One way to solve a system of 3 equations with 3 variables is to use Gaussian elimination or Gauss-Jordan elimination method.
Gaussian elimination method:
Write the augmented matrix of the system of equations.Use row operations to transform the matrix into an upper triangular matrix.Use back substitution to find the values of the variables.The steps for Gaussian elimination are as follows:
Write the system of equations in matrix form, where the coefficients of the variables are in the matrix and the constants are in the column vector on the right side.Use row operations to transform the matrix into an upper triangular matrix. These operations include adding or subtracting multiples of one row to another, and multiplying or dividing a row by a non-zero scalar.Use back substitution to find the values of the variables. Starting with the last equation, substitute the known values of the variables into the other equations to find the value of the next variable. Repeat until all variables are known.Gauss-Jordan elimination method is similar to Gaussian elimination, however in the final step, it converts the matrix into a Reduced Row Echelon Form (RREF) which leads to more easily solving the system of equations.
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Write a polynomial in intercept form so that P(x)=0 has the given roots.
7. 2, √√3
8. -i, -5
9. i, √7
11. --√6, √3
10. 2i, -i
12. 4DR, VII
The polynomial in intercept form so that P(x)=0 has the given roots is, x^2 - √3x - 2x + 2√3 = 0.
What is polynomial?
A polynomial is an expression in mathematics that only uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x^2 4x + 7 is an illustration of one with a single indeterminate x.
We have to find the polynomial in intercept form so that P(x)=0 has the roots 2 and √3.
Let 2 and √3 are the roots of the polynomial so,
x = 2, x = √3
⇒ x - 2 = 0, x - √3 = 0
⇒ (x - 2)(x - √3) = 0
x^2 - √3x - 2x + 2√3 = 0
Hence, the polynomial in intercept form so that P(x)=0 has the given roots is, x^2 - √3x - 2x + 2√3 = 0.
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At the end of a snowstorm, Peyton had 8 inches of snow on her lawn. The temperature then increased and the snow began to melt at a constant rate of 1 inch per hour. Assuming no more snow was falling, how much snow would Peyton have on her lawn 2 hours after the snow began to melt? How much snow would Peyton have on her lawn after t hours of snow melting?
The amount of snow on Peyton's lawn after 2 hours is 4 inches
amount of snow after t hours y = 8 - t
How to model the required equationA linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable = amount of snow remaking
m = slope = 1 inch per hour
x = input variable = number of hours
c = y intercept = 8 inches of snow on Peyton's lawn
The equation as described in the problem is represented using linear function as as follows
y = 8 - x
in 2 hours x = 2
y =8 - 2 = 4 inches
The quantity of snow after t hours
x = t
y = 8 - t
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SOME ONE HELP PLSSSS
which number line represents all of the values of x for the equation x2=100?
(picture below)
Eight packages of paper weigh a total of 38 pounds. What is the weight of 40 packages of the same kind of paper?
Answer:
1,520 pounds
Step-by-step explanation:
40x 38 = 1520
I NEED THIS ASAP ILL GIVE 100 POINTS
1. Gas stations A. B. C, and G are located
along a straight lighway.
Station B is between stations: A
and c The distance frim station A to
station C is 22 miles. BC is 5 miles less than twice AB
Station C is between stations B and C. 4 miles from C. Find AC.
Answer: 3
Step-by-step explanation:You can't start at station 0 or 1, as there is not enough gas to travel to the next station.
Let's start at station 2 and fill up with 4 unit of gas. Your tank = 0 + 4 = 4
Travel to station 0. Your tank = 4 - 3 + 2 = 3
Travel to station 1. Your tank = 3 - 3 + 3 = 3
You cannot travel back to station 2, as it requires 4 unit of gas but you only have 3.
Therefore, you can't travel around the circuit once no matter where you start.
25PTS don’t explain
Answer:
y = 2x+ 3
Step-by-step explanation:
The red line on this graph is y=-2x-1
The dotted line is y=x.
Write the equation of the inverse of this function
Answer:
Step-by-step explanation:
Name a pair of vertical angles and a pair of adjacent angles in each figure.
On solving the provided question we cans ay thatVertical Angles: TZU, XZW Adjacent Angles: TZU, UZV are Vertical angle and adjacent angle.
What is Vertical angle and adjacent angle,?
Vertical angles are two angles that share the same vertex and are formed by two intersecting lines. They are congruent (i.e. have the same measure) and are opposite each other
Adjacent angles are two angles that share a common vertex and side, but do not overlap. They are also called "next to" or "sharing an arm" angles.
Fig 1:
Vertical Angles: NMJ, LMK
Adjacent Angles: NMJ, JMK
Fig 2:
Vertical Angles: DEA, CEB
Adjacent Angles: DEA, AEB
Fig 3:
Vertical Angles: LQM, PQN
Adjacent Angles: LQM, MQN
Fig 4:
Vertical Angles: TZU, XZW
Adjacent Angles: TZU, UZV
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Hello can someone please help me with this
1. The best geometric model for the rail road is C. Line
2. Two straight lines cannot go through any two points. It is false.
3. The length of the cake is A. 5.5 inches.
4. The vertical angles are AHC and GHE.
How to illustrate the information?The best geometric model for a set of railroad tracks would likely be a line, as it represents the linear path that the tracks follow. A point would not be appropriate as it does not represent the length or direction of the tracks, and a plane would not be necessary as the tracks are linear and exist in a three-dimensional space.
It should be noted that two straight lines cannot go through any two points. Only one line can. The length of the cake will be:
= 6.0 - 0.5
= 5.5
It should be noted that vertical angles are equal. This was Illustrated as AHC and GHE.
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Slope = -7; (4, -30) step by step
Answer:
the equation of the line is y = -7x - 2.
Step-by-step explanation:
To find the equation of the line with slope -7 that passes through the point (4, -30), we can use the point-slope form of a line.
The point-slope form of a line is:
y - y1 = m(x - x1)
where:
(x1, y1) is a point on the line
m is the slope of the line
Substituting the given values, we get:
y - (-30) = (-7)(x - 4)
Expanding the right side, we get:
y + 30 = -7x + 28
Combining like terms, we get:
y = -7x - 2
So the equation of the line is y = -7x - 2.
Which shows that the set of irrational numbers under addition is not closed?
3+3
π + π
π +3
3π + (−3π)
The option that shows that the set of irrational numbers under addition is not closed is B. π + π.
What is an irrational number?All real numbers that are not rational numbers are referred to as irrational numbers in mathematics. In other words, it is impossible to express an irrational number as the ratio of two integers. The collection of real numbers known as irrational numbers, where p and q are integers, are those that cannot be expressed as fractions, such as p/q.
The example of "π + π" shows that the set of irrational numbers under addition is not closed, because the result of adding two irrational numbers (π + π) is an irrational number (2π) which is not included in the set of irrational numbers.
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I literally need so much help
Angie is working on solving the exponential equation 23x = 6; however, she is not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation.
Hint: Use the change of base formula: log base b of y equals log y over log b.
Answer:
[tex]x=\dfrac{\log 6}{\log 23}[/tex]
Step-by-step explanation:
Given exponential equation:
[tex]23^x=6[/tex]
[tex]\textsf{Apply the log law}: \quad a^c=b \iff \log_ab=c[/tex]
[tex]\implies\log_{23}6=x[/tex]
[tex]\textsf{Given change of base formula}: \quad \log_by=\dfrac{\log y}{\log b}}[/tex]
Apply the given change of base formula:
[tex]\implies x=\dfrac{\log 6}{\log 23}[/tex]
how do i do this qution
y = -1/2x is the equation of example of the direct variation.
What is polynomia?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively.
Given four linear equations in them we need to state which equation is an example of direct variation.
The direct variation equation has the form y = kx, where k is the constant proportionality. It is a linear equation with two variables. In a coordinate plane, the direct variation graph is a straight line. A constant is the ratio of two quantities that vary directly. Or in other words, the direct variation equation always passes through the origin point of a cartesian plane or (0, 0).
Therefore, in the given options y = -12/x is the only equation that is an example of direct variation.
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How many permutations are there of all the letters in each name?
a) Inverary
b) Beamsville
c) Mattawa
d) Penetanguishene
Permutations for each word can be calculated by considering the number of unique letters in it and taking factorial of it.
a) Inverary: There are 8 letters in the name "Inverary" (I, N, V, E, R, A, R, Y), so there are 8! (8 factorial) permutations of all the letters in the name. This equals 40320 permutations.
b) Beamsville: There are 9 letters in the name "Beamsville" (B, E, A, M, S, V, I, L, E), so there are 9! (9 factorial) permutations of all the letters in the name. This equals 362880 permutations.
c) Mattawa: There are 7 letters in the name "Mattawa" (M, A, T, T, A, W, A), so there are 7! (7 factorial) permutations of all the letters in the name. This equals 5040 permutations.
d) Penetanguishene: There are 14 letters in the name "Penetanguishene" (P, E, N, E, T, A, N, G, U, I, S, H, E, N), so there are 14! (14 factorial) permutations of all the letters in the name. This equals 87178291200 permutations.
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Help with these questions pls
The description of isometry and transformations is as follows,
isometry mean A distance-preserving transformation between metric spaces is known as isometry, congruence, or congruent transformation.
What is transformations?The transformation, or f, is a function that maps to itself: X X. Following the transformation, the pre-image X transforms into the image X. Any or all of the operations like translation, rotation, reflection, and dilation can be used in this transformation. A function is translated by moving it in a particular direction, rotated by spinning it about a point, reflection by reflecting the function, and dilation by scaling it.
Isometry: If two distinct points, a and b, were to be mapped to the same point, then the coincidence axiom of the metric d would be violated. This proof is similar to the proof that an order embedding exists between partially ordered sets. Clearly, a topological embedding exists for each and every isometry between metric spaces.
A bijective isometry is a global isometry, isometric isomorphism, or congruence mapping. A global isometry, like any other bijection, has a function inverse. A global isometry is also the inverse of a global isometry.
Types of transformations;
Transformation of Reflection: The term "reflection" refers to the kind of transformation that takes place when every point in the shape is reflected over a line. The image is on the opposite side of the line from the pre-image but at the same distance from the line when the points are reflected over it. An image point (q,p) is reflected from each point (p,q).
Transformation of Rotation: Rotation is the transformation that rotates each point of the shape by a predetermined number of degrees around that point. When the number of degrees is positive, the shape rotates counterclockwise, and when the number of degrees is negative, the shape rotates clockwise.
Transformation of Translation: Sliding occurs when a 2-d shape is translated. Let's look at how the vertices of the blue and red figures are positioned in relation to one another in order to describe their relative positions. By comparing its position to the positions of A, B, and C, we must determine their positions.
Hence the basic description of transformation is as follows.
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The Reed family is selecting a furniture set. A furniture set has a bed, a desk and a dresser. There are 4 beds, 3 desks, and 1 dresser to select from. How many different furniture sets could they select?
Answer:
12.
Step-by-step explanation:
right!!
An investment portfolio is shown below.
Investment Amount Invested ROR
Stock A $1,800 1.5%
Stock B $4,600 3.7%
Stock C $580 11.2%
Stock D $1,122 −2.8%
Using technology, calculate the weighted dollar amount of Stock C.
$27.00
$64.96
$170.20
$184.00
The required weight of the dollar amount of Stock C is $64.96.
The Correct option is (B).
What is simplification?In mathematics, the operation and interpretation of a function to make it simple or easier to grasp is known as simplifying, and the process is known as simplification.
Given:
Investment Amount Invested ROR
Stock A $1,800 1.5%
Stock B $4,600 3.7%
Stock C $580 11.2%
Stock D $1,122 −2.8%
According to the question,
Weight of dollar amount of Stock C
= 580 × 11.2%
= 580 x 0.112
= $64.96
Hence, the required weight is $64.96.
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Beth is making a garden plot which measures 6 open parentheses square root of x plus 2 end root close parentheses units in length and open parentheses 5 square root of x plus 2 end root close parentheses units in width. What is the area of the garden?
The area of the garden whose length and width as given in the task content is; 30 (x + 2) square units.
What is the area of the garden plot whose length and width are as described?It follows from the task content that the expression which represents the area of the garden plot whose dimensions are as given.
Recall that Area, A = length × width.
Therefore, since length = 6 (√(x + 2)) units
The width = (5 √(x + 2) ) units
Hence, the area of the garden plot as required in the task content is; 6 (√(x + 2)) × ( 5 √(x + 2) )
= 30 (x + 2) square units
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Pleas help me with #2, thanks
Toni invests money into an account which pays a fixed rate compound interest each year.
The total value, £V, of her investment after 't' years is given by the formula=1350 x 1.04t.
How much did Toney invest?
if u get this ur a genius
Answer: Toni invested in pounds= $1350
Step-by-step explanation:rate of compound interest=4%
Step-by-step explanation:
Toni invests money into an account which pays a fixed rate of compound interest each year. The total value, £V, of her investment after t years is given by the formula:
Given equation is in the form of
where P is the amount invested
'r' is the rate of interest
t is the time taken
P= 1350 is the initial amount invested
1+r= 1.04 (subtract 1 from both sides)
multiply it by 100 to get percentage
r= 4%
I just search it bc my brain dosent work any more
Which table shows a proportional relationship between x and y?
Answer:
C
Step-by-step explanation:
Put in the form y/x and you should have equivalent fraction
12/4 = 3
15/5 = 3
18/6 = 3
When the fractions are simplified, they all equal 3.
At 10:00 a.m. two planes leave an airport. if the northbound plane flies at 280 mph and the southbound at 320 mph, at what time will they be 1,000 miles apart? which equation can be used to solve for t, the time it takes the planes to be 1,000 miles apart?
280t + 320t = 1,000 is distance equation can be used to solve for t, the time it takes the planes to be 1,000 miles apart.
What does distance mean in a nutshell?
Distance is the overall movement of an object without consideration of direction.
Regardless of an object's starting or ending point, distance can be defined as the amount of ground it has traveled.
At 10:00 a.m. two planes leave an airport. If the northbound plane flies at 280 mph and the southbound at 320 mph
Let 't' be the time taken when they are 1000 miles apart
the northbound plane flies at 280 mph
Distance = speed * time
distance covered by northbound plane D1= 280 * t= 280t
the southbound at 320 mph
distance covered by southbound plane D2=320 t
Distance is 1000 miles apart
D1 + D2= 1000
280t + 320t = 1,000
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The population for Rainbow City is 36,000. The growth rate is 3%. About how many people will it have after 5 years
Answer:
41,500 people
Step-by-step explanation:
First you find 3% of 36,000= 1,080
Then you do 1080 x 5= 4,500
Then finally do 36,000 + 4,500= 41,500
How many terms are there in the expression 2p3 3p2 4p 7 *?
Answer: 4
Explanation:
In Algebra a term is either a single number or variable, or numbers and variables multiplied together.
Terms are separated by + or − signs, or sometimes by divide.
Colleen and Amy go shopping. The function below represents how much money each girl spent based on the number of hours they were shopping. If Colleen and Amy each go shopping for 3 hours, how much money did they spend together?
p(x)3x^4=x^4-3x^2+5
$32
$86
$248
$302
Answer:
$302
Step-by-step explanation:
p(x) 3x^4 = x^4-3x^2+5
We put 3 in for x and solve
3(3)^4 = 3^4 -3(3)^2 + 5
3(81) = 81 -3(9) + 5
243 = 81 - 27 + 5
243 = 59
Then we add 243 with 59 and get
$243 + $59 = $302
So, they spend together $302
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What is the solution of 2x 3 7?
Answer: It is a straight line
Step-by-step explanation:
Which expression is equivalent to 7(d - 4)?
Submit
7(-4+ d)
-4(d + 7)
(d + 7).-4
-28d + 7
The phrase that is identical to 7(d - 4) in option B is -4(d+ 7). A mathematical expression is a statement that contains a minimum of two numbers .
what is expression ?A mathematical expression is a phrase having a minimum of two numbers or variables and at least one mathematical operation. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: Expression is (Number/Variable, Math Operator, Number/Variable). A mathematical expression is a statement that contains a minimum of two numbers or variables and at least one mathematical operation. Let's learn how to write expressions. A number is 6 more than half of another number, and that other number is called x. In a mathematical expression, this statement is represented as x/2 + 6.
given
The correct response is 4 less than 7, since 4 is less than 7.
Thus, 7-4=3 could be considered.
The first section of 7–4 appears to be answer B.
The phrase that is identical to 7(d - 4) in option B is -4(d+ 7).
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•50 POINTS• don’t explain
-A
-B
-C
Answer:
C. Neither------------------------------------
There is no indication that the given triangles are congruent.
We can see one angle of each triangle is marked as congruent and that is is. No more evidences of congruence and therefore we state the triangles are not congruent.
This is a choice C.
what is 5x5+9x7
Whell help please i just wanted to put 5x5+9x7 but it didnt let me so yay
Answer: 88
Step-by-step explanation:
Answer: 88
Step-by-step explanation: 5x5=25 + 9x7=63 ----> 25+63= 88
It take Thorton 4 hour to edit a video for hi chool. If he ha already pent 2. 5 hour on thi video, what percent of the video i edited?
Using the concept of fraction, the percentage edited on the video is 62.5 percent.
What is Percentage
Percentage is a standard mathematical concept used to express a portion of a whole number in terms of a hundred. It is denoted by the symbol “%” and is often expressed as a fraction or a decimal. For example, 25% can be expressed as 0.25 or 1/4.
In this problem, Thorton has done a 2.5 hours work. The percentage he has edited can be calculated using fraction or ratio as;
percentage edited = (2.5 / 4) × 100
Percentage = 0.625 × 100
Percentage = 62.5 %
From the above, Thorton has edited 62,5 percent of the video for his school project.
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