where is the point on the number line?

The sketch of the function y = \(x^{2}\) - x - 3 for -3 <= x <= 3 reveals a parabolic curve that opens upwards. The turning point of the parabola, also known as the vertex, can be identified as (-0.5, -3.25).

To sketch the graph of y = \(x^{2}\) - x - 3, we consider the given domain of -3 <= x <= 3. The function represents a parabola that opens upwards. By calculating the coordinates of the turning point, we can locate the vertex of the parabola.

To find the x-coordinate of the turning point, we use the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. In this case, a = 1 and b = -1. Substituting these values, we have x = -(-1)/2(1) = -0.5.

To find the y-coordinate of the turning point, we substitute the x-coordinate (-0.5) into the equation y = \(x^{2}\) - x - 3. Evaluating this expression, we get y = \(-0.5^{2}\) - (-0.5) - 3 = -3.25.

Therefore, the turning point of the parabola is approximately (-0.5, -3.25).

From the sketch, we can estimate the approximate solutions to the equation \(x^{2}\)- x - 3 = 0 by identifying the x-values where the graph intersects the x-axis. These solutions are approximately x ≈ -2.5 and x ≈ 1.5.

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Answer:

x=25, y=19

Step-by-step explanation:

130+2x=180

x=25

54+2x+4y=180

y=19

Answer:

x = 25 , y = 19

Step-by-step explanation:

130° and 2x° are adjacent angles on a straight line and sum to 180° , so

130 + 2x = 180 ( subtract 130 from both sides )

2x = 50 ( divide both sides by 2 )

x = 25

--------------------------------------------------------------

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

130° is an exterior angle of the triangle , then

54 + 4y = 130 ( subtract 54 from both sides )

4y = 76 ( divide both sides by 4 )

y = 19

A relationship might exist in a sample even though it does not exist in the population, because of b) Sampling error

In statistical analysis, a relationship might appear in a sample even though it does not exist in the population due to sampling error. This occurs when the sample is not fully representative of the population, leading to discrepancies between the sample statistics and the true population parameters.

Sampling error can cause random fluctuations that mistakenly suggest a relationship, which may not be present in the larger population. It is important to consider the limitations and potential sources of error when generalizing findings from a sample to the broader population. So b option is correct.

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Answer:

-6/4

Step-by-step explanation:

equivalent, that means something that is equal to so if you break -6/4 to the lowest you get -6/4

The four levels of measurement in statistics are nominal, ordinal, interval, and ratio.

1. Nominal: The nominal level of measurement involves categorizing data into distinct categories or groups. Examples include gender (male or female), marital status (single, married, divorced), or types of fruits (apple, orange, banana).

2. Ordinal: The ordinal level of measurement allows for ranking or ordering of data based on a specific criterion. Examples include survey ratings (strongly agree, agree, neutral, disagree, strongly disagree) or educational levels (elementary, middle school, high school, college, postgraduate).

3. Interval: The interval level of measurement not only allows for ranking but also quantifies the intervals or differences between values.Examples include temperature measured in Celsius or Fahrenheit, where the intervals between values are equal but zero does not indicate the absence of temperature.

4. Ratio: The ratio level of measurement possesses all the properties of the interval level but also has a true zero point, which indicates the absence of the measured attribute. Examples include height, weight, or income, where zero represents the absence of the attribute and ratios between values are meaningful (e.g., someone twice as tall as another person).

Nominal: The nominal level of measurement involves categorizing data into distinct categories or groups. In this level, data are simply named or labeled without any quantitative value. Examples include gender (male or female), marital status (single, married, divorced), or types of fruits (apple, orange, banana).

Ordinal: The ordinal level of measurement allows for ranking or ordering of data based on a specific criterion. It indicates relative differences between the values but does not quantify the magnitude of those differences. Examples include survey ratings (strongly agree, agree, neutral, disagree, strongly disagree) or educational levels (elementary, middle school, high school, college, postgraduate).

Interval: The interval level of measurement not only allows for ranking but also quantifies the intervals or differences between values. However, it does not have a true zero point. Examples include temperature measured in Celsius or Fahrenheit, where the intervals between values are equal but zero does not indicate the absence of temperature.

Ratio: The ratio level of measurement possesses all the properties of the interval level but also has a true zero point, which indicates the absence of the measured attribute. It allows for comparisons of magnitude and ratios between values. Examples include height, weight, or income, where zero represents the absence of the attribute and ratios between values are meaningful (e.g., someone twice as tall as another person).

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Answer:

x/5 - 4

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

just took the test

The coordinates of the midpoint M of the segment FG is (-2,2).

This question is incomplete, the complete question is;

What is the midpoint M of a line having two endpoints F(-7, 12) and G(3, -8),

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point F (-7, 12)

Point G (3,-8)

To determine the midpoint, plug the given points into the formula above and simplify.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

M = ( (-7 + 3 )/2, ( 12 + (-8) )/2 )

M = ( ( -4 )/2, ( 12 - 8 )/2 )

M = ( ( -4 )/2, ( 4 )/2 )

M = ( -2, 2 )

Therefore, the  midpoint M of the segment is (-2,2)

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Quadrilaterals are closed shapes having four sides and four angles. The sides and angles of quadrilaterals may be of any degree and size. However, quadrilaterals having similar or identical properties are classified into different types. There are six types of quadrilaterals that exist, with each having its unique properties.

One such quadrilateral is the parallelogram. A quadrilateral is said to be a parallelogram if its opposite sides are parallel. Let's assume ABCD be a quadrilateral and AB is parallel to DC, then we can write AB||DC. Let's suppose the line segment AD intersects with BC at point E. Then we can write AE=CE and BE=DE. We can also write AD||BC. From triangle ABE, we can write angle ABE is congruent to angle CDE as AE=CE. Similarly, angle AEB is congruent to angle CED because BE=DE. So, from both these, we can say that the triangles ABE and CDE are congruent, which can be written as; ∆ABE ≅ ∆CDE.

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Moving counterclockwise around the rectangle, the labels and coordinates of the other  vertices are; E'(6, 8), C'(10, 10), T'(0, 10)

I have drawn an image of the given triangle RECT and attached it.

The length is 10 units and width is 6 units.

From the image of the triangle, we see that the coordinates are;

R(0, 0), E(10, 0), C(10, 6), T(0, 6)

Now, we are told that moving counterclockwise around the rectangle, and after rotation, we will now have the transformations as;

R'(0, 0), E'(6, 8), C'(10, 10), T'(0, 10)

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each cereal bar would cost Megan approximately $0.83 to make, assuming our initial assumptions about serving size and ingredient cost are correct.

Without knowing the dimensions of the pan, it's difficult to give a precise estimate for the appropriate length and width for each cereal bar. However, we can make some assumptions based on typical serving sizes for cereal bars and the number of bars that Megan wants to cut.

Assuming that Megan wants to make 12 cereal bars, a reasonable serving size would be around 1.5 inches by 3 inches. This would give a total area of 4.5 square inches per bar.

To calculate the cost per cereal bar, we need to know the total cost of ingredients and the total number of bars made. Let's assume that Megan spent $10 on ingredients and made 12 bars. Then the cost per bar would be:

Cost per bar = Total cost / Total number of bars

Cost per bar = $10 / 12 bars

Cost per bar = $0.83

So each cereal bar would cost Megan approximately $0.83 to make, assuming our initial assumptions about serving size and ingredient cost are correct.

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Answer:

-w+41

Step-by-step explanation:

5(w+4)-3(2w-7)

5w+20-6w+21

-w+41

Answer:

46080 ft²

Step-by-step explanation:

Given :

Scale :

1 in = 4 feets

Recall :

I foot =. 12 inches

Length of drawing = 4 feets

Length of drawing in inches = 4 * 12 = 48 inches

Width of drawing = 5 feets

Width of drawing in inches = 5 * 12 = 60 inches

Actual length of pool = 48 * 4 = 192 feets

Actual width of pool = 60 * 4 = 240 feets

The actual area of the pool :

Length * width

192 feets * 240 feets = 46080 ft²

Answer:

sup

Step-by-step explanation:

Answer:

a square

Step-by-step explanation:

a square has all right angles an no acute angles

The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin⁡(5x)dx. We are given that y=cos(5x)=π/30y=cos⁡(5x)=π/30 and x=0.055x=0.055.

We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:

Δy≈dy≈dy=-5sin(5x)dx

Plugging in the values of y, x, and dxdx, we get:

Δy≈-5sin(5(0.055))(0.005)≈-0.00679

Therefore, the estimated change in yy using differentials is -0.00679.

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By completing the square, we can determine the equation of a degenerate conic. The given equation, x² + 16 = 4(y² + 2x), can be simplified to (x - 2)² = -4(y - 2). This equation represents a degenerate conic, specifically a degenerate parabola with its vertex at (2, 2).

To determine the equation of the degenerate conic, we start by rearranging the given equation. We move the constant term, 16, to the right side to isolate the variable terms:

x² - 4(2x + y²) = -16.

Next, we complete the square for the x-terms. We take half of the coefficient of x, which is 2, square it to get 4, and add it to both sides:

x² - 4(2x) + 4 - 4y² = -16 + 4.

Simplifying further, we have:

(x - 2)² - 4y² = -12.

Rearranging the equation, we get:

(x - 2)² = 4y² - 12.

Now, we can divide both sides by 4 to simplify the equation:

(x - 2)² = -3(y² - 4).

The equation (x - 2)² = -3(y - 2) represents a degenerate conic, specifically a degenerate parabola with its vertex at (2, 2). It opens downward with no real solutions for y.

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Answer:

The first derivative of \(r(t) = 5\cdot t^{-2}\) (r(t)=5*t^{-2}) with respect to t is \(r'(t) = -10\cdot t^{-3}\) (r'(t) = -10*t^{-3}).

Step-by-step explanation:

Let be \(r(t) = \frac{5}{t^{2}}\), which can be rewritten as \(r(t) = 5\cdot t^{-2}\). The rule of differentiation for a potential function multiplied by a constant is:

\(\frac{d}{dt}(c \cdot t^{n}) = n\cdot c \cdot t^{n-1}\), \(\forall \,n\neq 0\)

Then,

\(r'(t) = (-2)\cdot 5\cdot t^{-3}\)

\(r'(t) = -10\cdot t^{-3}\) (r'(t) = -10*t^{-3})

The first derivative of \(r(t) = 5\cdot t^{-2}\) (r(t)=5*t^{-2}) with respect to t is \(r'(t) = -10\cdot t^{-3}\) (r'(t) = -10*t^{-3}).

The length of CD is \(15√(1 + 25x^2)\)

Describe length.

A measurement of length is the separation of two points or the size of an object. Units like centimeters, meters, and inches are frequently used to measure length. Time or the amount of space something occupies are other ways to measure length. Calculating area, volume, and other measurements can be done using length, a key idea in mathematics.

Let AB = 5+3x and BC = 20-2x.

To calculate the length of CD, we can use the distance formula. The distance formula states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of\((x2 - x1)^2 + (y2 - y1)^2\)

Therefore, to calculate the length of CD, we can use this formula with the given values:

CD = \(√(20 - 5)^2 + (-2x - 3x)^2\)

CD = \(√(15)^2 + (-5x)^2\)

CD =\(15√(1 + 25x^2)\)

Therefore, the length of CD is \(15√(1 + 25x^2)\)

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Answer:

5/2

Step-by-step explanation:

23x-19x+5=2x

23x-19x-2x=5

2x/2=5/2

x=5/2

Answer: The correct answer is 27

Step-by-step explanation: EDGE 2022

Sheila made 3, 3-point shots.

The correct answer to the given question is option G.

To find the number of 3-point shots Sheila made, we can use algebraic equations to represent the situation.

Let's assume Sheila made x shots worth 2 points and y shots worth 3 points. We know that the total number of shots made is 9, so we have the equation:

x + y = 9  -- Equation (1)

We also know that the total points Sheila scored is 21. Since each 2-point shot contributes 2 points and each 3-point shot contributes 3 points, we have another equation:

2x + 3y = 21  -- Equation (2)

To solve this system of equations, we can multiply Equation (1) by 2 and subtract it from Equation (2):

2x + 3y - 2x - 2y = 21 - 2(9)

y = 3

Therefore, the number of 3-point shots Sheila made is 3.

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This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

What is the standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a wider range.

Standard deviation determines how far numbers deviate from the mean. The Standard deviation of the two sets will be the same if the numbers from the respective means are placed in the same order.

This is what 10, 15, and 20 will be on a number line

10_ _ _ _15 _ _ _ _20

(15 is the mean and 10 and 20 are 5 steps away from the mean)

i) Z - X = 10

This is what Z and X will be on the number line

X _ _ _ _ _ Z

ii) Z - Y = 5

This is what Z and Y will on the number line.

Y_ _ _ _ _ Z

Together, their relative placement on the number line:

X _ _ _ _ _  Y  _ _ _ _ _  Z

This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

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Answer:

b

Step-by-step explanation:

Answer:

a). y = 3/2x - 3/4    b).-2/3       c).y = -2/3x + 3

Step-by-step explanation:

a). 6x – 4y = 3

-4y = -6x + 3

y = 3/2x - 3/4

 - The slope is 3/2.

b). The slope of a perpendicular line would be the opposite: -2/3

c). y = -2/3x + b

-1 = -2/3(6) + b

-1 = -4 + b

3 = b

y = -2/3x + 3

Based on the calculations on this arithmetic sequence, the value of the first term is equal to -8.

An arithmetic sequence can be defined as a series of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Given the following data:

Tenth term (a₁₀) = 30.

Common difference = 2.

Substituting the given parameters into the formula, we have;

10 =  a₁ + (10 - 1)2

10 =  a₁ + (9)2

10 =  a₁ + 18

a₁ = 10 - 18

First term, a₁ = -8.

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Answer: $2.08

Step-by-step explanation: First multiply $52 by 4% as a decimal or 0.04. Then, multiply that by the number of years.
=52(0.04)(1)

=2.08

Answer:

Does not pass the vertical line test, so its not a function.

Step-by-step explanation: