What is the solution to the system of equations below? x + 3 y = 15 and 4 x + 2 y = 30 (4, 10) (3, 6) (6, 3) (10, 4)

Possible rational zeros of the polynomial is

±1, ±1/2, ±1/4, ±2, ±5, ±5/2, ±5/4, ±10.

Polynomials are particular type of algebraic expressions which consists of variables and coefficients. Various arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions can be performed on polynomial but not division by variable. An example of a polynomial is x-12 . Here it has two  terms:  x and -12.

Given polynomial p(x)= 4x⁵-2x³+10

The polynomial can be rewritten as p(x)= 4x⁵+ 0x⁴-2x³+0x²+0x+10

Comparing the polynomial with

p(x) = aₙ xⁿ + aₙ₋₁xⁿ⁻¹+ ---------- + a₁ x + a₀ we get the  leading coefficient

aₙ= 4 and the constant term a₀= 10

So the possible zeros are=  ±( factors of a₀)/ (factors of aₙ)

Factors of 10:

1, 2, 5, 10

Factors of 4:

1, 2, 4

Hence, Possible rational zeros:

±1, ±1/2, ±1/4, ±2, ±5, ±5/2, ±5/4, ±10

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The Two figures are (Not similar) because 2/5 ( does not equal) 3/6.

What is similar rectangle?

If two rectangles are similar, their corresponding sides are proportionately equal.

Now comparing the length and width of the two rectangles then.

=> 2/5 = 3/6

Which is not equally proportional.

Hence the both rectangles are similar because 2/5 does not equal 3/6 .

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In a rectangle, there are 2 pairs of congruent sides. Therefore, the area of a rectangle can be found using:

[tex]\text{A}=\text{l} \times \text{w}[/tex]

We know that the length is 18 and the width is 12, so we can multiply 18 in for l, and 12 in for w.

[tex]\text{A}=\text{18} \times \text{12}[/tex]

Multiply the numbers together

[tex]\text{A}=216[/tex]

So, the area is 216 inches.

To find the area of a rectangular placemat, you multiply the length by the width. In this case, the length is 18 inches and the width is 12 inches. Therefore, the area of the tablecloth is:

Area = Length × Width

Area = 18 inches × 12 inches

Area = 216 square inches

So, the correct answer is option a. 216.

Adama can expect the die to land on a number less than 10 about 36 times in 40 rolls.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is essentially what probability means.

The die has 10 faces, with numbers 1 through 10, but we are interested in the number of times it will land on a number less than 10. That means, there are 9 possible outcomes for each roll to be less than 10.

The expected number of times the die will land on a number less than 10 can be calculated by multiplying the probability of getting a number less than 10 on each roll by the total number of rolls.

The probability of getting a number less than 10 on each roll is 9/10, since there are 9 faces with numbers less than 10 out of the total of 10 faces.

Therefore, the expected number of times the die will land on a number less than 10 is:

E = (9/10) x 40 = 36

Therefore, Adama can expect the die to land on a number less than 10 about 36 times in 40 rolls.

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☆ 36 times.

— your in college ? im in seventh grade and got this question !

Answer:

Area = π+4

Perimeter = 4π+4

Step-by-step explanation:

1) The two semi-circles make one whole circle

2) one square.

Area

1) formula for the area of a circle = [tex]r^{2}\pi[/tex]

The diameter is 2 which means the radius is 1

so the area of the circle is equal to π

2) to find the area of a square you multiply the sides

2x2=4

So to find the total area you add [tex]\pi +4[/tex]

which leaves us with [tex]\pi +4[/tex]

Perimeter

1) the formula for the perimeter of a circle = [tex]2\pi r[/tex]

Since the radius is 1

the perimeter of both circles is 4π

2) to find the perimeter of only part of the square (two sides), you have to add them together

2+2=4

So the total perimeter is 4π+4

Each student will read 2 1/2 pages aloud. The answer is option B, 2 1/2.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3, since each term after the first is found by adding 3 to the preceding term.

Ms. Avila's reading class has 18 students and they are going to read aloud from a book that has 45 pages. To determine the total number of pages that each student will read, we need to divide the total number of pages by the number of students.

So, 45 divided by 18 equals 2 1/2 pages per student.

This means that each student will read 2 1/2 pages aloud.

Therefore, the answer to the question is option B, 2 1/2.

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Answer:

The correct option is C. The best approximate for the given graph is [tex]\sqrt{28}[/tex].

Step-by-step explanation:

From the given graph it is noticed that the point lies between 5 and 6.

Let the square root of x is the best approximate for the given graph.

[tex]5 < \sqrt{x} < 6[/tex]

Taking square on each side.

[tex]5^2 < (\sqrt{x})^2 < 6^2[/tex]

[tex]25 < x < 36[/tex]

It means the value of x lies between 25 to 36 and the graph represents the approximate value between [tex]\sqrt{25}[/tex] to [tex]\sqrt{36}[/tex].

Therefore best approximate for the given graph is [tex]\sqrt{28}[/tex]. Option C is correct.

1. The reason is that E bisects line AC and is perpendicular to line AC.

2. The reason is that the angles are alternate interior angles.

What are alternate interior angles?

Alternate interior angles are made when a transversal joins two co-planar lines. These can be found on the inner side of the parallel lines, but on their transverse sides. The transversal goes through the two co-planar lines at two separate points.

1. We are given a statement that E is the midpoint of AC.

The reason is that E bisects line AC and is perpendicular to line AC, therefore it is the mid point of AC.

2. We are given that ∠D ≅ ∠B.

The reason is that DC ║ AB. We know that when two lines are parallel, alternate interior angles are equal.

The angle ∠D and ∠B are alternate interior angles and therefore they are equal.

Hence, the required solutions have been obtained.

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The complete question has been attached below.

Answer:

10.5

Step-by-step explanation:

250% = 2.5

What number is 250% of 4.2?
We Take

2.5 x 4.2 = 10.5

So, 10.5 is 250% of 4.2

The function f(2) from the piecewise function has a value of 0

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

The piecewise function

The x value of 2 belongs to the domain x > 2

So, we have

f(x) = -x + 2

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

f(2) = -2 + 2

Evaluate

f(2) = 0

Hence, the value iss 0

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Answer:

The triangles are similar by AA since vertical angles are congruent.

[tex] \frac{8}{12} = \frac{x}{7} [/tex]

[tex]12x = 56[/tex]

[tex]x = \frac{14}{3} = 4 \frac{2}{3} [/tex]

Answer:

5x + 12

Step-by-step explanation:

3(x + 2) + 2(x + 3)

= 3x + 6 + 2x + 6 (distributing the coefficients)

= 5x + 12 (combining like terms)

Answer:5x+12

Step-by-step explanation:

3(x+2)= 3x+6

2)x+3) = 2x+6

3x+2x+6+6=5x+12

HOPE I HELPED :)

The value of x in the given equation of the quadrilateral is 20.

The value of x is determined by applying the property of a quadrilateral which states that adjacent angles of a quadrilateral are supplementary while the opposite angles are equal.

(2x + 14) + 126 = 180

We can simplify the left side of the equation by combining the terms inside the parentheses:

2x + 140 = 180

Next, we can isolate the variable x by subtracting 140 from both sides of the equation:

2x = 40

Finally, we can solve for x by dividing both sides of the equation by 2:

x = 20

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Answer:

Step-by-step explanation:

Here is a step-by-step explanation of the solution and how it leads to the maximum revenue:

Let's start with the current revenue generated by the TV cable company, which is the product of the number of subscribers and the monthly fee:

Current revenue = Number of subscribers * Monthly fee

Current revenue = 6400 * $28

Current revenue = $179,200

To increase the revenue, the TV cable company can decrease the monthly fee by $0.50, which will result in an increase in the number of subscribers by 160 for each $0.50 decrease. Let's calculate the additional revenue generated by each $0.50 decrease in the monthly fee:

Additional revenue per decrease in monthly fee = Increase in subscribers * Decrease in monthly fee

Additional revenue per decrease in monthly fee = 160 * $0.50

Additional revenue per decrease in monthly fee = $80

The TV cable company can continue to decrease the monthly fee by $0.50 until the revenue stops increasing. Let's calculate the number of $0.50 decreases in monthly fee required to reach the maximum revenue:

Number of $0.50 decreases in monthly fee = (Total revenue - Current revenue) / Additional revenue per decrease in monthly fee

Number of $0.50 decreases in monthly fee = ($20,000,000 - $179,200) / $80

Number of $0.50 decreases in monthly fee = 248,525

The corresponding decrease in monthly fee is:

Decrease in monthly fee = Number of $0.50 decreases in monthly fee * Decrease in monthly fee

Decrease in monthly fee = 248,525 * $0.50

Decrease in monthly fee = $124,262.50

The corresponding increase in subscribers is:

Increase in subscribers = Number of $0.50 decreases in monthly fee * Increase in subscribers

Increase in subscribers = 248,525 * 160

Increase in subscribers = 39,764,000

The total number of subscribers at the maximum revenue point is:

Total subscribers = 6400 + Increase in subscribers

Total subscribers = 6400 + 39,764,000

Total subscribers = 39,770,400

The monthly fee at the maximum revenue point is:

Monthly fee = Current revenue / Total subscribers

Monthly fee = $179,200 / 39,770,400

Monthly fee = $0.0045

The maximum revenue is:

Maximum revenue = Total subscribers * Monthly fee

Maximum revenue = 39,770,400 * $0.0045

Maximum revenue = $178,966.80

Therefore, the TV cable company can generate maximum revenue of $178,966.80 per month by decreasing the monthly fee by $0.50 for each 160 additional subscribers.

The critical point of the function g is (0,0), the value of D(0,0) is -6272, and the critical point is a saddle point.

(a) To find the critical point of g, we need to find the partial derivatives of g with respect to x and y, and set them equal to zero:

[tex]∂g/∂x = -8xe^(-4x^2+7y^2+14√8y) = 0[/tex]

[tex]∂g/∂y = 14ye^(-4x^2+7y^2+14√8y) + 14√8e^(-4x^2+7y^2+14√8y) = 0[/tex]

From the first equation, we get x = 0. Substituting this value into the second equation, we get:

[tex]14ye^(7y^2+14√8y) + 14√8e^(7y^2+14√8y) = 0[/tex]

Dividing both sides by [tex]14e^(7y^2+14√8y)[/tex], we get:

y + √8 = 0

Thus, the critical point of g is (0, -√8).

(b) To find the value of D(a,b) from the Second Partials test, we need to compute the second-order partial derivatives of g with respect to x and y:

[tex]∂^2g/∂x^2 = 32x^2e^(-4x^2+7y^2+14√8y) - 8e^(-4x^2+7y^2+14√8y)[/tex]

[tex]∂^2g/∂y^2 = 98y^2e^(-4x^2+7y^2+14√8y) + 196√8ye^(-4x^2+7y^2+14√8y) + 686e^(-4x^2+7y^2+14√8y)[/tex]

[tex]∂^2g/∂x∂y = -112xye^(-4x^2+7y^2+14√8y) - 196√8xe^(-4x^2+7y^2+14√8y)[/tex]

At the critical point (0, -√8), we have:

[tex]∂^2g/∂x^2 = -8[/tex]

[tex]∂^2g/∂y^2 = 686[/tex]

[tex]∂^2g/∂x∂y = 0[/tex]

Therefore, D(0, -√8) =[tex](∂^2g/∂x^2)(∂^2g/∂y^2) - (∂^2g/∂x∂y)^2[/tex] = (-8)(686) - [tex](0)^2[/tex] = -5488.

(c) Since D(0, -√8) is negative, and [tex]∂^2g/∂x^2[/tex] is negative at the critical point, the Second Partials test tells us that (0, -√8) is a saddle point.

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C(N(x)) = 45 + 15(150 - x) = 45 + 2250 - 15x = 2295 - 15x. C(N(x)) = 2295 - 15x, which equals $2295 minus $15 for each guest fewer than 150. Therefore, $795 would be needed to prepare for 50 guests.

A group of terms joined with the operations +, -, x, or  form an expression, such as 4 x 3 or 5 x 2  3 x y + 17. A statement that starts with an equals sign, such as 4 b 2 = 6, says that two statements are equal in value and is known as an equation.

The functions are: C(x) = 45 plus 15x (Cost per guest)

N(x) = 150 - x (Number of guests)

We must simplify and replace the formula for N(x) with C(x) in order to evaluate C(N(x)):

C(N(x)) = 45 + 15(150 - x) = 45 + 2250 - 15x = 2295 - 15x

The expense of catering for x guests who are less than 150 is denoted by the expression 2295 - 15x.

The expense of catering a celebration for x guests fewer than 150 is denoted by the formula: C(N(x)) = 2295 - 15x, which equals $2295 minus $15 for each guest fewer than 150. This expression provides the total expense of catering for the number of guests defined by the function N.(x). For instance, if the event has 50 guests, then x = 100 and the expense of catering for 50 guests.

C(N(100)) = 2295 - 15(100)

= 2295 - 1500

= 795

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According to the question the value of the test statistic [tex]0.55[/tex]

Data variation from the mean is referred to as "standard deviation." If the standard deviation appears low, the data tend to cluster around the mean; on the other hand, if it appears large, the data are widely spread.

The data deviate from the mean value is indicated by the standard . It is useful for contrasting huge datasets with distinct ranges but the same mean.

The other, though, is without a doubt more spread. The standard deviation reveals the degree of data dispersion. It describes how far away from the mean each number obtained is.

We must compute the t-score, which is represented by: in order to determine the value of the test statistic.

[tex]t = x -[/tex] μ[tex]/(s/\sqrt{n}[/tex]

s= sampling standard deviation, n= sample size,[tex]x=[/tex] sampling rate μ = population mean

[tex]x = 69.5 bpm,[/tex] μ[tex]= 69 bpm, s = 11.4 bpm, n = 154[/tex]

[tex]t = (69.5- 69)/ 11.4/\sqrt{154} \\t = 0.5/ (11.4/12.4)\\t = 0.5/ 0.917\\t = 0.546[/tex]

Therefore the value of the test statistics is [tex]0.55[/tex]

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Answer: 165 degrees

Step-by-step explanation:

Let's start off and name the angle between the hour and minute hand x, representing the number of degrees between the hands. Next, let's look at the minute hand first. After exactly an hour, the minute hand does not change its position(since after one hour, it comes back to where it was previously). As for the hour hand however, its position differs by exactly "1 hour tick", which is equivalent to 30 degrees (360 / 12 hours). What that implies is that x would have to equal x + 30, which is clearly impossible. However, we can think about the problem in a different way: by looking at the acute angle only between the hands, that would indeed be possible. Assuming that x + 30 is greater than 180(since if it wasn't, that wouldn't be possible), we can write the following equation:

x = 360 - (x+30)

, with the right hand side coming from the fact that the obtuse angle of x + 30 must have an acute counterpart, of which both add up to 360.

Then, we can simplify to:

x = 330 - x

or:

2x = 330

x = 165.

This gives us our only answer of 165 degrees

a. Your friend's mistake is that the reflection of EFG to its image E'F'G' is not a reflection across the x-axis.

b. The correct description of the reflection is a reflection across the line y = x.

The correct description of the reflection are:

a. Your friend's mistake is that the reflection of EFG to its image E'F'G' is not a reflection across the x-axis.

b. The correct description of the reflection is a reflection across the line y = x.

This is because the line of reflection is the perpendicular bisector of the segment connecting each point to its image. In this case, the segment connecting E to E' has a slope of 1 (since it is a diagonal line), so the perpendicular bisector of this segment must have a slope of -1.

The line with slope -1 passing through the midpoint of this segment (which is the point on the line y = x) is the line of reflection. Therefore, the reflection of EFG to its image E'F' is a reflection across the line y = x, not the x-axis.

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1. The probability that a single randomly selected salary is less than 144000 dollars is 0.5129. 2. The probability for n=75 is randomly selected with a mean that is less than 144000 dollars is 0.8781.

The central limit theorem, which states that the distribution of sample means will be about normal regardless of how skewed the original population distribution was if the sample size is large enough and the population is not very skewed, is a foundational concept in statistics. The central limit theorem precisely states that the sample means' mean is equal to the population's mean and that the sample means' standard deviation (also known as the standard error) is equal to the population's standard deviation divided by the square root of the sample size.

The z-score us given by the formula:

z = (x - μ) / σ

1. For salary less than 144000 dollars:

z = (144000 - 143000) / 31000 = 0.0323

Using the z-table:

z-score < 0.0323 = 0.5129

Hence, the probability that a single randomly selected salary is less than 144000 dollars is 0.5129.

2. For n = 75:

z = (x - μ) / (σ / √(n))

z = (144000 - 143000) / (31000 / √(75)) = 1.164

Using z-table:

z-score is less than 1.164 = 0.8781.

Hence, the probability that a sample of size n=75 is randomly selected with a mean that is less than 144000 dollars is 0.8781.

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Answer: 5

Step-by-step explanation:

If the area of a square equals 25 square inches, then the side length of the square can be found by taking the square root of the area. The formula for the area of a square is A = s^2, where A is the area and s is the length of a side of the square.

So, in this case, we have:

A = 25 sq inches

s = sqrt(A) = sqrt(25 sq inches) = 5 inches

Therefore, the side of the square is 5 inches.

Answer:

Step-by-step explanation:

The solution to the set of equations can be found by solving the system:

3x + 3y = 12

x + y = 4

We can simplify the second equation by solving for y:

y = 4 - x

Substituting this expression for y into the first equation, we get:

The solution to the set of equations can be found by solving the system:

3x + 3y = 12

x + y = 4

We can simplify the second equation by solving for y:

y = 4 - x

Substituting this expression for y into the first equation, we get:

3x + 3(4 - x) = 12

3x + 12 - 3x = 12

12 = 12

This is a true statement, which means that the system is consistent and has infinitely many solutions. Therefore, the correct answer is:

There are infinitely many solutions.

Answer:

Step-by-step explanation:

To find:-

Answer:-

We are here given that there are two linear equations, namely,

[tex]\begin{cases} 3x+3y = 12 \\ x+y = 4 \end{cases}[/tex]

These can be rewritten as ,

[tex]\begin{cases} 3x+3y - 12 =0\\ x+y -4=0 \end{cases}[/tex]

Before we precede we must know that,

Conditions for solvability :-

If there are two linear equations namely,

[tex]\begin{cases} a_x + b_1y+c_1 = 0 \\ a_2x+b_2y+c_2=0\end{cases}[/tex]

Then ,

Case 1 :-

If we have,

[tex]\longrightarrow \boxed{ \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2} } \\[/tex]

Then , the lines are coincident and there are infinitely many solutions .

Case 2 :-

If we have,

[tex]\longrightarrow \boxed{ \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2} } \\[/tex]

Then, the linear equations are inconsistent and have no solutions , thus the lines are parallel .

[tex]\rule{200}2[/tex]

So here with respect to angle standard form of pair linear equations, we have;

Hence here we have,

[tex]\longrightarrow \dfrac{a_1}{a_2} = \dfrac{3}{1} \\[/tex]

[tex]\longrightarrow \dfrac{b_1}{b_2}=\dfrac{3}{1} \\[/tex]

[tex]\longrightarrow \dfrac{c_1}{c_2}=\dfrac{-12}{-4}=\dfrac{3}{1} \\[/tex]

Therefore we can clearly see that,

[tex]\longrightarrow \boxed{ \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2} =\boxed{\dfrac{3}{1}}} \\[/tex]

Hence there are infinitely many solutions and the lines are coincident .

Answer:

the area is 1000

Step-by-step explanation:

This one is for the boys with the booming system

Top down, AC with the cooler system

Answer:

Each bag of spinach weighs 0.833 kg or approximately 833 grams

Step-by-step explanation:

Fiona had 3 kg of spinach. She sold 1/2 kg of spinach to Mrs. Simon, which leaves her with:

3 kg - 1/2 kg = 2.5 kg

Fiona packed the remaining 2.5 kg of spinach equally into 3 bags. To find the mass of each bag of spinach, we can divide the total amount of spinach by the number of bags:

2.5 kg ÷ 3 = 0.833 kg

therefore, Each bag of spinach weighs 0.833 kg or approximately 833 grams

Answer: Given a 2x2 matrix A:

A = [a11 a12]

   [a21 a22]

The minor of any element a_ij is the determinant of the 1x1 matrix obtained by deleting the i-th row and j-th column from A. In other words, the minor of a_ij is given by:

M_ij = det(A_ij)

where A_ij is the matrix obtained by deleting the i-th row and j-th column from A.

For example, the minor of a11 is given by:

M_11 = det([a22])

    = a22

Similarly, we can find the minors of the other elements:

M_12 = det([a21])

    = a21

M_21 = det([a12])

    = a12

M_22 = det([a11])

    = a11

Therefore, the minors of the matrix A are:

M = [a22  a21]

   [a12  a11]

Step-by-step explanation:

Answer:

38.4 megabytes for 16 electronic books

Step-by-step explanation:

2.4 megabytes per electronic book

2.4 megabytes x 16 electronic books = 38.4 megabytes

The desalination plant can produce [tex]9.84*10^6[/tex] gallons of water in four day in scientific notation.

We must divide the daily production rate by the number of days in order to get the total volume of water that a desalination plant can generate in four days:

4. days at a rate of [tex]2.46*10^6[/tex] gallons equals [tex]9.84*10^6[/tex] gallons.

Hence, in four days, the desalination plant can produce [tex]9.84 * 10^6[/tex] gallons of water.

Large or small numbers can be conveniently represented using scientific notation, especially when working with measurements in science and engineering. A number is written in scientific notation as a coefficient multiplied by 10 and raised to a power of some exponent. For example, [tex]2.46*10^6[/tex] denotes 2,460,000, which is 2.46 multiplied by 10 to the power of 6.

The solution in this case is [tex]9.84*10^6[/tex], or 9,840,000, which is 9.84 multiplied by 10 to the power of 6. Large numbers can be written and compared more easily using this format, and scientific notation rules can be used to conduct computations with them.

In conclusion, the desalination plant has a four-day capacity of [tex]9.84 * 10^6[/tex] gallons of water production.

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we can conclude that the expression [tex]2x^2 + 3x -1[/tex] is the quadratic expression among the given options.

A quadratic expression is an algebraic expression in which the highest power of the variable is 2. The general form of a quadratic expression is:

[tex]ax^2 + bx + c[/tex]

where a, b, and c are constants and x is the variable. The coefficient a must be non-zero for the expression to be considered quadratic.

In the given options, we can see that only one expression has a degree of 2, which is the second term of the quadratic expression.

So, we can conclude that the expression [tex]2x^2 + 3x -1[/tex] is the quadratic expression among the given options.

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