The lines 2x-4y=4 and y=2x-3 are
A.
B.
C.
Parallel
Perpendicular
Neither

Step-by-step explanation:

\(length \: between \: ( - 2, - 1) \: and \: (6,4) \\ = \sqrt{(x _{1} - x _{2} )² + (y _{1} - y _{2})² } \\ = \sqrt{( - 2 - 6)²+ ( - 1 - 4)²} \\ = \sqrt{64 + 25} \\ = \sqrt{100} \\ = 10 \: units \\ radius = 10 \: units \\ diameter = 2 \times radius \\ d = 2 \times 10 \\ d = 20 \: units\)

Answer:

The lengths ( in feet ) of two sides of a regular quadrilateral are represented by th expresion

8x-6 and 4x+22 . find the length of a side of the quadrilateral

Answer by Alan3354(67447) (Show Source): You can put this solution on YOUR website!

A regular quadrilateral is a square, so

8x-6 = 4x + 22

Can you finish it?

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The length of a side of the quadrilateral is 38 feet.

Given that, The lengths (in feet) of two sides of a regular quadrilateral are represented by the expressions 8x + 6 and 4x + 22.

We need to find the length of a side of the quadrilateral.

The regular quadrilateral is a 4-sided polygon which is equiangular and equilateral. Square is a quadrilateral with all the sides equal and all angles equal to 90°. Hence, the square is a regular quadrilateral.

Now, 8x+6=4x+22

⇒8x-4x=22-6

⇒4x=16

⇒x=4

Then, 8x+6=38 feet and 4x+22=38 feet

Therefore, the length of a side of the quadrilateral is 38 feet.

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Answer:

Jsuusdi

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

The least amount of money he could pay for the conditions that he will for the given information is = £ 3053.4

What about least amount?

In mathematics, the term "least amount" is not commonly used. However, a similar term that is often used is "minimum".

The minimum value of a set of numbers or a function is the smallest value within that set or function. For example, if we have the set of numbers {2, 5, 7, 8, 10}, the minimum value is 2.

Similarly, in the context of optimization problems, we often seek to find the minimum value of a function to achieve the best possible outcome. This can involve finding the minimum value of a cost function in order to minimize the cost of a process, or finding the minimum value of a profit function to maximize the profit of a business.

According to the given information:

Set the number of party bags pack as x , toy pack as y

Since, 105 party bags in a pack , £1.32

84 toys in a pack £4.15.

Hence, 105x = 84y , cost = 105x × 1.32x + 84y × 4.15 = 763.35x

Find the least common multiple

Hence, 84 × 5 = 420 , 105 × 4 = 420

x  =4

y =5

least cost = 105 × 1.32 × 4 + 84×4.15 ×5

= £3053.4

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The net outward flux across the boundary of the tetrahedron is: 5, using the concept of gradient of function.

The gradient of a function is related to a vector field and it is derived by using the vector operator ∇ to the scalar function f(x, y, z).

Given vector field:

F = ( -x, 3y, 2 z )

Δ . F = (i δ/δx + j δ/δy + k δ/δz) (-x, 3y, 2 z )

Δ . F = [δ/δx(-x)] + δ/δy (3y) + δ/δz (2z)]

Δ . F = - 1 + 3 + 2

Δ . F = 4

According to divergence theorem;

Flux =  ∫∫∫ Δ . (F) dv

x+y+z = 1; so, 1st octant

∫₀¹∫₀¹⁻ˣ∫₀¹⁻ˣ⁻y (4) dz dy dx

= 4 ∫₀¹∫₀¹⁻ˣ (1 - x - y) dy dx

= 5

Therefore, we can conclude that the net outward flux across the boundary of the tetrahedron is: 5

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Answer:

The answer for this question is (-3.5,0.5)

The probability of a random patient being alcoholic with elevated cholesterol levels is 55/80, or 0.6875. The probability of a random patient being nonalcoholic is 320/400, or 0.8. Lastly, the probability of a random patient being nonalcoholic with Non elevated cholesterol levels is 248/400, or 0.62.

To calculate the probability of a random patient being alcoholic with elevated cholesterol levels, we must first determine the total number of patients with elevated cholesterol levels. This can be done by adding the number of alcoholic patients (55) with elevated cholesterol levels to the number of nonalcoholic patients (72) with elevated cholesterol levels.

The result is a total of 127 patients with elevated cholesterol levels. This means that out of 400 patients, 55 of them were alcoholic and had elevated cholesterol levels. Therefore, the probability of a random patient being alcoholic with elevated cholesterol levels is 55/400, or 0.6875.

The probability of a random patient being nonalcoholic is equal to the total number of nonalcoholic patients (320) divided by the total number of patients (400). This yields a probability of 0.8.

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Answer: The solutions of the absolute value equation are given by:

x = -41 and x = 49.

What is the absolute value function?

The absolute value function is defined by:

|x| = x, x >= 0.

|x| = -x, x < 0.

The absolute value function measures the distance of a point x to the origin, that is, the distance to x = 0. From this, we get that |x| = a can mean either that:

x = a, or;

x = -a.

In this problem, the equation is given by:

Hence:

0.2|x - 4| = 9

|x - 4| = 45

The first possible solution is:

x - 4 = 45

x = 49.

The second possible solution is:

-x + 4 = 45

-x = 41

x = -41.

Hence the solutions are x = -41 and x = 49.

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Step-by-step explanation:

(a) Yes, we can. We could work for two hours, study for five hours, and play sports/do workout for three hours.

(b) Yes, we can. We could play sports/do workout for five hours, study for three hours, and take a break for two hours.

(a) Yes, we can find a way to schedule the ten hours in order to achieve the goal of +1 happiness, +24 short-term benefit, and +15 long-term benefit. We can do this by working for two hours, studying for five hours, and playing sports/doing workout for three hours. Working for two hours would give us -4 happiness, +10 short-term benefit, and +2 long-term benefit. Studying for five hours would give us +5 happiness, +20 short-term benefit, and +4 long-term benefit. Playing sports/doing workout for three hours would give us +3 happiness, -6 short-term benefit, and +9 long-term benefit. This would give us a total happiness of +1, +24 short-term benefit, and +15 long-term benefit, which meets our goal.

(b) Similarly, we can find a way to schedule the ten hours in order to achieve the goal of +13 happiness, +8 short-term benefit, and +19 long-term benefit. We can do this by playing sports/doing workout for five hours, studying for three hours, and taking a break for two hours. Playing sports/doing workout for five hours would give us +5 happiness, -5 short-term benefit, and +15 long-term benefit. Studying for three hours would give us +15 happiness, +12 short-term benefit, and +3 long-term benefit. Taking a break for two hours would give us +2 happiness, -2 short-term benefit, and +1 long-term benefit. This would give us a total happiness of +13, +8 short-term benefit, and +19 long-term benefit, which meets our goal.

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Answer:

11

Step-by-step explaination

Start by subtracting 4-2 and you get 2

Then add 2+3 to get 5

Add 5+6 and get 11

4-2+3+6

4-2=2

2+3+6

5+6

11

Answer:

That formula is used to find the area of Trapezoids, so it would be "B"

The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.

The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.

For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).

The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).

To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.

The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

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Answer:

Step-by-step explanation:

Find the value of y when x = 2 or x = -2 to determine the system

It is easy to calculate and confirm the correct equations

See the attached to verify the answer

Check option C

Put (2,12)

And

Put(-2,12)

Hence verified

Option C is correct

The final two equations which represent the given situation are:

2x - y = -6 and 3x - y = -5.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a linear equation of two variables.

Suppose,

The larger number is 'y' and the smaller number is 'x'.

First relation,

'y' is equal to twice the sum of a smaller number (x) and 3. So we represent this as:

y = 2(x+3)

y = 2x + 6

2x - y = -6                     ............(1)

Second relation,

The larger number (y) is equal to 5 more than 3 times the smaller number (x). So we represent this as:

y = 5 + 3x

3x - y = -5                     .............(2)

Hence, the final two equations which represent the given situation are:

2x - y = -6 and 3x - y = -5.

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Answer:

Step-by-step explanation:

Abby can make 26 tie-dyed T-shirts.

We can start by setting up a linear equation to represent the total cost of making the tie-dyed T-shirts.

What is a linear equation?

First-order equations include linear equations. In the coordinate system, linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., just one variable).

Multiple variables may be present in a linear equation. Linear equations with two variables, for example, are used when a linear equation contains two variables.

Let x be the number of T-shirts Abby makes

The cost for each T-shirt is $3.95 + $0.50 = $4.45

The cost of the two boxes of salt is $4.50 * 2 = $9

So the total cost for x T-shirts is $4.45x + $9

We know that the total cost is 124.70 and we want to find the value of x, so we can set up the equation as:

$4.45x + $9 = 124.70

Solving for x:

$4.45x = 115.70

x = 115.70 / 4.45

x = 26

Therefore, Abby can make 26 tie-dyed T-shirts.

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Triangle b is a obtuse triangle.

A closed triangle has three vertices, three sides, and three angles. The symbol for a triangle with the three vertices P, Q, and R is PQR. Sandwiches and signboards in the shape of triangles are the most prevalent triangle-shaped objects.

A triangle has an obtuse angle if one of the inner angles is greater than 90 degrees. In an obtuse triangle, if one angle is greater than 90°, the total of the other two angles is also less than 90°.

As the triangle B have one interior angle as 126 degree which is greater than 90

so it follows the property of obtuse triangle

Hence, triangle b is a obtuse triangle.

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The couple's success can be attributed to aggressive saving, early mortgage repayment, budgeting, and strategic investments. They likely had high incomes, practiced disciplined saving, and diversified their investments for long-term growth. These strategies allowed them to pay off their mortgage quickly and accumulate substantial wealth.

The couple's achievement of paying off their mortgage and building substantial wealth in a relatively short period of time can be attributed to several savings and investment strategies. Here are some possible strategies they might have employed:

1. Aggressive Saving: The couple likely had a disciplined approach to saving money. They may have set aside a significant portion of their income towards savings and lived within their means, avoiding unnecessary expenses.

2. High Income: It's possible that the couple had high-paying jobs or multiple income streams, allowing them to save and invest more aggressively. A higher income provides more opportunities for saving and investing larger amounts.

3. Budgeting and Expense Management: The couple may have created a comprehensive budget to track their income and expenses. By closely monitoring their spending and identifying areas where they could cut back, they were able to allocate more funds towards their mortgage payment and investments.

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Answer:

The factors that multiply to equal

x^2  - 13x  + 42 = 0

is

(x-6)(x-7) = 0

So,

(x-6) = 0

x = 6

(x-7) = 0

x = 7

6, and 7, are the solutions. They are asking for PRODUCT of the solutions, which means to multiply.

So, 6 times 7 = 42.

The answer is 42

An IT company would like to investigate how a software developer's work experience, the dependent variable in the regression model described in the scenario is Work Performance.

In regression analysis, the dependent variable is the variable that is being predicted or explained by the independent variables. It is the outcome or response variable that is influenced by the independent variables. In this case, the CIO of the IT company wants to investigate how various factors contribute to the work performance of software developers.

The independent variables in this scenario are the software developer's work experience (in number of years), professional certifications (number of certificates), and knowledge of various computer languages (number of programming languages). These variables are used to explain or predict the work performance of the software developers.

Therefore, the dependent variable in this regression model is the Work Performance of the software developers. The CIO is interested in understanding how the independent variables, such as work experience, professional certifications, and knowledge of computer languages, affect the work performance of the developers.

By analyzing the data and performing the regression analysis, the CIO can determine the relationship and significance of these independent variables on the dependent variable, i.e., the impact of work experience, professional certifications, and knowledge of computer languages on the work performance of the software developers.

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The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.

To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.

(a) For A = 1, B = 0, and C = 1:

X = 1.¯¯¯¯¯¯01

To find the complement of BC, we replace B = 0 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001

(b) For A = B = C = 1:

X = 1.¯¯¯¯¯¯11

Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111

(c) For A = B = C = 0:

X = 0.¯¯¯¯¯¯00

Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:

X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000

In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.

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Answer:

I would divide the numerator and denominator by 2 to get it's simplest

Answer:

8

Step-by-step explanation:

To make 16/24 the simplest form you can find the GCF (greatest common factor) of 16 and 24:

16:

1 x 16

2 x 8

4 x 4

24:

1 x 24

2 x 12

3 x 8

4 x 6

They both have a factor of 8 in common, so 8 is your GCF

Divide the numerator and denominator by the greatest common factor (GCF) to get the most simplified fraction.

16 / 8 = 2

24 / 8 = 3

2/3 is the simplest form of 16/24

To increase by two times means also get double.

When something increases by two times, it means that it has multiplied by two or doubled in value. For example, if a person's salary increases by two times, it means that their salary has doubled.

Similarly, if the price of a product increases by two times, it means that the price has doubled.

It is important to note that "increase by two times" is not the same as "increase to two times". If something increases to two times its original value, it means that the new value is twice the original value.

For example, if the original value was 10 and it increased to two times its original value, the new value would be 20.

In mathematical terms, increasing by two times can be expressed as multiplying by a factor of 2, while increasing to two times can be expressed as multiplying by a factor of 2 or adding the original value to itself.

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Answer:

I believe (D)

Step-by-step explanation:

-5x + 7 = -13

-7 -7

-5x = -20

-5/-5 -20÷-5

x=4

Answer:

D.) x = 4

Step-by-step explanation:

-5x + 7 = -13

-5x + 7 (-7) = -13 (-7)

-5x = -20

-5x (-1/5) = -20 (-1/5)

x = 4

Answer:

Using distribute property

0.5(8a)(a) + 0.5(6b)(a) + 4b

4a^2 + 3ab + 4b

Step-by-step explanation:

Answer:

4a+3ab +4b

Step-by-step explanation:

0.5(8a+6b) a +4b

4a +3b*a +4b

4a+3ab +4b

the joint probability distribution for x and y is as follows:

f(x, y): x=0, y=0: 1/9

x=0, y=1: 2/9

x=1, y=0: 2/9

x=1, y=1: 4/9

Based on the given information, we can determine the marginal probability distributions for x and y:

For x:

f(x=0) = 1/3

f(x=1) = 2/3

For y, since it is independent of x, the probabilities remain the same:

f(y=0) = 1/3

f(y=1) = 2/3

To find the joint probability distribution, we multiply the probabilities for x and y since they are independent:

f(x=0, y=0) = f(x=0) * f(y=0) = (1/3) * (1/3) = 1/9

f(x=0, y=1) = f(x=0) * f(y=1) = (1/3) * (2/3) = 2/9

f(x=1, y=0) = f(x=1) * f(y=0) = (2/3) * (1/3) = 2/9

f(x=1, y=1) = f(x=1) * f(y=1) = (2/3) * (2/3) = 4/9

Therefore, the joint probability distribution for x and y is as follows:

f(x, y):

x=0, y=0: 1/9

x=0, y=1: 2/9

x=1, y=0: 2/9

x=1, y=1: 4/9

This represents the probabilities for each possible combination of x and y.

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Answer:

Piecewise

Step-by-step explanation:

For a piecewise function, the domain is broken into pieces, with a different rule defining the function for each piece.

Piecewise functions are usually a function that equals two or more equations depending on the x or the domain.

Google piecewise functions to see examples.

I hope this helps!

Answer: Piecewise

Step-by-step explanation:

There will be breaks and jumps in the curve, particularly when a value would undefined. So the solution curve looks like disconnected pieces.

ANSWER

EXPLANATION

For the first cylinder;

Recall, the formula for calculating the surface area of a cylinder is;

Now, substitute the values for the first cylinder;

The volume of the first cylinder is calculated using the formula;

Substitute the values of r and h for the first cylinder;

To get the surface area of the second cylinder, we need to calculate the height (h).

To get the height, we use the volume of the first cylinder to get the height of the second (since they have the same volume).

Hence;

Substitute the height to calculate the surface area is calculated thus;

Answer:

x = 5/3

Step-by-step explanation:

-3x+5

-5= -3x

-5/-3 = 5/3