How do you tell if a system of equations has no solution or infinitely many?

The total number of laps Sarah should run today is given by the equation A = 16 laps

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of laps be represented as A

Now , the equation will be

The total distance ran by Sarah yesterday = 3,682 m

The distance of one lap = 263 m

So , the number of laps ran by Sarah yesterday = total distance ran by Sarah yesterday / distance of one lap

Substituting the values in the equation , we get

The number of laps ran by Sarah yesterday = 3682 / 263

The number of laps ran by Sarah yesterday = 14 laps

Now ,

The distance Sarah wants to run today = 4,222 m

So , the number of laps Sarah should run today A = distance Sarah wants to run today / distance of one lap

Substituting the values in the equation , we get

The number of laps Sarah should run today A = 4,222 / 263

The number of laps Sarah should run today A = 16.05 laps

The number of laps Sarah should run today A = 16 laps

Therefore , the value of A is 16 laps

Hence , the number of laps is 16 laps

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The answers to each part is mentioned below.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is a straight line problem as shown in the question.

(a) -

Now, 12 oz of honey will cost $5.4. So, we can write that -

1 ounce of honey will cost - (5.4/12)

Cost of 1 oz honey will be - $(0.45)

(b) -

Now, 12 oz of honey will cost $5.4. So, we can write that -

For $1, you can buy - (12/5.4) oz of honey.

Amount of honey bought in 1 dollar - 2.22 ounces

(c) -

We can write the equation as -

c = 0.45h

(d) -

The graph for this function is attached with the answer.

Therefore, the answers to each part is mentioned above.

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The point (1, -2) is not a solution to the system of equation, 20·x + 20·y = -2, 2·x + 5·y = -8, the correct option is NO, the solution is (2.5, -2.6)

A system of equations are two (or more) equations that have common variables.

The system of equation is presented as follows;

20·x + 20·y = -2

2·x + 5·y = -8

The specified possible solution of the equation is; (1, -2)

Making y the subject of each of the equations, and plugging in the value of x = 1, for the first equation, we get;

20·x + 20·y = -2

20·y = -2 - 20·x

y = (-2 - 20·x)/20

Therefore; y = (-2 - 20 × 1)/20 = -1.1

When x = 1, y = -1.1, therefore, the point (1, -2), is not a solution to the first equation, 20·x + 20·y = -2

Evaluating the second equation, we get;

2·x + 5·y = -8

5·y = -8 - 2·x

y = (-8 - 2·x)/5

Plugging in x = 1, we get;

y = (-8 - 2 × 1)/5 = -2

When x = 1, y = -2, therefore, the point (1, -2), is a point on the graph of the second equation, 2·x + 5·y = -8, but it is not a solution to the system of equation

The solution to the system of equation, 20·x + 20·y = -2, 2·x + 5·y = -8, can by found by equating both expressions for y as follows;

y = (-2 - 20·x)/20 and y = (-8 - 2·x)/5

Therefore; (-2 - 20·x)/20 = (-8 - 2·x)/5

-10 - 100·x = -160 - 40·x

60·x = 150

x = 150 ÷ 60 = 2.5

x = 2.5

y = (-2 - 20 × 2.5)/20 = -2.6

y = -2.6

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The simplified form of radical √18 . 3√5 = 9√10

In mathematics, a radical expression is defined as any expression containing a radical (√) symbol. Many times it is used to determine the square root of a number. However, it can also be used to describe a cube root, a fourth root, or higher. When the radical symbol is used to denote any root other than a square root, there will be a superscript number in the 'V'-shaped part of the symbol.

For example, ³√(8) means to find the cube root of 8. If there is no superscript number, the radical expression is calling for the square root.

The term underneath the radical symbol is called the radicand.

Given radical

√18 . 3√5

⇒ √(9 × 2) . 3√5

⇒ 3√2 . 3√5

⇒ 9(√2.5)

⇒ 9√10

⇒ 28.46

Hence, The radical √18 . 3√5 can be simplified to 9√10 having value = 28.46

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Answer:

Any ordered pair #(x, y)# that satisfies #x>=6+4y#Or, in set notation, #Solution={(x, y)|x>=6+4y}#Explanation:Now, there is a little problem here - it is that you never specified which ordered pair needs to be evaluated to satisfy the condition #0.5x-2y>=3# Allow me to explain.Below is a graph of the inequality of your question:graph{0.5x-2y>=3 [-10, 10, -5, 5]}To answer which point is in the solution set, well the answer is that any point that is on or within the shaded area is part of the solution set.

Step-by-step explanation:

Sally's team score is 6.

We can determine Sally's team score by calculating the average of her team's finishing place positions.

From the information given, we know that:

If we assume that Peter's team finished in 1st, 2nd, 3rd, 4th and 5th places, then we can calculate Sally's team score as follows:

To find the average of the five finishing place positions, we add up all the places and divide by 5:

(2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6

So, Sally's team score is 6.

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Answer:

$400

Step-by-step explanation:

If $16 will be spent, then you should do 320/16=20 to find out how many times people are donating. Since that answer what 20, they need people to give 20*20=400 oo be able to raise enough money fOr playground equipment

The algebraic expression is represented as 4d - 2.5

An algebraic expression is simply defined as an expression that is composed of coefficients, factors, constants, terms, and variables.

They are also composed of mathematical operations, such as;

From the information given, we have that;

The variable = d

The constant = 2.5

The coefficient = 4

This is represented as;

4d - 2.5

Hence, the expression is 4d - 2.5

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Answer:

Step-by-step explanation:

You need to add both of the angles you already know (1 and 2). If you add angle 1 and angle 2 you get 74. This means m < J K M would be 74°.

Answer:

74 degrees

Step-by-step explanation:

You have to add angles 1 and 2

35 +39=74

Therefore, 74 is the answer

Answer:

slope = (3/2)

Step-by-step explanation:

point 1: (-1, 1); Point 2: (1, 4)

            (x₁, y₁)              (x₂, y₂)

y₂ - y₁         4 - 1            3            3

----------- = ------------ = --------- = -------

x₂ - x₁          1 - (-1)       1 + 1          2

I hope this helps!

Using percentage and equations, Greg has 734 songs, Raj has 426 songs and Mark has 720 songs

Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the percent symbol, "%". For example, 45% (read as "forty-five percent") is equal to 45/100, or 0.45. Percentages have no dimension, which it's why they are dimensionless number. for example 60% of a number, then it means 60 per cent of its whole.

In this problem, we can write an equations and solve to determine the number of songs Greg has on his computer.

Let;

Since Mark has 720 songs in his computer;

x = 14 + 720

x = 734

Greg has 734 songs

We can calculate the number of songs Raj has by;

y = 60%(720) - 6

y = [(0.6) * 720] - 6

y = 426

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The value of b is degree 104.we can find by using vertically opposite theorem.

Vertical Angles are when two lines intersect each other then the opposite angles formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.The point where they meet is called a vertex.

Vertical opposite angles that are opposite each other when two lines cross are also known as vertical angles because the two angles share the same corner. Opposite angles are also congruent angles meaning they are equal or have the same measurement.

Now we have

(b-308)=(-2b+4)

b+2b=4+308

3b=312

b=104

Hence the value of b is 104 degree.

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For a trigonometric equation. Cos^2x=3sin^2x, the solution is mathematically given as x = π/6 + 2nπ.

Trigonometry is the study of angles and the angular connections of planar and three-dimensional shapes. Trigonometry is made up of trigonometric functions (also known as circle functions) such as cosecant, cosine, cotangent, secant, sine, and tangent.

Generally, the equation for the trigonometric equation is mathematically given as:

Cos^2x=3sin^2x

Therefore

1 - sin^2(x) = 3 sin^2(x)

1/4 = sin^2(x)

Hence introducing \pi

x = arcsin(1/2) + 2nπ  

x = π/6 + 2nπ

In conclusion,

x = π/6 + 2nπ

For a trigonometric equation. Cos^2x=3sin^2x, the solution is mathematically given as x = π/6 + 2nπ.

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Answer:

Step-by-step explanation:

pull up in a monsta automobile gangsta

Answer:

7x = 33+2

7x = 35

x = 5

Step-by-step explanation:

A SIMPLE EQUATION

a) An equation to find the percent P of recorded music sold as full-length cassettes for any year x between 2001 and 2006 : y = -0.5x + 3.4

b) The percent of recorded music sold as full-length cassettes in 2004 = 1.9%

As, between 2001 and 2006, the percent of recorded music sold was decreased by about 0. 5% per year.

This means, the slope m = -0.5

In 2001, full-length cassettes represented 3. 4% of total music sales.

This means the y-intercept would be c = 3.4

So, an equation to find the percent P of recorded music sold as full-length cassettes for any year x between 2001 and 2006 would be,

y = mx + c

Substituting value of m and c,

y = -0.5x + 3.4

Now  to find the percent of recorded music sold as full-length cassettes in 2004

Here, the number of years x would be

x = 2004 - 2001

x = 3

So, the percent of recorded music sold would be,

y = (-0.5 × 3) + 3.4

y = 1.9%

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The sum of the interior angles of a nonagon (a 9-sided polygon) is 1,450°.

1. The interior angles of a polygon can be calculated by subtracting 2 from the number of sides, then multiplying the result by 180°.

2. For a nonagon (a 9-sided polygon), the calculation is

(9-2) × 180° = 1,450°.

The sum of the interior angles of any polygon can be calculated using the formula

(n-2) × 180°,

where n is the number of sides of the polygon. This formula works because the sum of the interior angles of any polygon is always equal to (n-2) times the measure of a single interior angle. For a nonagon, a 9-sided polygon, the calculation is

(9-2) × 180° = 1,450°.

This means that the sum of the interior angles of a nonagon is 1,450°.

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Han will make $57.75 for 7 hours of babysitting.

Given is a line segment RT.

We can write RT as -

RT = RS + ST

56 = (7y + 3) + (2y + 8)

(7y + 3) + (2y + 8) = 56

9y + 11 = 56

9y = 45

y = 5

Therefore, the value of {y} will be equivalent to 5.

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The probability that you correctly guess the letter section and then guess the correct number section where your car is located is 0.01.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Total possible outcomes.

= 8 x 22

= 176

Now,

Probability of guessing the correct letter.

= [tex]^8C_1[/tex] / 176

Probability of guessing the correct section.

= [tex]^{22}C_1[/tex] / 176

The probability that you correctly guess the letter section and then guess the correct number section.

= [tex]^8C_1 \times ^{22}C_1[/tex] / 176 x 176

= 8 x 22 / 176 x 176

=  1 / 176

= 0 .005

= 0.01

Thus,

The probability that you correctly guess where your car is located is 0.01.

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The solution is Option A.

Substitution is the second strategy for solving a system of equations

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A is

ax + by = c   be equation (1)

Let the second equation be represented as B

dx + ey = f   be equation (2)

On adding or subtracting both the equations , we can eliminate one of the variables from the system of equations

And , to calculate the other variable , substitute the value of the variable in either of the equations to solve the system of equations

So , we will get the value of the variable x and y

Hence , the system of equations can be solved by substitution

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The expression is 8n – 3; The 100th term is 797

The nth term of an arithmetic sequence is given by:

an=a1+(100-1)d          ....[1]

where

a1  is the first term

d is the common difference of two consecutive terms.

n is the number of terms.

Given the sequence:

5, 13, 21, 29, 37, 45, …

This is an arithmetic sequence with first term  = 5 and common difference(d) = 8

Since;

13-5 = 8,

21-13 = 8,

29-21 = 8  and so on....

We have to find the 100th term in the sequence

Substitute in [1] we have;

an=a1+(100-1)d

an=5+(n-1)8=5+8n-8 = 8n-3

Substitute the given values and n=100 we have;

a100= 800 - 3 = 797

Therefore, the 100th term in the sequence is, 797 and an expression to describe a rule for the sequence is, 8n – 3;

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We know that the derivative means the rate of change of the function. Graphically, this means that the derivative is the slope of the graph of that function.

The derivative of a function is the slope of the curve for the specified function. Physically speaking, the derivative of a function is the instantaneous rate of change of a function with respect to the variable at a location.

A securities with a price that is based on or derived from one or more underlying assets is referred to as a derivative. A contract between two or more parties based on the asset or assets constitutes the derivative itself. Changes in the underlying asset's value affect its value.

The instantaneous pace at which a function changes with regard to one of its variables is known as the derivative. Finding the slope of the tangent line to the function at a certain location is equal to doing this.

lim/h→0f(x+h)−f(x)h=f'(x).

lim/h→06−6/h=0.

f'(x)=limΔx→0

f'(x)=limΔx→0

f(x+Δx)−f(x)Δx=

f'(x)=limΔx→06−6Δx=0

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Therefore ,the ordered pairs which are the solutions of the system of equations shown in the graph below are (1,-4) and (4,-7).

The term "ordered pair" refers to a pair of two variable that are shown in a way that they convey a specific order.

In an order pair, the first term denotes the x- and second term, the y-coordinates. The ordered pair is written in close brackets as shown in the example below.

Here ,

Is an equation system:

A set of equations is referred to as a system of equations when a limited set of equations is available and a common solution is sought.

The intersection of two lines, for the two equations drawn on a graph, represents the system's solution.

In the given graph, one linear line and one parabola is shown. In this graph the parabola intersect with the line at point (1,-4) and (4,-7).

Therefore ,the ordered pairs which are the solutions of the system of equations shown in the graph below are (1,-4) and (4,-7).

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The number of possible different sequences of heads and tails is 1024.

A list of numbers (or other components) that follow a specific pattern is called a sequence. An arithmetic progression is one of the common examples of sequence and series.

A sequence can be arranged in either ascending or descending order.

Each flip has two outcomes H or T, so in ten flips you can get a sequence like HTHHTHTTTH

The number of possible different sequences is simply 2*2*2*2*2*2*2*2*2*2 = 2^10 = 1024

Thus, The number of possible different sequences of heads and tails is 1024.

Complete question:

If you flip a coin ten times, how many different sequences of heads and tails are possible?

a. 2° = 512

b. 10 = 100

C. 102 = 1024

d. 210 = 1024

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The perimeter of a closed shape is the overall length of the boundary. As a result, the perimeter of that shape is determined by adding up all of its sides. Therefore, Perimeter(P) = Sum of All Sides is the perimeter formula.

The formula is:

Perimeter = (the distance all the way around the outside of the figure).

How to calculate the distance all the way around the outside of the figure

is different for every shape.

A few of them are:

The perimeter of a Square, (P) = 4 × Side units.

The perimeter of a Rectangle, (P) = 2(l + b) units.

The perimeter of a Triangle is = Sum of all three sides.

The perimeter of a Circle = 2 π r = π d.

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Therefore because of this, the answer to the speed problem is that a family can travel 31.875 miles in 3/4 of an hour.

Speed is a tempo that is determined by the distance an entity travels in a predetermined period of time. Numerous methods exist for measuring speed, including miles per hour, laps per minute, and meters per second. The measurements of speed, distance, and time are related. The relationship can be expressed in three different ways:

D = RT, R = DT, & T = DR.

Here,

We are given that

Distance drives by a family=4[tex]\frac{1}{4}[/tex] miles

Time = 1/10

We have to find the rate of speed in miles per hour.

The speed formula will be used to get the velocity in miles per hour.

Distance traveled in a given amount of time equals speed.

=> Speed = 17/4 * 10

=> Speed = 42.5

So, using the calculation, we arrive at 42.5 miles per hour.

The miles traveled in 3/4 miles are therefore:

Distance is calculated as speed times time,

therefore 42.5 * 3/4 would equal 31.875 miles in distance.

Because of this, the answer to the speed problem is that a family can travel 31.875 miles in 3/4 of an hour.

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Lisa needs to sell fifty nine (59) cards on Friday to make a profit, based on total 140 cards and the information on number of cards sold per day.

The total number of cards to be sold for profit = number of cards sold till Thursday + Remaining cards

We need to calculate remaining cards, but before that, we will find the sum of sold cards.

Number of cards sold = 15 + 7 + 14 + 45

Performing addition on Right Hand Side of the equation

Number of cards sold = 81

Remaining cards = 140 - 81

Performing subtraction on Right Hand Side of the equation

Remaining cards = 59

Thus, required number of cards is 59.

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The complete question is-

Lisa need to sell at leat 140 card to make a profit. Monday-thursday she sell 15,7,14,45 card. How many more will she need to sell on friday to make a profit?

If two even integers are multiplied, then the product is also even. Hypothesis: Two even integers are multiplied. Hypothesis starts after the word "if". Conclusion starts after the word "then".

The sentence that comes just after the word "if" in a conditional statement is known as the hypothesis. The sentence that comes after the word then in a conditional statement is the conclusion.

If you earn high grades, the portion that follows the "if" is referred to as a hypothesis, and if you get good grades, the part that follows the "then" is referred to as a conclusion.

An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion.

p → q

Read this: if p, then q.

If the hypothesis is correct but the conclusion is untrue, a conditional statement is false. If the statement in the example above read, "If you achieve good marks then you will not get into a good college," it would be untrue.

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If two even integers are multiplied, then the product is also even. Hypothesis: Two even integers are multiplied. Hypothesis starts after the word "if". Conclusion starts after the word "then".

The sentence that comes just after the word "if" in a conditional statement is known as the hypothesis. The sentence that comes after the word then in a conditional statement is the conclusion.

If you earn high grades, the portion that follows the "if" is referred to as a hypothesis, and if you get good grades, the part that follows the "then" is referred to as a conclusion.

An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion.

p → q

Read this: if p, then q.

If the hypothesis is correct but the conclusion is untrue, a conditional statement is false. If the statement in the example above read, "If you achieve good marks then you will not get into a good college," it would be untrue.

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