How many solutions can a system of 3 linear equations have?

Eleri wants to be fit for the adventure holiday and to achieve that she runs 2 laps of a running track. Each lap is 400m and she thinks she has run 1km in total. To determine if Eleri is correct, we must first understand the basic units of measurement for distance and how they relate to one another.

A lap of a running track is a distance of 400m. The prefix "kilo" in the unit "kilometer" represents 1000. Therefore, a kilometer is equal to 1000 meters. To convert meters to kilometers, we divide the number of meters by 1000. To convert kilometers to meters, we multiply the number of kilometers by 1000.

To determine the total distance Eleri ran, we must multiply the number of laps by the distance of each lap. 2 laps x 400m per lap = 800m. This is the total distance Eleri ran in meters.

To determine if Eleri ran 1km, we must convert 800m to kilometers. Therefore, to convert meters to kilometers, we divide 800 by 1000. 800m / 1000 = 0.8km.

Therefore, Eleri did not run 1km, she ran 0.8km.

To further demonstrate the accuracy of our calculation, we can use dimensional analysis by using the conversion factor of 1000m = 1km.

800m / (1000m/1km) = 0.8km

This confirms that Eleri ran 0.8km, not 1km.

In conclusion, Eleri is not correct in her assumption that she ran 1km. She actually ran 0.8km which is 800 meters. This was determined by understanding the basic units of measurement for distance, converting the distance from meters to kilometers, and using dimensional analysis to verify our calculations.

Answer:

Step-by-step explanation:

no she is not correct she only ran 0.8 km

The correct dotplot for the given data is option D, which displays the number of errors for the week for each workstation.

Error in math is any mistake made in the process of solving a mathematical problem or problem-solving process. It could mean a mistake in the calculations, incorrect steps taken, or incorrect assumptions made. It can also include making a wrong interpretation of the problem, or not being able to solve it at all. Errors in math can occur due to a lack of understanding of the concepts, mistakes in calculations, errors in reasoning, or incorrect application of the rules and formulas. Errors can also be made in the process of writing down the equations, or in the process of simplifying the equation.

The graph begins with 0 and goes up to 254201 in intervals of 5. The data points for each work station are marked on the graph, showing the number of errors each work station made. This visual display of data points allows for an easy comparison of the number of errors across all workstations.

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The 100W bulb will have a lower brightness than the 60W bulb because the resistance of the 100W bulb is less than that of the 60W bulb, so it will have the lowest voltage drop.

Since the power of a lamp of nominal voltage V can be defined as [tex]\bold{P = \frac{V {}^{2} }{R}}[/tex], where R is the resistance to hot, this means that the resistance of the lamp is inversely proportional to its power, that is, the greater the power of the lamp, the lower its resistance.

Applying Kirchoff's second law to a series circuit with resistors R1 and R2 and power supply E we have:

[tex] \bold{E = I.R1 + I.R2}[/tex]

Since the current I is the same for all elements connected in series. In this expression we see that the smallest resistance will have the smallest voltage drop.

Now, in our circuit with two bulbs in series, the 100W bulb will have less resistance than the 60W bulb, so it will have less voltage drop. As it has a lower voltage drop, the power developed in the 100W lamp will be less than that developed in the 60W lamp and the 100W lamp will have a weaker brightness than the 60W lamp.

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The mean number of accidents that would be expected to be more than 7 accidents is 0.6554.

By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.

A statistical measurement known as the Z-score indicates how closely a value relates to the mean of a collection of values. The Z-score is calculated using standard deviations from the mean. When a data point's Z-score is 0, it means that it has the same score as the mean. One standard deviation from the mean would be indicated by a Z-score of 1.0.

Given that mean is 6.4 and the standard deviation is 1.5.

The z score is used to determine the accidents:

z = 7 - 6.4 / 1.5

z = 0.4

Using the table of normal distribution we have, P(x > 7 ) = P(z > 0.4) = 0.6554

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The given equation rearranged so that the variable q is the independent variable is 12r + 4r = 3q + 7q OR 16r = 10q

From the question, we are to rearrange the given equation so that the variable q is the independent variable

From the given information,

The give equation is

−7q + 12r = 3q − 4r

Add 7q to both sides of the equation

−7q + 7q + 12r = 3q + 7q − 4r

12r = 3q + 7q − 4r

Add 4r to both sides of the equation

12r + 4r = 3q + 7q − 4r + 4r

12r + 4r = 3q + 7q

Simplifying

16r = 10q

The equation rearranged is 12r + 4r = 3q + 7q OR 16r = 10q

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The cost in dollars if a cab ride 49 miles long is $ 110.

The question is not complete, a table of travel costs and distance data should be provided. A table that is similar to the table that should be provided is in the attachment. From the table, it can be seen that if the mileage increases by 5 miles, the cost will increase by $ 12.5. The data graph will be in the form of a straight line.

The equation of the line if two points are known

(y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)

(c - c₁)/(c₂ - c₁) = (d - d₁)/(d₂ - d₁)

(c - 12.5)/(25 - 12.5) = (d - 5)/(10 - 5)

(c - 12.5)/12.5 = (d - 5)/5

5 × (c - 12.5) = 12.5 × (d - 5)

5c - 62.5 = 12.5d - 125

5c = 12.5d - 125 + 62.5

5c = 12.5d - 62.5

c = 2.5d - 12.5

If a cab ride is 49 miles long,

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Answer:

Let x be the length of one side of the square field.

Since the field is divided into two squares, the total length of the fencing is 2x + 2x = 4x.

And since the problem states that it takes 406 yards of fencing to enclose the field,

we can set up the equation: 4x = 406.

Solving for x, we get x = 101.5

So the dimensions of the field would be 101.5 yards by 101.5 yards.

Step-by-step explanation:

The simplified polynomial is 6w^2 - 18w + 10.

A polynomial is an expression consisting of variables and coefficients and are used to model real-world situations. It is an equation of degree greater than one, where the exponents of the variables can be any non-negative integer. For example, the polynomial equation x2 + 3x + 2 represents a parabola when graphed. Polynomials are used in a variety of fields, such as mathematics and physics.

It is in standard form because it is written as ax^2 + bx + c, where a, b, and c are the coefficients of the terms and x is the variable. The coefficients are in decreasing order of powers of the variable, and there are no fractions or radicals in the equation.

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Rate of the jet in still Air is 716 miles per hour and

wind speed is 80 miles/hour.

The velocity of an item in relation to another observer is known as its relative velocity. It is the pace at which one item's relative location changes in relation to another object over time. When two bodies are travelling in opposing directions, their relative velocity is at its highest. They are approaching one another.

Let ‘X’ be speed of jet and

'Y’ be speed of Wind

Relative velocity when jet travels against wind: X - Y = ( 2544 / 4 ) = 636 miles/hour

Relative velocity when jet travels with wind is: X + Y = ( 3184 / 4 ) = 796 miles/hour

By adding these two equations we will get

2 X = 1432 or X = 716 miles /hour and

or, Y = 796 - 716 = 80 miles/hour

Hence,

Rate of the Jet in still Air is 716 miles per hour and

Wind speed is 80 miles/hour.

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Answer: [tex](0,-9)[/tex]

Step-by-step explanation:

The vector from [tex](-4,2)[/tex] to [tex](3,-4)[/tex] is [tex]\langle 7, -6 \rangle[/tex].

Applying this transformation to [tex](-7, -3)[/tex] yields that the fourth vertex has coordinates [tex](-7+7, -3-6)=(0,-9)[/tex].

Correct answers are - A, B, D, F, G.The volume of oblique cone is same as normal cone and volume of oblique cylinder is same as normal cylinder due to Cavalier's principle.

Cavalieri's principle is a method for determining the volume of an object by comparing it to the volume of another object of known volume. It was introduced by the Italian mathematician Bonaventura Cavalieri in the early 17th century. The principle states that if two solids have the same height and the same cross-sectional area at every height, then the two solids have the same volume.

The principle is based on the idea of slicing the solids into thin slices and comparing the areas of the cross-sections of the slices. If the cross-sectional areas are the same at every height, then the solids have the same volume.

Cavalieri's principle was one of the early precursors to the development of calculus and the concept of the definite integral. It is also a powerful tool in geometry and is used in many problems involving the calculation of volumes of irregular shapes.

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The complete question is as follows:

Answer:

a. The length and width of the smaller wall are 14 feet and 8 feet, respectively.

b. The area of the smaller wall is 14 feet x 8 feet = 112 square feet.

c. The area of the larger wall is 20 feet x 8 feet = 160 square feet.

d. The total area of the four walls in the room is 112 square feet + 112 square feet + 160 square feet + 160 square feet = 544 square feet.

e. To find the cost of painting the room walls with two coats of paint, we need to know the total area of the walls, and the cost of one gallon of paint. We can use the information provided: a gallon of paint covers 350 square feet on average and the cost of one gallon of paint is $36.50.

We can divide the total area of the walls by the coverage of one gallon of paint, then multiply that by the cost of one gallon of paint.

544 square feet / 350 square feet/gallon * $36.50/gallon = $38.34

So the cost of painting the room walls with two coats of paint is $38.34.

Answer:

250 and 10

Step-by-step explanation:

substitute x = 10 into the expressions

a = [tex]\frac{5x^2}{2}[/tex]

  = [tex]\frac{5(10)^2}{2}[/tex]

  = [tex]\frac{5(100)}{2}[/tex]

  = [tex]\frac{500}{2}[/tex]

  = 250

-----------------------------------------------

b = [tex]\frac{2x^2(x-5)}{10x}[/tex]

  = [tex]\frac{2(10)^2(10-5)}{10(10)}[/tex]

  = [tex]\frac{2(100)(5)}{100}[/tex] ( cancel 100 on numerator and denominator )

  = [tex]\frac{2(5)}{1}[/tex]

  = 10

Answer: [tex]18p^{4}[/tex]

Step-by-step explanation:

I wrote the steps in the image

Answer:

56.5 cm

Step-by-step explanation:

Circumfrence= pi× diameter

= 3.14×18 = 56.52 cm

3SF: 56.5 cm

The equation to determine the number of hours it will take to fill the pool, given the current level of the pool, the rate at which the pool is being filled, and the pool's capacity can be found using the following steps.

To write an equation that can be used to find the number of hours it will take to fill the pool from its current level, we need to use the following information:

The pool's capacity: 43,000 gallons

The current level of the pool: 20,000 gallons

The rate of filling the pool: 130 gallons per minute

We can start by using the formula:

time = (amount needed to fill)/(rate of filling)

The amount needed to fill the pool is the difference between the pool's capacity and the current level of the pool.

amount needed to fill = 43,000 - 20,000 = 23,000 gallons

Now we can substitute this value in the formula above:

time = (23,000 gallons)/(130 gallons/minute)

To convert the time to hours, we divide the time in minutes by 60

time = (23,000 gallons)/(130 gallons/minute) × (1 hour/60 minutes)

So, the equation that can be used to find h, the number of hours it will take to fill the pool from its current level is:

h = (23,000 gallons) / (130 gallons/minute) × (1 hour/60 minutes)

Note that this equation is not simplified, you can simplify it by canceling out common factors, you'll get:

h = (23000 / 130) × (1/60)

This equation can be used to find the number of hours it will take to fill the pool, given the current level of the pool, the rate at which the pool is being filled, and the pool's capacity.

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Answer:

t + c <= 17

Step-by-step explanation:

This inequality states that the total number of tables and chairs sold (t + c) must be less than or equal to 17, in order to satisfy the constraint that the store can ship at most 17 pieces of furniture per day.

The coordinate point T' the reflection of T over the y-axis is (4, -5).

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given that, the point T is plotted on the coordinate grid.

The coordinate point on the grid is (-4, -5).

The reflection of point (x, y) across the y-axis is (-x, y).

Here, (-4, -5)→(4, -5)

Therefore, the coordinate point T' the reflection of T over the y-axis is (4, -5).

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The likelihood of selecting a second ball is 2/8 or 1/4 if that ball is now eliminated.

Probability theory, a subfield of mathematics, gauges the likelihood of an event or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty.  Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a comprehensive set of equally likely outcomes that result in a certain occurrence compared to the total number of outcomes.

given

The ratio of the number of balls of that color to all the balls is the likelihood of selecting a ball from a bag.

In the first case, the likelihood of a red ball is therefore 3/9, or 1/3. The likelihood of selecting a second ball is 2/8 or 1/4 if that ball is now eliminated.

Therefore, the chance of getting a white ball is 1/2*1 plus 1/2*49/99, or roughly 3/4.

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The expression will be;

n = 8 x 5 / 4.

The correct option is A.

Algebraic expressions shows us how to express an unknown value using letters such as t, a, y, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Number of friends = 4

Bags sold = 8

Amount sold = $5

The expression will be;

n = (8 x 5) / 4

to find the amount sold for each of the friends.

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The equation of function after a horizontal translation is y = 2*4ˣ⁺².

Initially, functions represented the idealized relationship between two changing quantities. A planet's position, for instance, depends on time. In the past, the idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity).

The realms of application of the concept of a function were substantially expanded at the conclusion of the 19th century when it was defined in terms of set theory.

An assignment of an element from set Y to each element of set X constitutes a function from set X to set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

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The final equation of the line using the point-slope formula is y = (1/5)x + (6/5) = (1/5)x + 1.2.

The point-slope form of a line is given by y - y1 = m(x - x1) where m is the slope of the line and (x1, y1) is a point on the line.

First, we need to find the slope of the line that is perpendicular to 5y = x − 4. A line is perpendicular to another line if the product of their slopes is -1. The slope of 5y = x − 4 is x/5y=-1. Therefore, the slope of the line that is perpendicular to 5y = x − 4 is 1/5

Now we can use the point-slope form of a line with a slope of 1/5 and the point (-2, 1) to find the equation of the line.

y - 1 = (1/5)(x + 2)

y = (1/5)x + (2/5) + 1

y = (1/5)x + (6/5)

To write the equation in slope-intercept form, we need to solve for y:

y = (1/5)x + (6/5) = (1/5)x + 1.2

That's the final equation.

Therefore, The final equation of the line using the point-slope formula is y = (1/5)x + (6/5) = (1/5)x + 1.2.

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Using the given function V(x) = 15,000(0.87)^x , the value of Mr.Dulaney's car 5 years after its purchase will be approximately equal to given option $7500.

A mathematical phrase, rule, or law that establishes the relation between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

A mathematical function is a rule that assigns a unique output, also called the function value, to each input value within a certain set called the domain. The output is determined by the instructions, also called the function rule, that defines the relationship between the input and output values. It can be represented by an equation, such as y = f(x), where x is the input, y is the output, and f is the function symbol. The graph of a function is a set of points, where each input in the domain corresponds to a unique output. It helps to express the relationship between two variables and allows to make predictions and analyze patterns in mathematical problems.

Given,

V(x) = 15,000(0.87)^x where x denotes number of years after its purchase.

So, to find the value of Mr. Dulaney's car 5 years after its purchase,

let x =5

so V(x) = 15,000(0.87)^5 = $7476.31

Which is approximately equal to given option , $7,500

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-7.4 degrees celsius is less than the temperatures Susan recorded.

To explain, temperatures are measured on a scale, with 0 degrees celsius being the point at which water freezes and 100 degrees celsius being the point at which water boils. A temperature of -7.4 degrees celsius is therefore less than the recorded temperatures of -7.4 and 1.8 degrees celsius.

The temperature is a measure of the thermal energy of a substance or system, and is typically measured on a scale, such as the Celsius scale or the Fahrenheit scale.

In other words, the number -7.4 is less than 1.8 and -7.4 on the scale of temperature, meaning that -7.4 degrees celsius is less than the temperatures Susan recorded.

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The equation be 38.67 + 13.6 then we get 52.27.

A different way to represent a fractional value in mathematics is to use decimal notation. It denotes that base-10 fractional representation is being used. It is possible to change fractions into decimals and vice versa.

The same thing applies to decimals: they each represent a portion of a whole number. The distinction is in the notation used to write decimals vs fractions. By using decimal notation, we can graphically express how much of a whole number we are working with.

The decimal point must be moved till it is to the left of the first non-zero number in order to be written in scientific notation. The exponent is the amount of places the decimal point advances since each movement signifies a "power of 10".

Let the equation be 38.67 + 13.6 then we get 52.27.

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The angles and sides are in order from smallest to largest is written as,

For first triangle;

Sides = ZY, XZ, XY

Angles = ∠X, ∠Y, ∠Z

For second triangle;

Sides = MQ, MP, PQ

Angles = ∠P, ∠Q, ∠M

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We know that;

In triangle, The opposite side of large angle is large and opposite angle of a large side is large.

So, By above conclusions we get;

The angles and sides are in order from smallest to largest is written as,

For first triangle;

Sides = ZY, XZ, XY

Angles = ∠X, ∠Y, ∠Z

For second triangle;

Sides = MQ, MP, PQ

Angles = ∠P, ∠Q, ∠M

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hope this helps you understand !!

Answer:

x + 2

Step-by-step explanation:

Ben : x cm

Kieran: (x + 8) cm

Bianca: (x - 2) cm

Mean of their heights = [tex]\frac{Sum of their heights}{Number of people} = \frac{x + (x + 8) + (x - 2)}{3}[/tex]

                                   = [tex]\frac{x + x + 8 + x - 2}{3}[/tex]    (Expand the brackets)

                                   = [tex]\frac{x + x + x + 8 - 2}{3}[/tex]  (Bring all the like terms together)

                      = [tex]\frac{3x + 6}{3}[/tex] (Simplify the two sets of like terms)

                        = [tex]\frac{3(x + 2)}{3}[/tex]  (Extract the common factor '3' in the numerator)

                      = (x + 2) cm  ([tex]\frac{3}{3} = 1[/tex])

Therefore , the solution of the given problem of function comes out to be it is compatible with P(J(y)) = 1/3J(y) +4.

Math is a science that studies numbers, their variants, math and the tissues in the area, shapes, and both their real and possible locations. 'Function' refers to the relationship between a set of inputs, which each have a corresponding output. A function is a relationship between inputs in which each input yields a single variable, distinct output.

Here,

Given:

The quantity of paintings is returned by the function P, which accepts a number of months as an argument.

The function J returns the number of weeks in a year after accepting an undefined parameter.

P(weeks annually) = P(J(y)) seems to be the composites function that will provide the annual number of paintings.

Choice C is compatible with P(J(y)) = 1/3J(y) +4.

Therefore , the solution of the given problem of function comes out to be it is compatible with P(J(y)) = 1/3J(y) +4.

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Answer:

angle 1 = 120

Step-by-step explanation:

5x-5

x=25

5x=125

125-5=120

angle 1 = 120

you can check this by figuring out the second angle:

2x+10

x=25

2x=50

50+10=60

120+60=180  we know that all angles on a straight line add up to 180, so we know they are both correct

the rate of change of height at h = 15cm, 0. 0159 cm/s

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

Beads are dropped to create a conical pile such that the ratio of its radius to the height of the pile is constant at 2:3.

Volume is increasing at a rate of 5 cm3/s.

The volume of a Cone: 1/3 pi r^2 h

given r/h =2/3

V =0. 0159 cm/s

Hence the rate of change of height at h = 15cm, 0. 0159 cm/s

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