g(x) = {-2x+1, x <3
(-x+3, X23
What is g(2) ?

Answer:

x = 6.5

Step-by-step explanation:

The image below shows that the equation y = 2x - 2 (which has a slope of 2) passes the the points (3, 4) and (6.5, 11); when x = 6.5

Hope this helps! :)

Answer:

\(y = 2x - 2 \\ y = mx + c\)

When the point is (3,4) and slope=2

\(4 = 2 \times 3 + c \\ 4 = 6 + c \\ \boxed{c = - 2}\)

Now, when the point is (x,11) and slope=2

\(11 = 2x - 2 \\ 2x = 13 \\ x =\frac{13}{2} \\ \boxed{x = 6.5 }\)

An equation in slope-intercept form for the perpendicular bisector of the line segment with endpoints (-1, -8) and K (5, 4) is y = 2x - 6.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 + 8)/(5 + 1)

Slope (m) = 12/6

Slope (m) = 2.

At data point (-1, -8) and a slope of 2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-8) = 2(x - (-1))

y + 8 = 2x + 2

y = 2x - 6.

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The equation of the ellipse in standard form with center at the origin, focus (0,3√2), and height 19 is
x²/a² + y²/(361/4) = 1.

The equation of an ellipse in standard form with center at the origin is:

x²/a² + y²/b² = 1

Where a is the distance from the center to the horizontal axis, and b is the distance from the center to the vertical axis.

Given that the center is at the origin, the equation becomes:

x²/a² + y²/b² = 1

To find the values of a and b, we can use the given information about the focus and the height of the ellipse.

The distance from the center to the focus is given as 3√2. Since the focus lies on the vertical axis, this means that b = 3√2.

The height of the ellipse is given as 19, which means that 2b = 19. Solving for b, we get b = 19/2.

Substituting the value of b into the equation, we get:

x²/a² + y²/(19/2)² = 1

Simplifying, we have:

x²/a² + y²/(361/4) = 1

To find the value of a, we can use the fact that the distance from the center to a vertex is a. Since the center is at the origin and the vertex lies on the horizontal axis, this means that a = 0. Therefore, the equation simplifies to:

y²/(361/4) = 1

Thus, the equation of the ellipse in standard form with center at the origin, focus (0,3√2), and height 19 is
x²/a² + y²/(361/4) = 1.

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The two intervals that show f(x) increasing are [–2.5, –1.6) and [0, 0.8).

A function is said to be increasing in an interval if the function values increase as we move from left to right through the interval.

Mathematically, a function f(x) is increasing in an interval I if, for any two numbers x1 and x2 in the interval I such that x1 < x2, then f(x1) < f(x2).

To determine the intervals where the function is increasing, we should find the intervals where the function values increase.

If f(x) is increasing in an interval I, then the graph of f(x) over the interval I rises from left to right.

Below are the given intervals[–2.5, –1.6) [–2, –1] (–1.6, 0] [0, 0.8) (0.8, 2)

We need to check which intervals satisfy the condition "increasing."

Let's evaluate f(x) at the left endpoint and the right endpoint for each interval:

a. f(–2.5) = 2, f(–1.6) = 5b. f(–2) = 1, f(–1) = 3c. f(–1.6) = 5, f(0) = 2d. f(0) = 2, f(0.8) = 3.2e. f(0.8) = 3.2, f(2) = 1

The intervals that satisfy the condition "increasing" are [–2.5, –1.6) and [0, 0.8).

Hence the options to choose from are [–2.5, –1.6) and [0, 0.8).

Therefore, the two intervals that show f(x) increasing are [–2.5, –1.6) and [0, 0.8).

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The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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Answer:

22

Step-by-step explanation:

By the segment addition postulate, FH=8+14=22.

The equation will be,

→ FH = FG + GH

Then the value of FH will be,

→ FH = 8 + 14

→ [ FH = 22 ]

Hence, the value of FH is 22.

Answer:

24

Step-by-step explanation:

To find the area of a rectangle, it is     Area=l x w

The answer is 24.

You can just count all of the squares (grid).

Hope this helps!! :)

Ingrid used 2.125 pints of blue paint to paint her bedroom walls.

Let's solve the problem given to us by using the method given below: Firstly, we need to calculate how many pints of paint Ingrid uses to paint her bedroom walls. Total pints of paint used = 8.5 pints3/4 of paint used is white. Using this information we can calculate the amount of white paint Ingrid uses. white paint used = 3/4 × 8.5 pints white paint used = 6.375 pints.

Now that we know the amount of white paint used, we can calculate the amount of blue paint used by subtracting the amount of white paint used from the total amount of paint used.pints of blue paint used = Total pints of paint used - white paint usedpints of blue paint used = 8.5 pints - 6.375 pintspints of blue paint used = 2.125 pintsTherefore, Ingrid used 2.125 pints of blue paint to paint her bedroom walls.

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When we describe relationships between variables, a correlation nearer to 1.00 (plus or minus) indicates the relationship between variables is strong.

The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.

When correlation is known, predictions can be made using it. Knowing a score on one measure helps us predict another that is closely related to it more accurately. The forecast will be more accurate the stronger the correlation between/among the variables.

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Answer: AB≈10,8,  C(-1;0,5).

Step-by-step explanation:

4.

\((-2,-2)\ \ \ \ (8,-6)\ \ \ \ \overline {AB}=?\\\)

                     Equation of a straight line

                  \(\boxed {\overline {AB}=\sqrt{(x_B+x_A)^2+(y_B-y_A)^2} }\)

\(x_A=-2\ \ \ \ x_B=8\ \ \ \ y_A=-2\ \ \ \ \ y_B=-6\\\\\overline{AB}=\sqrt{(8-(-2))^2+(-6-(-2))^2} \\\\\overline{AB}=\sqrt{(8+2)^2+(-6+2)^2} \\\\\overline{AB}=\sqrt{10^2+(-4)^2} \\\\\overline{AB}=\sqrt{100+16} \\\\\overline{AB}=\sqrt{116} \\\\\overline{AB}\approx10,8.\)

5.

\((-2,-2)\ \ \ \ (0,3)\ \ \ \ the\ midpoint\ C\ of\ AB=?\\\)

                                 Line Midpoint Equation

                           \(\boxed {C_x=\frac{X_A+X_B}{2} }}\ \ \ \boxed {C_y=\frac{Y_A+Y_B}{2} }\)

\(X_A=-2\ \ \ \ \ X_B=0\ \ \ \ \ Y_A==-2\ \ \ \ Y_B=3\\\\C_x=\frac{-2+0}{2} \\\\C_x=\frac{-2}{2} \\\\C_x=-1.\\\\C_y=\frac{-2+3}{2}\\\\C_y=\frac{1}{2}\\\\ C_y=0,5.\\\\Hence,\ \ \ \ C_{AB}(-1;0,5).\)

You can use either a numerical (integer or floating-point) variable or a Boolean variable to store the value of a logical expression.

Numerical Variable: You can use a numerical variable, such as an integer or floating-point variable, to store the result of a logical expression. In this case, the logical expression would be evaluated and assigned a numerical value, typically 0 or 1, representing false or true, respectively. For example, if you have a logical expression "x > 5", you can assign the result to a numerical variable like "result = (x > 5)", where the value of "result" would be 0 if the expression is false and 1 if it is true.

Boolean Variable: Alternatively, you can use a Boolean variable to directly store the truth value of a logical expression. A Boolean variable can only have two possible values: true or false. In this case, the logical expression would be evaluated and directly assigned to the Boolean variable. For example, if you have a logical expression "x > 5", you can assign the result to a Boolean variable like "isGreaterThanFive = (x > 5)", where "isGreaterThanFive" would be true if the expression is true and false if it is false.

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Answer:

A) eight legs per one spider (56/7)

B) one pretzel is 2.25 (6.75/3)

Step-by-step explanation:

56 divided by 7 is 8

6.75 divided by 3 is 2.25

After solving the expression ∛ (27 • 250), we get that option (C) 15 ∛2 is the correct option.

We are given the expression:

(27 • 250)^1/3

We need to evaluate the expression.

We can also write this expression as:

∛ (27 • 250)

First we will make factors of 27 and 250:

27 = 3 × 3 × 3

250 = 2 × 5 × 5 × 5

Now, we can write the expression as:

∛2 × 3 × 3 × 3 × 5 × 5 × 5

Now solving the cube root we get that:

= 3 × 5 × ∛2

= 15 ∛2

Therefore, after solving the expression ∛ (27 • 250), we get that option (C) 15 ∛2 is the correct option.

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Answer:

292 and 2092

Step-by-step explanation:

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

Total : 240 + 600 + 90 = 730

So, cost of painting = 730/25 x 10 = 29.2 x 10 = 292

Total: 292 + 1800 = 2092

The total cost of paint would be 2092 dollars.

The area of the cuboid is the sum of product of the length, breadth of the given prism.

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

The Total area: 240 + 600 + 90 = 730

So, The cost of painting = 730/25 x 10

= 29.2 x 10

= 292

Total: 292 + 1800 = 2092

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Answer:

2.6 kilometers

Step-by-step explanation:

To find the circumference of a circle, we can use the formula:

Circumference = π * diameter

Given that the diameter of the volcanic crater is 840 meters, we can substitute this value into the formula:

Circumference = π * 840

Using the approximate value of π as 3.14159, we can calculate the circumference:

Circumference = 3.14159 * 840

Circumference ≈ 2643.1796 meters

To convert the circumference to kilometers, we divide the value by 1000:

Circumference in kilometers = 2643.1796 / 1000

Circumference ≈ 2.6432 kilometers

Therefore, the circumference of the rim of the volcanic crater is approximately 2.6 kilometers (rounded to 1 decimal place).

Answer:

\( \huge{ \boxed{ \bold{ \tt{k = 12}}}}\)

Step-by-step explanation:

\( \rm { \frac{k}{2} - 5 = 1}\)

Move 5 to right hand side and change it's sign

\( \rm{⇢ \: \frac{k}{2} = 1 + 5}\)

Add the numbers : 1 and 5

\( \rm{⇢ \: \frac{k}{2} = 6}\)

Apply cross product property

\( \rm{⇢ \: k \: = 6 \: \times \: 2}\)

\( \rm{⇢ \: k = 12}\)

Hope I helped!

Best regards! :D

~\( \text{TheAnimeGirl}\)

Answer:

Similar to the question: They figure that they will drive 792 miles round trip. If their car gets 25 miles per gallon and the current cost of gasoline is $2.35, what will the gas for their trip cost? $74.45 George is taking the same trip to San Antonio (792 miles)

Step-by-step explanation:

Hope it helps :)

The ratio of the final surface charge density (ηf) to the initial surface charge density (ηi) is given by 3.68 * \(Q_i / (A_i \times A_i).\)

To understand the concept and solve this problem, we need to consider the relationship between surface charge density, area, and charge. Surface charge density (σ) is defined as the charge (Q) per unit area (A). Mathematically, we can express this relationship as σ = Q/A.

Let's assume the initial area of the irregular shape is \(A_i\), and the final area after each dimension is reduced is \(A_f\). Since each dimension (x and y) is reduced by a factor of 3.68, we can write the relationship between the initial and final areas as:

\(A_f = (1/3.68) \times A_i\)

Now, let's consider the relationship between charge and area. Since the charge remains constant for a given area, we can express it as \(Q_i = Q_f\), where \(Q_i\) is the initial charge and \(Q_f\) is the final charge.

Since the charge remains constant, the ratio of the surface charge densities can be expressed as:

ηf/ηi = \(\sigma _f/\sigma _i = Q_f/A_f / Q_i/A_i\)

Substituting the expressions for area into the equation, we have:

ηf/ηi = \(Q_f/A_f / Q_i/A_i = Q_f / (A_f * Q_i) * (A_i / Q_i)\)

Canceling out the \(Q_i\) terms, we get:

ηf/ηi = \(Q_f / (A_f * Q_i) * (A_i / Q_i) = Q_f / (A_f * A_i)\)

Since \(Q_i = Q_f\), we can simplify further:

ηf/ηi = \(Q_f / (A_f * A_i) = Q_i / (A_f * A_i)\)

Now, substituting the expressions for area into the equation, we have:

ηf/ηi = \(Q_i / (A_f * A_i) = Q_i / ((1/3.68) * A_i * A_i)\)

Simplifying, we find:

ηf/ηi = 3.68 x \(Q_i / (A_i \times A_i).\)

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Complete Question:

The irregularly shaped area of charge in the figure has surface charge density ηi. Each dimension (x and y) of the area is reduced by a factor of 3.68.

What is the ratio ηf/ηi where ηf is the final surface charge density?

The "dead spot" is 19.04 thousand miles from the center of the earth

To find the "dead spot" where no net gravitational force acts upon the object, we need to find the value of x that makes F equal to 0.

We know that F = −K x2 + 0.012K (239 − x)2

So, we set F equal to 0 and solve for x:

0 = −K x2 + 0.012K (239 − x)2

0 = −K x2 + 0.012K (239 − x)2

K x2 = 0.012K (239 − x)2

x2 = 0.012 (239 − x)2

x2 = 2.888 (239 − x)2

x2 = 2.888 (239 − x)2

x2 = 2.888 x2 - 676.8 x + 568.976

x2 - 2.888 x2 = 676.8 x - 568.976

-1.888 x2 = 676.8 x - 568.976

x2 = 361.6 x - 303.504

x = √(361.6 x - 303.504)

x = √(361.6 x - 303.504)

x = 19.04

So the "dead spot" is 19.04 thousand miles from the center of the earth

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Answer:

Trinomial——2

i just took it

Answer:

4+12v or 12v+4

Step-by-step explanation:

you distribute (multiply 2 with 2 and 6v)

Answer:

54

Step-by-step explanation:

18x3

Answer:

i might be wrong but 54

Step-by-step explanation:

i hope i helped sorry if i didnt :(

Answer: 2n^2. let me know if you need the explanation :).

Step-by-step explanation:

The solution to the given inequality expression is: x ≥ -8 and it is shown on the number line attached

To represent inequalities on a number line we show the range of numbers by drawing a straight line and indicating the end points with either an open circle or a closed circle. An open circle shows it does not include the value. A closed circle shows it does include the value.

We are given the inequality expression as:

8x - 4 ≥ -68

Add 4 to both sides to get:

8x ≥ -64

Divide both sides by 8 to get:

x ≥ -8

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The answer is: True. When matrix A is upper triangular, its eigenvalues are located on its main diagonal. If you find the eigenvectors corresponding to each eigenvalue, you can construct an eigenvector matrix S.

An upper triangular matrix is a square matrix in which all entries below the main diagonal are zero. An eigenvector of a matrix A is a nonzero vector x such that Ax is a scalar multiple of x. That is, there exists a scalar λ such that Ax = λx.
For a complete upper triangular matrix, all of its eigenvalues are on the diagonal. To see this, consider the characteristic polynomial of a complete upper triangular matrix:
p(λ) = det(A - λI)
where I is the identity matrix. Since A is upper triangular, its determinant is the product of its diagonal entries, and det(A - λI) is a polynomial of degree n (the size of the matrix) in λ. Therefore, there are n roots of p(λ), which correspond to the eigenvalues of A. Since A is completely upper triangular, all of its eigenvalues are on the diagonal.

Now, let's consider the eigenvector matrix S of A. This is a matrix whose columns are the eigenvectors of A. Since A is upper triangular, any eigenvector of A must also be upper triangular (or zero). Therefore, the eigenvector matrix S must also be upper triangular. In summary, if a is a complete upper triangular matrix, then all of its eigenvalues are on the diagonal, and its eigenvector matrix S is upper triangular. Therefore, the statement is true.
"If A is a complete upper triangular matrix, then it has an upper triangular eigenvector matrix S." When a matrix A is upper triangular, its eigenvalues are located on its main diagonal. If you find the eigenvectors corresponding to each eigenvalue, you can construct an eigenvector matrix S. Since A is upper triangular, the eigenvector matrix S will also be upper triangular.

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The Year 1 Incremental EBIT for Project Q is $15.73 million. The NPV for Project Q needs to be calculated by discounting the cash flows considering

The total revenue can be calculated by multiplying the number of units sold by the price per unit. In this case, the revenue would be 3 million units multiplied by $24.99, which equals $74,970,000.The COGS can be calculated by multiplying the number of units sold by the cost per unit. In this case, the COGS would be 3 million units multiplied by $17.08, which equals $51,240,000.The operating expenses for Year 1 are given as $8 million.

Therefore, the Year 1 Incremental EBIT can be calculated as follows:

Revenue - COGS - Operating Expenses = $74,970,000 - $51,240,000 - $8,000,000 = $15,730,000.The NPV (Net Present Value) for Project Q can be determined by calculating the present value of the cash flows generated by the project. We need to consider the initial cost of machinery, annual operating expenses, incremental EBIT, and net working capital.Using the WACC (Weighted Average Cost of Capital) of 10%, we can discount the cash flows to their present value. The net cash flow in each year would be the incremental EBIT minus taxes plus the depreciation and amortization expense. The net cash flow in Year 4 would also include the recovery of net working capital.

By discounting the net cash flows and summing them up, we can calculate the NPV. The margin of error is given as 0.05, so the result should be within that range.

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Answer:

Y=3x-2

Step-by-step explanation

Answer:

Step-by-step explanation:

The limiting distribution of yn is a point mass at β.

To find the limiting distribution of yn, we will use the Central Limit Theorem (CLT), which states that the sum of a large number of independent and identically distributed (i.i.d.) random variables, each with finite mean and variance, will be approximately normally distributed.

First, we need to find the mean and variance of yn:

E(yn) = E(xn/n) = (1/n)E(xn) = (1/n)(αβ) = β

Var(yn) = Var(xn/n) = (1/n^2)Var(xn) = (1/n^2)(αβ^2) = β^2/n

Now, we can apply the CLT to yn:

(zn - β) / (σ / sqrt(n)) ~ N(0,1)

where zn = yn, σ^2 = Var(yn) = β^2/n.

As n approaches infinity, the distribution of yn approaches a normal distribution with mean β and variance 0, since σ^2 approaches 0:

lim n->∞ P(zn ≤ z) = Φ((z-β)/0) = Φ(∞) = 1, for any z.

Therefore, the limiting distribution of yn is a point mass at β. In other words, yn converges in probability to β as n approaches infinity.

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One reason for using a t distribution instead of the standard normal curve to find critical values when calculating a level c confidence interval for a population mean is that (b) z requires that you know the population standard deviation s.

The t distribution is used when the population standard deviation is unknown and is estimated from the sample. The t distribution has fatter tails than the standard normal curve, which makes it more appropriate for smaller sample sizes. When the sample size is large, the t distribution approaches the standard normal curve, and the z distribution can be used instead.

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