Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y > 5x + 5 y is greater than negative 1 over 2 times x plus 1 Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points) Part B: Is the point (−2, 5) included in the solution area for the system? Justify your

57 packets will be wasted during the distribution process. It is essential to ensure efficient distribution to minimize wastage and provide adequate support to those affected by the flood.

In order to distribute the food packets equally among all the people in the buildings affected by the flood, we need to calculate the number of packets each person will receive and the amount that will be wasted.

Let's calculate the distribution for each group separately:

1. Group 1: 13 people with 419 packets

  Packets per person: 419 / 13 = 32 packets per person

  Packets wasted: 419 % 13 = 0 packets wasted

2. Group 2: 35 people with 1771 packets

  Packets per person: 1771 / 35 = 50 packets per person

  Packets wasted: 1771 % 35 = 6 packets wasted

3. Group 3: 16 people with 260 packets

  Packets per person: 260 / 16 = 16 packets per person

  Packets wasted: 260 % 16 = 4 packets wasted

4. Group 4: 100 people with 145 packets

  Packets per person: 145 / 100 = 1 packet per person

  Packets wasted: 145 % 100 = 45 packets wasted

5. Group 5: 20 people with 4982 packets

  Packets per person: 4982 / 20 = 249 packets per person

  Packets wasted: 4982 % 20 = 2 packets wasted

In summary, the distribution of food packets and the amount wasted in each group are as follows:

Group 1: 32 packets per person, 0 packets wasted

Group 2: 50 packets per person, 6 packets wasted

Group 3: 16 packets per person, 4 packets wasted

Group 4: 1 packet per person, 45 packets wasted

Group 5: 249 packets per person, 2 packets wasted

Overall, 57 packets will be wasted during the distribution process. It is essential to ensure efficient distribution to minimize wastage and provide adequate support to those affected by the flood.

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The equivalent matrix of the matrix operations can be given by [tex]\left[\begin{array}{ccc}35&14\\-70&42\end{array}\right][/tex].

Matrix operations are fundamental mathematical operations performed on matrices, which are rectangular arrays of numbers or symbols arranged in rows and columns. Matrix operation includes addition, subtraction, scalar multiplication, matrix multiplication, transposition, determinant, inverse, etc.

Given matrices are written below:

[tex]A=\left[\begin{array}{ccc}1&5\\-5&3\end{array}\right][/tex] and [tex]B=\left[\begin{array}{ccc}4&-3\\-5&3\end{array}\right][/tex].

Given matrices operation to be performed: [tex]7(A)+7(B)[/tex].

[tex]7(A)+7(B)=7\left[\begin{array}{ccc}1&5\\-5&3\end{array}\right] +7\left[\begin{array}{ccc}4&-3\\-5&3\end{array}\right][/tex]

First, perform the scalar multiplication. Multiply both matrices by the scalar [tex]7[/tex].

[tex]\Rightarrow7(A)+7(B)=\left[\begin{array}{ccc}(1\times7)&(5\times7)\\(-5\times7)&(3\times7)\end{array}\right] +\left[\begin{array}{ccc}(4\times7)&(-3\times7)\\(-5\times7)&(3\times7)\end{array}\right]\\\Rightarrow7(A)+7(B)=\left[\begin{array}{ccc}7&35\\-35&21\end{array}\right] +\left[\begin{array}{ccc}28&-21\\-35&21\end{array}\right]\\[/tex]

Now, perform the addition of two matrices.

[tex]\Rightarrow7(A)+7(B)=\left[\begin{array}{ccc}(7+28)&(35-21)\\(-35-35)&(21+21)\end{array}\right]\\\Rightarrow7(A)+7(B)=\left[\begin{array}{ccc}35&14\\-70&42\end{array}\right]\\[/tex]

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The x = 6 is not a valid solution because it violates the restriction. So x = 6 is an extraneous solution.Therefore, the only acceptable solution is x = 1.

The equation is:(x)/(x - 2) = (4)/(x² - 8x + 12) - (1)/(x - 6)To solve the above equation, we have to find the LCD (least common denominator) and then convert all terms into a single fraction with the LCD as its denominator. Then we can simplify and solve for x.To find the LCD of the given terms, we need to factorize the denominator of the second term, which is a quadratic equation.x² - 8x + 12 = (x - 6)(x - 2)So the LCD is (x - 2)(x - 6).

Multiplying the first term by (x - 6) / (x - 6), we get:(x)(x - 6) / (x - 2)(x - 6) = (4)(x - 2) / (x - 2)(x - 6) - (1)(x - 2) / (x - 2)(x - 6)Multiplying both sides by (x - 2)(x - 6), we obtain:x(x - 6) = 4(x - 2) - (x - 2)(x - 6)Expanding the brackets, we get:x² - 6x = 4x - 8 - x² + 8x - 12Simplifying and rearranging terms, we get:2x² - 18x + 20 = 0Dividing both sides by 2, we get:x² - 9x + 10 = 0Factoring the equation, we get:(x - 1)(x - 10) = 0So the solutions are:x = 1 or x = 10.

However, we need to check both solutions since there is a restriction in the original equation:x ≠ 2 and x ≠ 6.If we substitute x = 2 in the original equation, we get a 0 in the denominator, which is not defined. So x = 2 is not a valid solution.If we substitute x = 6 in the original equation, we also get a 0 in the denominator.

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To calculate the rate of change or slope between two points, we use the formula:

slope = (change in y) / (change in x)

In this case, the initial gas price in 2001 is $1.75, and twelve years later in 2013, the gas price is $4.35. So, the change in y (change in gas price) is 4.35 - 1.75 = $2.60. The change in x (change in years) is 2013 - 2001 = 12 years.

Now we can calculate the slope:

slope = (change in y) / (change in x) = 2.60 / 12 = 0.2167

Therefore, the rate of change or slope between the two points is approximately 0.2167, or 21.67%.

Answer:1800

Step-by-step explanation:

Answer:

 $900

Step-by-step explanation:

You want to know the cost of supplying tyres to twelve cyclists if the cost per pair is $75.

Each cyclist requires one pair of tyres, so 12 cyclists will need 12 pairs. At $75 per pair, the total cost is ...

  ($75/pair) × (12 pairs) = $900

It would cost $900 to supply these tyres to 12 cyclists.

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The most appropriate viewing window for determining the domain and range of the function f(x) = (x^2 - 81)/(x^2 - 11x + 18) would be:

Xmin: -10, Xmax: 10

Ymin: -10, Ymax: 10

This window allows you to see a wide range of x-values and y-values, giving you a comprehensive view of the graph and helping you determine the domain and range of the function accurately.

In the given similar triangles below, we have to find the measure of Dwrite. Triangle 1, ABC, is similar to Triangle 2, DEF. The two triangles are similar because their corresponding angles are congruent and their sides are proportional.

In order to find the measure of Dwrite, we can use the concept of proportionality. The sides of similar triangles are proportional to each other.

This means that if we know the ratio of the sides of one triangle, we can use that ratio to find the corresponding sides of the other triangle. We can use this property to find the value of Dwrite.

To start, let's write down the ratio of the sides of Triangle 1 and Triangle 2. We can choose any two corresponding sides to do this, but we'll choose AB and DE because they are easiest to measure: AB/DE = 6/8.5We know that the measure of AB is 6, so we can solve for the measure of DE: DE = AB x (DE/AB)DE = 6 x (8.5/6)DE = 8.5Now we know that the measure of DE is 8.5.

We can use this to find the measure of Dwrite. We know that DE and Dwrite are corresponding sides of Triangle 2 and Triangle 1, respectively.

So we can write a proportion using the ratio of DE to Dwrite: DE/Dwrite = 8.5/xWe know that DE is 8.5, so we can substitute that in:8.5/Dwrite = 8.5/Now we can solve for x by cross-multiplying:8.5x = 8.5Dwrite = 1Therefore, the measure of Dwrite is 1.

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The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle [tex]= \frac{180}{3} = 60\)[/tex] degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

[tex]V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2][/tex]] evaluated from 0 to 1

V = [tex]2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)][/tex]

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

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Answer:

Step-by-step explanation:

total interest paid is given as $4,643.46.

total payments = $429.95 x 36 months = $15,478.20

total lease payments = total payments - total interest

total lease payments = $15,478.20 - $4,643.46 = $10,834.74

Remaining balance = Total cost of the lease - Total lease payments

$23,495 - $10,834.74 = $12,660.26

We have proven that △ABD ≅ △CBD based on the given information and the SAS congruence criterion.

To prove that △ABD ≅ △CBD, we can use the SAS (Side-Angle-Side) congruence criterion.

Given:

∠BDA ≅ ∠BDC (Both are right angles)

D is the midpoint of AC¯¯¯¯¯

AB¯¯¯¯¯ ≅ BC¯¯¯¯¯

BD¯¯¯¯¯ bisects ∠B

Proof:

Since D is the midpoint of AC¯¯¯¯¯, we have AD ≅ CD by the definition of a midpoint.

AB¯¯¯¯¯ ≅ BC¯¯¯¯¯ (Given)

BD¯¯¯¯¯ is a common side for both triangles.

∠BDA ≅ ∠BDC (Given)

To apply the SAS congruence criterion, we need to show that one pair of corresponding sides and the included angle are congruent in both triangles.

AD ≅ CD (Side) - This is true as D is the midpoint of AC¯¯¯¯¯.

∠BDA ≅ ∠BDC (Included Angle) - Both are right angles.

By the SAS congruence criterion, we can conclude that △ABD ≅ △CBD.

Therefore, we have proven that △ABD ≅ △CBD based on the given information and the SAS congruence criterion.

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Answer: -14

Step-by-step explanation:

If u have 4 x's divided by 4 = -4 that shows all the temperatures in total for the first 4 days would equal -16.

if u do the same for the first 5 days you get 5x's and say all of them divided by 5 equals -6 which shows that the temperature for the first 5 days in total equals -30.

You then find the difference between -30 and -16 which equals -14

Hope that answered your question.

Best Of Luck

Building 1: 13 people received 32 packets, with 3 packets wasted.

Building 2: 35 people received 50 packets, with 21 packets wasted.

Building 3: 16 people received 16 packets, with 4 packets wasted.

Building 4: 4 people received 36 packets, with 1 packet wasted.

Building 5: 20 people received 249 packets, with 2 packets wasted.

Let's analyze the given information to determine how many food packets each person receives and the amount wasted during the flood.

Building with 419 packets:

People: 13

Packets per Person: 419 / 13 = 32

Packets Wasted: 419 - (13 * 32) = 419 - 416 = 3 packets

Building with 1771 packets:

People: 35

Packets per Person: 1771 / 35 = 50

Packets Wasted: 1771 - (35 * 50) = 1771 - 1750 = 21 packets

Building with 260 packets:

People: 16

Packets per Person: 260 / 16 = 16

Packets Wasted: 260 - (16 * 16) = 260 - 256 = 4 packets

Building with 145 packets:

People: 4

Packets per Person: 145 / 4 = 36.25 (rounded to the nearest whole number)

Packets Wasted: 145 - (4 * 36) = 145 - 144 = 1 packet

Building with 4982 packets:

People: 20

Packets per Person: 4982 / 20 = 249.1 (rounded to the nearest whole number)

Packets Wasted: 4982 - (20 * 249) = 4982 - 4980 = 2 packets

Therefore, during the flood, the distribution of food packets and the amount wasted in each building is as follows:

Building 1: 13 people received 32 packets, with 3 packets wasted.

Building 2: 35 people received 50 packets, with 21 packets wasted.

Building 3: 16 people received 16 packets, with 4 packets wasted.

Building 4: 4 people received 36 packets, with 1 packet wasted.

Building 5: 20 people received 249 packets, with 2 packets wasted.

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Yes, Pascal's Triangle can be used to expand the binomial [tex](2x+3y)^{15.[/tex] Pascal's Triangle is a triangular arrangement of numbers in which each number is the sum of the two numbers directly above it.

The coefficients in the expansion of a binomial can be found by using the corresponding row of Pascal's Triangle.

To expand[tex](2x+3y)^{15[/tex], we will use the 15th row of Pascal's Triangle. The first term will have the exponent of[tex](2x)^{15[/tex], and the second term will have the exponent of (3y)^0. Each subsequent term will have decreasing exponents of (2x) and increasing exponents of (3y).

The expansion of (2x+3y)^15 using Pascal's Triangle is as follows:

[tex](2x)^{15} + 15(2x)^{14}(3y) + 105(2x)^{13}(3y)^{2} + 455(2x)^{12}(3y)^{3} + ... + 455(2x)(3y)^{12} + 105(3y)^{13 }+ (3y)^{15[/tex]

We can simplify each term by calculating the coefficients and combining like terms. The coefficients are determined by the corresponding numbers in the 15th row of Pascal's Triangle: 1, 15, 105, 455, ...

So, the expanded form of (2x+3y)^15 is:

[tex](2x)^{15} + 15(2x)^{14}(3y) + 105(2x)^{13}(3y)^{2} + 455(2x)^{12}(3y)^{3} + ... + 455(2x)(3y)^{12} + 105(3y)^{13 }+ (3y)^{15[/tex]

Simplifying further would involve performing the necessary calculations and combining like terms.

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Answer:

See below

Step-by-step explanation:

I'm assuming by your prompt you're looking to convert (3,-2) into polar coordinates and (2, 5pi/4) into rectangular coordinates (assuming θ is in radians and not degrees).

For converting rectangular to polar coordinates, recall [tex]r=\sqrt{x^2+y^2}[/tex] and [tex]\theta=\tan^{-1}(\frac{y}{x})[/tex], therefore, [tex]r=\sqrt{3^2+(-2)^2}=\sqrt{9+4}=\sqrt{13}[/tex] and [tex]\theta=\tan^{-1}(\frac{-2}{3})\approx-0.588[/tex], making [tex](r,\theta)=(\sqrt{13},0.588)[/tex]

For converting polar to rectangular coordinates, recall [tex](x,y)=(r\cos\theta,r\sin\theta)[/tex], therefore, [tex](2\cos(\frac{5\pi}{4}),2\sin(\frac{5\pi}{4}))\approx(-\sqrt{2},-\sqrt{2})[/tex].

The length of the line segment AB is 5 units.

Unfortunately, you haven't provided any information about PQ such as its location or any other data to help solve the question.

Therefore, it's impossible to determine the length of PQ using the given options. However, here is an explanation of how to find the length of a line segment using the distance formula, which may help you in solving similar questions in the future.

The distance formula is used to find the distance between two points in a coordinate plane, such as the length of a line segment. The formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where d is the distance, (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

To use the distance formula, you first need to find the coordinates of the two points that make up the line segment. Then, substitute these coordinates into the formula and simplify to find the distance.

For example, let's say you have two points: A(1, 2) and B(4, 6), and you want to find the length of the line segment AB. Using the distance formula:

d = √((4 - 1)² + (6 - 2)²)
d = √(3² + 4²)
d = √(9 + 16)
d = √25
d = 5

Remember, the distance formula can be applied to any two points in a coordinate plane to find the distance between them.

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Answer:

$31.50

Step-by-step explanation:

To calculate the new cost of the jeans after a discount, we can use the formula:

New cost = Original cost - (Discount percentage * Original cost)

In this case, the original cost of the jeans is $45.00, and the discount is 30% off. So, the discount percentage is 30/100 = 0.30.

Substituting these values into the formula, we have:

New cost = $45.00 - (0.30 * $45.00)

= $45.00 - $13.50

= $31.50

Therefore, the new cost of the jeans after a 30% discount is $31.50.

In a sprint race, Manuel covered 2/3 of the total distance, and his friend José covered 3/5 of the distance. The fraction which represents the total distance covered by Manuel and José in the sprint race is 19/15

To find the fraction that represents the total distance covered by Manuel and José, we need to add their individual fractions together.

Let's start by finding a common denominator for the fractions 2/3 and 3/5. The least common multiple (LCM) of 3 and 5 is 15.

Now, we can convert the fractions to have a common denominator of 15:

2/3 = (2/3) * (5/5) = 10/15

3/5 = (3/5) * (3/3) = 9/15

Next, we add the fractions together:

10/15 + 9/15 = 19/15

The fraction 19/15 represents the total distance covered by Manuel and José. However, we can simplify this fraction to its simplest form.

To simplify the fraction, we divide the numerator and denominator by their greatest common divisor, which is 1 in this case:

19/15 ÷ 1/1 = 19/15

Therefore, the final answer is 19/15, which represents the total distance covered by Manuel and José in the sprint race.

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The probable question in english:

In a sprint race, Manuel covered 2/3 of the total distance, and his friend José covered 3/5 of the distance. What fraction represents the total distance covered by the two friends?

b = 7. The equation of the hyperbola is thus:$(y - 0)^2/6^2 - (x - 0)^2/7^2 = 1$.

A hyperbola is a set of points in the Cartesian plane whose difference of distances from two fixed points, called foci, is a positive constant.

The distance between the center of the hyperbola and its vertices is a fixed distance, known as the semimajor axis, a.

A transverse axis is perpendicular to the major axis and passes through the center of the hyperbola. For a hyperbola, the distance between its foci is always greater than the length of its transverse axis.

Since the co-vertices of the hyperbola are at (0,7) and (0,-7), the center is at (0,0). The length of the transverse axis is 12, which is equal to 2a, where a is the semimajor axis.

Therefore, a = 6. The equation of the hyperbola is given by the standard form equation:$(y - k)^2/a^2 - (x - h)^2/b^2 = 1$,where (h, k) is the center of the hyperbola, and a and b are the lengths of the semimajor and semi minor axes, respectively.

For this hyperbola, h = 0, k = 0, and a = 6. The length of the semi minor axis can be determined using the co-vertices.

The distance between the center and each co-vertex is equal to b. Therefore, b = 7. The equation of the hyperbola is thus:$(y - 0)^2/6^2 - (x - 0)^2/7^2 = 1$.

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