The best method to use to solve the system of equation will be Elimination method.
What is elimination method?According to the description of the elimination approach, it involves removing a phrase that contains any of the variables from the equation in order to simplify the computations. To achieve this, multiply or divide a number by the equation(s) until all of the variable terms' coefficients are the same. The term is then eliminated or removed from the result by adding or subtracting from both equations. Because of this, the addition technique is another name for the elimination approach. For illustration, let's use the elimination approach to resolve two linear equations with two variables.
The two equations are:
3x+7y=-19
-3x+4y=12
From the above equations we can observe that the value of the coefficient of x is same, as well as, they have opposite sign.
Hence, the best method to use to solve the system of equation will be Elimination method.
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What is the properties of.
|+-8|-5=7
The expression after applying distributive property is
[(-5/8) × (-3)] + [(-5/8 ) × (-7)] = 50/8
What is Distributive Property?Distributive property shows us how to multiply an arithmetic number or an algebraic expression with two or more numbers or expressions within brackets.
This can be symbolically represented as :
X ( Y + Z ) = XY + XZ
here, we have,
The expression given here is -5/8 (-3 + (-7)).
Applying distributive property, we get,
-5/8 (-3 + (-7)) = [(-5/8) × (-3)] + [(-5/8 ) × (-7)]
= (15/8) + (35/8)
= 50/8
The expression - 5/8(-3 + (-7)) after applying distributive property changes to the expression [(-5/8) × (-3)] + [(-5/8 ) × (-7)] = 50/8.
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Hence determine the circumference of the base of the tin In mm
The required real diameter οf the tin is 250 mm.
What is the diameter?Diameter is a measurement οf the length οf a straight line that passes thrοugh the center οf a circular οbject, such as a circle οr a sphere. It is the distance between twο pοints οn the οbject's edge that are furthest frοm each οther and that pass thrοugh the center οf the οbject.
Here,
If the diameter οf the tin in the picture is 10 cm, then the actual diameter οf the tin can be calculated as:
Actual Diameter = 2.5 × Picture Diameter
Actual Diameter = 2.5 × 10 cm
Actual Diameter = 25 cm
Tο cοnvert the actual diameter tο millimeters (mm), we can multiply by 10:
Actual Diameter in mm = Actual Diameter × 10
Actual Diameter in mm = 25 cm × 10
Actual Diameter in mm = 250 mm
Therefοre, the real diameter οf the tin is 250 mm.
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Complete question:
I. Simplify the following fully 1.1 ,(2x-1)(x^(2)-3x+1) 12(2x+3)(5-x) 13(x^(3)-1)/((x+2)+x(x+2))+(x-1)/(2x+4) 1.4(3)/(x^(2)-9)+(2)/((x-3)^(2)) 2. Factorise : 2.1,6x^(2)+7x-20 2.2,x^(3)+x^(2)-x-1
I. Simplify the following fully:
1.1 (2x-1)(x^(2)-3x+1)
= 2x^(3) - 6x^(2) + 2x - x^(2) + 3x - 1
= 2x^(3) - 7x^(2) + 5x - 1
1.2 12(2x+3)(5-x)
= 12(-2x^(2) + 7x + 15)
= -24x^(2) + 84x + 180
1.3 (x^(3)-1)/((x+2)+x(x+2))+(x-1)/(2x+4)
= (x^(3)-1)/(x^(2)+3x+2)+(x-1)/(2(x+2))
= (x-1)(x^(2)+x+1)/(x+2)(x+1)+(x-1)/(2(x+2))
= (2(x-1)(x^(2)+x+1)+(x-1)(x+1))/(2(x+2)(x+1))
= (2x^(3)+x^(2)-x-1+x^(2)-1)/(2(x+2)(x+1))
= (2x^(3)+2x^(2)-x-2)/(2(x+2)(x+1))
1.4 (3)/(x^(2)-9)+(2)/((x-3)^(2))
= (3)/((x+3)(x-3))+(2)/((x-3)^(2))
= (3(x-3)+2(x+3))/(x+3)(x-3)^(2)
= (3x-9+2x+6)/(x+3)(x-3)^(2)
= (5x-3)/(x+3)(x-3)^(2)
2. Factorise:
2.1 6x^(2)+7x-20
= (2x-4)(3x+5)
2.2 x^(3)+x^(2)-x-1
= (x+1)(x^(2)-1)
= (x+1)(x+1)(x-1)
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In Exercises 17-24, for each matrix A. find (a) a permutation matrix P such that PA has an LU decomposition and (b) an LU decomposition of PA. -1 2 -2 2 3 5 17. 18. TO 2 26 3 19. 2. 2 -3 - 2 :: 8 to s
A permutation matrix is a square matrix that has exactly one entry of 1 in each row and each column, and all other entries are 0. When a permutation matrix is multiplied with another matrix, it rearranges the rows of the other matrix.
For matrix A = \begin{bmatrix}-1 & 2 & -2\\ 2 & 3 & 5\\ 1 & 2 & 2\end{bmatrix}
(a) A permutation matrix P that allows for an LU decomposition of PA is P = \begin{bmatrix}0 & 1 & 0\\ 1 & 0 & 0\\ 0 & 0 & 1\end{bmatrix}
When we multiply P and A, we get PA = \begin{bmatrix}0 & 1 & 0\\ 1 & 0 & 0\\ 0 & 0 & 1\end{bmatrix}\begin{bmatrix}-1 & 2 & -2\\ 2 & 3 & 5\\ 1 & 2 & 2\end{bmatrix} = \begin{bmatrix}2 & 3 & 5\\ -1 & 2 & -2\\ 1 & 2 & 2\end{bmatrix}
(b) An LU decomposition of PA is L = \begin{bmatrix}1 & 0 & 0\\ -0.5 & 1 & 0\\ 0.5 & 0 & 1\end{bmatrix} and U = \begin{bmatrix}2 & 3 & 5\\ 0 & 3.5 & 4.5\\ 0 & 0 & -0.5\end{bmatrix}
So, PA = LU = \begin{bmatrix}1 & 0 & 0\\ -0.5 & 1 & 0\\ 0.5 & 0 & 1\end{bmatrix}\begin{bmatrix}2 & 3 & 5\\ 0 & 3.5 & 4.5\\ 0 & 0 & -0.5\end{bmatrix} = \begin{bmatrix}2 & 3 & 5\\ -1 & 2 & -2\\ 1 & 2 & 2\end{bmatrix}
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you have three grades in your report card that you want to
interpret to your parents in terms of performance: Mathematics
(75), English (85), and Science (90). The means are 72, 82, 88, and
the standa
Therefore , the solution of the given problem of unitary method comes out to be 6.10 is the standard deviation.
What is an unitary method?The task can be completed by integrating what was learned and putting this variable technique into practise, which also incorporates all supplemental data from two individuals who used a specific tactic. Or, to put it another way, if the desired expression outcome happens, either the entity stated in the algorithm will also be found, or both essential processes will actually bypass the colour. For forty pens, a refundable charge of Rupees ($1.01) might be required.
Here,
Using the ideas of mean and standard deviation, we can interpret the three grades in terms of achievement.
The three categories' mean (average) is:
=> Mean = (75 + 85 + 90) / 3 = 83.33
This indicates that the achievement as a whole is above average (since the mean of 72, 82, and 88 is 80).
Which is:
=> Variance = [(75 - 83.33)² + (85 - 83.33)² + (90 - 83.33)²] / 3
=> [67.11 + 1.36 + 44.11] / 3
=> 37.19
The variance's square root equals the standard deviation.
=> SD= √(37.19)
=> 6.10 is the standard deviation.
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1.In a circle of radius 6cm a chord is drawn 3cm from the center
a) Calculate the angle subtended by the chord at the centre of the circle b)Find the length of the minor and the perimeter of the minor segment formed by a chord and minor
Answer:
a) The angle subtended by the chord at the centre of the circle is 120°.
b) The length of the minor arc is 12.57 cm (2 d.p.).
The perimeter of the minor segment formed by a chord and minor arc is 22.96 cm (2 d.p.).
Step-by-step explanation:
The chord of a circle is the base of an isosceles triangle, where its congruent sides are the radii of the circle.
The height of the isosceles triangle is the perpendicular bisector of the chord from the central angle.
The angle subtended by the chord at the centre of the circle is twice the angle formed by the radius and the perpendicular bisector (marked θ on the attached diagram).
To find the measure of angle θ, use the cosine trigonometric ratio.
[tex]\begin{aligned}\implies \cos \theta&=\sf \dfrac{adjacent\;side}{hypotenuse}\\\\\cos \theta &=\sf \dfrac{3}{6}\\\\\cos \theta &=\sf \dfrac{1}{2}\\\\\theta &=\arccos\left(\sf \dfrac{1}{2}\right)\\\\\theta &=60^{\circ}\end{aligned}[/tex]
As the angle subtended by the chord at the centre of the circle is twice angle θ:
[tex]\implies 2\theta=2 \cdot 60^{\circ}=120^{\circ}[/tex]
Therefore, the angle subtended by the chord at the centre of the circle is 120°.
A minor arc is less than 180° and is equal to the central angle.
Therefore, as the angle subtended by the chord at the centre of the circle is 120°, the minor arc is the part of the circumference between the two endpoints of the chord (marked in red on the attached diagram).
To find the length of the minor arc, use the arc length formula.
[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Arc length}\\\\Arc length $= \dfrac{\pi r\theta}{180^{\circ}}$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}[/tex]
Therefore:
[tex]\begin{aligned}\implies \textsf{Arc length}&= \dfrac{\pi \cdot 6 \cdot 120^{\circ}}{180^{\circ}}\\\\&= 4 \pi\\\\&= 12.57\; \sf cm\;(2\;d.p.)\end{aligned}[/tex]
Therefore, the length of the minor arc is 12.57 cm (2 d.p.).
To calculate the perimeter of the minor segment formed by the chord and minor arc, we need to calculate the length of the chord.
[tex]\boxed{\begin{minipage}{10.2 cm}\underline{Chord length}\\\\Chord length $=2r\sin\left(\dfrac{\theta}{2}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle (in degrees) subtended at the center by the chord.\\\end{minipage}}[/tex]
Therefore:
[tex]\begin{aligned}\implies \textsf{Chord length}&= 2 \cdot 6 \cdot \sin \left(\dfrac{120^{\circ}}{2}\right)\\\\&= 12 \cdot \sin \left(60^{\circ}\right)\\\\&= 12 \cdot \dfrac{\sqrt{3}}{2}\\\\&= 6\sqrt{3}\; \sf cm\end{aligned}[/tex]
Therefore, the perimeter of the minor segment formed by the chord and minor arc is:
[tex]\begin{aligned}\implies \textsf{Perimeter}&=\textsf{Minor arc length}+\textsf{Chord length}\\&=4 \pi + 6 \sqrt{3}\\&=22.96\; \sf cm\;(2\;d.p.)\end{aligned}[/tex]
The expression below shows how to convert 12 gallons to cups with one part missing 4 cups 1 quart Which value completes the expression? 12 gallons 1 4 gallons 1 quart 1 gallons 4 quarts 4 quarts 1 gallon 16 cups 1 gallon
Answer: 4 quarts / 1 gallon
Step-by-step explanation: or C!! hope this helps!!
A convention center is in the shape of a rectangular pyramid with a height of 332 m. Its base measures 475 m by 571 m. Find the volume of the convention center. If necessary, round your answer to the nearest tenth.
The convention centre has a volume of approximately 30,085,616.8 cubic metres as a result.
What is the formula for volume?As opposed to length, width, and height for a rectangle's surface, the basic formula for volumes is length, breadth, and height. It doesn't matter how you refer to the different dimensions; for example, using "depth" instead of "height" wouldn't affect the calculation.
V = base area ×height (1/3)
The pyramid's height is disclosed to be 332 meters. We multiply the base's length and width to determine the base area:
Base area = 475 m × 571 m = 271525 m²
We can now enter the values into to the formula as follows:
V = (1/3) × 271525 m² × 332 m
V = 30085616.7 m³
This is rounding up to the closest tenth, giving us:
V ≈ 30085616.7 ≈ 30085616.8 m³
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The map shows the distance in air miles from Houston to both Austin and San Antonio.What is the greatest possible distance to Austin to san Antonio
a. The greatest possible distance from Austin to san Antonio is 335.77 mi, b. the Least possible distance to Austin to san Antonio is 120.03 mi.
Describe Distance?Distance refers to the physical length or space between two points or objects. It is an important concept in mathematics, physics, and everyday life. Distance can be measured in various units such as meters, feet, kilometers, miles, or light-years, depending on the context and scale of the measurement.
In mathematics, distance is often measured using the Euclidean distance formula, which calculates the distance between two points in a plane or in three-dimensional space. The formula is given by:
d = √((x2 - x1)² + (y2 - y1)²)
where d is the distance between the two points, (x1, y1) and (x2, y2).
In physics, distance is often used to describe the separation between two objects or particles. The distance between two objects can affect the strength of gravitational or electromagnetic forces between them. Distance is also an important concept in special relativity, where it is affected by the relative motion of observers and the distortion of spacetime.
a. Greatest possible distance from Austin to san Antonio= Distance from Austin →Houston → san Antonio.
Austin - Houston = 146.43 mi
Houston - San Antonio = 189.34 mi
Total distance= 146.43+ 189.34= 335.77 mi
b. Least possible distance to Austin to San Antonio = the shortest distance = x
By Pythagoras theorem
(189.34)² = (146.43)²+ x²
x² = (189.34)²- (146.43)²
x² = 35849.63- 21441.744
x² = 14407.89
x =√14407.89
x = 120.03
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The complete question is:
Select the correct answer. Which inequality represents all the solutions of 10(3x + 2) > 7(2x − 4)?
Answer:
x > -3
Step-by-step explanation:
10(3x + 2) > 7(2x − 4)
30x + 20 > 14x - 28
16x + 20 > -28
16x > -48
x > -3
So, the answer is x > -3
Geometry help needed!
In the figure below, what are the measures of ∠A and ∠B?
Answer:
[tex]\huge\boxed{\sf \angle A = 43\°}[/tex]
[tex]\huge\boxed{\sf \angle B = 59\°}[/tex]
Step-by-step explanation:
Finding Angle B:Interior angles of a triangle add up to 180 degrees.In ΔDBC,
98 + ∠B + 31 = 180°
∠B + 121 = 180
∠B = 180 - 121
∠B = 59°Finding Angle A:The measure of exterior angle is equal to the sum of non-adjacent interior angles.So,
∠C (Exterior Angle) = ∠A + ∠B
102 = ∠A + 59
Subtract 59 from both sides102 - 59 = ∠A
43 = ∠A
∠A = 43°[tex]\rule[225]{225}{2}[/tex]
A. What is the name of this 3-D shape below?
B. What is one way we could find the surface area of this figure?
Please help me with this thanks
You do not have to find the surface area
Answer:
A. This shape is a rectangular prism — a rectangle with a third dimension of depth. In technical terms, it is "a polyhedron with two congruent and parallel bases." - BYJU's Maths
B. We could find the area of its net, since the surface area of a shape is the sum of the areas of its sides.
Please show your work.
In the triangle DEF the measure of angle E is obtained as (183 - 9x)°.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
In the triangle DEF the value for ∠D = (4x + 1)°.
In the triangle DEF the value for ∠F = (5x - 4)°.
According to the properties of a triangle, the sum of angles of a triangle is equal to 180°.
So, the equation will be -
(4x + 1)° + (5x - 4)° + ∠E = 180°
Evaluate the expression -
(9x - 3)° + ∠E = 180°
∠E = 180° - (9x - 3)°
∠E = 180° - 9x + 3°
∠E = (183 - 9x)°
Therefore, the value for angle E is (183 - 9x)°.
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Function r is an input-output machine that uses the rule "3(t^4)-19". Write the machine's function using function notation.
The given function 3(t^4)-19 is thus written using the function rule in notations as: f(t) = 3(t^4)-19 for the input-output machine.
Explain about the function notation?Although equations are frequently used to represent functions, a sequence of equations all beginning with y = may make it difficult to distinguish between different functions.
So, giving functions names is a great touch. Functions and their variables are named in function notation.A function that involves the variables x and y can be expressed in the form y = "some expression involving x," or y = f(x) .By reading the last sentence as "y equals f of x," it is indicated because y is a function of x.A function called f is defined by the notation f(x).
This should be understood as "y is a function of x."The input value, called independent variable, is represented by the letter x.The output value, meaning dependent variable, is represented by f(x) in place of the letter y.The given function 3(t^4)-19 is thus written using the function rule in notations as:
f(t) = 3(t^4)-19.
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Sandy decided to do an experiment with a sandwich she left in her locker. She found it 4 days after she had put it there, took it to the lab, and counted 71 bacteria. 3 days later she counted 185 bacteria.
Write the exponential equation that represents this problem.
She estimates that it will take 500 bacteria to completely cover her sandwich. How many days would it take this to happen, starting from the day she first put her sandwich in her locker?
The respοnse tο the given questiοn wοuld be that As a result, it will take equatiοn arοund 9.7 days frοm the day Sandy placed her sandwich in her lοcker fοr 500 bacteria tο cοmpletely cοver it.
What is equatiοn?When twο statements are cοnnected by a mathematical equatiοn, the equals sign (=) implies equality. An equatiοn in algebra is a mathematical statement that prοves the equivalence οf twο mathematical expressiοns. Fοr instance, the equal sign separates the numbers in the equatiοn 3x + 5 = 14. It is pοssible tο determine the relatiοnship between the twο sentences οn either side οf a letter using a mathematical fοrmula. The lοgο fοr the particular piece οf sοftware is frequently the same. as 2x - 4 = 2, fοr dinstance.
This issue's expοnential equatiοn is as fοllοws:
N(t) = N0 × [tex]e^{(kt)[/tex] × (kt)
We can utilise the abοve infοrmatiοn tο determine the values οf N0 and k:
N(4) = 71 × N(7) = 185
When we enter these numbers intο the equatiοn, we οbtain:
71 = N0 × [tex]e^{(4k)[/tex] × (4k)
185 = N0 × [tex]e^{(7k)[/tex] × (7k)
185/71 = [tex]e^{(3k)[/tex] × (3k)
As a result, the equatiοn fοr this issue is:
N(t) = 23.77 × [tex]e^{(0.3056t)}[/tex] × (0.3056t)
We may set N(t) equal tο 500 and sοlve fοr t tο see hοw many days it will take fοr 500 germs tο grοw:
500 = 23.77 × [tex]e^{(0.3056t)}[/tex] × (0.3056t)
9.7 days based οn t = ln(500/23.77) / 0.3056.
As a result, it will take arοund 9.7 days frοm the day Sandy placed her sandwich in her lοcker fοr 500 bacteria tο cοmpletely cοver it.
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Helpp pleasee i added an attachment
The graphs when classified are decay and growth functions
The complete solution is shown below
Classifying the functions by graphA graph that represents an exponential growth would increase as the input value (x) increases, while graphs of exponential decay would decrease with increment in x
This means that:
Graph 5 = DecayGraph 6 = GrowthGraph 7 = DecayClassifying the functions by equationAn exponential function is represented as
y = abˣ
If b > 1, then it is a growth function, otherwise it is a decay function
This means that:
Equation 8: y = 0.1(7)ˣ = GrowthEquation 9: y = 3(0.25)ˣ = DecayEquation 10: y = (3/4)ˣ = DecayEquation 9: y = 1/2(5/3)ˣ = GrowthCompleting the missing blanksFor the equation y = abˣ, we have
Initial value = a
Decay rate (if b < 0) = 1 - b
Growth rate (if b > 0) = b - 1
This means that
Function (12) is unclear
13. f(x) = 11(0.4)ˣ:
Initial value = 11
Decay factor = 0.4
Decay rate = 6%
14. f(x) = (1/4)ˣ:
Initial value = 1
Decay factor = 1/4
Decay rate = 75%
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10
#6
Three vertices of parallelogram MNPQ are M(2,2). N(4,0), and P(1,-1). Plot points M, N, P, and Q in the coordinate plane below.
The points M, N, P, and Q have been plotted in the coordinate plane below.
How to determine the midpoint of a line segment?In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Substituting the given parameters into the midpoint of a line segment formula, the midpoint of the diagonal is given by;
Midpoint MP = [(2 + 1)/2, (-1 + 2)/2]
Midpoint MP = [3/2, 1/2]
Midpoint MP = (1.5, 0.5).
For the fourth vertex Q, we have:
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
(1.5, 0.5) = [(4 + x₂)/2, (0 + y₂)/2]
4 + x₂ = 2(1.5)
x₂ = -4 + 3
x₂ = -1.
0 + y₂ = 2(0.5)
y₂ = 1.
Therefore, vertex Q = (-1, 1).
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Use long division to find the quotient
(2x^3-5x^2+3x-6) divided by (x+4)
Using long division the quotient of (2x^3-5x^2+3x-6) divided by (x+4) is 2x^2 - 13x + 55.
What is quotient?Quotients are often used in algebra and other branches of mathematics to solve equations and expressions involving division. They are also commonly used in everyday life, such as when calculating the cost per unit of a product, or the average speed of a journey.
For example, if we divide 10 by 2, the quotient would be 5, since 10 divided by 2 equals 5. Similarly, if we divide 12 by 3, the quotient would be 4, since 12 divided by 3 equals 4.
Now let find the quotient using long division:
2x^2 - 13x + 55
_______________________
x + 4 | 2x^3 - 5x^2 + 3x - 6
- (2x^3 + 8x^2)
---------------
- 13x^2 + 3x
- (-13x^2 - 52x)
---------------
55x - 6
- (55x + 220)
-----------
-226
Therefore, the quotient is 2x^2 - 13x + 55 and the remainder is -226.
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Hi due today pls help! Ty! question attached
Snails to Newts iz
There are 36 Snails present in the pond.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Ratio of Snail to Newts = 3:4
So, Number of Snail= 3x and number of Newts = 4x
If 12 more newts added then the ratio is 3:5
So, 3x/ 4x+ 12 = 3/5
15 x = 3(4x+ 12)
15x = 12x + 36
15x - 12x = 36
3x = 36
x= 12
So, the number of Snails in pond are 3x = 3(12)= 36.
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Help me find the g(x)
This is exponential function
The function g(x) is given as follows:
g(x) = -7x + 15What is the value of g(x) if the exponential function f(x) = -7ˣ⁺¹ shifts two units to the right?To shift the exponential function f(x) = -7x+1 two units to the right, we need to replace x with (x-2) in the equation.
This is because when x is replaced with (x-2), the function will have the same output value as before when x was 2 units less.
Thus, the shifted function g(x) can be written as:
g(x) = f(x-2)
g(x) = -7(x-2) + 1
g(x) = -7x + 15
So, the function g(x) is given by g(x) = -7x + 15, and it is the same as f(x) shifted 2 units to the right.
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condense the expression log3 2x+3 log3 4x
Answer:
The expression log3 2x + 3 log3 4x can be condensed to log3 8x + 3. This is because log3 4x = 2 log3 2x, so when we add the two logarithms together, the result is log3 8x + 3
Step-by-step explanation:
(1 point) Lelv1=−123−3,v2=16−4−4,v3=−1640Are the vectorsv1,v2andv3linearly independent? If the vectors are independent, enter zero in every answer blank since zeros are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer.000=−123−3+16−4−4+−1640
v1, v2, and v3 are linearly independent
Yes, the vectors v1, v2, and v3 are linearly independent.
To verify this, we can set up the equation:
a1v1 + a2v2 + a3v3 = 0
If the vectors are linearly independent, then the only way to solve this equation is if a1 = a2 = a3 = 0.
Substituting the values for v1, v2, and v3 into the equation yields:
-123 - 3a1 + 16 - 4a2 - 4a3 - 1640a3 = 0
Solving for a1, a2, and a3, we get:
a1 = 0, a2 = 0, a3 = 0
Therefore, the vectors v1, v2, and v3 are linearly independent.
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A certain type of insect was introduced into a protected area. The population of the insect t months after being introduced is given by 50+251 P(t) = 2+0.011 a. What is the equation of the horizontal asymptote of P?
b. Explain in words what the horizontal asymptote tells you about the insect population. Include a unit of measure for the asymptote value in your explanation.
The equation of the horizontal asymptote of P isy = 22818.18. This means that the insect population will approach a maximum value of approximately 22818 insects, no matter how many months have passed since they were introduced. The unit of measure for this value is insects per month.
a. The equation of the horizontal asymptote can be found by taking the limit of P(t) as t approaches infinity.
lim P(t) as t approaches infinity = lim (50+251)/(2+0.011t) as t approaches infinity
Since the denominator grows without bound as t approaches infinity, the limit of P(t) approaches 251/0.011 = 22818.18. Therefore, the equation of the horizontal asymptote is:
y = 22818.18
b. The horizontal asymptote tells us the maximum population that the protected area can sustain for this type of insect. In other words, as time goes on, the insect population will approach a maximum value of approximately 22818 insects. The unit of measure for the asymptote value is insects.
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I WILL GIVE YOU BRAINLIEST IF YOU ANSWER THIS!
Identify the asymptotes of the rational function.
[tex]y = \frac{1}{3x + 9} - 9[/tex]
A. Vertical asymptote: x = −3
Horizontal asymptote: y = –9
B. Vertical asymptote: x = –9
Horizontal asymptote: y = −3
C. Vertical asymptote: x = 0
Horizontal asymptote: y = 9
D. Vertical asymptote: x = 3
Horizontal asymptote: y = 9
Answer:
A) vertical asymptote: X = -3
Horizontal asymptote: y = -9
Step-by-step explanation:
sorry I don't know how to explain it
What the 3 basic operations used to simplify a linear system?
Answer:
Simplify both sides of the equation and combine all same-side like terms.
Combine opposite-side like terms to obtain the variable term on one side of the equal sign and the constant term on the other.
Divide or multiply as needed to isolate the variable.
The three basic operations used to simplify a linear system are elimination, substitution, and augmentation.
The 3 basic operations used to simplify a linear system are:
1. Swapping the order of equations: This operation is used to rearrange the equations in the system to make it easier to solve.
2. Multiplying or dividing an equation by a constant: This operation is used to make the coefficients of the variables in the equation equal to 1 or -1, which makes it easier to solve the system.
3. Adding or subtracting equations: This operation is used to eliminate one of the variables in the system, which reduces the number of equations and makes it easier to solve the system.
These operations are used to manipulate the equations in the system in order to find the values of the variables that satisfy all of the equations in the system. By using these operations, we can simplify the system and solve it more easily.
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What 's the area which has sides of length 6and8
Answer: 48
Step-by-step explanation:
6 x 8 = 48
provealgebraically that the square of any odd number is always 1more than a multiple of 8
Answer:
Let's assume that we have an odd integer represented by the variable "n". Then, according to the definition of an odd integer, we can write it as follows:
n = 2k + 1
Where "k" is any integer.
Now, we need to find the square of "n". We can write it as follows:
n^2 = (2k + 1)^2
n^2 = 4k^2 + 4k + 1
Now, we can simplify the expression:
n^2 = 4k(k + 1) + 1
We can observe that the expression 4k(k + 1) is always an even number. This is because when we multiply two consecutive integers (k and k + 1), we always get an even result. Therefore, we can write:
4k(k + 1) = 8m
Where "m" is any integer. Substituting this expression into the previous equation, we get:
n^2 = 8m + 1
This shows that the square of any odd number is always 1 more than a multiple of 8, which is what we wanted to prove.
Answer:
The answer is 8
Step-by-step explanation:
If n is "any integer", then 2n+1 is "any odd number."
The square of any odd number is then ...
(2n+1)² = 4n² +4n +1 = 4n(n+1) +1
Since n is any integer, one of n and n+1 will be an even integer, so the product 4n(n+1) will be divisible by 8.
Then the sum 4n(n+1) +1 is one more than a number divisible by 8, hence ...
the square of an odd number is 1 more than a multiple of 8.
How do I solve this?
The value of x is 4 using the trigonometric function.
What is hypotenuse?The term "hypotenuse" refers to a right-angled triangle's longest side as compared to the base and perpendicular lengths. The right angle, the largest angle of the three angles in a right triangle, lies opposite the hypotenuse side. In essence, only the right triangle possesses the hypotenuse feature, not any other triangles. When we study the right-angled theorem, Pythagoras Theorem, or Pythagorean Theorem, this is better understood. The main use of these ideas is in trigonometry.
The triangle is a right-triangle.
Thus, using the trigonometric functions we have:
Sin (30) = opposite / hypotenuse
sin (30) = 2 / x
1/2 = 2/x
x =2(2)
x = 4
Hence, the value of x is 4 using the trigonometric function.
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NEED HELP FAST! 20 POINTS!!
The value of x is 57 degrees. This was obtained by the use of the trigonometric ratios.
What is a right angle triangle?A right triangle, also known as a right-angled triangle, is one that we can say that an angle in this triangle would be 90 degrees.
The Pythagorean theorem can be used to obtain the lengths of the various sides that we have in the right angled triangle. This is one of the fundamental theories in the right angled triangle.
Let us now use the cosine to find the angle as shown below;
We know that;
Cos x = 11/20
x = Cos-1(11/20)
x = 57 degrees
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[tex]G(3)=4^{2}[/tex]
Answer:
G = 5.333
Step-by-step explanation:
Given: G(3) = 4^2
3 times G is 3G:
3G = 4^2
4 squared is 16:
3G = 16
Divide both sides by 3:
G = 5.333