What is one of the solutions to the following system?

StartLayout Enlarged left-brace 1st Row y minus 3 = x 2nd row x squared minus 6 x + 13 = y EndLayout

The expressions that show the number of students for each activity are;

Note that this is a fraction problem.

We are given;

Total number of students in the middle school = x

A) From the given table, we can deduce that;

B: Now, the expression to show the students that like either drama or dance is;

(1/7)x + 26 + (1/7)x + 22

⇒(2/7)x + 48

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Full Question:

A middle school with x students ran a survey to determine the students' favorite activities. The table indicates the number of students who enjoy each activity. Answer parts A and B.

Table:

Activity:

Dance- 22 more than one-seventh of the students

Baseball- 24 fewer than four-sevenths of the students

Drama- 26 more than one-seventh of the students.

The equation of the line to commute the time is written as y = -1/2x + 24.5.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The given points are (1,24) and (15,17). To write the equation of the line first calculate the slope of the line and then find the y-intercept of the line.

Slope =  ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 17 - 24 ) / ( 15 - 1 )

Slope = -7 / 14

Slope = -1 / 2

The y-intercept is:-

y = mx + c

24 = -1/2 + c

c = ( 48 + 1 ) / 2

c = 49 / 2

c = 24.5

The equation of the line can be written as:-

y = mx + c

y = -1/2x + 24.5

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The rational number representation of Micah withdrawing $4.50 from his bank account is -4.5.

A rational number is any fraction with non-zero denominators. A rational number can be written as a fraction with a numerator and denominator that are both integers.

In this case, we can write $-4.50$ as the fraction $\frac{-450}{100}$, where the numerator represents the amount of money withdrawn (in cents) and the denominator represents the unit of currency used (in this case, 100 cents = 1 dollar).

So, the rational number representing the amount of money withdrawn from Micah's bank account is {-450} / {100}$ = -4.5.

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The probability of picking a green ball on the first pick, given that at least one red is chosen, is 11/19.

The probability of picking a green ball on the first pick, given that at least one red is chosen, can be calculated by finding the total number of possible outcomes and then dividing by the number of outcomes that include at least one red ball. In this bag, there are 11 green balls and 5 red balls, for a total of 16 balls. Since two balls are taken out successively without replacement, the total number of outcomes is 16 choose 2, or 120. Of those, there are 10 outcomes that include at least one red ball, so the probability of picking a green ball on the first pick, given that at least one red is chosen, is 11/19. This can be calculated by dividing the number of outcomes that include at least one red ball (10) by the total number of outcomes (120).

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As a result, on a graph of dP/dt vs P, the curve would be concave down for P b/a and concave up for P > b/a. The curve would reach its maximum when P = b/a, with dP/dt equal to zero.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

The equation dP/dt = aP² - bP represents the rate of change of the population P over time t.

When dP/dt is positive, the population is increasing. When dP/dt is negative, the population is decreasing.

To find when dP/dt is positive and negative, we need to find the critical points where dP/dt = 0.

Solving the equation dP/dt = aP² - bP = 0, we get:

aP² - bP = 0

aP(P - b/a) = 0

This equation has two solutions: P = 0 and P = b/a.

For P < b/a, dP/dt is negative (the population is decreasing). For P > b/a, dP/dt is positive (the population is increasing).

So, on a graph of dP/dt against P, the curve would be concave down for P < b/a and concave up for P > b/a. At P = b/a, the curve would have a maximum and dP/dt = 0.

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Both graphs show the same relationship between Clem's waist height and time, but the exponential graph shows a more rapid increase in Clem's waist height over time.

Both graphs depict the relationship between Clem's waist height and time. The first graph is linear and is represented by the equation y = 2x + 3, where y is Clem's waist height and x is the amount of time that has passed. The second graph is exponential and is represented by the equation y = 2^x + 3. Both graphs show that Clem's waist height increases with time – the difference is that the linear graph shows a steady, linear increase, while the exponential graph shows an exponential increase. For example, if Clem's waist height was 3 inches at the start, then after 1 hour it would be 5 inches on the linear graph, but 8 inches on the exponential graph. This difference can be seen in the calculations: 1 hour on the linear graph would be 3 + (2 x 1) = 5 inches, while 1 hour on the exponential graph would be 3 + (2^1) = 8 inches.

In summary, both graphs show the same relationship between Clem's waist height and time, but the both graphs show the same relationship between Clem's waist height and time, but the exponential graph shows a more rapid increase in Clem's waist height over time.

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Answer:

40.6428571429

Step-by-step explanation:

To evaluate the expression for the given value of the variable when t = -1/2, we just need to substitute the value of t into the expression:

41 + 5/7 * (-1/2) = 41 - 5/14
41 - 5/14 = 40.6428571429

So the answer is 40.6428571429.

Answer: The lateral surface area of the cylinder can be found using the formula: πr h, where r is the radius and h is the height of the cylinder.

Given that the height of the cylinder is 22 ft, and the diameter is 6 ft, the radius can be found by dividing the diameter by 2: r = 6 / 2 = 3 ft.

So the lateral surface area of the cylinder is: πr h = π * 3 * 22 = 66 * π ≈ 208.36 sq ft.

Rounding to the nearest hundredth, the lateral surface area of the cylinder is 208.36 sq ft.

Step-by-step explanation:

The measures of x, y and z are 40⁰, 90⁰ and 50⁰

A triangle is a three-sided polygon that consists of three edges and three vertices.

We know that co-interior angles are supplementary.

∠APQ+∠CPQ=180⁰

x+∠CPQ=180⁰

x+140⁰=180⁰

x=40⁰

∠BPR+∠PRD=180⁰

z+130⁰=180⁰

z=50⁰

Now, angles x, y and z form a line, hence they sum up to 180∘.

x+y+z=180⁰

40⁰+y+50⁰=180⁰

y=90⁰

Hence, the measures of x, y and z are 40⁰, 90⁰ and 50⁰

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The question is not complete, similar kind of question is given below.

In the given figure, AB || CD. Find the measure of x, y and z.

The missing angles in the figure are:

∠XVR = 125°

∠RVS = 55°

∠WVS = 125°

∠RST = 110°

∠RSV = 70°

∠VSU = 110°

∠UST = 70°

∠TUS = 39°

Angle geometry is a branch of mathematics that deals with the study of angles and their properties in two-dimensional figures such as circles, triangles, and polygons.

∠XVW + ∠XVR = 180° (sum of angles on a straight line is 180° )

Thus, ∠XVR = 180 - 55 = 125°

∠RVS = 55° (vertically opposite angles are equal)

∠WVS = 125° (vertically opposite angles are equal)

∠RST =  55 + 55 = 110°  (exterior angle of a triangle)

∠RSV = 180-55-55 = 70° (sum of angles in a triangle is 180°)

∠VSU = 110° (vertically opposite angles are equal)

∠UST = 70° (vertically opposite angles are equal)

∠TUS = 180 - 70 -71 = 39° (sum of angles in a triangle is 180°)

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Answer:

Step-by-step explanation:

99x99= 9801

Answer: 9,801

Step-by-step explanation: first you write the numbers down like this

99

x99

then you multiply the numbers

When solving problems that contain exponents, we must know the value of both elements for the result to be correct. This ability can be improved by knowing how to multiply very well.

An exponent is a mathematical expression that tells us that a value must be multiplied by itself a certain number of times, the most common exponent is the square in which a value must be multiplied by itself once, for example:

To improve in problems with exponents we must know how to multiply very well because this is the basic operation that is most related to solving exponents.

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Step-by-step explanation:

14 for every 3 would be the same as 14/3

If we make that equal to x/15, what follows...

[tex] \frac{chickens}{geese} = \frac{14}{3} = \frac{x}{15} [/tex]

If we cross multiply

[tex]3x = 14(15)[/tex]

[tex]3x = 210[/tex]

And lastly we divide by 3

[tex]x = 70 \: chickens[/tex]

The total Messages that Tammy, Felipe, and David sent are 30, 50, and 45 messages respectively.

Let's denote the number of text messages sent by Tammy as x, Felipe as y, and David as z. Based on the information given, we have:

y < x and z = 3y.

The total number of messages they sent is x + y + z = x + y + 3y = 4y + x.

Since the total number of messages sent is not specified, we can choose an arbitrary value for the total number of messages. Let's choose 90 messages. Then, we have:

4y + x = 90

x = 90 - 4y.

Substituting z = 3y into x = 90 - 4y, we get:

3y = 90 - 4y

7y = 90

y = 90/7 = 15.

Plugging y = 15 into x = 90 - 4y, we get:

x = 90 - 4 * 15 = 30.

Therefore, Tammy sent 30 messages, Felipe sent 15 messages, and David sent 45 messages.

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Not merely a cluster of random elements, a narrative presents an ordered series of events connected by the logic of cause and effect.

A narrative depicts an ordered set of events linked by the logic of cause and effect, not just a collection of random pieces. In tales, the sequence of events is linear, making it evident to the viewer the motivation behind and effects of character behavior.

The sequence of events in a story is referred to as the story. Simply put, sequencing a story is determining the beginning, middle, and end of the story as a first step toward retelling the events in a logical order.

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Step-by-step explanation:

A line that is parallel to another line has the same slope but a different y-intercept. The slope of the line through the points (1,-2) and (-6,3) can be found using the slope-point formula:

slope = (y2 - y1) / (x2 - x1) = (3 - (-2)) / (-6 - 1) = 5/7

So, a line that is parallel to this line would have the same slope of 5/7. To find an equation for a line with this slope that passes through a different point, we can use the point-slope formula:

y - y1 = m * (x - x1)

Where m is the slope and (x1, y1) is a point on the line. We can choose any point to use in this formula, but a common choice is the origin (0,0). So, plugging in the values we have:

y - 0 = 5/7 * (x - 0)

y = 5/7 * x

This is the equation for a line that is parallel to the line through the points (1,-2) and (-6,3) and passes through the origin.

Step-by-step explanation:

I just answered this. how often was that posted ?

the distance of a vertex to its 2 neighboring circle touching points is the same, because tangents emanating from the same point to the same circle must have the same distance to the touching points.

so, AB splits into a (from A to the circle touching point on AB) and b (from the circle touching point on AB to B).

b = AB - a

BC splits into b (from B to the circle touching point on BC) = AB - a, and c (from the circle touching point on BC to C).

c = BC - (AB - a) = BC - AB + a

CD splits into c (from C to the circle touching point on CD) = BC - AB + a, and d (from the circle touching point on CD to D).

d = CD - (BC - AB + a) = CD - BC + AB - a

DA now splits into d (from D to the circle touching point on DA) and ... a (from the circle touching point on DA to A).

a = DA - (CD - BC + AB - a) = DA - CD + BC - AB + a

0 = DA - CD + BC - AB

DA = CD - BC + AB = 8 - 5 + 4 = 7

Answer:

  DA = 7

Step-by-step explanation:

You have quadrilateral ABCD with an inscribed circle and side lengths AB=4, BC=6, CD=8, and you want to know the length of DA.

The tangents from each vertex of the quadrilateral to the inscribed circle are the same length, so we can work our way around the quadrilateral to find the missing length. The attached figure shows the tangent lengths working counterclockwise from vertex A.

The sum of the tangents from A and D is ...

  x + (7 -x) = 7

The length of DA is 7 units.

__

Additional comment

The sum of the lengths of opposite sides is the same in any quadrilateral with an inscribed circle. Here, that sum is 4+8 = 12, so the unknown side is 12-5 = 7.

The area of the shaped portion of the given diagram(circle) would be = 153.86cm²

The formula which is used to calculate the area of a circle = πr²

where π = 3.14

radius = 7 cm

Therefore the area of the shaded part of the circle ;

= 3.14 × 7²

= 3.14 × 49

= 153.86cm²

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The solution of the piecewise function at the given values of the independent variable g(0) is 5, g(-7) is 12 and g(2) is 7.

This is an example of a piecewise function, which is a function composed of two or more parts, each part being defined by a separate equation.

In this function, the first part is defined as g(x) = x+5 if x >= -5, and the second part is defined as g(x) = -(x+5) if x < -5.

To evaluate the function at the given values of the independent variable, we can simply substitute the values into the appropriate equation.

At x = 0,

=> g(0) = 0+5 = 5.

At x = -7,

=> g(-7) = -(-7+5) = 12.

And at x = 2,

=> g(2) = 2+5 = 7.

Therefore, the values of the function are 5, 12, and 7 respectively

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Andy should write $507.18 for the balance on January 30. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

Four fundamental mathematical operations can be used to express any real number.

1. To determine the total of the numbers, use the addition operator ('+').

2. Use the sign "-" when subtracting to find the differences between the numbers.

3. Multiply when the result is the product of the numbers.

4. Dividing the numbers produces their quotient.

We are given that the amount balance on January 24 is $104.47 and she deposited $407.71 on January 30.

So, the amount Andy should write for the balance on January 30 is

⇒$104.47 + $407.71

⇒$507.18

Hence, Andy should write $507.18 for the balance on January 30.

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The original price of the bracelet, before tax $0.68

From the question, we have the following parameters that can be used in our computation:

Amount = $0.72

Sales tax = 6%

Using the above as a guide, we have the following:

Amount = Original amount * (1 + Sales tax)

Substitute the known values in the above equation, so, we have the following representation

0.72 = Original amount * (1.06)

So, we have

Original amount = 0.68

Hence, the original amount = 0.68

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The pattern tells that the amount raised by Robert in 26th mile is $90.

What is a pattern?

A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern.

The amount of money raised by Robert for first mile = $5

The amount of money raised by Robert for second mile = $6

The amount of money raised by Robert for third mile = $7.2

The difference between amount raised in first and second mile = $1

The difference between amount raised in second and third mile = $1.2

Similarly, the difference between amount raised in third and fourth mile will be = $1.4

Similarly, the difference between amount raised in fourth and fifth mile will be = $1.8

Following this pattern the difference between 25th and 26th mile will be = (26 × 0.2) + 0.4 = $5.8

Now, the amount raised in 26th mile = 84.2 + 5.8 = 90

Therefore, the amount raised is $90.

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Answer:

-6

Step-by-step explanation:

using the rules of exponents

• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

• [tex]a^{\frac{1}{2} }[/tex] = [tex]\sqrt{a}[/tex]

then

- 18 × [tex]9^{-\frac{1}{2} }[/tex]

=-  18 × [tex]\frac{1}{9^{\frac{1}{2} } }[/tex]

= - 18 × [tex]\frac{1}{\sqrt{9} }[/tex]

= - 18 × [tex]\frac{1}{3}[/tex]

= -6

Answer: The answer should be -6

Step-by-step explanation:

18(9^−1/2)

= −18(9^−1/2)

= (−18)(0.333333)

= −6

So, what you want to do is first solve 9^-1/2, it will come out to be about 0.333333

You are going to put 0.333333 in for 9^-12 and then multiply:

-18(9^-1/2) = (-18)(0.333333)

(-18)(0.333333) = -6

The median of the data collected is 1.5. Option B

It is important to note that the median of a given set of data is the middle number or the sum of the pair of numbers arranged in the order from the least to the greatest value.

From the information given, we have the data set;

1/3 2 4 1 7 2/3 4/5 5/2

Arrange the values in an ascending order from the least to the greatest value

1/3, 2/3, 4/5, 1, 2, 5/2, 4, 7

Since the total number is odd, take the two middle number and divide by 2, we get;

1 + 2/2

add the values

3/2

Divide the values

1. 5

Hence, the value is 1.5

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The value of the exponents will be (x²)³ = x^6 and the value of 7² will be 49.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

The value of (x²)³ will be:

= x^(2 × 3)

= x^6

The value of 7² will be:

7 × 7

= 49

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Miguel buys a dozen (12) bagels for $9.99. How much money did he spend on each bagel?

Answer:.83

Answer:

80 percent of people don't like the turkey sandwich because 80 plus 20 equals 100 so think about it as a subtraction equation

Answer: 80% of students don't like turkey sandwiches.

the sin(Ф) trigonometric function can be used to calculate its y component.

What is vector?

Latin word for "carrier" is "vector." Point A is transported to point B by vectors. The direction of the vector AB is the direction in which point A is moved in relation to point B, and the magnitude of the vector is the length of the line connecting the two points A and B. The terms Euclidean vectors and spatial vectors are also used to refer to vectors. Having both magnitude and direction, vectors are geometrical objects. An arrow pointing in the direction of a vector's magnitude and a line representing the vector's direction can be used to depict a vector. Since they have starting and ending points, vectors are symbolized by arrows.

component of a vector along the y-axis is a product of the length of vector and the sine of the angle of a vector with the x-axis.

the trigonometric function can be used to calculate its y component.

Then sin(Ф) trigonometric function can be used to calculate its y component.

Hence the sin(Ф) trigonometric function can be used to calculate its y component.

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the Domain of f divided by g of x  (-∞, -2) to (-2 , ∞)

A function is described as a relation among a fixed of inputs having one output every. In easy words, a feature is dating among inputs in which every entry is associated with precisely one output.

Given, The function f(x) = 20x + 80 represents the distance in miles a drone flew.

The function g(x) = x + 2 represents the time the drone flew in hours

Part A:

f(x) = 20x + 80

F(2) = 20*2 + 80

F(2) = 120

g(x) = x + 2

g(2) = 2 + 2

g(2) = 4

Part B: f(x) divided by g(2)

=> f(x) / g(2)

=> (20x + 80 ) /4

=> 5x + 20 (since, g(2) is 4)

Part C:  the domain of f divided by g of x

So,

f(x) / g(x ) = (20x + 80)/(x +2)

=>  (20x + 80)/(x +2)

Since Denominator can not be zero.

Therefore, the Domain of f divided by g of x  (-∞, -2) to (-2 , ∞).

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