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Solve for x.

3.4>x+2/3

You have points R(2, 10) and S(6, - 8).

There two ways to construct a right triangle with RS being a hypotenuse.

Please see both ways reflected in the attached.

One triangle is RST and another one is RSU with red or blue legs.

When x = 10 the equations are equal and when x gets any value the two equations are equal.

What is equation ?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

The equals sign is a part of mathematical expressions known as equations. Often, algebra is used in equations. When a calculation requires an exact number but you don't know it, algebra is utilized.

When x = 10 the equation becomes

6x³ + 9x² + 4x + 7

6(10)³ + 9(10)² + 4(10) + 7

= 6000 + 900 + 40 + 7

= 6947

6x³ + 3x² + 6x² + 4x + 5 + 2

= 6x³ + 9x² + 4x + 7

= 6(10)³ + 9(10)² + 4(10) + 7

= 6000 + 900 + 40 + 7

= 6947

Both the equations are equal when x = 10

When x = -3/2 the equation becomes

6x³ + 9x² + 4x + 7

6(-3/2)³ + 9(-3/2)² + 4(-3/2) + 7

= -20.25 + 20.25 + 6 + 7

= 13

6x³ + 3x² + 6x² + 4x + 5 + 2

= 6x³ + 9x² + 4x + 7

= 6(-3/2)³ + 9(-3/2)² + 4(-3/2) + 7

= -20.25 + 20.25 + 6 + 7

= 13

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If the first two Gauss-Markov assumptions are met and heteroskedasticity exists in the error term, Var(ui|xi) = i2.

Examples. When there is a significant disparity in the magnitude of the observations, heteroscedasticity frequently develops. An old-fashioned illustration of heteroscedasticity is the relationship between income and food expenses. The variability of eating habits will rise as income does as well.

Because normal regression model (OLS) regression presumes that all royalties are taken from a population with constant variance, heteroscedasticity is a concern (homoscedasticity). The particles ought to have a standard deviation in order to meet the plugs and be capable of relying on the results.

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Answer:

see explanation

Step-by-step explanation:

- 1x + 4y = 12 , that is

- x + 4y = 12 ( add x to both sides )

4y = 12 + x ( divide each term by 4 )

y = 3 + [tex]\frac{1}{4}[/tex] x

Answer:

x = 4

Step-by-step explanation:

7x = 3x + 16

7x - 3x = 16

4x = 16

4/4 x = 16/4

x = 4

Answer:

a) 9/5

Step-by-step explanation:

Formula we use,

→ Slope (m) = (y2 - y1)/(x2 - x1)

Now required slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (-16 - 2)/(-10 - 0)

→ m = (-18)/(-10)

→ m = 18/10

→ [ m = 9/5 ]

Hence, the slope is 9/5.

Answer:

13 and 15

Step-by-step explanation:

We set up equations.

X=Y-2

2Y=3X-9

We change X=Y-2 into Y=X+2.

Substituting for Y, we get 2Y=2X+4=3X-9

We now solve for x.

2X+4=3X-9  |-2X

4=X-9  |+9

13=X.

X=13

Substituting for Y, we get that Y =15 from the equation Y=X+2.

So, X=13 and Y=15

a) The percentage of scores that are less than 19 is of: 34.09%.

b) The amount out of the 1500 scores that would be greater than 21 is of: 774.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of the scores in this problem are given as follows:

[tex]\mu = 21.2, \sigma = 5.4[/tex]

The proportion of scores that are less than 19 is the p-value of Z when X = 19, hence:

Z = (19 - 21.2)/5.4

Z = -0.41.

Z = -0.41 has a p-value of 0.3409.

Hence the percentage is of 34.09%.

The proportion of scores that are greater than 21 is one subtracted by the p-value of Z when X = 21, hence:

Z = (21 - 21.2)/5.4

Z = -0.04

Z = -0.04 has a p-value of 0.484.

1 - 0.484 = 0.516.

Hence the amount out of the 1500 scores is given as follows:

0.516 x 1500 = 774 scores.

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The required length of the third side should be less than the sum of the other two sides or less than 37 in.

As mentioned, Kelsey is welding 3 metal rods to make a triangle. If the lengths of two rods are 15 in. and 22in.,

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Let the length of the third side,
The property of the triangle states that the sum of the two sides of a triangle is always greater than the length of the third side.
So
x < 15 + 22
x < 37

Thus, the required length of the third side should be less than the sum of the other two sides or less than 37.

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The different combinations of 5 friends could possibly receive the tickets are 56.

What is combination?

A combination is a choice made from a set of distinct items in mathematics where the order of the choices is irrelevant.

The definition of a combination is "An arrangement of objects where the order in which the objects are chosen does not matter." A combination is a "selection of things" where the importance of the order of the things is negligible.

Given:

A group of 8 friends (5 girls and 3 boys) plans to watch a movie.

We have to find the different combinations of 5 friends could possibly receive the tickets.

Here there are total 8 friends.

We have to select 5 from 8 in 8C5 ways.

[tex]8_C_5 = \frac{8!}{5!*(8-5)!} \\8_C_5 = \frac{8!}{5!*3!} \\8_C_5 = \frac{6*7*8}{1*2*3}\\ 8_C_5 = 56[/tex]

Hence, the different combinations of 5 friends could possibly receive the tickets are 56.

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Answer:

<B, <C, <A

Step-by-step explanation:

The order from smallest to largest angle is the same as the order from shortest to longest opposite side.

Sides from shortest to longest:

120, 130, 180

Angles from smallest to largest:

<B, <C, <A

The cost of the five-minute call will be equal to $0.72.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Ron got a cell phone rate of C(a)=0.22+0.10a. The cost of a five-minute call will be calculated as,

Cost = 0.22+0.10a

Cost = 0.22 + ( 5 x 0.10 )

Cost = 0.22 + 0.50

Cost = $0.72

The five-minute call will cost $0.72.

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Answer:

The axis of symmetry of a parabola is the line that divides the parabola into two mirror images. This line always passes through the vertex of the parabola. For a parabola with an axis of symmetry at x = 5/12, the vertex of the parabola is at the point (5/12, 0).

The distance between the roots of a parabola is the distance between the x-coordinates of the two points where the parabola crosses the x-axis. In this case, the distance between the roots is 13/6.

To find the equation of the parabola, we can use the vertex form of the equation, which is given by y = a(x - h)^2 + k, where (h, k) is the coordinates of the vertex and a is a constant. In this case, the coordinates of the vertex are (5/12, 0) and the constant a can be determined using the distance between the roots.

To find a, we can use the fact that the distance between the roots of a parabola is equal to the square root of the product of the coefficients of the quadratic terms in the equation. In the vertex form, the coefficient of the x^2 term is a, so we can set up the following equation to find a:

(13/6)^2 = a * (5/12)^2

Solving for a, we find that a = -1/3.

Therefore, the equation of the parabola is y = -1/3(x - 5/12)^2.

In the unit rate between two units, the denominator is always one.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

Unit rate is written in a fraction form where the denominator is always one.

Example:

6 miles in 3 minutes.

This can be written as,

6 miles = 3 minutes

Dividing 3 on both sides.

2 miles = 1 minute

= 2 miles per minute

Thus,

In the unit rate between two units, the denominator is always one.

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The number of times that the actual flag is wider than the Reagan's model would be = 3 times.

A rectangle is defined as a type of quadrilateral that has opposite sides that are parallel and equal to each other and all four angles are right angles.

The actual length of the rectangular flag = 39 inches long.

The length of Reagan's model = 13 inches.

To find the number of times wider than the actual flag the model is, use the formula:

= Length of actual flag / Length of model

= 39/13 = 3.

Therefore, the number of times that the actual flag is wider than the Reagan's model is 3 times.

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Answer:

36

Step-by-step explanation:

Answer:10x+2y=38, where x is the dollar cost of cinnamon and y the dollar cost of the spice.1

6x+8y=80multiply the top by -4-40x-8y=-15216x+8y=80.

Add them and y is eliminated.-24x=-72

Step-by-step explanation:

Answer: 7/8

Step-by-step explanation:

n represents the number of friends, there must have been 2 friends with Matthew at the concert.

What is the arithmetic operation?

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

Let's call the number of friends n. The cost of the car service for the friends is 75 - 25 = 50 dollars. Since this cost is divided equally among the friends, each friend pays 50/n dollars.

The total cost for each friend, including the cost of the car service and the cost of dinner, is 25 dollars. Therefore, the cost of dinner for each friend is 25 - 50/n dollars.

Since the cost of dinner was divided equally among the friends, each friend paid 60/n dollars for dinner. Therefore, 25 - 50/n = 60/n.

Solving this equation for n, we get:

25 - 50/n = 60/n

50/n - 60/n = -25

10/n = 25

n = 2.5

Hence, n represents the number of friends, there must have been 2 friends with Matthew at the concert.

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Answer:

To find three integer or decimal solutions to the equation 5x + 4y = 20, we can first divide both sides of the equation by the GCF of the coefficients, which is 1. This gives us the equation 5x + 4y = 20/1, which can be rewritten as 5x + 4y = 20. We can then use the substitution method to solve for x in terms of y, by setting 4y = 20 - 5x and solving for x. This gives us x = (20 - 4y) / 5. Substituting this expression for x into the original equation, we get 5((20 - 4y) / 5) + 4y = 20, which simplifies to 20 - 4y + 4y = 20, or 20 = 20. This means that any value of y that satisfies the equation will also satisfy the original equation.

For example, if we choose y = 3, then x = (20 - 4 * 3) / 5 = 2, and the solution (x, y) = (2, 3) satisfies the equation 5x + 4y = 20. Similarly, if we choose y = 0, then x = (20 - 4 * 0) / 5 = 4, and the solution (x, y) = (4, 0) satisfies the equation. Finally, if we choose y = -1, then x = (20 - 4 * -1) / 5 = 5, and the solution (x, y) = (5, -1) satisfies the equation.

The solution set for the equation 5x + 4y = 20 is the set of all ordered pairs (x, y) that satisfy the equation. The three solutions we found are (2, 3), (4, 0), and (5, -1), and these solutions can be plotted on a coordinate grid to show the solution set. The graph of the solution set is a line that passes through the points (2, 3), (4, 0), and (5, -1).

Step-by-step explanation:

After 2 hours, Zoe and Wanda will complete the same total number of shirts.

Each tailor will finish 18 shirts.

What is linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given that,

Zoe can embroider 2 shirts per hour, and Wanda can get through 6 shirts per hour. Zoe has already completed 14 shirts, and Wanda has completed 6 shirts.

Assume that after x hours they have finished the same total number of shirts.

The number of shirts that Zoe finished is

Z(x) = 14 + 2x ....(i)

The number of shirts that Wanda finished is

W(x) = 6 + 6x ...(ii)

When they make same number of shirts, then Z(x) = W(x)

14 + 2x = 6 + 6x

6 + 6x = 14 + 2x

Subtract 2x from both sides:

6x - 2x = 14 - 6

4x = 8

Divide both sides by 4

x = 8/4

x = 2.

Putting x = 2 in Z(x) = 14 + 2x:

Z(2) = 14 + (2×2)

Z(2) = 18

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The value of the numbers 'x' and 'y' will be 6 and 17, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

One number is 5 more than twice another and their sum is 23.

Let the two numbers be 'x' and 'y'. Then the equations are given as,

y = 2x + 5            ...1

x + y = 23           ...2

From equations 1 and 2, then we have

x + 2x + 5 = 23

3x + 5 = 23

3x = 23 - 5

3x = 18

x = 6

Then the value of the variable 'y' will be given as,

6 + y = 23

y = 23 - 6

y = 17

The value of the numbers 'x' and 'y' will be 6 and 17, respectively.

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Answer: S wanted points I

Step-by-step explanation:

Answer:

y = 1/2x² - 2x - 6

Answer:

See below.

Step-by-step explanation:

The given functions f(x) and g(x) are linear functions.  Therefore, their inverses are a reflection about the line y = x.

The mapping rule for reflecting a point about the line y = x is:

To determine if f(x) and g(x) are inverses of each other:

If the y-value of one function equals the x-value of the other function (and the x-value of one function equals the y-value of the other function), the functions are inverses of each other.

Given functions:

[tex]\begin{cases}f(x) = 2x+5\\\\g(x)=\dfrac{x-5}{2} \end{cases}[/tex]

Ordered pair: (2, 9)

Substitute x = 2 into f(x):

[tex]\implies f(2)=2(2)+5=9[/tex]

Substitute x = 9 into g(x):

[tex]\implies g(9)=\dfrac{9-5}{2}=2[/tex]

Therefore, the functions are inverses of each other since the x-value of function f equals the y-value of function g, and the y-value of function f equals the x-value of function g.

The inequality that describes the base length of the triangle is b ≤ 28/h

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

The area of a triangle can be calculated using the following formula

Area = 1/2 * Base * Height

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

Area = 1/2 * b * h

Evaluate the products

Area = 1/2bh

Recall that

Area = At most 14 square feet

This means that

Area ≤ 14

So, we have

1/2bh ≤ 14

Multiply through by 2

bh ≤ 28

Divide both sides by h

b ≤ 28/h

Hence, the inequality is b ≤ 28/h

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The differentiation of the given function x² + xy + y² + 1 = 0 will be 2x + y + dy/dx(x + 2y) = 0.

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time.

As per the given,

x² + xy + y² + 1 = 0

Take the first derivative on both sides with respect to x as,

d/dx(x² + xy + y² + 1) = d/dx(0)

2x + xdy/dx + ydx/dx + 2ydy/dx + 0 = 0

2x + x(dy/dx) + y + 2y (dy/dx) = 0

2x + y + dy/dx(x + 2y) = 0

Hence "The provided function x2 + xy + y2 + 1 = 0 will be differentiated as 2x + y + dy/dx(x + 2y) = 0.".

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Answer:yes

Step-by-step explanation: