Find the rate of change of a circle diameter with respect to radius. (Give your answer as a whole or exact number.) d' (n) =
The rate of change of a circle's diameter with respect to its radius is a constant value of 2.
The diameter (d) of a circle is twice the radius (r), so we can write:
d = 2r
To find the rate of change of diameter with respect to radius, we can take the derivative of both sides of this equation with respect to r using the chain rule:
d/dx [d] = d/dx [2r]
d' = 2r'
Here, d' is the derivative of diameter with respect to radius, and r' is the derivative of radius with respect to some independent variable (e.g. time).
Since r' is simply equal to 1 (because the derivative of a variable with respect to itself is always 1), we have:
d' = 2
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What is 30 Meters in Feet?
Around 98.4 feet are equal to 30 metres.
The common formula 1 metre (m) = 3.28 feet (ft) will be used to convert measurements from metres to feet. Here, the conversion value is 3.28. To convert 10 metres to feet, for instance, multiply 10 by 3.28, which is 32.8 ft. Therefore, 10 meters = 32.8 feet.
Converting from metres to feet: 3.28084 metres are nearly equal to one metre. Add 3.28084 feet to the given metre value to convert it to feet. Add 3.28084 feet to the given metre value to convert it to feet. For instance, the conversion of 5 metres to feet is as follows: We are aware that the conversion factor for 5 metres to feet is 3.28084.
30 m * 3.280839895 ft/m =98.4251968504 ft
So, 30 metres is roughly equivalent to 98.4 ft.
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what is rhombus angle sum
Answer:
360 degrees
Step-by-step explanation:
I remember learning this in Math class. The rhombus angle sum will make 360 degrees.
The mean and the median are closely related concepts. The median is the numerical value separating the higher half of your data from the lower half. You can find the median by arranging all of the observations from lowest value to highest value and picking the middle value​ (assuming you have an odd number of​ observations). Although the mean and median are closely​ related, the difference between the mean and the median is sometimes of interest.
Suppose Country A has five families. Their incomes are $9000, $21,000, $29,000, $39,000, and $50,000.
Country A's median income is _______, and its mean income is ______.
Suppose country B also has five familities. Their incomes are $9000, 21000, 29000, 39000, and 151000.
Country B's median income is _____ and its mean income is ____.
Country _____ has a greater income inequality
Based on your answers to this​ question, would you expect the ratio of the mean income in the United States to the median income has risen or​ fallen? Explain.
A.
​Fallen, because means change less with standard deviation.
B.
​Risen, because means change more with extreme values.
C.
​Risen, because means increase but medians decrease with income.
D.
​Risen, because medians increase with variance but means do not.
Mean of country A is $29600 and median $29000. Mean of country B is $49800 and median is $29000. Country B has greater income inequality. So option B is the correct answer.
Mean of incomes in country A = (9000+ 21000+ 29000 + 39000+ 50000)/5 = $29600
Median income of country A = (5+1)/2 th term = 3rd term = $29000
Mean to median ratio = 29600/ 26000= 1.02
Mean income of country B = ( 9000+ 21000+ 29000+ 39000+ 151000)/5 = $ 49800
Median income = (n+1)/2 th term = (5+1)/2 = 3rd term = 29000
Mean to median ratio of country B = 49800/29000 = 1.71
Since mean and median are closer to each other, standard deviation is less. The mean to median ratio is greater for country B. So country B has greater income inequality.
If the income inequality has been increasing, then the mean-median ratio will increase, due to the extreme values, mean will increase. So option B is the correct answer.
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how to convert microliters to milliliters
Using the formula 1 millilitre = 10⁻³ microliters, we can convert millilitres to microliters.
The volume unit is milliliters (mL). One microliter (uL) is likewise a volume unit, although it is a smaller unit.
We already know that Milli equals 10⁻³.
As a result, we may write the relationship using the unit conversion idea.
One microliter equals 10⁻³ milliliters.
For example, if we have 2 microliters, it is equal to 2 x 10⁻³ milliliters.
Thus, we now have a standard formula that we can use to calculate the time in microliters to milliliters and milliliters to microliters.
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If there were two runners running a race, one along the inside and one along the outside, how far apart they start so the race is fair?
Answer:
I would believe inside of a race track is smaller than the outside. They are staggered so the runners all run the same distance.
Step-by-step explanation:
Darrel receives a weekly salary of $289. In addition, $13 is paid for every item sold in excess of 100 items. How much will Darrel earn for the week if he sold 122 items?
Daren will earn $286 for the week if he sold 122 items.
What is mean by Multiplication?Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.
Given that;
Darrel receives a weekly salary of $289.
And, In addition, $13 is paid for every item sold in excess of 100 items.
Hence, The cost to earn for the week if he sold 122 items is,
⇒ (122 - 100) × $13
⇒ 22 × $13
⇒ $286
Thus, Daren will earn $286 for the week if he sold 122 items.
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PLEASE HELP I RLY RLY NEED HELP
Answer: x= 155 degrees
Step-by-step explanation:
All angles in a triangle add up to 180. That is how we find angle a
a + b = 120 degrees as 60 degrees is taken for a straight angle or 180 degrees.
Use Algebra to find angle b
To find c we do the same thing as for a.
x is everything remaining from 180 degrees after c is taken from it.
x = 155 degrees
The cost of a car rental is $40 per day plus 18(cents) per mile. You are on a daily budget of $67. Write and solve an inequality to find the greatest distance you can drive each day while staying within your budget. Use pencil and paper. Find 2 other two-step inequalities with the same solutions.
PLEASE HELP (30 POINT REWARD) PLEASE.
The inequality that represents the greatest distance that can be driven while staying within the daily budget is:
0.18x + 40 ≤ 67
Solving for x, we get:
0.18x ≤ 27
x ≤ 150
Therefore, the greatest distance that can be driven in a day while staying within the daily budget is 150 miles.
Two other two-step inequalities with the same solutions are:
0.18x ≤ 27.5 x ≤ 153.50.18x + 39 ≤ 670.18x ≤ 28
x ≤ 155
Please help , I do not understand this at all
The frequency of the sine function is given as follows:
F = 0.5/π Hz.
How to obtain the frequency of a sine function?The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.For the function y = sin(x), we have that B = 1, hence the period is given as follows:
P = 2π/B
P = 2π.
The frequency is one divided by the period, hence:
F = 1/P
F = 1/2π
F = 0.5/π Hz.
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Answer:
[tex]F=\dfrac{1}{2\pi}\; \sf Hz[/tex]
Step-by-step explanation:
The frequency of a sinusoidal wave refers to the rate at which the wave completes one full cycle, typically measured in Hertz (Hz), where 1 Hz signifies one complete oscillation of the wave in one second.
The period of a sinusoidal wave is the amount of time it takes for the wave to complete one complete oscillation.
The frequency (F) of a sinusoidal wave can be determined from its period (P) using the formula:
[tex]\boxed{F=\dfrac{1}{P}}[/tex]
The sine function y = sin(x) completes one full cycle over the interval [0, 2π]. Therefore, its period is P = 2π.
To calculate the frequency (F), substitute P = 2π into the frequency formula:
[tex]F=\dfrac{1}{P}=\dfrac{1}{2\pi}\; \sf Hz[/tex]
In the notation "s(x) = ...," what does "s(x)" represent? A. The value found when s is multiplied by the value x. B. There is not enough information to answer this question. C. The value of s(x) depends on the value of x, since s is a function of x. D. The value of x depends on the value of s(x), since x is a function of s.
s(x) represents the value of s(x) depending on the value of x since s is a function of x.
The first thing you should be aware of in this situation is that the following is contained in the provided expression:
S: stands for a function whose value we are interested in.
In order to understand the function s, we must use the term (numerical value) represented by x.
S is therefore dependent on X.
So, we have:
As s is a function of x, its value depends on the value of x.
As s is a function of x, the value of s (x) depends on the value of x.
Consider the provided notation.
Since s is a function of x. The s(x) value depends on the x value.
For any function f(x); The independent variable is x.
i.e. it depends on the variable x.
Similarly, here s(x) is the dependent variable. which is defined for the corresponding variable x.
Hence, s(x) represents the value of s(x) depending on the value of x, since s is a function of x.
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The diameter of a circle is 8 m. Find its circumference in terms of iπ.
c=25.1327
Step-by-step explanation:
c=2pir
r=1/2 d
r=4
2pi*4= 25.1327
jessica is bisecting a segment. first, she places the compass on one endpoint and opens it to a width larger than half of the segment. what is her next step? brainly
The next step would be to draw an arc with the compass centered at the endpoint.
This arc should intersect the segment at two points.
We have,
After Jessica places the compass on one endpoint of the segment and opens it to a width larger than half of the segment, her next step would be to draw an arc with the compass centered at the endpoint.
The concept used in Jessica's next step is the compass-and-straightedge construction method.
By opening the compass wider than half of the segment and drawing an arc with the compass centered at one endpoint, she creates two points of intersection between the arc and the segment.
These points will divide the segment into two equal halves, allowing her to bisect the segment.
Thus,
The next step would be to draw an arc with the compass centered at the endpoint.
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Ernesto measured a house and its lot and made a scale drawing. The scale of the drawing was 5 inches : 6 feet. The house's driveway is 35 inches long in the drawing. How long is the actual driveway?
With the provided scale, the driveway's true length is 7/6 feet, and 1 and 1/6 feet.
Inch Calculator: What is It?The height of any unit can be converted to inches using the free online tool known as an inch calculator. Both inches and centimetres are units used to measure length; inches are abbreviated as "in" and centimeters as "cm".
To determine the real length of the driveway, we can use the provided scale.
The scale indicates that 5 inches just on illustration corresponds to 6 feet in everyday life.
Now, let's change 35 inches just on picture to feet:
35 inches / 5 inches for every 6 feet equals 7/6 feet.
The driveway is therefore 7/6 feet in length in actuality. We can condense.
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What is the Taylor series for Sinx?
The Taylor series for sin(x) is an infinite series expansion that represents the trigonometric function sin(x) as a sum of infinite terms involving the powers of x.
The Taylor series for sin(x) can be written as:
sin(x) = x - (x^3 / 3!) + (x^5 / 5!) - (x^7 / 7!) + ...where n! represents the factorial of n.
The series converges for all values of x, which means that it can be used to calculate the value of sin(x) to any desired degree of accuracy. The series is based on the idea that any continuous function can be represented as an infinite sum of terms involving the function's derivatives at a particular point, in this case, x=0.
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Given square PQRS, determine the missing information.
P
R
4 cm
1
S
X =
y=
Ox= 4y = 4
Ox + 4y = 2 sqrt(2)
x = 4y = 4 sqrt(2)
x = 4y - 8 sqrt(2)
The missing information in the square is option(b) x = 4y = 4 √(2) and y = 4.
Given square PQRS, the task is to determine the missing information. A square is a quadrilateral with four equal sides and four equal angles.
The coordinates of the vertices of a square are (x,y), (x+4,y), (x+4,y+4) and (x,y+4).
The missing information, x and y, can be found by solving the equations that represent the sides of the square. We can start by solving for x.
The equation for the side PQ is x + 4y = 2 √(2). Solving this equation for x gives x = 4y - 8 √(2).
Similarly, the equation for the side RS is x + 4y = 4 √(2). Solving this equation for x gives x = 4y = 4 √(2).
Therefore, the missing information is x = 4y = 4 √(2) and y = 4.
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How to convert 95 confidence z score?
The z-score associated with a 95% confidence level is approximately 1.96.
The z-score associated with a 95% confidence level is the value of the standard normal distribution that corresponds to an area of 0.95 to the left of the z-score.
Using a standard normal distribution table or calculator, we can find that the z-score associated with a 95% confidence level is approximately 1.96.
Therefore, if we want to calculate the z-score for a 95% confidence level, we can use the formula
z = invNorm(1 - α/2)
where α is the significance level (α = 0.05 for a 95% confidence level), and inv Norm is the inverse normal cumulative distribution function. Using this formula, we can calculate the z-score as:
z = inv Norm(1 - 0.05/2)
= inv Norm(0.975) ≈ 1.96
Therefore, the z-score is 1.96
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Help me pls I don’t understand I am in need of assistance pls
Work Shown:
a = change in distance = 492-300 = 192 miles
b = change in time = 12 weeks
c = a/b = rate of change of distance over time = speed of growth
c = (192 miles)/(12 weeks)
c = (192/12) miles per week
c = 16 miles per week
In other words, each time a week goes by, Ryan has walked another 16 miles.
For a related math concept, check out the slope formula. The slope represents the rate of change. It's useful for graphing linear equations.
suponga que usted se mueve sobre una pista rectilinea y se dezplaza a partir de un punto fijo 12 metro hacia la derecha avanza en la misma dirección 5 metro y luego se regresa en sentido contraria 18 metros la distancia entre el punto fijo y usted es
You are 1 meter behind the fixed point.
What is distance in kinematics?The total path length covered by the moving body is called distance covered.
Given is that you move on a rectilinear track and move from a fixed point 12 meters to the right, advance in the same direction 5 meters and then return in the opposite direction 18 meters.
Total displacement = 12 + 5 - 18 = - 1
So, you are 1 meter behind the fixed point.
Therefore, you are 1 meter behind the fixed point.
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{Question in english -
Suppose you move on a rectilinear track and move from a fixed point 12 meters to the right, advance in the same direction 5 meters and then return in the opposite direction 18 meters, the distance between the fixed point and you is}
Sin descuento, esta casaca cuesta $80 por lo que luiscomenta. Voy acomprar la casac, ya que por ella pagaré solo $55 luego del descuento. ¿es correcto lo que dice luis? ¿por qué? explica tu respuesta
No es posible determinar si lo que dice Luis es correcto sin conocer el porcentaje de descuento aplicado en la compra de la casaca.
Si el precio original de la casaca es de $80 y después de aplicar un descuento el precio final es de $55, entonces se puede determinar el porcentaje de descuento utilizando la fórmula:
descuento = (precio original - precio final) / precio original
descuento = (80 - 55) / 80 = 0.3125 = 31.25%
Si el porcentaje de descuento es del 31.25%, entonces Luis tiene razón en su afirmación de que está comprando la casaca con un descuento. Sin embargo, si el porcentaje de descuento es diferente, entonces su afirmación podría ser incorrecta.
Por lo tanto, es importante conocer el porcentaje de descuento para determinar si lo que dice Luis es correcto o no.
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
A librarian is expanding some sections of the city library. He buys books at a special price from a dealer who charges one price for any hardback book and another price for any paperback book. For the children's section, Mr. Howard purchased 100 new hardcover books and 72 new paperback books, which cost a total of $1,760. He also purchased 97 new hardcover books and 72 new paperback books for the adult fiction section, spending a total of $1,718. What is the special price for each type of book?The special price is $ for hardcover books and $ for paperback books.
The system of equation is 100x + 72y = 1760 and 97x + 72y = 1718. The special price is $14 for hardcover books and $5 for paperback books.
What is linear equation?Equations are declarations of equality between two mathematical expressions containing one or more variables. A linear equation is one in which the maximum power of the variable is one. Any arithmetic equation can be solved using linear equations, which can also be used to find the precise value or root of the variable that answers the question.
Let us suppose the price of hardback covers = x.
Let us suppose the price of paperback covers = y.
Given that, Mr. Howard purchased 100 new hardcover books and 72 new paperback books, which cost a total of $1,760.
100x + 72y = 1760........(1)
He also purchased 97 new hardcover books and 72 new paperback books for the adult fiction section, spending a total of $1,718.
97x + 72y = 1718.........(2)
The system of equation to describe the situation is:
100x + 72y = 1760.
97x + 72y = 1718
To find the solution subtract the two equations:
100x + 72y = 1760.
- (97x + 72y = 1718)
Thus,
3x = 42
x = 14
Substitute the value of x in equation 1:
100(14) + 72y = 1760
1400 + 72y = 1760
72y = 360
y = 5
Hence, the special price is $14 for hardcover books and $5 for paperback books.
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What are the coefficients of the product
(5y-3)^2 ?
A: -30
B: -6
C: 9
D: 10
E: 25
The value of the coefficient of the product is equal to - 30. (Correct choice: A)
How to determine the value of coefficient in a quadratic equation
The expanded form of a quadratic equation includes three real coefficients, whose definition is shown below:
(a · x + b)² = a · x² + 2 · a · b · x + b · x²
The coefficient of the product is the element 2 · a · b of the expanded form. If we know that a = 5 and b = - 3, then the coefficient of thre product is:
2 · a · b = 2 · 5 · (- 3)
2 · a · b = - 30
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Let v = (- 5,8) Calculate the magnitude of - v
The magnitude of -v is [tex]\sqrt{(89)}[/tex]
Describe magnitude ?In physics and mathematics, magnitude refers to the size or quantity of a physical or mathematical property. It can be represented by a scalar value or a vector with a scalar magnitude.
In the case of scalar magnitude, it represents a property's absolute value, which is always positive. For example, the magnitude of a force, velocity, or acceleration represents its absolute value without any direction.
In contrast, vector magnitude represents the length or size of a vector, including both its magnitude and direction. It can be calculated using the Pythagorean theorem, where the magnitude of a vector V with components (Vx, Vy, Vz) is:
[tex]|V| = sqrt(Vx^2 + Vy^2 + Vz^2)[/tex]
The magnitude of a vector is always positive and can be used to determine the distance between two points in space.
Overall, magnitude is an essential concept in many fields, including physics, mathematics, engineering, and computer science, and it plays a crucial role in understanding various physical and mathematical phenomena.
The magnitude of a vector is its length, which is calculated using the Pythagorean theorem. For a vector v = (a, b), the magnitude is given by:
[tex]|v| = sqrt(a^2 + b^2)[/tex]
The negative of a vector simply reverses its direction, but not its magnitude. Therefore, the magnitude of -v is the same as the magnitude of v.
Using this information, we can calculate the magnitude of -v as follows:
[tex]|-v| = |-( -5, 8)| = |(5, -8)|\\\|-v|\ = \sqrt{(5^2 + (-8)^2)} = \sqrt{(25 + 64) }= \sqrt{(89)}Therefore, the magnitude of -v is \sqrt{(89)}[/tex]
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Solve for one two three and four
For the given rectangle, the angles are:
1 = 72°
2 = 36°
3 = 18°
4 = 144°
What is a rectangle?
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length. A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
The given figure is a rectangle.
The angle 3 = 18°
This is because they are alternate angles.
In triangle ADC,
∠DAC = 180 - ( 18 + 90) = 72°
The angles ∠DAC and ∠BCE are alternate angles.
∠BCE and 1 are congruent angles.
1 = 72°
2 = 180 - ( 72+72) = 36°
From triangle BDC,
∠CDE = 180 - (72+90) = 18
So 4 = 180 - ( 3+∠CDE ) = 180 - (18+18) = 144°
Therefore for the given rectangle, the angles are:
1 = 72°
2 = 36°
3 = 18°
4 = 144°
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write in standard from
Answer:
(D.) [tex]5x^{5} -5x^{3} +4[/tex]
Step-by-step explanation:
Adding Polynomials:
To add both of these two polynomials together, all we need to do is add like terms. All of the other options are wrong, since we do not add the exponents.
[tex]5x^{5} -5x^{3} +4[/tex]
Find the missing side length. Round to the nearest tenth.
The missing side length is 22.6.
From the given figure, We can observe that it is a right-angled triangle.
We are provided with two angles in the triangles,
So, We can evaluate the third angle by the sum of the angles property of
a triangle.
∠ABC + ∠BAC + ∠ACB = 180°
90° + 37° + ∠ACB = 180°
∠ACB = 180° - 127°
∠ACB = 53°
By the property of the triangle,
tanα = Perpendicular/Base of the triangle
tanα = AB/BC
tan53° = x/17
x = tan53°×17
x = 22.6
Therefore, The missing side length is 22.6.
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The missing side length of right angled triangle is 22.6.
Given,
Right angled triangle
Here
Two angles in the triangles : 37 and 90 degrees .
So, We can evaluate the third angle by the sum of the angles property of a triangle.
∠ABC + ∠BAC + ∠ACB = 180°
90° + 37° + ∠ACB = 180°
∠ACB = 180° - 127°
∠ACB = 53°
By the property of the triangle,
tanα = Perpendicular/Base of the triangle
tanα = AB/BC
tan53° = x/17
x = tan53°×17
x = 22.6
Therefore, The missing side length is 22.6.
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Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.30 and P(B) =0.40.
What is P(A Assume that we have two
events, A and&nbB)?
What is P(A | B)?
Is P(A | B) equal to P(A)?
Are events A and B dependent or independent?
A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate?
What general conclusion would you make about mutually exclusive and independent events given the results of this problem?
The probability of A given B is 0, and P(A | B) is not equal to P(A). Events A and B are mutually exclusive, meaning that they cannot both occur at the same time, and thus they are not independent. Mutually exclusive events are not necessarily independent and independent events may or may not be mutually exclusive.
P(A) = 0.30 and P(B) = 0.40, so P(A and B) = 0 because the events A and B are mutually exclusive. This means that the probability of A given B is 0, and P(A | B) = 0. P(A | B) is not equal to P(A).Events A and B are mutually exclusive, meaning that they cannot both occur at the same time, and thus they are not independent.The statement that mutually exclusive events and independent events are the same is not accurate. Mutually exclusive events are not necessarily independent and vice versa.Given the results of this problem, we can conclude that mutually exclusive events are not independent, and independent events may or may not be mutually exclusive. The two concepts are not necessarily related as mutually exclusive events do not necessarily need to be independent and independent events do not necessarily need to be mutually exclusive.
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1. What are the Math 1 essential skills and/or concepts relevant to this task?
2.Name the strategy you will use to solve the problem:
3. Describe the strategy:
Justify your thinking. (This means: justify the strategy or justify your final solution.)
The number of solutions in the equation is One solution
The number of solutions in the equationFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have two lines that intersect at a point
This means that the number of solutions is one
The essential skillsHere, the skills needed are:
Being able to solve a system of equations using graphsUnderstanding the concept of a unique solution of equationsThe strategy used to solve the problemThe strategy to solve the problem is to use the graph method to solve the system of linear equations and check if the resulting solution satisfies all the equations in the system.
If it does, then the system has one unique solution.
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Round 0.002391 to 2 significant figures
To round 0.002391 to 2 significant figures, we need to look at the digits after the first two significant digits (which are 2 and 3 in this case).
The digit in the third decimal place is 2, which is less than 5. Therefore, we leave the second significant digit (3) as it is, and we drop all the digits after that.
So, rounding 0.002391 to 2 significant figures, we get:
0.0024
complete both transformations below then enter the final coordinaties of the figure below A(-6,-3) b (-1,-4) c (-5,-1) 1. reflect across x-axis 2. <3,-2>
The coordinates of the figure are A''(-3, 1),B''(2,2), C''(-2, -1).
What is the transformation of a point?
The transformation, or f: X →X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the image X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one direction or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.
Given that the coordinates of the points A, B, C are A(-6,-3), B(-1,-4), C(-5,-1).
The rule of a reflection across the x-axis is (x,y)→(x,-y).
After reflection across the x-axis,
A(-6,-3)→ A'(-6,3)
B(-1,-4)→B'(-1,4)
C(-5,-1)→C'(-5,1)
A rule of translation of 3 units right and 2 units down is (x,y)→(x+3,y-2).
Thus the new coordinates are:
A'(-6,3)→ A''(-6+3,3-2)=A''(-3,1)
B'(-1,4)→ B''(-1+3,4-2)=B''(2,2)
C'(-5,1)→ C''(-5+3,1-2)=C''(-2,-1)
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