What is an equation of the line that passes through the points (-3, 7) and (3, 3)?

Step-by-step explanation:

I call the law of cosine the extended Pythagoras for general triangles (not just right-angled).

c² = a² + b² - 2ab×cos(C)

with C being the angle opposite of the side C.

we can use this, when we know all 3 side lengths and need to know the angles.

and we can use this when we know 2 sides and their enclosed angle to get the third side length.

Answer:

it is true.................

Answer: Your answer is TRUE

Step-by-step explanation:

There are 127 subsets of {1,2,3,4,5,6,7} that do not contain two consecutive integers, including the empty set.

Each number in the set {1,2,3,4,5,6,7} can either be included or not included in a subset.

So, the number of subsets of this set is:

However, we need to exclude the subsets that contain two consecutive numbers, such as {2,3} or {5,6}. This can be achieved by considering each number as the starting point of a subset and appending it with a number of non-consecutive numbers that can follow.

For example, if 1 is the starting point, the next numbers can only be 3, 4, 5, 6, or 7. Hence, the number of subsets starting from 1 is 5.

By repeating this process for each number in the set, we obtain a total of 5555551 = 127 subsets.

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Answer:

QR = 15

Step-by-step explanation:

The product of the length of the secant segment and its external part equals the square of the length of the tangent segment.

(QR+5) *5 = 10^2

(QR+5) *5 = 100

Divide each side by 5.

(QR+5) *5/5 = 100/5

(QR+5)  = 20

Subtract 5 from each side.

QR = 20-5

QR = 15

Answer:

a)  0.356

b)  1.1397

Step-by-step explanation:

a) log₇2

b) log₇ (¹⁴⁷/₁₆)

          log (7)

43% of elementary students chose something other than blue, red, or yellow as their favorite color.

Blue: 24%

Red: 17%

Yellow: 16%

Total: 24% + 17% + 16% = 57%

Percentage chose something other:

100% - 57% = 43%.

Therefore, 43% of elementary students chose something other than blue, red, or yellow as their favorite color.

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Answer:

( 3,1)

Step-by-step explanation:

To rotate the point (-1, 3) 90 degrees clockwise around the origin, we can use the following formula:

(x', y') = (y, -x)

where (x, y) are the coordinates of the original point, and (x', y') are the coordinates of the rotated point.

So, for the point (-1, 3), we have:

x = -1

y = 3

Using the formula, we get:

x' = 3

y' = -(-1) = 1

Therefore, the coordinates of the point after rotation are (3, 1).

To graph this point, we can plot it on the coordinate plane. The point (3, 1) is located 3 units to the right of the origin and 1 unit above the origin.

The graph of the point (-1, 3) and its image (3, 1) after rotation 90 degrees clockwise around the origin is shown below:

     |

     |   (3, 1)

     |

     |

------O------  

     |

     |

     |

     |   (-1, 3)

Answer: x ≤ -4

Step-by-step explanation: The explination  will be placed in the comment area :)

Answer:

Step-by-step explanation:

\(-5-3x \geq 2(10+2x)+3\\\)

Expand

\(2\left(10+2x\right)+3:\quad 4x+23\\\\-5-3x\ge \:4x+23\\\\\mathrm{Add\:}5\mathrm{\:to\:both\:sides}\\-5-3x+5\ge \:4x+23+5\\\\Simplify\\-3x\ge \:4x+28\\\\\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}\\-3x-4x\ge \:4x+28-4x\\\\Simplify\\-7x\ge \:28\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\left(-7x\right)\left(-1\right)\le \:28\left(-1\right)\\\\Simplify\\7x\le \:-28\\\\\mathrm{Divide\:both\:sides\:by\:}7\\\frac{7x}{7}\le \frac{-28}{7}\)

\(Simplify\\x\le \:-4\)

Answer:

(y-1)

Step-by-step explanation:

lets take the expression

1st expression: y²-11y+10

y²-10y-y+10

y(y-10)-1(y-10)

(y-10)(y-1)

2nd expression:y²+9y-10

y²+10y-y-10

y(y+10)-1(y+10)

(y+10)(y-1)

3rd expression:y²-1

(y-1)(y+1)

*HCF=(y-1)

*LCM=(y-1)(y+1)(y-10)(y+10)

(y²-1)(y²-10²)

True. The equation Ax = 0 gives an explicit description of its solution set.

When A is a matrix and x is a vector, the equation Ax = 0 represents a homogeneous system of linear equations. The solution set of this system consists of all vectors x that satisfy the equation and make the left-hand side equal to zero.

The explicit description of the solution set can be obtained by using techniques such as Gaussian elimination or matrix factorizations. These methods allow you to perform row operations on the augmented matrix [A | 0] to obtain the reduced row echelon form. The reduced row echelon form reveals the structure of the solution set by identifying pivot and free variables.

If there are no free variables (all columns of A are pivot columns), then the solution set consists of only the zero vector, x = 0. In this case, the solution set is a singleton set {0}.

If there are one or more free variables, you can express the solutions in terms of those variables. The free variables introduce parameters that allow for infinitely many solutions. The explicit description of the solution set will involve expressing the dependent variables (those corresponding to pivot columns) in terms of the free variables.

In summary, the equation Ax = 0 gives an explicit description of its solution set, either as the singleton set {0} or as a set of vectors expressed in terms of free variables.

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The surface area of the composite figure is 714 sq. in.

Let, a be the edge of the cube.

Then, surface area of the cube = 6a² square unit

Let, length of the cuboid = l unit

Width of the cuboid = w unit

Height of the cuboid = h unit

Then, surface area of the cuboid = 2(lw+lh+hw) square unit

Given, edge of cube = 4 in.

∴ Surface area of cube = (6×4²) sq. in. = 96 sq. in.

Now, given, length of cuboid = 15 in.

Width of the cuboid = 10 in. & height of the cuboid = 7 in.

∴ Surface area of the cuboid = 2{(15×10)+(15×7)+(10×7)} sq. in.

                                                = 2{150+105+70} sq. in.

                                                = 2{325} sq. in. = 650 sq. in.

Here, we have to find the surface area of the composite figure.

We have to subtract the surface area from both of cube & cuboid, where they are attached.In that case, we have to subtract (4×4) from both.

So, we have to subtract 2(4×4) sq. in. = 32 sq. in.

∴ The surface area of the composite figure = (650+96-32) sq. in.

                                                                        = 714 sq. in.

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The total cost of both meals including tip is 24.61, from the information provied.

Total cost (TC), in the field of economics, is the lowest possible cost in terms of money for producing a given output. This is the total economic cost of production, which is made up of two types of costs: fixed costs, which are independent of the quantity of a good produced and include costs such as buildings and machinery, as well as perhaps sunk costs, and variable costs, which vary depending on the amount of a good produced and include inputs such as labour and raw materials.

Every factor of production has a total cost that, depending on whether it has fixed costs or variable costs, includes the total opportunity cost (benefits from the next-best alternative) of each factor.

Marginal cost is the added sum of the costs resulting from adding one more unit of production.

Based on the said conditions, formulate 21.4 × {15%+1}

= 21.4 × {0.15+1}

= 21.4 × 1.15

= 24.61

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The value of f(-3) for the function f(a)  = -2a² - 5a + 4 is 1.

Function relates input and outputs. The outputs are called the ranges of dependent variables while the input are called domain or independent variables.

Therefore,

f(a)  = -2a² - 5a + 4

Hence,

f(-3) = -2(-3)² - 5(-3) + 4

Therefore,

f(-3) = -18 + 15 + 4

f(-3) = -3 + 4

f(-3) = 1

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To calculate the probability that at least two people in a class of 30 share the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to one minus the probability of the event not happening.

If we assume that birthdays are uniformly distributed throughout the year (i.e., each day is equally likely to be someone's birthday), then the probability that no two people in the class share the same birthday is:

365/365 * 364/365 * 363/365 * ... * 336/365

This is because the first person can have any birthday (probability of 365/365), the second person must have a different birthday (probability of 364/365), the third person must have a different birthday than the first two (probability of 363/365), and so on, up to the 30th person, who must have a different birthday than the first 29 (probability of 336/365).

Calculating this probability gives us:

(365/365) * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937

So the probability that no two people in the class share the same birthday is approximately 0.2937.

Using the complement rule, the probability that at least two people in the class share the same birthday is:

1 - 0.2937 = 0.7063

Therefore, the probability that at least two people in a class of 30 share the same birthday is approximately 0.7063, or 70.63%.

This law can be used to find the unknown side of a triangle given the ratio of two sides and the angle opposite one of them.

A polygon is a closed two-dimensional figure that has three or more straight sides. A polygon method is a method of determining an unknown angle or side in a triangle using trigonometric ratios. The cosine law, also known as the Law of Cosines, is used to determine the side lengths or angle measures in any triangle. It relates the length of each side of a triangle to the cosine of one of its angles. The law of cosines states that

`a² = b² + c² − 2bc cos A` or

`b² = a² + c² − 2ac cos B` or

`c² = a² + b² − 2ab cos C`

where a, b, and c are the side lengths of the triangle, and A, B, and C are the angles opposite those sides.

In essence, this law is used to solve a triangle given one side and two angles, two sides and an included angle, or three sides. On the other hand, the sine law, also known as the Law of Sines, is used to solve triangles in which you know the ratio of the lengths of two sides and the measure of the angle opposite one of those sides.

The sine law states that `a/sin A = b/sin B = c/sin C`

where a, b, and c are the side lengths of the triangle, and A, B, and C are the angles opposite those sides.

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The game described has multiple Nash equilibria.

In this game, each daughter has to choose an integer number of dollars between 1 and 50, and their goal is to maximize their own payoff. The total amount of money they can receive is limited to 51 dollars. If the total amount asked for exceeds 51, both daughters get nothing.

The Nash equilibria in this game occur when neither daughter can increase their payoff by unilaterally deviating from their chosen strategy. In other words, if both daughters have made their choices and neither has an incentive to change their choice, then it is a Nash equilibrium.

The number of Nash equilibria in this game depends on the choices made by the daughters. Since they do not coordinate and only care about their own payoffs, there can be multiple combinations of choices that result in Nash equilibria.

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A rational equation is defined as the quotient of two polynomials, with the denominator not being zero. It is a type of algebraic expression that involves variables and rational functions with rational exponents.

The error in the given rational equation is that it's not allowed to cancel out the x-2 and X+2 terms, as they are in the denominators. It is because of the fact that it may make the denominator zero, which would result in undefined expressions. Therefore, we need to find the least common multiple (LCM) of the denominators and then convert the equation into equivalent forms with the same denominator.B):

Correction of the error1-2/x-2 = x+1/X+2Given rational equation can be re-written as:((1 - 2)/(x - 2)) = ((x + 1)/(X + 2))The LCM of x - 2 and X + 2 is (x - 2) (X + 2).Multiplying the numerator and denominator of the left side by (X + 2) and the numerator and denominator of the right side by (x - 2) we get,(1 - 2)(X + 2) = (x + 1) (x - 2)Now simplify the equation:2X - 3x = -3The given rational equation becomes 2X - 3x = -3 after correction.Note: You should always double-check if the obtained solution satisfies the initial equation.

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When two consecutive whole numbers are randomly selected, the probability that one of them is a multiple of 4 is 1/2.

To find the probability that one of the two consecutive whole numbers selected is a multiple of 4, follow these steps:
Identify the pattern of multiples of 4.
Multiples of 4 follow this pattern: 4, 8, 12, 16, and so on.
Observe the consecutive whole numbers that include a multiple of 4.
When selecting two consecutive whole numbers, they will be in one of the following forms:
a) (Multiple of 4) and (Multiple of 4 + 1)
b) (Multiple of 4 - 1) and (Multiple of 4)
Determine the probability of each form.
a) For every 4 consecutive whole numbers, there is one pair of the form (Multiple of 4) and (Multiple of 4 + 1). Thus, the probability of this form is 1/4.
b) Similarly, for every 4 consecutive whole numbers, there is one pair of the form (Multiple of 4 - 1) and (Multiple of 4). The probability of this form is also 1/4.
Calculate the total probability.
The total probability is the sum of the probabilities of both forms:
Total Probability = (Probability of form a) + (Probability of form b)
Total Probability = (1/4) + (1/4) = 2/4
Simplify the fraction.
The total probability can be simplified to 1/2.
So, when two consecutive whole numbers are randomly selected, the probability that one of them is a multiple of 4 is 1/2.

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The interpretation of the 1001 measurements in the third set of data vary due to reasons are as follow,

Measurement error, Random variation and Sampling error.

Measurement error: The measurand being measured may have inherent variability, but measurement error can also contribute to variation in the data set.

Random variation: Even if the same measurand is being measured under the same conditions, there may be random fluctuations in the system or the environment that can cause variation in the data.

Sampling error: If the 11 measurements were not taken at random from the population of interest, then the variation could be due to sampling error.

For the 1001 measurements in the second and third data sets, some possible explanations for the variation could be measurement error, systematic variation, changes in the measurand and Sampling error.

Thus, variation in data can have many different causes, and it is important to carefully consider the context and specific factors that may be contributing to the variation when interpreting the results.

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The most important factor economists study when measuring a country's development is A. Gross Domestic Product (GDP).

Gross Domestic Product is a widely used economic indicator that measures the total value of all goods and services produced within a country's borders over a specific time period, usually a year. It represents the economic output and productivity of a nation.

GDP is considered a crucial measure of a country's development because it reflects the overall economic activity and the standard of living within a nation. A higher GDP generally indicates a larger economy, more production, higher income levels, and potentially greater access to goods and services.

While factors such as crime rate, literacy rate, and life expectancy are important in assessing the overall well-being and development of a country, GDP is often seen as a primary indicator of economic development. It provides insights into a nation's economic growth, investment potential, income distribution, and overall economic health, which are crucial for understanding and comparing the development levels of different countries.

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The minimum that could be earned is $150. The required inequalities are solved below:

What is an inequality?

An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line. There are multiple notations used to denote various types of inequalities: The symbol a b indicates that an is smaller than b. The symbol a > b indicates that an is more than b. In either scenario, a and b are not equal. These are characterized as stringent inequalities because an is either strictly less than or strictly bigger than b. Equivalence is not allowed.

(a) The minimum that could be earned is $150.

(b) The required inequality is given as 150+20x≥630

or, 20x≥630-150

or, x≥480/20

or, x≥24

(c) The required inequality is given as 150+20x≥750

or, 20x≥750-150

or, x≥600/20

or, x≥30

(d) The required inequality is given as 150+20x≤950

or, 20x≤950-150

or, x≤800/20

or, x≤40

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Answer:

its A

Step-by-step explanation:

on edge

In the word problem , the number of students in each group is 16.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here Number of student in first class = 21

Number of students in second class = 25

Number of students in third class = 18

Total number of students = 21+25+18 = 64

Now the group is split into 4. Then number of students in each group is,

=> 64 / 4 = 16

Hence the number of students in each group is 16.

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the new value of the house is $225,500. we can solve this by  substituting the given information into the equation from part (a)

what is equation ?

An equation is a mathematical statement that uses an equal sign to show that two expressions have the same value. Equations are used to represent a wide range of relationships between variables

In the given question,

(a) To write the new value in terms of the old value, we can use the fact that the value decreased by 18%, which means that the new value is equal to 100% - 18% = 82% of the old value. So, we can write:

New value = 0.82 x Old value

(b) To determine the new value, we can substitute the given information into the equation from part (a):

New value = 0.82 x 275,000

New value = 225,500

Therefore, the new value of the house is $225,500.

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The  statement about probability that is true is option The probability of landing on orange is equal to the probability of landing on yellow.

From the  question, the spinner has:

8 sections, with:

So probability of one getting on any section is  = 1/8, or 0.125.

Therefore, the  probability of getting on orange will still be the same as the probability of landing on yellow and as such option C is correct.

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Answer:

\(a=12\)

Step-by-step explanation:

Work backwards with synthetic division with remainder 0 and then solve for a:

-3 | 2 a 19 3

_________

      2       | 0

-3 | 2 a 19 3

_______ -3

      2      | 0

-3 | 2 a 19 3

_______ -3

      2    1 | 0

-3 | 2 a 19 3

_____-18 -3

     2     1 | 0

-3 | 2 a 19 3

_____ -18 -3

     2  6  1 | 0

-3 | 2 a 19 3

_____ -18 -3

     2  6  1 | 0

-3 | 2 a 19 3

____-6 -18 -3

     2  6  1 | 0

a - 6 = 6

a = 12

To find the average value of a function f(x, y) over a rectangle R, we need to calculate the double integral of the function over the region R and divide it by the area of the rectangle.

The double integral represents the total value of the function over the region, and dividing it by the area gives the average value.

To find the average value of f(x, y) over the rectangle R = {(x, y) | a ≤ x ≤ b, c ≤ y ≤ d}, we start by calculating the double integral of f(x, y) over the region R. The double integral is denoted as ∬R f(x, y) dA, where dA represents the differential area element.

We integrate the function f(x, y) over the region R by iterated integration. We first integrate with respect to y from c to d, and then integrate the resulting expression with respect to x from a to b. This gives us the value of the double integral.

Next, we calculate the area of the rectangle R, which is given by the product of the lengths of its sides: (b - a) * (d - c).

Finally, we divide the value of the double integral by the area of the rectangle to obtain the average value of f(x, y) over the rectangle R. This is given by the expression (1 / area of R) * ∬R f(x, y) dA.

By following these steps, we can find the average value of f(x, y) over the rectangle R.

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