This graph displays a linear function. What is the rate of change?

Rate of change= _____

The point, (5, -4), is the solution to the given system of equations because the lines intersect at the point.

From the question, we are to determine why the given point is a solution to the system of equations

The given system of equations is

4y = -3x - 1

2y = x - 13

When solving system of equations by the graphical method, the point where the lines intersect gives the solution to the system of equations.

From the given graph,

The two lines intersect at the point where x = 5 and y = -4.

That is,

The lines intersect at (5, -4), and thus, (5, -4) is the solution to the system of equations.

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Using linear approximation, we estimate that f(5.1) is approximately 9.8.

To estimate f(5.1) using linear approximation, we can use the formula: f(x) ≈ f(a) + f'(a)(x - a)
where x is the value we want to estimate, a is a known value close to x, f(a) is the known value of the function at a, and f'(a) is the known value of the derivative at a. In this case, we have:

a = 5
f(a) = 10
f'(a) = -2
x = 5.1

Plugging these values into the formula, we get:

f(5.1) ≈ f(5) + f'(5)(5.1 - 5)
f(5.1) ≈ 10 + (-2)(0.1)
f(5.1) ≈ 9.8

Therefore, using linear approximation, we estimate that f(5.1) is approximately 9.8. It's important to note that this is just an estimate and may not be exact, but it gives us a good idea of what the function value could be close to 5.1. This technique is often used in calculus and other mathematical fields to make quick approximations without having to evaluate complex functions.

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Answer:

28

Step-by-step explanation:

60-32=28

Answer:

60-32

Step-by-step explanation:

She saves 32 so subtract 60-32

Answer:

3/5 3/4

3/5*4/3=12/15=4/5

4/5 cups of water

because 4/3 is the reciprocal of 3/4 and so 3/4*4/3=1

The measure of central tendency that better describes the typical test score depends on the shape of the distribution of the scores - it can be median or mean.

The measure of central tendency that better describes the typical test score is the median. The median is the middle value in a data set when the data is arranged in ascending or descending order. It is a better measure of central tendency for test scores because it is not affected by extreme values or outliers, which can skew the mean.

To find the median, first, arrange the test scores in ascending or descending order. If there is an odd number of test scores, the median is the middle value. If there is an even number of test scores, the median is the average of the two middle values.

For example, if the test scores are 85, 90, 92, 95, and 98, the median is 92. If the test scores are 85, 90, 92, 95, 98, and 100, the median is (92 + 95)/2 = 93.5.

If the distribution of test scores is approximately symmetrical or bell-shaped, then the mean (arithmetic average) is a good measure of central tendency to describe the typical test score.

In conclusion, the choice of measure of central tendency to describe the typical test score depends on the shape of the distribution of the scores. If the distribution is approximately symmetrical or bell-shaped, the mean is preferred, and if it is skewed or contains outliers, the median is preferred.

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Answer: C. Buenos Aries-Tucuman-Bahia Blanca-Salta-Buenos Aries

Step-by-step explanation:

Edg 2022

The correct graph would be a straight line with a slope of 45 and passing through the origin (0, 0).

We have,

The graph that models the cost, y, in cents of making x minutes of international calls would be a linear graph, as the cost is directly proportional to the number of minutes.

The equation of the linear graph would be:

y = 45x

Here, y represents the cost in cents, and x represents the number of minutes.

Therefore,

The correct graph would be a straight line with a slope of 45 and passing through the origin (0, 0).

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Answer:

B

Step-by-step explanation:

Hope this helps :D

The area of the rectangular parking lot is 929.03 square meters.

Use the formula for the area of a rectangle to calculate the area of the rectangular parking lot, which is given as:

Area = length × width

We know that the parking lot is 67.5 ft wide and 148 ft long, the area can be calculated as follows:

Area = 67.5 ft × 148 f

t= 9990 sq. ft

However, the question asks for the area in square meters, so we need to convert square feet to square meters. 1 square foot is equal to 0.092903 square meters, so we can use this conversion factor to convert square feet to square meters.

Area in square meters = Area in square feet × 0.092903

= 9990 sq. ft × 0.092903

= 929.03 sq meters

Therefore, the area is 929.03 square meters.

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The time taken by the rocket to reach its maximum height is 3.25 seconds. The maximum height reached by the rocket is 174 feet.

A toy rocket is shot vertically into the air from a launching pad 5 feet above the ground with an initial velocity of 104 feet per second. The height h, in feet, of the rocket above the ground at "t" seconds after launch is given by the function h(t) = -16t² + 104t + 5. We need to calculate the time taken by the rocket to reach its maximum height and the maximum height.

Let the time taken and the maximum height be denoted by the variables "T" and "H". We will differentiate the given function to get the velocity of the rocket as a function of time.

v(t) = (d/dt)h(t)

v(t) = (d/dt)(-16t² + 104t + 5)

v(t) = -32t + 104

The velocity of the rocket must be equal to zero when it reaches its maximum height.

v(t) = 0

-32t + 104 = 0

32t = 104

t = 3.25

Hence, the time taken to reach the maximum height is 3.25 seconds.

The maximum height is calculated below.

H = h(3.25)

H = -16*(3.25)² + 104*(3.25) + 5

H = -16*10.5625 + 338 + 5

H = -169 + 343

H = 174

Hence, the maximum height reached by the rocket is 174 feet.

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So, let's judge the items one by one, to see which one is true:

a)Triangle BFD is an acute scalene triangle. False, the triangle is isosceles.

b)Triangle BCF is a right isosceles triangle. False, it is right, but scalene.

c) Triangle DEF is an obtuse scalene triangle. True, Angle EDF is the obtuse one.

d) Triangle ABF is an obtuse isosceles triangle. False, it's not isosceles.

e) Triangle BFE is an acute equilateral triangle.​ False, it's not equilateral.

Step-by-step explanation:

REFER TO THE ATTACHMENT

HEY IN WHICH CLASS YOU ARE ROSA

Answer:

my answer is 7.5

Step-by-step explanation:

let me know if I'm incorrect

Anna looks at the clock for the second time to clock at 11:50.

To determine the time Anna looks at the clock for the second time, we need to consider the rotation of the minute hand.

The minute hand on a clock completes a full rotation (360°) in 60 minutes, or 1 hour. So, if the minute hand has rotated 270°, it means it has traveled 270° out of the total 360°.

To find the elapsed time, we can set up a proportion:

270° / 360° = x / 60 minutes

Cross-multiplying, we get:

360x = 270 * 60

Dividing both sides by 360, we find:

x = (270 * 60) / 360

Simplifying the equation further:

x = 45 minutes

Therefore, the minute hand has rotated 270° in 45 minutes. Adding this to the initial time of 11:05, we find that Anna looks at the clock for the second time at:

11:05 + 45 minutes = 11:50

So, Anna looks at clock for second time at 11:50.

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(A) The basis in which the space work is done is around 2. The powers of 10's logarithmic values can be used to determine this. (b) They could have two fingers for each hand, giving infants a total of five fingers.

a. The space creatures are most likely employed in a base other than base 10. The values of log 10, log 100, and log 1000 do not match the expected values for base 10, which should be 1, 2, and 3, respectively. Instead, the values given indicate that the base is slightly less than ten, because log 10 is less than one, log 100 is less than two, and log 1000 is less than three.

To be more specific, using the calculator's approximation, we can use the change of base formula to find the value of log base b for each of these numbers:

log base b of 10 = log 10 / log b ≈ 0.926628408

log base b of 100 = log 100 / log b ≈ 1.853256816

log base b of 1000 = log 1000 / log b ≈ 2.779885224

By dividing the known values of log 10, log 100, and log 1000, we can find log b:

0.473606797 log b = log 1000 / log 100

As a result, the space creatures are most likely based on 9.526.

b. It is impossible to determine how many fingers the space creatures have based solely on the calculator information and logarithm values. The space creatures' base could be related to the number of fingers they have, but we don't have enough information to tell.

The inverses of exponential functions, or those that "undo," the exponential functions, are the logarithmic functions.

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The solution to the given system of equations is x = 2, y = -1, and z = 1.

To solve the system of equations, we can use methods such as substitution or elimination. Here, we will use the method of elimination to find the values of x, y, and z.

First, let's eliminate the variable x by multiplying equation (1) by 2 and equation (3) by -1. This gives us:

2x + 4y - 2z = -6 (4)

-x + y - z = -4 (5)

Next, we can subtract equation (5) from equation (4) to eliminate the variable x:

5y - z = 2 (6)

Now, we have a system of two equations with two variables. Let's eliminate the variable z by multiplying equation (2) by 2 and equation (6) by 1. This gives us:

4x - 2y + 2z = 10 (7)

5y - z = 2 (8)

Adding equation (7) and equation (8), we can eliminate the variable z:

4x + 5y = 12 (9)

From equation (6), we can express z in terms of y:

z = 5y - 2 (10)

Now, we have a system of two equations with two variables again. Let's substitute equation (10) into equation (1):

x + 2y - (5y - 2) = -3

x - 3y + 2 = -3

x - 3y = -5 (11)

From equations (9) and (11), we can solve for x and y:

4x + 5y = 12 (9)

x - 3y = -5 (11)

By solving this system of equations, we find x = 2 and y = -1. Substituting these values into equation (10), we can solve for z:

z = 5(-1) - 2

z = -5 - 2

z = -7

Therefore, the solution to the given system of equations is x = 2, y = -1, and z = -7.

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The value of  x² -2x +1 when x= -3 is 16

Note that algebraic expressions are defined as expressions that are composed of terms, variables, coefficients, constants and factors.

They are also made up of arithmetic operations like addition, division, subtraction, multiplication, bracket, parentheses.

From the information given, we have that;

x² -2x +1 when x= -3

Substitute the value of x as - 3, we get;

(-3)²- 2(-3) + 1

expand the bracket

9 + 6 + 1

Add the values

16

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Hi there!  

»»————-　★　————-««

I believe your answer is:  

d – 22 ≥ 28

d ≥ 50  

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(\boxed{\text{Information Given:}}\\\\d - \text{Initial amount of money}\\\\\text{22 dollars was spent, and there are 'at least' 28 dollars left.}\)

⸻⸻⸻⸻\(\boxed{\text{Setting up an inequality:}}\\\\\text{22 dollars was spent from the initial amount, 'd'.}\\\\d - 22\\\\\text{There are \textbf{at least} 28 dollars left. "At least" indicates a \underline{greater than or equal to} sign.}\\\\\rightarrow \boxed{d-22\geq 28}\)

⸻⸻⸻⸻

\(\boxed{\text{Solving the inequality:}}\\\\d - 22\geq 28\\-------------\\\rightarrow d - 22 + 22 \geq 28 + 22\\\\\rightarrow \boxed{d \geq 50}\)

⸻⸻⸻⸻

\(\text{Your answer should be: }\boxed{d-22\geq 28; \text{ }d \geq 50}\)

⸻⸻⸻⸻

»»————-　★　————-««

Hope this helps you. I apologize if it’s incorrect.  

Answer:

120 cm^2

Step-by-step explanation:

The area of a rectangle is it's length(l)  times its width(w):  

Area = l*w

Area = (12 cm)*(10 nm) = 120 cm^2

Question :-

Answer :-

\( \rule {180pt} {2pt} \)

Given :-

To Find :-

Solution :-

As per the provided information in the given question, we have been given that the Lenght of Rectangle is 12 cm . Breadth of Rectangle is given 10 cm . And, we have been asked to calculate the Area of Rectangle .

For calculating the Area , we will use the Formula :-

Therefore , by Substituting the given values in the above Formula :-

⇒ Area of Rectangle = Lenght × Breadth

⇒ Area of Rectangle = 12 × 10

⇒ Area of Rectangle = 120

Hence :-

\( \underline {\rule {180pt} {4pt}} \)

Yes, there will be a collision between Speedy Sue's car and the slow-moving van in the tunnel. The collision will occur at a distance of approximately 146.5 meters into the tunnel, and the time of the collision will be around 7.72 seconds.

To determine whether there will be a collision, we need to calculate the time it takes for Speedy Sue to reach the van and compare it with the time it takes for the van to exit the tunnel.

First, we calculate the time it takes for Sue to reach the van. The relative velocity between Sue and the van is (33.0 m/s - 5.40 m/s) = 27.6 m/s. Using the formula time = distance / velocity, the time it takes for Sue to reach the van is approximately 175 m / 27.6 m/s ≈ 6.34 seconds.

Next, we calculate the time it takes for the van to exit the tunnel. The distance the van needs to travel to exit the tunnel is the sum of the distance from its initial position to the end of the tunnel and the distance Sue needs to travel to reach the end of the tunnel. The total distance is 175 m + 175 m = 350 m. The velocity of the van is 5.40 m/s. Using the formula time = distance / velocity, the time it takes for the van to exit the tunnel is approximately 350 m / 5.40 m/s ≈ 64.81 seconds.

Since 6.34 seconds is less than 64.81 seconds, Sue will collide with the van before it exits the tunnel. To determine the distance into the tunnel where the collision occurs, we subtract the distance Sue travels in 6.34 seconds from the initial distance between Sue and the van. The distance Sue travels is (33.0 m/s - 1.90 m/s^2 * 6.34 s^2 / 2) * 6.34 s ≈ 146.5 meters.

Therefore, the collision between Sue's car and the van will occur at a distance of approximately 146.5 meters into the tunnel, and the time of the collision will be around 7.72 seconds.

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Function notation is a way of representing mathematical functions using symbols. In function notation, a function is represented by a single letter, such as "f" or "g," followed by a set of input values in parentheses. For example, f(x) represents a function of x, where the value of f for a given x can be found by evaluating the function.

Function notation is commonly used in mathematics to simplify expressions and make it easier to understand mathematical relationships between variables.

The following function notations represent the following given conditions:

a) N(5) represents the population of Miami 5 years after 1990.

b) N(9) represents the population of Miami 9 years after 1990, or in the year 1999.

c) N(1997) + 45,000 represents the population of Miami which is 45,000 more than the population in 1997.

d) N(1990 + k) represents the population of Miami k years after 1990.

e) N(1998) - N(1995) represents the change in the population of Miami from 1995 to 1998.

f) N(11) - N(7) represents the change in the population of Miami from 7 years after 1990 to 11 years after 1990.

g) N(2008) = 431,200 represents the population of Miami in 2008 as being 431,200.

h) The solution of the equation N(t) = 412,000 represents the year (or years) when the population of Miami was 412,000.

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The point prevalence of brilliance at the end of Week 1 is 0.08 or 8%.

The point prevalence of brilliance at the end of Week 2 is 0.17 or 17%.

The point prevalence of brilliance at the end of Week 3 is 0.33 or 33%.

Using person-weeks as denominator, the incidence of brilliance over the course of the 10-week course is 0.017 or 1.7%

In epidemiology context, brilliance can be calculated through calculating point prevalence, cumulative incidence, and incidence rate. The provided data table can be used to determine the point prevalence, incidence, and incidence rate of brilliance among PHE 450 students. So, the calculations of point prevalence, cumulative incidence, and incidence rate based on the provided data are as follows:

The point prevalence of brilliance at the end of Week 1 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #8 was the only existing case of brilliance at the beginning of Week 1, so the point prevalence of brilliance at the end of Week 1 is; Point prevalence = 1 ÷ 12 = 0.08 or 8%.

The point prevalence of brilliance at the end of Week 2 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #3 and Student #8 were existing cases of brilliance at the beginning of Week 2, so the point prevalence of brilliance at the end of Week 2 is; Point prevalence = 2 ÷ 12 = 0.17 or 17%.

The point prevalence of brilliance at the end of Week 3 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #3, #4, #6, and #8 were existing cases of brilliance at the beginning of Week 3, so the point prevalence of brilliance at the end of Week 3 is; Point prevalence = 4 ÷ 12 = 0.33 or 33%.

The incidence of brilliance can be calculated by the following formula; Incidence = Total number of new cases ÷ Total person-weeks of observation

Student #5 and Student #7 developed brilliance during the 10-week course, so the incidence of brilliance over the course of the 10-week course is; Incidence = 2 ÷ 120 = 0.017 or 1.7%.

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Answer:

-17

Step-by-step explanation:

(-12)+(-5)

Answer: Your answer is -17.

Step-by-step explanation: -12+(-5)

Have a wonderful day, good luck on your question! Bye!

using exponents, On simplifying the equation, we get =4m+8.

The PEMDAS order of operations must be followed when you want to simplify a mathematical equation without using parenthesis (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). There are no parenthesis in the expression, so you may start looking for exponents. If it does, first make that simpler.

Work simplification is to develop better work processes that boost output while cutting waste and costs.

Simplifying an expression is the same as solving a mathematical issue. When you simplify an equation, you essentially try to write it as simply as you can. There shouldn't be any more multiplication, dividing, adding, or deleting to be done when the process is finished.

Given equation,

m-(8-3m)

=m-8+3m

=4m+8

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The characteristic polynomial of T splits,  the characteristic polynomial of the restriction of T to any T-invariant subspace of V also splits.

To prove the given statement, we need to show that if the characteristic polynomial of a linear operator T on a finite-dimensional vector space V splits, then the characteristic polynomial of the restriction of T to any T-invariant subspace of V also splits.

Let U be a T-invariant subspace of V. We want to show that the characteristic polynomial of T restricted to U splits.

First, let's consider the minimal polynomial of T, denoted by \(m_T_{(x).\)Since the characteristic polynomial of T splits, we know that it can be written as \(c(x-a_1)^{m_1}(x-a_2)^{m_2}...(x-a_k)^{m_k}\), where \(a_1, a_2, ..., a_k\) are distinct eigenvalues of T, and \(m_1, m_2, ..., m_k\) are their respective multiplicities.

Since U is T-invariant, it means that for any u ∈ U, T(u) ∈ U. Thus, the restriction of T to U, denoted by \(T|_U,\) is a well-defined linear operator on U.

Now, let's consider the minimal polynomial of T restricted to U, denoted by m_{T|U}(x). We want to show that m{T|_U}(x) splits.

For any eigenvalue λ of T|_U, there exists a nonzero vector u ∈ U such that T|_U(u) = λu. This implies that T(u) = λu, so u is also an eigenvector of T associated with the eigenvalue λ.

Since the characteristic polynomial of T splits, we have λ as one of the eigenvalues of T. Hence, the minimal polynomial m_T(x) must have a factor of (x-λ) in its factorization.

Since m_T(x) is also the minimal polynomial of T restricted to U, it follows that m_{T|_U}(x) must also have a factor of (x-λ) in its factorization.

Since this argument holds for any eigenvalue λ of T|_U, we conclude that the characteristic polynomial of T restricted to U,

given by det(xI - T|_U), can be factored as (x-λ_1\()^{n_1}\)(x-λ_2\()^{n_2}\)...(x-λ_p\()^{n_p},\)

where λ_1, λ_2, ..., λ_p are the distinct eigenvalues of T|_U, and n_1, n_2, ..., n_p are their respective multiplicities.

Therefore, we have shown that if the characteristic polynomial of T splits, then the characteristic polynomial of the restriction of T to any T-invariant subspace of V also splits.

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1. The skaters are approximately 2.53 feet apart.

2. The adjusted equation using the Law of Cosines would be:

(5 - x)² + (7 - y)² - 2 * (5 - x) * (7 - y) * cos(15°) = 2²

Q1: The distance between Jackie and Peter can be found using the Law of Cosines. Let's denote the distance between them as d. According to the Law of Cosines, we have:

d² = 5² + 7² - 2 * 5 * 7 * cos(15°)

Calculating the cosine of 15 degrees, we find:

cos(15°) ≈ 0.9659

Plugging in the values, we get:

d² = 25 + 49 - 70 * 0.9659

d² ≈ 25 + 49 - 67.613

d² ≈ 6.387

d ≈ √6.387

d ≈ 2.53 feet

Therefore, the skaters are approximately 2.53 feet apart.

Q2: The given distance between the skaters is 2 feet, and we have found that they are currently 2.53 feet apart. Hence, they are unable to complete the trick at their current positions because they are farther apart than the allowed distance.

To adjust the distances skated by one or both skaters, we can decrease their individual distances so that their total distance is 2 feet. Let's assume that Jackie reduces her distance by x feet and Peter reduces his distance by y feet.

The adjusted equation using the Law of Cosines would be:

(5 - x)² + (7 - y)² - 2 * (5 - x) * (7 - y) * cos(15°) = 2²

By solving this equation, we can find the values of x and y that satisfy the condition. To do so, we would need to substitute the value of cos(15°) and solve for x and y using algebraic methods.

Once we find the values of x and y, we can determine the adjusted distances for Jackie and Peter. These adjustments will allow them to complete the trick while being 2 feet apart.

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Answer:

y =4x+ 18

Step-by-step explanation:

Slope intercept form: y = mx + b

y -6 = 4(x + 3)

y - 6 = 4x + 12

Add 6 to both side

y = 4x + 12 + 6

y = 4x + 18

______________

\( \: \)

y - 6 = 4(x + 3)

y - 6 = 4x + 12

y = 4x + 12 + 6

y = 4x + 18✔

Answer:

D. 12 units

Step-by-step explanation:

For a point to be translated x units to the left, we must subtract x from the original point, so the x coordinate for M' is -4 as 4 - 8 = -4

For a point to be translated x units down, we must subtract x from the original point, so the y coordinate for M' is -3 as 6 - 9 = -3

Thus, the coordinates for M' is (-4, -3)

The formula for distance, d, between two points is

\(d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\), where (x1, y1) is one point and (x2, y2) is another point.

If we allow M (4, 6) to be our x1 and y1 point and M' (-4, -3) to be our x2 and y2 point, we can find the distance between the two points:

\(d=\sqrt{(4-(-4))^2+(6-(-3))^2}\\ d=\sqrt{(4+4)^2+(6+3)^2}\\ d=\sqrt{(8)^2+(9)^2}\\ d=\sqrt{64+81}\\ d=\sqrt{145}\\ d=12.04159458\)