This system of inequalities models the scenario: 4x + 2y ≤ 16 x + y ≥ 4 Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution set. (4 points) Part B: Is the point (2, 3) included in the solution area for the system? Justify your answer mathematically. (3 points) Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context. (3 points) Source StylesFormatFontSize

Answer: C

Step-by-step explanation: C



Answer:

 a.  1492 kg

  b.  20.8 m

Step-by-step explanation:

Given a tree is initially 20 m high and has a diameter of 0.5 m, you want the mass of the trunk if its density is 380 kg/m³. If it adds a growth ring of 4 mm per year and adds height of 0.2 m in the first year, you want the height of the tree after 5 years, assuming the same amount of wood is added each year.

The volume of the tree trunk is that of a cylinder. The formula is ...

  V = (π/4)d²h

  V = (π/4)(0.5 m)²(20 m) ≈ 3.9270 m³

The mass is the product of volume and density:

  M = Vρ

  M = (3.9270 m³)(380 kg/m³) ≈ 1492 kg

The mass of the tree trunk is about 1492 kg.

In the first year, the diameter of the tree increases by 8 mm, and the height increases by 0.2 m,. This means the volume of the tree increases to ...

  V = (π/4)(0.508 m)²(20.2 m) ≈ 4.0942 m³

The volume increase is the same each year for 5 years, so after 5 years, the volume is ...

  3.9270 m³ + 5(4.0942 -3.9270) m³ ≈ 4.7630 m³

At that time, the diameter is about 0.540 m. Solving the volume equation for the height, we find it to be ...

  h = 4v/(π·d²)

  h = 4(4.7630 m³)/(π·(0.54 m)²) ≈ 20.797 m

The height of the trunk after 5 years is about 20.8 m.

__

Additional comment

We note that the wood added in the first year includes the cylindrical shell represented by the tree ring, and a cylindrical "plug" that is 0.2 m high and equivalent in diameter to the rest of the tree. This seems an odd way for the tree to grow, but may be a reasonable approximation to the actual growth.

The height, diameter, and growth are all given to 1 significant figure. Hence the 4- and 3-significant figures used in the answers may be unsupported by the precision of the given numbers. Keeping 2 significant figures, we might report the initial mass as 1500 kg, and the final height as 21 m.

The graph is drawn by a function formulated to have the correct height at the x-intercept: v(d, h) - (final volume) = 0.

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Answer:

3 (x + y) (x - y)

Step-by-step explanation:

3x²-3y²​

GCF is 3

3(x² - y²)

Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = (a+b) (a−b) where a = x  and b = y.

So, the answer is 3 (x + y) (x - y)

Answer:

please let me know what is the name of the shape. Thank you

Answer:

To find the lower and upper quartiles and the interquartile range, we first need to order the data from smallest to largest:

20, 22, 25, 28, 29, 30, 32, 33, 34

Next, we find the median (middle value) of the entire dataset:

Median = (29 + 30) / 2 = 29.5

This median value divides the data into two halves. We then find the median of the lower half of the data, which includes all values less than or equal to 29.5:

Lower half: 20, 22, 25, 28, 29

Median of lower half = (25 + 28) / 2 = 26.5

This value, 26.5, is the lower quartile (Q1).

Similarly, we find the median of the upper half of the data, which includes all values greater than or equal to 29.5:

Upper half: 30, 32, 33, 34

Median of upper half = (32 + 33) / 2 = 32.5

This value, 32.5, is the upper quartile (Q3).

Finally, we can calculate the interquartile range (IQR) as the difference between the upper and lower quartiles:

IQR = Q3 - Q1 = 32.5 - 26.5 = 6

Therefore, the lower quartile is 26.5, the upper quartile is 32.5, and the interquartile range is 6.

Aaron's algebraic expression is:

14 * (18 - 3x)

an algebraic expression is an expression built up from constant algebraic numbers, variables, and the addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number.

This expression represents the product of 14 and the difference of 18 and 3x. The factors of this expression are:

14: This is a constant factor that multiplies the difference of 18 and 3x.

(18 - 3x): This is the distinction of 18 and 3x, which is being duplicated by 14. It is a two-term binomial expression: 18 and -3x. The first term, which has a coefficient of -3, is a variable, while the second term, which has a coefficient of -3, is a constant.

To work on the articulation, we can utilize the distributive property of augmentation to get:

14 * (18 - 3x) = 14*18 - 14*3x = 252 - 42x

In this worked on structure, the elements are as yet 14 and (18 - 3x). However, additional factors of the simplified expression, such as 2 and 21, which are factors of 42 (the coefficient of x), can also be identified.

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Answer: GL = [tex]\sqrt{61}[/tex]

Step-by-step explanation:

     Since this is a right triangle, we can use the Pythagorean theorem. GL is the hypotenuse.

Given:

     a² + b² = c²

Substitue:

     AL² + AG = GL²

Find side lengths (count via the coordinate plane given):

     6² + 5² = GL²

Square:

     36 + 25 = GL²

Add:

     61 = GL²

Square root both sides:

     [tex]\sqrt{61}[/tex] = GL

We can see here that if Jared wants to make fruit punch and he has 8 pints each of orange juice, pineapple juice, and cranberry juice, we can deduce here that the following is true: B. He has enough of each type of juice to make 1 recipe.

Fruit punch is a non-alcoholic drink that is created by combining different fruit juices. It is a well-liked beverage for parties and other social occasions and is normally served chilled.

Fruit punch's exact ingredients might vary, but typically it consists of a mixture of juices including orange, pineapple, cranberry, and/or grapefruit that have been combined with sugar, water, or carbonated water.

We can see here that in order to make 1 recipe of fruit punch, we need 2 pints of orange juice, 2 pints of pineapple juice, and 1 pint of cranberry juice.

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The piecewise function graphed is defined as follows:

C)

A piecewise function is a function that is defined by multiple equations, each of which applies to a specific interval or set of inputs. The equations are pieced together to form a single function that describes the behavior of the function over its entire domain.

The intervals for this problem are given as follows:

For the first interval, we have a linear function with a slope of 1/2 and an intercept of 2, hence:

y = 1/2x + 2, x ≤ -1.

For the second interval, we have a quadratic function with a vertex of -1, hence:

y = 1/2x² - 1, x > -1.

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The expression that can be used to find out the amount of time it would take Sal to finish the remaining homework is C. 4 / 9 x 3 / 5 .

To find the expression that would show the time it would take for Sal to finish his homework, the formula would be:

= Proportion of questions remaining x Time taken to finish one question

Proportion of questions remaining:

= 1 - 5 / 9

= 4 / 9

Time taken to finish one question:

= 3 / 5 minutes

The expression is therefore:

4 / 9 x 3 / 5

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Applying the Two-Tangent Theorem, the length of segment LM in the circle is: A. 18.

What is the Two-Tangent Theorem?

If two tangent segments are drawn to one circle from the same external point, the Two-Tangent Theorem states that both segments are congruent together.

Applying the theorem, we have:

4x - 2 = 3x + 3

Find the value of x:

4x - 3x = 2 + 3

x = 5

Find the length of LM:

LM = 3x + 3

Plug in the value of x:

LM = 3(5) + 3

LM = 18

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according to the question the distance between the points (1, 5) and (3, 8) is √13 units.

Distance is an object's total, aimless movement. Without regard to whether an object represents a starting or finishing point, distance can be defined as the total distance travelled. Distance is referred to as the breadth or height of the difference between two locations. It should be highlighted that the distance between each of the vantage points as well as the distance travelled from one to the other are not the same thing. The total length of a path connecting two locations counts as the distance travelled. Distance is the real distance that a body travels. It also goes by the name "path length." For instance, the length of the route for an object moving from point O to point P would be OP = 360 m.

given,

To find the distance between the points (1, 5) and (3, 8), we can use the distance formula:

distance = √[(x2 - x1)² + (y2 - y1)²]

Substituting the given values, we get:

distance = √[(3 - 1)² + (8 - 5)²]

distance = √[4 + 9]

distance = √13

Therefore, the distance between the points (1, 5) and (3, 8) is √13 units.

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We can use the formula for the volume of a cylinder: V = Ah, where A is the base area and h is the height.

Substituting the given values, we have:

720 cm³ = 36 cm² x h

Simplifying, we can divide both sides by 36 cm²:

20 cm = h

Therefore, the height is 20 cm.

Based on the intersecting chords, the calculated value of x on the circle is 11

The given shape in the question is a circle

As a general rule, a circle is a shape with all points on its boundary equidistant from a central point called the center

In this case, the center is point W

The sum of angles on the circumference is 360

So, we have

17x - 20 + 75 + 2 * 59 = 360

Evaluating the like terms, we have

17x = 187

Divide by 17

x = 11

Hence. the value of x is 11

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The value of x unknown for the given shape with given measurements 131°, 122°, 125°, 148°, 107°, 126° is equal to 141°.

The attached figure is seven sided polygon.

Seven sided polygon is called Heptagon.

Sum of all the interior angles of seven sided polygon = 900 degrees

Measurements are,

131°, 122°, 125°, 148°, 107°, 126°

Measurement of seventh angle is unknown.

let the measure of seventh angle be x°

⇒ x° + 131° + 122° + 125° + 148° + 107° + 126° = 900°

⇒ x° + 759° = 900°

⇒ x° = 900° - 759°

⇒ x° = 141°

Therefore, the value of x for the given shape with measurements is equal to 141°.

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The above question is incomplete , the complete question is:

what is the value of x if a shape has sides measuring 131, 122, 125, 148, 107, 126.

Attached figure.

Answer: 8x^2 + 2y^2 = 7

Step-by-step explanation:

The equation R = 7/8cosθ + 2sinθ can be rewritten in terms of x and y using the conversions x = Rcosθ and y = Rsinθ.

Substituting R = 7/8cosθ + 2sinθ into these equations, we get:

x = (7/8)cosθ cosθ + 2sinθ cosθ

y = (7/8)cosθ sinθ + 2sinθ sinθ

Simplifying these expressions using trigonometric identities, we get:

x = (7/8)cos^2θ + (4/8)sin2θ

y = (7/8)sinθ cosθ + (4/8)sin2θ

Multiplying both sides of the x equation by 8/7 and simplifying, we obtain:

8x^2 + 2y^2 = 7cos^2θ + 8sin^2θ

Using the identity cos^2θ + sin^2θ = 1, we get:

8x^2 + 2y^2 = 7(1)

Therefore, the Cartesian form of the equation is 8x^2 + 2y^2 = 7.

Answer:y=−4x+7/2

Step-by-step explanation:

Multiply each side of the equation by 8cosθ+2sinθ to get 8rcosθ+2rsinθ=7. Using the relationships x=rcosθ and y=rsinθ, the equation becomes 8x+2y=7. Solving this equation for y shows that y=−4x+7/2.

Answer:

C. 84.8 m

Step-by-step explanation:

Circumference of circle = D x 3.14

D = 27 m

Let's solve

27 x 3.14 = 84.78 m

So, the circumference of the circle is C. 84.8 m

Answer:

Option C) 84.8 is the correct answer.

Step-by-step explanation:

Here we have given that the diameter of circle is 27 m and we have to find the circumference of circle. The formula to find circumference of circle is :

[tex]\dashrightarrow\sf{C = \pi d}[/tex]

Where :

Thus, finding the circumference of circle by substituting the given values in the formula :

[tex]\dashrightarrow\sf{C = \pi d}[/tex]

[tex]\dashrightarrow\sf{C = \pi \times d}[/tex]

[tex]\dashrightarrow\sf{C = 3.14 \times 27}[/tex]

[tex]\dashrightarrow\sf{C = 84.78 \: m}[/tex]

[tex]\dashrightarrow\sf{C \approx 84.8\: m}[/tex]

Hence, the circumference of circle is 84.8 m.

The total number of 6 tickets will be earned when 54 points are earned.

Given that the total number of tickets earned for 9 points was earned = 1 ticket

the tickets earned when every 18 points are earned = 2 tickets

the tickets earned when every 27 points are earned = 3 tickets

Let's divide the points by tickets to find out how many points are earned for each ticket.

9/1 = 18/2 = 27/3 = 9

This shows for every ticket 9 points are earned. So, to find out the no. of tickets for 54 points, we can divide the 54 by 9.

no. of tickets earned for 54 points = 54/9 = 6 tickets.

From the above analysis, we can conclude that the 6 tickets are earned for 54 points.

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The answer of the given question based on the circle and rectangle is , the perimeter of the shape is approximately 83.8 feet, and its area is approximately 148.4 feet².

Perimeter is a measurement of the distance around the edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. The perimeter is often measured in units of length, such as centimeters, meters, or feet.

To find the perimeter and area of the composite shape formed by a rectangle and two semicircles, we can break it down into its individual components and then add them up.

First, let's find the perimeter. The shape consists of two semicircles, each with a diameter of 15 feet, and a rectangle with a width of 4 feet and a length equal to the diameter of the semicircles, which is 15 feet. The perimeter can be calculated as:

Perimeter = 2 × (semicircle circumference) + rectangle perimeter

The circumference of circle is by the formula 2πr, where r is the radius. Since each semicircle has a diameter of 15 feet, its radius is 7.5 feet. Therefore, the circumference of each semicircle is:

C = 2πr = 2π(7.5) = 15π feet

The perimeter of the rectangle is simply the sum of its four sides, which is:

P = 2(length + width) = 2(15 + 4) = 38 feet

Putting it all together, we have:

Perimeter = 2 × 15π + 38 ≈ 83.8 feet

Now let's find the area. The shape consists of two semicircles, each with a diameter of 15 feet, and a rectangle with a width of 4 feet and a length equal to the diameter of the semicircles, which is 15 feet. The area can be calculated as:

Area = (semicircle area) + rectangle area

The area of a circle is given by the formula πr². Since each semicircle has a diameter of 15 feet, its radius is 7.5 feet. Therefore, the area of each semicircle is:

A = (1/2)πr² = (1/2)π(7.5)² = 44.18 feet²

The area of the rectangle is simply its length multiplied by its width, which is:

A = length × width = 15 × 4 = 60 feet²

Putting it all together, we have:

Area = 2 × 44.18 + 60 = 148.4feet²

Therefore, the perimeter of the shape is approximately 83.8 feet, and its area is approximately 148.4 feet².

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Thus, the interquartile range of the given data set. are -

1st quartile (Q1) = 6.8 ; 2nd quartile (Q2) = 7.6 and 3rd quartile (Q3) = 8.4 .interquartile range = 1.60.

The interquartile range in descriptive statistics reveals the spread of your distribution's middle half.

Each distribution that is sorted from low to high is divided into four equal portions using quartiles. The third and second quartiles, or the centre half of your data set, are contained in the interquartile range (IQR).

The interquartile range provides the range of a middle half of a data set, whereas the range provides the spread of the entire data set.

Given data set:

8.4, 7.1, 6.3, 6.8, 9.2, 7.3, 8.8, 7.9, 5.3, 8.2

arrange the data set in ascending order:

5.3, 6.3, 6.8, 7.1, 7.3, 7.9, 8.2, 8.4, 8.8, 9.2

Total term = 10 (even)

2nd quartile (Q2) 50% quartile - (5th + 6th) /2 = (7.3 + 7.9) /2 = 7.6

Now:

1st quartile (Q1) 25% quartile - 3rd term = 6.8

3rd quartile (Q3) 75% - 8th term = 8.4

Thus, the  interquartile range of the given data set. are -

1st quartile (Q1) = 6.8 ; 2nd quartile (Q2) = 7.6 and 3rd quartile (Q3) = 8.4 .

interquartile range = maximum  - minimum

interquartile range = 8.4 - 6.8 = 1.60.

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Equation: [tex]6xt^4yz^3 + 10a = 1[/tex]. Number of terms: 2, Coefficients: 6, 10 and Constants: 1.

Equation: [tex]25abc^2ab + 3ac6bc + 25[/tex], Number of terms: 3. Coefficients: 25, 3, 6. Constants: 25

What is equation and an expression?

A random combination of integers, variables, functions, etc. can be described as an expression. An expression is, for instance, 3x - 2. An equation, on the other hand, is created when two independent expressions are joined by the equal to sign. An equation, for instance, is when 3x - 2 = 5 + x.

Equation/Expression: 6xt⁴yz³ + 10a = 1

Number of terms: 2

Coefficients: 6, 10

Constants: 1

Equation/Expression: 25abc²ab + 3ac6bc + 25

Number of terms: 3

Coefficients: 25, 3, 6

Constants: 25

Equation/Expression: 25y³xy + 5 = 100

Number of terms: 2

Coefficients: 25, 1

Constants: 5, 100

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The angle that is vertical to angle DEB is A.

A vertical angle is an angle formed by two intersecting lines or planes that are perpendicular to each other. Specifically, it is the angle between two straight lines or planes that intersect each other and are perpendicular to the horizontal plane.

The measure of a vertical angle is always the same as the measure of the other vertical angle formed by the same two intersecting lines or planes. This is because vertical angles are always congruent, meaning they have the same size and shape. Vertical angles are commonly used in geometry and trigonometry to solve problems involving angles, lines, and plane.

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A feature of function gif g(x) = f(x-4) is D. horizontal asymptote of y = 4

A horizontal asymptote is a straight line on a graph that a function approaches but never touches as the independent variable (usually denoted as x) increases or decreases without bound. In other words, the function gets closer and closer to the horizontal line as x becomes very large or very small, but it never actually touches or crosses it.

A function can have at most two horizontal asymptotes - one on the left side of the graph and one on the right side. The horizontal asymptotes of a function are determined by the highest degree of the polynomial in the numerator and the denominator of the function.

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Hence ,the basketball team  scored 83 points in  the first game.

Basketball is a team sport in which two teams,  most commonly of five players each,  opposing one another on a rectangular court,  compete with the primary objective of shooting a basketball through the defender's hoop,  while preventing the opposing team from shooting through their own hoop.

A team is a group of individuals (human or non-human) working together to achieve their goal.As defined by Professor Leigh Thompson of the Kellogg School of Management, team is a group of people who are interdependent with respect to information, resources, knowledge and skills and who seek to combine their efforts to achieve a common goal

Let x be  the number of points  scored in the first game.

According  to the  question,

747 = 9 x

now  9 divided by both sides,

x = [tex]\frac{747}{9}[/tex]

than we get:

x = 83

Therefore,  the basketball team  scored 83 points in  the first game.

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Complete question is:

A basketball scored 747 points for the season.This was 9 times the number of points they scored in the first game.How many points were scored in the first game.

The conclusion of the given hypothesis is: we FAIL to reject the null hypothesis and conclude that there is not enough evidence to reject the claim that the mean lifetime of the newest model is 12 years

The parameters given are:

Population mean: μ = 12

Sample mean: x' = 12.5

Population standard deviation; σ = 3.5

Sample size: n = 35

Let's define the hypotheses:

Null Hypothesis: H₀: μ = 12

Alternative Hypothesis: Hₐ: μ ≠ 12

Let us find the z-score from the formula:

z = (x' - μ)/(σ/√n)

z = (12.5 - 12)/(3.5/√35)

z = 0.845

The p-value from online p-value from z-score calculator using two tailed hypothesis and a significance level of 0.1 gives:

p-value = 0.398

The p-value is greater than the significance value and we FAIL to reject the null hypothesis and conclude that there is not enough evidence to reject the claim that the mean lifetime of the newest model is 12 years

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Answer:

Area of a rectangle = Length x Width

Step-by-step explanation:

Length = 25 cm

Width = 8 cm

25 x 8 = 200

So the area of a rectangle = 60 cm^2

If the function f(x) = x, the effect of f(x) - 8 is: is (D) The y intercept decreases.

The function f(x) = x is a linear function with a slope of 1, which means that for every increase of 1 in the x-value, the y-value also increases by 1.

If we subtract 8 from the function, we get:

f(x) - 8 = x - 8

This is still a linear function with a slope of 1, but it has been shifted downwards by 8 units.

Therefore, the effect of f(x) - 8 is that the y-intercept decreases by 8 (since the y-intercept of f(x) is 0 and the y-intercept of f(x) - 8 is -8), while the slope remains the same.

So the correct answer is (D) The y intercept decreases.

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Using the functions, we can find the graphs for each function as follows:

Graph 3 is: g (x) = [tex]4^{x}[/tex]

Graph 4 is: h (x) = [tex]-4^{x}[/tex]

Graph 2 is: f (x) = [tex]-(\frac{1}{4})^{x}[/tex]

Graph 1 is: k (x) = [tex](\frac{1}{4})^{x}[/tex]

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain. For all values of a and b, f = (a,b)|

Based on elements like the domain and range of a function, as well as the function expression, the function y = f(x) is categorised into many categories of functions. The domain x value is referred to as input for the functions. The domain value can be a fraction, decimal, angle, integer, or decimal. The range is also represented by the y value or the f(x) value.

Graph 3 is: g (x) = [tex]4^{x}[/tex]

Graph 4 is: h (x) = [tex]-4^{x}[/tex]

Graph 2 is: f (x) = [tex]-(\frac{1}{4})^{x}[/tex]

Graph 1 is: k (x) = [tex](\frac{1}{4})^{x}[/tex]

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Answer:

Step-by-step explanation:

Perimeter: 34 yd

Area: 37 yd²