The converse of the Pythagorean Theorem states that if two sides of a triangle are congruent, then the angles opposite to them are also congruent. This property is known as the Corresponding Angles Postulate.
The Pythagorean Theorem states that the sum of the squares of the lengths of the two sides of a right triangle are equal to the square of the length of the hypotenuse. The theorem is written as a^2 + b^2 = c^2. The converse of the Pythagorean Theorem states that if two sides of a triangle are congruent, then the angles opposite to them are also congruent. This property is known as the Corresponding Angles Postulate. To prove this postulate, we can start with an arbitrary triangle ABC. If we extend the side AC to D, then we can create a line parallel to BC, creating two similar triangles, ABC and ADC. Since similar triangles have corresponding angles that are congruent, then angle A = angle D. Since side AC is congruent to side AD, then angle A is also congruent to angle B. This proves the Corresponding Angles Postulate.
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1.
If
z
y
=
x
, which of the following statements is true?
z - x = y
z - y = x
x · y = z
Answer:b
Step-by-step explanation:
There are three boxes one of them contains gold. In each box, there is amessage
Answer:
Gold is in Box 1
Step-by-step explanation:
There are 3 boxes. One of them contains gold
In each box, there is a message, and one of them is true.
Box 1: "The gold is not in Box 2".
Box 2: "The gold is in this box"
Box 3: "The gold is not in this box".
Which box has the gold?
Answer:
O Box 1
O Box 3
O Box 2
There's not enough info
Assume each statement to be true at a time, and check for contradictions.
Box 1: "The gold is not in Box 2".
Assume True. Gold in 1 or 2.
Box 2: "The gold is in this box"
False. Gold not in 2.
Box 3: "The gold is not in this box".
False. Gold in 3
Contradiction between box1 and box 3 message.
Box 2: "The gold is in this box"
Assume true. Gold in 2.
Box 1: "The gold is not in Box 2".
False. Gold in 2.
Box 3: "The gold is not in this box".
False. Gold in 3.
Contradiction between boxes 2 and 3. Box 2 message cannot be true.
Box 3: "The gold is not in this box".
Assume true. Gold in 1 or 2.
Box 1: "The gold is not in Box 2".
False. Gold in 2.
Box 2: "The gold is in this box"
False. Gold not in 2.
No contradictions.
Gold must be in 1.
Answer: Gold is in Box 1
using the definitions and diagram, determine which sets each number belongs to. circle the symbol if the number belongs to that set. the first one has been done for you as an example. g
The number 9 does not belong to the set g, so it does not get circled. The number 9 belongs to the set A, so it should be circled.
The number 9 does not belong to the set g, so it does not get circled. The number 9 belongs to the set A, so it should be circled.
g = {2, 4, 6, 8}
9
A: A
The number 9 does not belong to the set g, so it does not get circled. The number 9 belongs to the set A, so it should be circled.
The number 9 does not belong to the set g, which consists of the numbers 2, 4, 6, and 8. Instead, the number 9 belongs to the set A, so the symbol should be circled to indicate this. The set A includes all the numbers from 1 to 10, so the number 9 is included. This means that the circle should be placed around the symbol for set A to indicate that 9 belongs to this set.
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perpendicular to line y=1/2x-8 passes through (7,-6) point slope form
The equation of line is y = -2x + 8 and the slope is m = -2
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
The equation of line perpendicular to the line is y = ( 1/2 )x - 8
Now , the slope of the line m₁ = 1/2
For perpendicular lines , the product of the slopes is -1
So , m₁ x m₂ = -1
So , the value of Slope m₂ = -2
And , the line passes through the point P ( 7 , -6 )
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - ( -6 ) = ( -2 ) ( x - 7 )
On simplifying the equation , we get
y + 6 = -2x + 14
Subtracting 6 on both sides of the equation , we get
y = -2x + 8
Hence , the equation of line is y = -2x + 8
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if there are 5 people and 2 have to sit next to each other and 2 others cant sit next to each other, how many combinations
if there are 5 people and 2 have to sit next to each other and 2 others cant sit next to each other, then 30 combinations possible
What are combinations?
A combination is a calculation that determines the number of possible arrangements in a collection of items in which the order of the selection does not matter. In combinations we can select the items in any order.
nn!/r!(n-r)!
Number of ways=5
=5!/2!2!
=5!/2*2
=5*4*3*2/2*2
=30
=30 ways
if there are 5 people and 2 have to sit next to each other and 2 others cant sit next to each other, then 30 combinations possible
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Two 3 x 4 rectangles overlap, as shown below. Find the area of the overlapping region (which is shaded).
Rectangles
The Area of a Rectangle
In geometry, a figure is defined as a rectangle if it is a quadrilateral and it has four right angles and two pairs of parallel sided. The area of such a figure is calculated as A=l w, where l represents the length and w represents the width.
719/64 unit² is the area of the overlapping region (which is shaded)
Rectangles .
What is a rectangle, exactly?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral.
Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.
the Pythagorean theorem as follows to calculate the value of x .
( 4 - x )² = 3² + x ²
16 - 8x + x² = 9 + x²
16 - 8x = 9
16 - 9 = 8x
7/8 = x
Thus, the area of the shaded region will be equal to the area of rectangle ABDC minus the area of the two triangles on the same rectangle. The area of rectangle ABDC is equal to
A = l * w
= 4 * 3
A = 12
The area of each of the two triangles is equal to
A = 1/2bh
= 1/2 ( 7/8) ( 7/8 )
= 49/128
The area of the two triangles is equal to
A = 2 * 49/128
A = 49/64
Therefore, the area of the shaded region is equal to
12 - 49/64 = 719/64 unit²
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HELP ASAP!!!! NO LINKS OR SPAM
Willa earns a bi-weekly gross income of $2,417.00 and has total monthly debt payments of $1,623.00. Determine Willa's current debt-to-income ratio. Round the final answer to the nearest whole percent. (2 points)
28%
31%
34%
35%
Willa's debt to income ratio is 34%.
What is Debt to Income Ratio?Debt to income ratio is usually calculated as a percentage of the gross monthly debt payments divided by the gross monthly income.
Given that,
Willa earns a bi-weekly gross income of $2,417.00
Monthly gross income = 2 × $2,417.00 = $4834
Monthly debt payments = $1,623.00
Debt to income ratio = $1,623.00 / $4834.00
= 0.3357
= 33.57%
= 34%
Hence the debt to income ratio of Willa is 34%.
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4. Alfonso surveyed several students in his school. He asked them to give the grade that they are in and the number of pets they have at home. The results are shown in the table below.
Survey Results
Grade
5
6
2
1
4
2
4
1
4
3
5
Number of
Pets
0
4
2
3
5
1
2
2
0
5
2
Find the correlation coefficient for the data. Round to the nearest hundredth
EDIT: IT ISNT 0.35 , 0.36 nor 0.37 SOOO PLEASE REFRAIN FROM GIVING ME THISE ANSWERS!!!
Answer: sorry would help ya but i can't because i have no clue what the question is asking me to round...
BRAINLIEST ANSWER
please help me answer this question
thanks
-Jake
Answer:
I1 ≈ 103.6∠68.7° mA
I2 ≈ 163.7∠50.3° mA
Step-by-step explanation:
Given equations for mesh currents, you want to find their values in polar form.
(2+j6)I1 -(j4)I2 = 0(j1)I1 +(8-j10)I2 = 2SolutionThe coefficients of these equations can be used to fill an augmented matrix, which can then be reduced by a suitable calculator to give the values of the variables.
I1 = (14+j36)/373 ≈ 0.1036∠68.7°
I2 = (39+j47)/373 ≈ 0.1637∠50.3°
__
Additional comment
The equations can be solved "by hand" using any of the usual methods: substitution, elimination, Cramer's Rule, and others. The complex arithmetic makes it tedious, but not significantly more difficult. A suitable calculator reduces the work substantially.
The second attachment shows more working using the "cross multiplication method", similar to Cramer's Rule.
Square ABCD has a diagonal AC with the given vertices. Find the coordinates of the remaining vertices.
A(2, 2) and C(6, - 2)
The coordinates are (_,_) and (_,_)
Square ABCD has a diagonal AC with the given vertices. Find the coordinates of the remaining vertices. A(2, 2) and C(6, - 2)
The coordinates are B(4,-2,) and (4,0)
What do you mean by coordinates?Coordinates are two numbers (Cartesian coordinates), or sometimes a letter and a number, that locate a specific point on a grid, known as a coordinate plane. A coordinate plane has four quadrants and two axes: the x axis (horizontal) and y axis (vertical). (One way of helping children to remember which of these is which is to tell them that the x axis goes across because ‘x’ is a cross.)
The Cartesian Coordinate System is the name of the two-dimensional plane that is used in math to calculate points using a set of perpendicular lines and basing the points on the place where the line meet. The plane is called a Cartesian plane and Perpendicular lines are lines that intersect at exactly 90 degrees, which makes a right angle.
If A(2,2) and C(6,-2) are the coordinates of two opposite vertices of the square, then the square is a rectangle with a diagonal AC. The remaining vertices of the square can be determined by using the fact that opposite sides of a square are parallel and congruent.
If A(2,2) is one vertex of the square, then the vertex opposite it is C(6,-2)
If C(6,-2) is one vertex of the square, then the vertex opposite it is A(2,2)
The vertex B(x,y) can be found by moving 2 units left from C(6,-2)
x = 6 - 2 = 4
y = -2
so B(4,-2)
The vertex D(x,y) can be found by moving 2 units up from B(4,-2)
x = 4
y = -2+ 2 = 0
so D(4,0)
Therefore, the coordinates of the remaining vertices of the square are B(4,-2) and D(4,0)
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The radioactive substance cesium-137 has a half-life of 30 years. The amount A(t) (in grams) of a sample of cesium-137 remaining after t years is given by the following exponential function.
A(t)=458(1/2 (is written as a fraction) t/3) also written as a fraction
Find the initial amount in the sample and the amount remaining after 50 years.
Round your answers to the nearest gram as necessary.
Answer:
1818886278282871728282882
Differentiation stationary points please help
A stationary point can be found by solving d y d x = 0 , i.e. finding the x coordinate where the gradient is 0.
How do you find the coordinates of a stationary point of a curve?When the derivative of a function, f(x), equals 0, it is said to be stationary. Because the function is neither increasing nor decreasing at these locations, they are referred to be "stationary" points.
This graphically correlates to locations on the graph of f(x) where the horizontal line that forms the tangent to the curve is present.When the derivative of a function, f(x), equals 0, it is said to be stationary. Because the function is neither increasing nor decreasing at these locations, they are referred to be "stationary" points.
Stationary Points Defined. Remember that a stationary point is a value of x0 for x at which f′(x0)=0 f ′ (x 0) = 0 for a univariate function y=f(x) y = f (x).
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Repeated addition:
1 3 + 1 3 + 1 3= a b
a =
b =
Answer:
[tex]\frac{1}{3} + \frac{1}{3} + \frac{1}{3} = \frac{3}{3} = 1[/tex]
a=3
b=3
Third part
Commutative property
Fourth part
Inverse property
Fifth part
Identity property
Step-by-step explanation:
Answer:
1st part is a= 3
b= 9
Second part
x=16
y= -24
Third part
Commutative property
Fourth part
Inverse property
Fifth part
Identity property
Step-by-step explanation:
What is 2015 in Roman numeral
Answer:
MMXV
Step-by-step explanation:
(◕ᴗ◕✿)(◕ᴗ◕✿)(◕ᴗ◕✿)
1.in a multivariate regression, which of the following is a true statement concerning the f-statistic?
In multiple regression,
a. The F statistic is only appropriate if errors are homoskedastic.b. The F statistic can never be negative.d. The F statistic has approximately an X² distribution in large samplesThus, option (a), (b), and (d) is correct.
What is F-Test?The F-test is done to check for the equality of variances for the samples given whereas the F-distribution is a positively skewed distribution involving the numerator and the denominators degrees of freedom
a. The F statistic is only appropriate if errors are homoskedastic.
b. The F statistic can never be negative.
c. The F statistic has approximately a normal distribution in large samples.
d. The F statistic has approximately an X² distribution in large samples
In the given question, parts (a), (b), and (d) are true.
As the F-distribution is always positively skewed and is the ratio of the mean squares of between and within errors, it can never be negative and the assumptions of the samples having equal variances need to be fulfilled before proceeding with the test
Hence, in multiple regression,
a. The F statistic is only appropriate if errors are homoskedastic.
b. The F statistic can never be negative.
d. The F statistic has approximately an X² distribution in large samples
option (a), (b), and (d) is correct.
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Full question:
Which of the following is true about the F statistic in the multiple regression model? (Select all that apply.)
a. The F statistic is only appropriate if errors are homoskedastic.
b. The F statistic can never be negative.
c. The F statistic has approximately a normal distribution in large samples.
d. The F statistic has approximately a χ² distribution in large samples.
Find the volume of a cone that has a radius of 8 inches and a slant height of 10 inches. Round your answer to the nearest tenth of a cubic inch.
Answer:
401.9 in³------------------------------------
Volume of the cone:
V = πr²h/3We have a slant height and radius. They represent a hypotenuse and one of the legs of the right triangle.
Use Pythagorean to find the other leg, the height h of the cone:
[tex]h = \sqrt{10^2-8^2}=\sqrt{100-64} =\sqrt{36}=6\ in[/tex]Find the volume:
V = 3.14*8²*6/3 = 401.92 ≈ 401.9 in³The volume of the cone is calculated as: 671.0 cubic inches.
How to Find the Volume of a Cone?The volume of a cone can be found using the formula:
V = (1/3) * pi * r^2 * h
Where V is the volume, pi is approximately 3.14, r is the radius of the base, and h is the height (or slant height) of the cone.
In this case, the radius of the base is 8 inches and the slant height is 10 inches. So, the volume of the cone can be found by:
V = (1/3) * pi * 8^2 * 10
V = (1/3) * 3.14 * 64 * 10
V = (1/3) * 201.12 * 10
V = 671.04 cubic inches
Rounding the answer to the nearest tenth of a cubic inch, the volume of the cone is approximately 671.0 cubic inches.
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which point represents the center of the circle shown below?
O A Point M
• B. Point K
• C. Point R
• D. Point T
Point K is the point that marks the centre of the circle depicted below. This is due to the fact that the centre of a circle is the place from which all of its points are equally far. As a result, Point K is the circle's midpoint and consequently its centre.
What is a Circle?To put it simply, a circle is a spherical shape without any edges or line segments. In geometry, it has the shape of a closed curve. The circle's points are set apart from the center by a specified amount.
A circle is a closed, two-dimensional object in which all points in the plane are equally spaced apart from the center. The symmetry line of reflection is formed by each line that traverses the circle. Additionally, it is rotationally symmetric about the center for all angles.
A circle is a figure with a round shape, all of its points lying on the same plane and all of its points being equally spaced from the circle's center.
The center of the circle can be found by finding the midpoint of the diameter, which passes through points K and T.
The midpoint of the diameter can be found by taking the average of the x and y coordinates of points K and T.
Midpoint of AB = (x1+x2/2 , y1+y2/2)
Midpoint of K and T = ((-2 + 4)/2 , (1 + 7)/2)
Midpoint of K and T = (1 , 4)
Therefore, the center of the circle is point K.
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Determine whether the following system of linear equations have no solution, infinitely many solution or unique solutions.x+2y=3,2x+4y=15A.No solutionB.Infinitely many solutionC.Unique solutionD.Cannot be determined
C. Unique solution. The system of linear equations have a unique solution because the equations are consistent and have the same number of variables and equations.
The given system of linear equations is x+2y=3 and 2x+4y=15. To determine whether the system of linear equations have no solution, infinitely many solution or unique solutions, we need to solve the system of equations. Firstly, we expand and simplify both equations to get x+2y=3 and 2x+4y=15. Then, we compare the coefficients of the equations to determine if the system of equations is consistent, inconsistent or dependent. Since the equations are consistent and have the same number of variables and equations, we can solve the system of equations. By isolating the variables and using the substitution method, we can solve the system of equations to get x=3 and y=3. This means that the system of linear equations have a unique solution.
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a jar holds five lollipops: three red and two yellow. if you remove and replace three lollipops after every draw, find the probability of drawing the same color lollipop twice.
The probability of drawing the same color lollipop twice is 0.72.
According to the given question, 3 lollipops were picked up one by one, but after every draw, the lollipop is kept back in the jar. So it is a case of sampling with replacement.
Thereby, there will be 6 cases when the same color i.e red & yellow lollipops will be picked up 2 times i.e, rry, ryr, yrr, yry, yyr, ryy
(where r & y stand for red and yellow lollipops respectively)
And the corresponding probabilities for these six situations will be
(i) 3/5∗3/5∗2/5=18/125
(ii) 3/5∗2/5∗3/5=18/125
(iii) 2/5∗3/5∗3/5=18/125
(iv) 2/5∗3/5∗2/5=12/125
(v) 2/5∗2/5∗3/5=12/125
(vi) 3/5∗2/5∗2/5=12/125
Hence, the required probability will be the sum of all these probabilities i.e,
(i)+(ii)+(iii)+(iv)+(v)+(vi)
=3∗(18/125)+3∗(12/125)
=90/125
so, the probability that the same color Lollipop will be drawn two times is 90/125 or 0.72.
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Which of the following could represent consecutive even integers, given x =1?
x + 1, x + 2
x+1, 2x + 1
2x, 2x + 2
Answer:
2x, 2x + 2
Step-by-step explanation:
2x is even
2x + 2 = 2(x+1)
x and x+1 are consecutive integers
So multiplying both by 2 makes them consecutive even integers
For example with x = 1
2x = 2, 2(x+1) = 2 . 2 = 4 which is next even consecutive integer
Answer:
2x, 2x + 2
Step-by-step explanation:
Each expression is divisible by 2, so it is even.
In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points is in the same quadrant as the fourth vertex of the square?A. (-5, -3)B. (-5, 3)C. (5, -3)D. (3, -5)E. (3, 5)
The point (-5,3) is in the same quadrant as the fourth vertex of the square.
The given points are representing the points in the quadrant of the cartesian coordinate system. According to this any location on a 2-D plane is represented by 2 numbers, x and y, where x represents the horizontal displacement from the origin of the plane and y represents the vertical displacement from the origin.
Since the given points are the vertices of a square they must be in the form (c, d), (c, -d), (-c, -d), and (-c,d). So, from the given points only the B (-5,3) satisfies the given condition and forms the square.
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8. ABC has vertices A(0, 0), B(0, -2), and C(-3, 0). What are the coordinates
of the orthocenter of ABC?
Answer:
(-1,-1)
Step-by-step explanation:
join the mid points of AB, BC & AC ...
you got the orthocenter point, then we can read the coordinates from X-axis and Y-axis.
find the distance between dallas, texas, whose latitude is n, and omaha, nebraska, whose latitude is n. assume that earth is a sphere of radius 4000 miles and that the cities are on the same longitude (omaha is due north of dallas). City Latitude
Dallas, Texas 32° 47' 39'' N.
Omaha, Nebraska 41° 15' 50'' N.
The distance between Dallas, Texas and Omaha, Nebraska is 631.4 miles.
The distance between Dallas, Texas and Omaha, Nebraska can be calculated using the Haversine Formula. This formula calculates the great circle distance between two points on a sphere, taking into account the curvature of the Earth. The formula is as follows:
d = 2r arcsin( sqrt[ sin^2((lat2 - lat1)/2) + cos(lat1)cos(lat2)sin^2((lon2 - lon1)/2)] )
In this case, the latitude of Dallas, Texas is 32° 47' 39'' N and the latitude of Omaha, Nebraska is 41° 15' 50'' N. Since the two cities are on the same longitude, we can assume that the longitude for both cities is 0°.
Plugging these values into the formula, we get:
d = 2(4000 miles) arcsin[ sqrt[ sin^2((41° 15' 50'' N - 32° 47' 39'' N)/2) + cos(32° 47' 39'' N)cos(41° 15' 50'' N)sin^2((0° - 0°)/2)] ]
d = 631.4 miles
Therefore, the distance between Dallas, Texas and Omaha, Nebraska is 631.4 miles.
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Mains 10 kilograrA company uses copper and zinc in a ratio of 3:2 to manufacture bronze. How many kilograms of copper is needed to make a bronze sheet that contains 10 kilograms of Zinc?
Using the ratio, if a certain piece of brass requires 10kg of zinc, the weight of the copper required for the same piece is 15 kg.
What is ratio?A ratio expresses the frequency with which one number contains another. If a fruit dish contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the orange to lemon ratio is 6:8, while the orange to total fruit ratio is 8:14.
Here,
Given that a company uses copper and zinc in a weight-to-weight ratio of 3:2 to make bronze. As a result, the metal ratio can be written as,
3/2 = copper/zinc
Now, because the zinc weighs 10 kilograms.
As a result, the ratio can be depicted as,
3/2 = copper / zinc
3/2 = copper / 10kg
3 x 10 /2 =copper
30/2 = copper
15 = copper
As a result, if 10kg of zinc is required for a specific piece of bronze, the weight of copper required for the same piece is 15kilograms.
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The average temperature during the winter in three states is given.
• Maine: 8.4°C below zero
• Minnesota: 10.9°C below zero •Georgia: 8.8°C
Part A Order these temperatures from least to greatest. Select your answers from the drop-down lists. Least to Greatest:
Part B Explain how you determined the order of the temperatures.
Answer:
10.9 8.4 8.8
Step-by-step explanation:
Both 10.9C and 8.4C are below zero. We can identify both are in negative temperatures. 8.8C was not labeled as below zero, which indicates a positive unit.
Assignment Scoring
Your best submission for each question part is used for your score.
4.
DETAILS AUFEXC4 10.4.025. 28/100 Submissions Used
Find the minimum or maximum value of the quadratic function.
f(x) = x² - 6x + 9
(-2,11)
x Your answer cannot be understood or graded. More Information
State whether the value is a minimum or a maximum.
minimum
O maximum
Submit Answer
The quadratic function f(x) = x² - 6x + 9 has a minimum at point (3,0).
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The given quadratic function is - f(x) = x² - 6x + 9.
Find the differentiation of f(x) -
dy/dx = d/dx (x² - 6x + 9)
d/dx (x²) - d/dx (6x) + d/dx (9)
2x - 6 + 0
2x - 6 = 0
For stationary values, dy/dx = 0
2x - 6 = 0
2x = 6
x = 6/2
x = 3
At x = 3 we get stationary values.
Now, d²y/dx² = 2x - 6
d/dx (2x - 6)
d/dx (2x) - d/dx (6)
2 - 0 = 0
2 = 0
(d²y/dx²) x=3 = 2 (positive)
Therefore, at x = 3 the function is minimum.
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Pls help please pls please
Answer:
x=5/3 0r 1 2/3
Which of these classes do the matrices A and B belong to (more than one answer is possible for each matrix: invertible; orthogonal; projection; permutation; diagonalizable; Markov.A = [0 0 1]0 1 01 0 0B = 1/3[1 1 1]1 1 11 1 1
Matrix A belongs to the permutation and Markov classes. A permutation matrix is a square matrix with exactly one 1 in each row and each column, and 0s everywhere else.
This is the case for matrix A, as it has one 1 in each row and column and 0s everywhere else. Matrix A is also a Markov matrix, which means that all the entries are non-negative and the sum of each row is equal to 1. This can be seen by summing each row, which yields 1+0+0 = 1, 0+1+0 = 1, and 1+0+0 = 1.
Matrix B belongs to the orthogonal, projection, and diagonalizable classes. Matrix B is orthogonal, which means that it is a square matrix whose columns and rows are orthonormal unit vectors (i.e. the dot product of any two columns or rows is 0). This is the case for matrix B, as the dot product of any two columns or rows yields 0. Matrix B is also a projection matrix, which means that it is a square matrix whose columns are all of unit length (i.e. the dot product of any two columns or rows is 1). This can be seen by taking the dot product of any two columns or rows, which yields 1. Finally, matrix B is diagonalizable, which means that it can be transformed into a diagonal matrix using a similarity transformation. This can be seen by calculating the eigenvalues and eigenvectors of matrix B, which yields the same diagonal matrix.
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Solve equation 9x-3(x-5)=6x+3
Answer: x= -1
Step-by-step explanation:
9x-3(x-5)=6x+3
9x-3x+15=6x+3
9x+6x-3x= 3-15
15x-3x= -12
12x= -12
x= -1
2x+y=30
x+3y=36
by elmination methods
The solution to the system of equations 2x + y = 30 and 2x + 6y = 72 is (10.8, 8.4)
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Given the equations:
2x + y = 30 (1)
x + 3y = 36; multiplying by 2 gives:
2x + 6y = 72 (2)
To solve by elimination method, subtract equation 2 from 1, hence:
-5y = -42
Dividing by -5:
y = 8.4
Put y = 8.4 in equation 2:
2x + 6(8.4) = 72
2x = 21.6
x = 10.8
The solution is (10.8, 8.4)
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