m
2
4
107
m
2
start fraction, 107, divided by, 4, end fraction, start text, m, end text, squared. Let
�
gg represent the total area of the garden.
Select
1
11 multiplication and
1
11 division equation to represent the relationship.
Answer:hewwo
Step-by-step explanation:hewwo
Answer: The answer is b and c
Step-by-step explanation:
the sum of 8 and 11 times a number
The sum of 8 and 11 times a number will be (8+11x).
What does a math sum mean?A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms. The result or conclusion of adding two or more numbers or sentences is known as the sum.
Let x be the number.
The result is 11 times the number, or 11x.
The result of adding the number's multiples of 8 and 11 is 8+11x.
What is sum, for instance?The result that is produced when we add numbers, objects, or other things is referred to in mathematics as the sum. For instance, the sum of addends 14 and 6.
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What expression is equivalent to 4/9(2n -3)
8n/9-4/3 is the equivalent expression of 4/9(2n -3)
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 4/9(2n -3)
Four by nine times the 2n minus three.
n is the variable in the given expression and minus is the operator.
Apply distributive property
4/9(2n)-4/9(3)
8n/9-12/9
8n/9-4/3
Hence, 8n/9-4/3 is the equivalent expression of 4/9(2n -3)
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The town of Madison has a population of 25{,}00025,00025, comma, 000. The population is increasing by a factor of 1.121.121, point, 12 each year.
Write a function that gives the population P(t)P(t)P, left parenthesis, t, right parenthesis in Madison ttt years from now.
The population after 12 years is 98448 and the formula is[tex]P(t) = 25000(1.121)^{t}[/tex].
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the population of the town is 25000 and increasing at the rate of 1.121.
The expression will be written as:-
[tex]P(t) = 25000(1.121)^{t}[/tex]
[tex]P(12) = 25000(1.121)^{12}[/tex]
P(12) = 98448
Hence, the population after 12 years will be 98448.
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use the following sample data to calculate the measures of central tendency and dispersion: two decimal places. 10 12 15 22 22 34 42
The measures of central tendency are Mean: 22.14, Median: 22.00, Mode: 22.00, and dispersion are Range: 32, Variance: 183.14, Standard deviation: 13.53 Interquartile range: 12.00
According to the question
The mean, median, and mode values for this collection of data are 22, 14, and 22, respectively. The median is the midway value when the data are arranged, while the mode is the value that occurs the most frequently. The mean is the average of the data set. Range = 32, Variance = 183.14, Standard deviation = 13.53, and Interquartile Range = 12.00 are the metrics of dispersion for this data set. The variance measures the spread of the data, the standard deviation is the square root of the variance, and the interquartile range is the difference between the median of the upper half and the median of the lower half of the dataset. The range is the difference between the highest and lowest values.
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