Two matrices are row equivalent if they can be transformed into each other using elementary row operations.
Elementary row operations are operations such as the addition or subtraction of two rows, the multiplication or division of a row by a non-zero constant, or the interchange of two rows. Row equivalent matrices are equal in terms of row space, meaning any linear combination of the rows of one matrix will yield the same linear combination of the rows of the other matrix. An example of two row equivalent matrices is given below:
Matrix A =
[tex]\begin{bmatrix} 1 & 2 & 3 \\4 & 5 & 6 \end{bmatrix}[/tex]
Matrix B =
[tex]\begin{bmatrix} 1 & 2 & 3 \\2 & 3 & 4 \end{bmatrix}[/tex]
These matrices are row equivalent because adding the first row of Matrix A to the second row of Matrix B yields Matrix A. To show this mathematically, let row 1 of Matrix A be represented as r1, and row 2 of Matrix B be represented as r2. We can then say that r2 + r1 =
[tex]\begin{bmatrix} 1 & 2 & 3 \\6 & 8 & 10 \end{bmatrix}[/tex]
which is equal to Matrix A.
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How do you graph logarithms?.
Step 1: Find some points on the exponential f(x). The more points we plot the better the graph will look.
Step 2: Switch the x and y values to obtain points on the inverse.
Step 3: Determine the asymptote.
Graph the following logarithmic functions. State the domain and range.
A logarithmic scale (or log scale) is a way of displaying numerical facts over a completely extensive range of values in a compact manner—typically the biggest numbers inside the data are loads or even lots of times large than the smallest numbers.
Logarithmic scales are useful for quantifying the relative alternate of a fee in place of its absolute distinction. moreover, because the logarithmic feature log(x) grows very slowly for huge x, logarithmic scales are used to compress massive-scale scientific statistics.
A logarithm is an exponent or power to which a base need to be raised to yield a given quantity. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logo n. for example, 23 = 8; therefore, 3 is the logarithm of eight to base 2, or 3 = log2 eight.
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Under what conditions is a radical expression in simplest form?.
Algebraic expressions involving radicals are known as radical expressions. The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both).
Three conditions must be satisfied for a radical expression to be in its simplest form, that is, first, No radicands other than 1 have perfect square factors.
Secondly, there isn't a fraction in any radicand and finally, the fraction's denominator has no radicals.
A radical expression can be reduced to a simple form by first factoring it into primes, then finding the radical's index, and finally moving the group of numbers either inside or outside the radical.
The expressions both inside and outside the radical can then be made simpler by adding up all the numbers inside the radical.
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URGENT!
find the value of x in each supplementary angle pair
Answer: X=9
180 -108=72
72/8=9
Answer:
x = 9° (or) 8x = 72°
Step-by-step explanation:
Now we have to,
→ find the required value of x.
We know that,
→ Straight line is always 180°.
Forming the equation,
→ 8x + 108° = 180°
Then the value of x will be,
→ 8x + 108° = 180°
→ 8x = 180° - 108°
→ 8x = 72°
→ x = 72° ÷ 8
→ [ x = 9° ]
Hence, the value of x is 9°.
Mikaela wants to do a poll of everyone at Martin Luther King High School. Which of
these is the best way to get an accurate response?
A.Poll only students in 9th and 11th grades.
B.Poll a random selection of teachers, students and staff.
C.Poll only female teachers and students.
D.Poll only staff who have worked at the school for less than five years.
Poll only students in 9th and 11th grades would be the best way to get an accurate response. Thus, option A is correct.
What is poll?In electoral campaigns, math is frequently used. The goal of polling is to predict how the electorate will vote overall by taking a small sample of voters and extrapolating their results to the entire population. Pollsters must ensure that their sample of respondents is representative of the entire electorate, or if it is not, they must use a variety of statistical techniques to increase the representativeness of their findings.
In essence, this means that a survey is conducted, and not only are respondents' voting intentions recorded, but also their age, gender, race, and other demographics. As a result, it is possible to make predictions about the voting intentions of various social groups.
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for each sequence,find the first 4th terms and the 10th terms.
a)10-n
b)6-2n.
The numbers for the sequences are 10-n = 9, 8, 7, 6, 0, and 6-2n = 4,2, 0, -2, and -14.
What is a sequence?A sequence is a series of numbers that follow the sample principle in terms or order. In this case, the sequence is determined by the equations given, and based on this the numbers are calculated.
What are the numbers in these sequences?10-n:
10 - 1 = 9
10 - 2 = 8
10 - 3 = 7
10 - 4 = 6
And the 10th term is
10- 10 = 0
6-2n:
6 - 2 = 4
6 - 4 = 2
6- 6 = -0
6 - 8 = -2
And the 10th term is
6 - 20 = -14
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What is also called Avogadro's number?.
The numerical value of both the mole and Avagadro’s number is 6.022 x 10²³. That is why the mole is also called Avogadro's number.
The Avogadro constant, A, is the number of particles (such as atoms, molecules, or ions) in one mole of something. Its value is modernly defined as exactly 6.022 140 76 × 10²³. (As it is a pure number, it has no units.)
So, in 1 mol of helium, which has a mass of (very close to) 4 g, there are A
atoms; in 1 mol of sucrose, with a mass of 342 g, there are A molecules.
We can have moles of other kinds of things, including subatomic particles. The amount of charge known as the faraday is the charge of one mole of electrons (A of them; about 96 500 C).
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What is inverse 2x2?.
If a 2×2 matrix A is reverse and is multiplied by its inverse (indicate by the symbol A−1), the develop product is the Identity matrix which is indicate by I.
In fact, I can control the order or direction of multiplication between matrices A and A−1, and I would still get the Identity matrix I. That means reverse matrices are commutative.
A×A^-1= I.
In normal, the inverse of a matrix A is found using the formula (adj A)/ (det A), where "adj A" is the "adjoint of A" and "det A" is the "determinant of A".
the inverse of a 2x2 matrix, say A, is a matrix of the similar order known by A^-1 such that AA^-1 = A^-1A = I, where I is the identity matrix of order 2x2.
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Which of the following uses the reciprocal property to rewrite
x/6 = 28/3?
Answer:
6/x = 3/28
Step-by-step explanation:
How do you multiply mixed numbers step by step?.
1: Convert the mixed number into an improper fraction.
2: Multiply the numerators and denominators of the two fractions separately.
3: Simplify by eliminating the common factors to get the lowest form of the result.
Now, According to the question:
A mixed number is a whole number and a proper fraction represented together. It generally represents a number between any two whole numbers.
For Example:
[tex]4\frac{1}{2}[/tex] and [tex]3\frac{1}{3}[/tex]
[tex]4\frac{1}{2}[/tex] = (4 × 2 +1)/2 = 9/2
[tex]3\frac{1}{3}[/tex] = (3 × 3 + 1)/3 = 10/3
[tex]4\frac{1}{2}[/tex] × [tex]3\frac{1}{3}[/tex] = 9/2 × 10/3 = 90/6 = 15
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2x^ 3 +17x^ 2 +20x+6 is divided by 2 x + 1
Answer:
The quotient is x^2 + 9x + 6 with a remainder of 6.
Step-by-step explanation:
I used the polynomial long division method to divide the polynomial 2x^3 + 17x^2 + 20x + 6 by 2x + 1.
First, I divided the leading coefficient of the dividend (2x^3) by the leading coefficient of the divisor (2x). This gave me x^2 as the first term of the quotient.Next, I multiplied the divisor (2x + 1) by the first term of the quotient (x^2) to get 2x^3 + x^2.I then subtracted this product from the dividend (2x^3 + 17x^2 + 20x + 6) to get 17x^2 + 20x + 6 as the new dividend.I then brought down the next term of the dividend (17x^2) and divided it by the leading coefficient of the divisor (2x) to get 8.5x as the next term of the quotient.I then multiplied the divisor (2x + 1) by this term (8.5x) to get 17x^2 + 8.5x.I subtracted this product from the new dividend (17x^2 + 20x + 6) to get 0.5x + 6 as the new dividend.I brought down the next term of the dividend (0.5x) and divided it by the leading coefficient of the divisor (2x) to get 0.25x as the next term of the quotient.I multiplied the divisor (2x + 1) by this term (0.25x) to get 0.5x.I subtracted this product from the new dividend (0.5x + 6) to get 6 as the remainder.So the quotient is x^2 + 8.5x + 0.25x which simplifies to x^2 + 9x + 6 and the remainder is 6.
Answer:
[tex] \sf x^ 2 +17x^ 2 +20x+6[/tex]
Step-by-step explanation:
[tex] \sf \frac{2x^ 3 +17x^ 2 +20x+6}{ 2 x + 1}[/tex]
2x³/2x = x²
[tex] \sf \frac{x^ 2 +17x^ 2 +20x+6}{ 1}[/tex]
[tex] \sf x^ 2 +17x^ 2 +20x+6[/tex]
Which of the following could be the vertex of a parabola with x-intercepts of (-12, 0) and (14, 0)?
A: (1, 9)
B: (3, 7)
C: (7, 3)
D: (9, 1)
What is the value of f of 2?.
The value of f of 2, which means f(2), is 6.
As we know,
f'(x) = [tex]\[ \lim_{h\to0}[/tex] [f(x+h) - f(x)]/h
= [tex]\[ \lim_{h\to0}\\[/tex] [f(3x + 3h)/3 - f(3x + 0)/3]/h
= [tex]\[ \lim_{h\to0}\\[/tex] [{2 + f(3x) + f(3h)}/3 - {2 + f(3x) + f(0)}/3]/h
∴f'(x) = [tex]\[ \lim_{h\to0}\\[/tex] [f(3h) - f(0)]/3h-0 = f'(0)
⇒ f′(2) = f′(0) = 2 [∵f′(2) = 2]
⇒f′(x) = 2
Now, apply integration on the above equation with respect to x
∴f(x) = 2x + c (1)
Substituting x = 0 = y in f{(x+y)/3} = {2 + f(x) + f(y)]/3
⇒3f(0) = 2 + f(0) + f(0)
∴f(0) = 2
By equation (i) f(0) = 2.0 + c
∴c = 2 [∵f(0) = 2]
Now (1) becomes
∴f(x) = 2(x + 1)
Put x = 2
f(2) = 2(2 + 1) = 2 × 3 = 6
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A fruit juice company include 1. 751 ounce of juice in a 6. 45
-ounce bottle of a mixed fruit juice. How much of the bottle of mixed fruit juice i NOT juice?
73.14 % of the 6.45-ounce bottle of mixed fruit juice is not juice.
To find out how much of the 6.45-ounce bottle is not juice, we need to subtract the amount of juice in the bottle, which is 1.751 ounces, from the total volume of the bottle, which is 6.45 ounces.
6.45 ounces - 1.751 ounces = 4.699 ounces
So, 4.699 ounces of the 6.45-ounce bottle is not juice.
Alternatively, we can express the answer as a percentage of the total volume of the bottle:
(4.699 / 6.45) x 100 = 73.14 %
So, 73.14 % of the 6.45-ounce bottle of mixed fruit juice is not juice.
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How do you know if the inverse of a function is a function?.
Answer:
function-function relation
Step-by-step explanation:
To determine if the inverse of a function is a function, we can use the horizontal line test.
A function is a set of ordered pairs (x, y) where each x value corresponds to one and only one y value. The inverse of a function is a set of ordered pairs (y, x) where each y value corresponds to one and only one x value.
To use the horizontal line test, we draw a horizontal line on a graph of the original function. If the line intersects the graph in more than one point in any vertical section, the inverse is not a function. But if the horizontal line intersects the graph in at most one point in any vertical section, the inverse is a function.
Another way to check if the inverse of a function is a function is to check that the original function is a one-to-one function, meaning that each x value corresponds to one and only one y value. If the original function is not one-to-one, then the inverse is not a function.
It's also possible to check if the inverse of a function is a function by analyzing the equation of the function. If the original function is a one-to-one function, its inverse is also a function
10. Christian sold tickets to the Golden Knights hockey game. Lower Level seats were $50 each and Upper
Level seats cost $20 each. 2100 people attended and paid $66000. Write a system of linear equations that
can be used to find how many Lower Level seats (x) and how Upper Level seats (y) were sold. How many
of each type of seat were sold?
1500 Lower Level seats and 600 Upper Level seats were sold.
What is linear equation?Linear equation is an equation that can be written in the form ax + b = 0, where a and b are real numbers and x is a variable. In this equation, a is referred to as the coefficient of x and b is referred to as the constant. Linear equations are used to represent relationships between two variables and can be used to solve for either variable. Linear equations are used in many different fields of mathematics, including algebra, calculus, and geometry.
System of linear equations:
50x + 20y = 66000
x + y = 2100
Solving the system of equations gives:
x = 1500
y = 600
Therefore, 1500 Lower Level seats and 600 Upper Level seats were sold.
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Find the bearing of d from a
Please help!
The bearing of D from A is given as follows:
24º.
How to obtain the bearing of D from A?The bearing of D from A is obtained using the angle addition postulate, which states that if two angles share a common vertex and a common angle, forming a combination, the larger angle will be given by the sum of the smaller angles.
The angle measures for this problem are given as follows:
x, 166, 15 and 155.
The total of these measures is of 360º, hence the value of x, representing the bearing of D from A, is given as follows:
x + 166 + 15 + 155 = 360
x + 336 = 360
x = 24º.
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what is 345 divided by 2:3
Answer:
Est: 517
Answer: 517.499999974
Step-by-step explanation:
Put the following equation of a line into slope-intercept form, simplifying all fractions. 3x-3y=18
The slope intercept form of a line is,
⇒ y = x - 6
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
The equation is,
⇒ 3x - 3y = 18
Now, We know that;
The slope intercept form of the equation is,
⇒ y = mx + b
Here, The equation of line is,
⇒ 3x - 3y = 18
Take 3 as common,
⇒ 3(x - y) = 18
Divide by 3;
⇒ x - y = 18/3
⇒ x - y = 6
⇒ x - 6 = y
⇒ y = x - 6
Thus, The slope intercept form of a line is,
⇒ y = x - 6
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Could someone please help me on this? The answer is NOT c.
Answer:
The answer is D the second quadrant.
Step-by-step explanation:
HAVE A GREAT DAY!!!!!
Choose the expression that is equivalent to the expression shown below. n/4+n/4+n/4+n/4
The expression that is equivalent to the expression n/4+n/4+n/4+n/4 is,
⇒ n
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
The expression is,
⇒ n/4 + n/4 + n/4 + n/4
Now, We can simplify the expression as;
⇒ n/4 + n/4 + n/4 + n/4
⇒ (n + n + n + n) / 4
⇒ 4n/4
⇒ n
Thus, The expression is equivalent to n.
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Louis has 1 green counter, 2 white counters
and 2 yellow counters in a box.
Louis takes one counter at random from the
box, puts it back, and takes another
counter from the box.
The probability that Louis takes two green counters is 1/9, since there is only one green counter in the box.
What is random probability? Random probability is a mathematical concept that describes the likelihood of a given event occurring. It is a measure of the chance that a certain event will happen, expressed as a percentage or a fraction. Random probability is based on the idea that all outcomes of a situation are equally likely to occur, and the probability of any event occurring is the same as any other event. For example, the probability of rolling a six on a standard die is 1/6, or 16.7%. Random probability is used in many different fields, from gambling to weather forecasting. It is also used in scientific experiments and research, to determine the likelihood of a certain outcome occurring. Random probability can be used to measure the probability of success in any given situation. For example, a company may use random probability to determine how likely it is for a particular product to be successful in the market. By understanding random probability, companies can make more informed decisions about their products and services, and gain a better understanding of their risks and rewards.To learn more about probability refer to:
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triangle k a p is congruent to Triangle akr by rule
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. The rules to show this include SSS, SAS, ASA.
How to explain the triangle congruenceSide-Side-Side (SSS) Rule The SSS rule states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent
The SAS rule states that if two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.
The ASA rule states that if two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent.
An overview was given due to the incomplete information.
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The scatter plot shows the systolic blood pressure of people of several different ages. The equation represents the linear model for this data. Y = x + 95 according to the model, how much does the systolic blood pressure increase for each year of age? responses 1 mm hg per year 1 mm hg per year 5 mm hg per year 5 mm hg per year 15 mm hg per year 15 mm hg per year 95 mm hg per year 95 mm hg per year 110 mm hg per year 110 mm hg per year.
The true statement is that blood pressure increases by 1 mm HG per year.
In geometry, we have seen the lines drawn on the coordinate plane. To predict whether the lines are parallel or perpendicular or at any angle without using any geometrical tool, the best way to find this is by measuring the slope. In this article, we are going to discuss what a slope is, slope formula for parallel lines, perpendicular lines, slope for collinearity with many solved examples in detail.
What is a Slope?
The equation that represents the linear model is:
y =x+95
Linear regression is represented as:
y=mx+b
Where:
m represents the slope
b represents the y-intercept
By comparison, we have: m=1
This means that:
The blood pressure increases by 1 mm HG per year.
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The jazz band sells 30 large boxes of fruit and 75 smallboxes of fruit for a fundraiser
a. Use the Distributive Property to write and simplify an expression for
the profit
b. A large box of fruit costs $7 and a small box of fruit costs $3. What is the juz band's profit?
Jazz Band Makes $785 in Profit.
What is the juz band's profit ?31 huge boxes and 74 little boxes of fruit are sold by the jazz band.
The cost is $x and the price is $20 for each huge fruit box.
Price minus Cost is referred to as profit.
Profit therefore equals 20 - x for one large fruit box.
31 huge fruit boxes at a profit (20 - x)
Each little fruit box costs $10 and costs $10 per small fruit box.
Each tiny fruit box has a profit of 10–y.
74 little fruit boxes worth of profit (10 - y)
For 74 small boxes and 31 large boxes, the overall profit will be:
Profit overall equals 31 (20-x) + 74. (10 - y)
We can reduce the problem above by using the distributive property as follows:
Total profit is equal to 31(20)-31x + 74(10)-74y.
Profit total = 1360 - 31 x - 74 y
Part B)
Each large package is estimated to cost $9.
Accordingly, x = 9.
Each tiny box is stated to cost $4.
Therefore, y = 4.
We can determine the Jazz Band's profit by using the x and y numbers from the profit equation.
Profit of Jazz Band = 1360 - 31(9) - 74. (4)
Jazz Band Makes $785 in Profit
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x+y=4 in slope intercept form
Answer:
y=-x+4
Step-by-step explanation:
have a good day
Answer:
y=-x+4
slope intercept form is y = mx+c
m is 1 and c is 4
y=- x +
Step-by-step explanation:
PLEASE HURRY!!!
Question- A circle has a circumference of 10π inches and a center of (9, 2). What is the standard form equation of this circle?
Answers:
A. (x-9)^2 + (y-2)^2 = 10
B. (x-9)^2 + (y-2)^2 = 25
C. (x-9)^2 + (y-2)^2 = 3.14
D. (x-9)^2 + (y-2)^2 = 100
Answer:
[tex]\sf{Choice \;B.\;\; (x-9)^2 + (y-2)^2 = 25[/tex]
Step-by-step explanation:
The standard form equation of a circle with center (a, b) and radius r is
[tex](x-a)^2 + (y-b)^2 = r^2[/tex]
where (a, b) is the center of the circle.
Here we are given that the circle has center (9, 2)
So the equation becomes
[tex](x-9)^2 + (y-2)^2 = r^2\cdots(1)[/tex]
All we have to do is find the radius and we are done
Circumference of a circle with radius r
[tex]= 2 \pi r\\[/tex]
Given circumference [tex]= 10\pi[/tex]
[tex]10\pi = 2\pi r\\\implies r = 10/2 = 5[/tex]
Substitute this into equation (1):
[tex](x-9)^2 + (y-2)^2 = 5^2\\\\(x-9)^2 + (y-2)^2 = 25\\[/tex]
This corresponds to option B.
The equation of a circle is (x - 9) + (y - 2) = 25.
Option B is the correct answer.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
We have,
The equation of a circle is (x - h) + (y - k) = r² _____(A)
Where (h, k) is the center and r is the radius.
Now,
Centre = (9, 2)
This means,
(h, k) = (9, 2) _____(1)
Circumference = 10π
This means,
2πr = 10π
2r = 10
r = 5 in ____(2)
Now,
Substituting (1) and (2) in (A).
(x - h) + (y - k) = r²
(x - 9) + (y - 2) = 5²
(x - 9) + (y - 2) = 25
Thus,
The equation of a circle is (x - 9) + (y - 2) = 25.
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4. Triangle XYZ with vertices X(-6, 4), Y(0, 6), and Z(-4, 2):
a) 180° counterclockwise rotation about the origin
b) dilation with scale factor of 3/2 centered at the origin
X')
Y')
Z'
a) X'(-6, -4), Y'(0, -6), Z'(-4, -2)
b) X'(-9, -6), Y'(0, -9), Z'(-6, -3)
Rotation and dilation in geometry
This question uses the concepts of rotation and dilation in geometry.For the rotation of 180° counterclockwise about the origin, we will use the rotation formula:
(x, y) → (xcosθ - ysinθ, xsinθ + ycosθ)
Where θ is the angle of rotation.
For our 180° rotation, θ = 180°.
We calculate the new coordinates for each vertex:
X(-6, 4) → X'(-6, -4):
(-6cos180° - 4sin180°, -6sin180° + 4cos180°)
Y(0, 6) → Y'(0, -6):
(0cos180° - 6sin180°, 0sin180° + 6cos180°)
Z(-4, 2) → Z'(-4, -2):
(-4cos180° - 2sin180°, -4sin180° + 2cos180°)
For the dilation of the triangle with a scale factor of 3/2 centered at the origin, we will use the dilation formula:
(x, y) → (kx, ky)
Where k is the scale factor.
For our dilation, k = 3/2.
We calculate the new coordinates for each vertex:
X(-6, 4) → X'(-9, -6):
(-6*3/2, 4*3/2)
Y(0, 6) → Y'(0, -9):
(0*3/2, 6*3/2)
Z(-4, 2) → Z'(-6, -3):
(-4*3/2, 2*3/2)
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Is the domain of a function always all real numbers?.
The domain of a function is not always all real numbers.
We know that the domain of function is the set of all possible input values for which the function is well defined.
And the range of function is the set of all possible output values for given input.
As we know the domain of a function, f(x), is all real numbers when there are no restrictions on what we can take input for x, as all real numbers would make function f(x) true.
But the domain of a function is not always all real numbers.
consider the function f(x) = 1/x
This function is not defined for x = 0
So, the domain of above function f(x) is R - {0}
Also, we know that the domain of a logarithmic function is all non-zero positive real numbers.
Thus, the domain is not always set of all real numbers.
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Rina ha been viiting the coffee hop everyday for 7 day. Each day, he pent a dollar more than he did the day before. If he tarted going to the coffee hop on Monday, pending $ 1, how much did he pend on average daily for that week?
Rina has been visiting the coffee shop every day for 7 days and he spent an average of $1 each day he visited the coffee shop during the week.
He started on Monday, spending $1, and each day he spent a dollar more than he did the day before. By the end of the week, he had spent $7. To calculate the average amount he spent each day, add up the total amount of money he spent that week and divide it by 7 (the total number of days he visited the shop).
7/7=1
In this case, the total amount of money spent was $7, so when divided by 7, the average amount spent each day is $1. Therefore, Rina spent an average of $1 each day he visited the coffee shop during the week.
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Wyatt is typing his science paper. He can type 50 words per minute. Write an equation that shows the relationship between the number of minutes Wyatt types, x, and the number of words he types, y. y=
Answer:
Step-by-step explanation:The equation that shows the relationship between the number of minutes Wyatt types, x, and the number of words he types, y, is:
y = 50x
This equation shows that the number of words Wyatt types is directly proportional to the number of minutes he types. For every 1 minute he types, he types 50 words.
This equation can also be read as "y is equal to 50 multiplied by x" which means that for any given number of minutes, x, that Wyatt types for, the number of words he types will be 50 times that value.
