7 27. MODELING REAL LIFE Find the length of the slide.
(See Example 6.)
MTR
12 ft
53°

The equation of the context is, 3.5x + 2y = 42 and

The y-intercept is when x = 0, indicating that no funnel cakes were purchased, and the x-intercept is when y = 0, indicating that no deep-fried Oreos were purchased.

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.

Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.

An example of a non-linear function is a quadratic function.

From, The given information the equation can be modeled as,

3.5x + 2y = 42.

The x-intercept is when y = 0 which states no deep fried oreos bought and the y-intercept is when x = 0, states no funnel cakes bought.

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The axis of symmetry, vertex, domain, and range of each of the quadratic function are as follows;

Axis of symmetry = 3.

Vertex = (3, 3).

Domain = {-∞, ∞}.

Range = {-∞, 3}.

Axis of symmetry = 4.

Vertex = (4, -2).

Domain = {-∞, ∞}.

Range = {-2, ∞}.

Mathematically, the axis of symmetry (vertex) of a quadratic function can be calculated by using this mathematical expression:

Axis of symmetry (vertex), Xmax = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

Note: The domain of a quadratic function (parabola) is always all real numbers on the x-axis of a cartesian coordinate.

For the given quadratic function y = -2x² + 12x - 15, we have:

Axis of symmetry (vertex), Xmax = -b/2a

Axis of symmetry (vertex), Xmax = -12/2(-2)

Axis of symmetry (vertex), Xmax = -12/-4 = 3.

Vertex (h, k) = (3, 3).

Domain = {-∞, ∞} or x ∈ R.

Range = {-∞, 3}.

x      y

1      2

1      4

3     3

For the given quadratic function y = 2x² - 16x + 30, we have:

Axis of symmetry (vertex), Xmax = -b/2a

Axis of symmetry (vertex), Xmax = -(-16)/2(2)

Axis of symmetry (vertex), Xmax = 16/4 = 4.

Vertex (h, k) = (4, -2).

Domain = {-∞, ∞} or x ∈ R.

Range = {-2, ∞}.

x      y

3     0

5     0

4     -2

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The required equation model for the given situation is 1/6 (c + 24) = 15. Option C is correct.

The concept of the equation model is a fundamental part of mathematics, and it is used in a wide range of applications. Here are some ways in which the equation model is used,
1. Solving equations    2. Modeling real-world situations 3.Understanding relationships between variables.

here,
According to the question let the Pokémon cards Mark intially had be c,
So as per the given condition, Mark has c + 24 card and he gives 1/6 of his card to his little brother, which is 15 cards
The equation model of the situation is given as,
1/6(c + 24) = 15

Thus, the required equation model for the given situation is 1/6 (c + 24) = 15. Option C is correct.

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The doubling time formula is used to calculate the time required for a quantity to double in size at a constant growth rate. The formula is: doubling time = ln(2) / r

Where ln(2) is the natural logarithm of 2, and r is the annual growth rate expressed as a decimal. The doubling time represents the number of time units it takes for the quantity to double, such as years, months, or days, depending on the time unit used for the growth rate. This formula is commonly used in many fields, such as finance, biology, and demography, to estimate the future growth of a quantity based on its current growth rate.

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Answer: SSS (Side- Side- Side) Congruence Postulate

Step-by-step explanation:

The coordinates of equation y is (0, 3), (1, 4) and (3,5).

The graph is attached below.

The graph's x-axis (horizontal line) should contain the independent variable, and the y-axis should contain the dependent variable (vertical line). At the origin, where the coordinates are, the x and y axes intersect (0,0).

Given:

y= x+ 3.

Now, put x= 0

y= 0+3

y=3

and, x= 1

y= 1+3

y= 4

and, x= 2

y= 2+ 3

y= 5

Thus, the coordinates of equation y is (0, 3), (1, 4) and (3,5).

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The Questions attached here is seems to incomplete, the options for the graph is attached below.

The slope of the line is -1/4, So correct option is B.

It is defined as the ratio of the change in the vertical coordinate (y) to the change in the horizontal coordinate (x) between any two points on the line or curve. The letter m is typically used to indicate a line's slope.

The formula for the slope of a line between two points (x1, y1) and (x2, y2) is:

m = (y2 - y1) / (x2 - x1)

The slope can be positive, negative or zero, depending on the direction of the line. A positive slope indicates that the line is moving upwards from left to right, while a negative slope indicates that the line is moving downwards from left to right. A slope of zero indicates that the line is horizontal.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1)/(x2 - x1)

Using the coordinates (-4, 2) and (4, 0), we have:

slope = (0 - 2)/(4 - (-4)) = -2/8 = -1/4

Therefore, the answer is option B, -1/4.

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Answer:

The polygon has 8 sides, so the sum of its interior angles is 1080 degrees. Each interior angle is equal to 135 degrees

the interior angle of a regular polygon is equal to the total number of its sides minus two, multiplied by 180 degrees divided by the number of sides. For example, in a regular polygon with 8 sides, one interior angle would equal 1080 degrees (8 - 2) x 180/8 = 1080.

The expression 1/2 × 5/4 has the value greater than 1/2. Therefore, option D is the correct answer.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Here,

A) 1/2 × 4/5

= 2/5

= 0.4

B) 1/2 × 4/4

= 1/2

= 0.5

C) 1/2 × 5/5

= 1/2

= 0.5

D) 1/2 × 5/4

= 5/8

= 0.625

Therefore, option D is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Which expression has the value greater than 1/2

A) 1/2 × 4/5

B) 1/2 × 4/4

C) 1/2 × 5/5

D) 1/2 × 5/4

The tangent of the smaller acute angle in a right triangle is tanФ = 5/12 taking side 5 as opposite side and 12 as adjacent side.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent or (base and perpendicular)

The Formula of tangent is opposite side/ adjacent side

Given, a right triangle with side lengths 5, 12, and 13.

We can see that largest side i.e., 13 is a hypotenuse of triangle and other two sides are base and perpendicular length.

Tangent taking side 5 as opposite side and 12 as adjacent side

tanФ = 5/12.

Tangent taking side 12 as opposite side and 5 as adjacent side

tanФ = 12/5

so, the  tangent of the smaller acute angle in a right triangle is 5/12.

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The number of cup servings in a bag of trail mix is 5[tex]\frac{1}{5}[/tex] cups.

Math operations include division as one of its types. This technique involves splitting the phrases or numbers into the same amount of components.

Given:

There are 1[tex]\frac{1}{4}[/tex] cup servings in a bag of trail mix.

And a bag of trail mix contains 6 ½ cups of mix.

The number of cup servings in a bag of trail mix is,

= 6 ½ ÷ 1[tex]\frac{1}{4}[/tex]

= 13/2 ÷ 5/4

= 26/5

= 5[tex]\frac{1}{5}[/tex]

Therefore, the required number of cups is 5[tex]\frac{1}{5}[/tex].

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The formula for converting Celsius (°C) to Fahrenheit (°F) is °F = (°C × 9/5) + 32. To convert 37 degrees Celsius to Fahrenheit, you must multiply 37 by 9/5 and then add 32.

The calculation is: 37°C × 9/5 = 66.6 and 66.6 + 32 = 98.6°FTherefore, 37 degrees Celsius is equal to 98.6 degrees Fahrenheit.The formula for converting Celsius (°C) to Fahrenheit (°F) is °F = (°C × 9/5) + 32. To convert 37 degrees Celsius to Fahrenheit, you must multiply 37 by 9/5 and then add 32. To convert Celsius to Fahrenheit, the formula is simple and easy to remember. Multiply the Celsius temperature by 9/5, then add 32. This formula is useful for many applications, such as measuring air and water temperature, cooking and baking, and more. Knowing how to convert from Celsius to Fahrenheit is important for many everyday tasks.

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The required solution is given as,

f(x) = 22 + x   = Linear

f(x) = x²+1       = Non-linear

f(x) = x³ +2x+1 = Non-linear

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Linear functions are functions that can be represented by a straight line on a graph. These functions have a constant rate of change and can be written in form f(x) = mx + b, where m is the slope of the line and b is the y-intercept.

Non-linear functions are functions that do not have a constant rate of change and cannot be represented by a straight line on a graph.

Thus, the required solution is given as,

f(x) = 22 + x   = Linear

f(x) = x²+1       = Non-linear

f(x) = x³ +2x+1 = Non-linear

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Step-by-step explanation:

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A multiple intelligences test is an assessment that identifies an individual's strengths and weaknesses across different types of intelligence, as defined by Howard Gardner's theory of multiple intelligences.

The test aims to help individuals understand their unique strengths and learning styles, and to guide educators in developing personalized teaching strategies. Multiple intelligences test is an assessment that identifies an individual's strengths and weaknesses across different types of intelligence, as defined by Howard Gardner's theory of multiple intelligences. The test is designed to go beyond traditional IQ tests, which focus on logical-mathematical and linguistic intelligence, and assess a wider range of abilities, such as musical, spatial, bodily-kinesthetic, interpersonal, and intrapersonal intelligence. The test is intended to help individuals better understand their unique strengths and learning styles, and to guide educators in developing more personalized teaching strategies that cater to a diverse range of intelligences.

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Answer:

The answer is B.

The owner's claim is incorrect. Since the highest bar is those that make between $50,000 and $100,000, the average salary would be about $75,000 since that is the mode.

If (63, x, 105) generate a Pythagorean Triple, the value of x is 84.

Before starting to solve this problem we must know that the Pythagorean theorem is a theorem that realizes the sides of a right triangle and has many applications for it.

A Pythagorean Triple is a set of three integers that satisfy the Pythagorean Theorem, [tex]a^2 + b^2 = c^2[/tex]. In this case, 63 and 105 are two sides of a right triangle, and x is the third side. We can plug in the values and solve for x:
63² + x² = 105²
3969 + x² = 11025
x² = 7056
x = √7056
x = 84

Therefore, the value of x is 84, and the Pythagorean Triple is (63, 84, 105).

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4.571 billion years is equals to  1.4415 × 10⁷ seconds.

To calculate the number of seconds in 4.571 billion years, we first need to determine how many seconds there are in a year. There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 365 days in a year. Multiplying these together gives us 31,536,000 seconds in a year.

Next, we multiply the number of seconds in a year by the number of years in 4.571 billion years. This gives us:

31,536,000 seconds/year x 4,571,000,000 years = 1.4415 × 10¹⁷ seconds

Therefore, there are approximately  1.4415 × 10¹⁷ seconds  in 4.571 billion years.

It's worth noting that this calculation assumes a standard year of 365 days. In reality, a year is slightly longer than 365 days, and so the actual number of seconds in 4.571 billion years would be slightly higher. Nonetheless, this calculation provides a good approximation.

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Jada can get 4 albums or she can get 80 individual songs for $20. The equation will be written as 0.25s + 5a = 20.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that It costs $0.25 to download an individual song and $5 to download an album. Jada has $20 to spend downloading music.

The equation will be written as,

0.25s + 5a = $20

The number of individual songs will be,

0.25s = 20

s = 20 / 0.25

s = 80

The number of albums,

5a = 20

a = 20 / 5

a = 4

The complete question is given below.

It costs $0.25 to download an individual song and $5 to download an album. Jada has $20 to spend downloading music.

a. Make a table showing three ways Jada can spend $20 downloading individual songs and albums. (s the being number of individual songs and a being the number of albums.)

b. Write an equation relating the number of individual songs (s) and the number of albums(a) in standard form.

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The mean of the stem and leaf plot and the meaning of this mean is B. 3.875 feet; The value means that a typical throw of the ball results in 3.875 feet.

To find the mean, add up all the values of feet that the heavy ball was thrown in the air and then divide by the number of times the ball was thrown.

The mean is therefore :

= ( 20 + 22 + 25 + 31 + 33 + 34 + 41 + 41 + 45 + 50 + 56 + 67 ) / 12

= 465 / 12

= 38. 75 ft

This mean is the value that the typical throw of the ball results in.

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As a rule of thumb, altitude corrections of less than 100 feet should be corrected by using "less than a full bar width on the attitude indicator".

C. is the answer.

The attitude indicator (also known as an artificial horizon) is a key instrument in an aircraft that displays the aircraft's pitch and bank attitude. The instrument typically consists of a gyro that indicates the aircraft's attitude relative to the horizon.

When flying an aircraft, it's important to maintain a specific altitude, and to make adjustments as needed to stay on course. The altitude is typically measured in feet above sea level, and can be affected by a number of factors, such as temperature, pressure, and wind.

As a rule of thumb, altitude corrections of less than 100 feet can be corrected using the attitude indicator by making adjustments that are less than a full bar width on the instrument. This means that the correction is relatively small and does not require a significant adjustment of the aircraft's pitch or bank.

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Answer: For Jon, buying 3 shirts for $20 can be written as a rate as follows:

The number of shirts Jon buys per dollar spent = 3 shirts / $20 = 3/20 shirts/dollar

For Brenda, recording 76 songs on 4 albums can be written as a rate as follows:

The number of songs Brenda records per album = 76 songs / 4 albums = 19 songs/album

So, the rate of songs Brenda records per album can be written as 19 songs/album.

Step-by-step explanation:

If Two high schools, A and B, are each trying to raise at least $3,000 for new computers. The inequality  for each school is : x ≥ 250, x ≥ 233.33.

1. For School A, the inequality representing the number of stuffed bears they must sell to reach their goal is:

500 + 10x ≥ 3000

10x ≥ 2500

x ≥ 250

Where:

x = number of stuffed bears they must sell.

For School B, the inequality representing the number of stuffed monkeys they must sell to reach their goal is:

1250 + 7.5x ≥ 3000

7.5x ≥ 1750

x ≥ 233.33

Where:

x= number of stuffed monkeys they must sell.

2. To compare the minimum number of stuffed animals each school must sell, we round up the number of stuffed animals for School B to the nearest whole number:

x ≥ 234 for School B

Since 234 > 250, School B must sell more stuffed animals to reach their goal of $3,000.

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Answer:

Many test takers have found the Reading and English section to be moderately difficult. However, many TEAS takers vouch that the Science and Math section are more complex and challenging. The timed nature of the exam can be difficult for some.

Step-by-step explanation:

The value of x where both curve and line intersect with each others are -0.44 and 1.69

Using the linear-quadratic system, both curve and line are intersecting in 2 points where:

f(x) = g(x)

8x2 - 13x + 8 = 14 - 3x

8x2 - 10x - 6 = 0

We will use the ABC theorem, where:

x = -b ± √(b2 - 4ac)

               2a

x = - (-10) ± √((10)2 - 4(8)(-6))

                  2(8)

x = 10 ± √(100 + 192)

             16

x = 10 ± 2√73

           16

x1 = 10 - 2√73  = -0.44

           16

x2 = 10 + 2√73 = 1.69

             16

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44 °F was found out to be equivalent to approximately 6.67 °C using conversion formula of Fahrenheit to Celsius.

To convert a temperature from Fahrenheit to Celsius, you can use the following formula:

°C = (°F - 32) x 5/9

where °C is the temperature in Celsius, and °F is the temperature in Fahrenheit.

Using this formula, we can convert 44 °F to Celsius as follows:

°C = (44 - 32) x 5/9

= 12 x 5/9

= 6.67 °C (rounded to two decimal places)

Therefore, 44 °F is equivalent to approximately 6.67 °C.

On the Fahrenheit scale, water freezes at 32 degrees Fahrenheit (°F) and boils at 212 °F, at standard atmospheric pressure.

On the Celsius scale, the freezing point of water is defined as 0 degrees Celsius (°C), and the boiling point of water is defined as 100 °C, at standard atmospheric pressure.

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The approximate percent increase in consumption from 1986 to 1997 is 30%.

Percent refers to a ratio or proportion expressed as a fraction of 100. When we talk about the percent increase or decrease of a quantity, we are interested in finding out by how much it has grown or declined relative to its original value.

In this case, we are asked to determine the approximate percent increase in consumption from 1986 to 1997.

To answer this question, we would need to have data on the consumption levels in both years and calculate the difference between the two.

Then, we would divide the difference by the consumption level in 1986 and multiply by 100 to express the result as a percentage.

From the options given, it appears that the closest answer is C, with a 30% increase in consumption.

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The equation represents the line that has a slope of 3 and passes through the point (-4,-7) is Y = 3X - 5.

The equation of a line is a mathematical expression that describes the relationship between the x and y coordinates of any point on the line.

The slope of a line is the steepness of the line and can be calculated by finding the ratio of the change in y to the change in x for any two points on the line. In this case, the slope of the line is 3. The line also passes through the point (-4,-7), which means that we can use this point to find the equation of the line.

To find the equation of the line, we need to use the slope-intercept form, which is given by

=> Y = mX + b,

where m is the slope and b is the y-intercept. To find the y-intercept, we can use the point (-4,-7) and substitute it into the equation:

=> -7 = 3 * -4 + b.

Solving for b, we find that b = -5.

Therefore, the equation of the line is Y = 3X - 5.

So, the correct answer is b. Y = 3x + 5.

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Answer:

Step-by-step explanation:

The length of a curve can refer to the arc length of a function, or the distance along a curved path between two points.

Arc Length of a Function:

For a continuous and differentiable function y = f(x) defined over an interval [a, b], the arc length of the curve between x = a and x = b can be found using the following definite integral:

L = ∫_a^b √(1 + (dy/dx)^2) dx

Where L is the arc length, dy/dx is the derivative of the function with respect to x, and the integral is taken from x = a to x = b.

Length of a Curved Path:

For a curved path defined by a continuous and differentiable function y = f(x), the length of the path between two points (x1, y1) and (x2, y2) can be found using the same definite integral formula as the arc length of a function:

L = ∫_(x1)^(x2) √(1 + (dy/dx)^2) dx

Where L is the length of the path and the integral is taken from x = x1 to x = x2.

Note that finding the exact length of a curve can sometimes be difficult and may require numerical methods such as numerical integration or approximation techniques like Simpson's rule.