On a number line, point S is at -2, and point T is at 7. Point R is the midpoint of ST. Where does point R lie on the number line?
OA. 2.5
O
O
O
B.
4.5
C. -2.5
D. -4.5
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The range of a function refers to the set of all possible output values that the function can produce for its corresponding input values. In this case, the function is:

f(x) = 6x / (x^2 - 9)

To find the range of this function, we need to consider the restrictions on the denominator (x^2 - 9) that would make the function undefined.

The denominator (x^2 - 9) can be factored as a difference of squares:

x^2 - 9 = (x + 3)(x - 3)

So, the function is undefined when the denominator is equal to zero, i.e., when:

(x + 3)(x - 3) = 0

This occurs when x = -3 or x = 3.

Now, we need to consider the behavior of the function as x approaches these values. As x approaches -3 or 3 from the left, the function becomes increasingly negative, and as x approaches -3 or 3 from the right, the function becomes increasingly positive. This is because the numerator (6x) remains constant while the denominator approaches zero, resulting in a very large positive or negative value for f(x).

Since the function can approach arbitrarily large positive or negative values as x approaches -3 or 3, respectively, the range of the function is (-∞, ∞), which represents all real numbers except for the values -3 and 3. In interval notation, the range of the function can be written as:

Range of f(x): (-∞, ∞) \ {-3, 3}

Answer:

Step-by-step explanation:

4:1 and 6:1

Note that the value of C that satisfies the mean value theorem is -11/6

The mean value theorem in mathematics says that for each given planar arc between two end points, there exists at least 1   point where the tangent to the arc   is parallel to the secant between its ends. It is one of the most significant findings in real -  world analysis.

To apply the mean value theorem, we need to check 2 conditions

f(x) is continuous on [-3, -1]

f(x) is differentiable on (-3, -1)

f(x) = (x^2-1/3x) satisfies both conditions.

Now, let's find the value of c that satisfies the mean value theorem:

f(-1) - f(-3) = f'(c)(-1 - (-3))

(2/3) - (-26/3) = f'(c)(2)

f'(c) = -4

To find the value of c, we need to solve for c in f'(c) = -4 ...  

f '(x) = d/d x(x²  -1/3x)

= 2x - 1/3

2c - 1/3 = -4

2c = -4 + 1/3

c = -11/6

So we can state that  the value of c that satisfies the mean value theorem is -11/6

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Step-by-step explanation:

Area of a kite = D1 × D2/2

D1 = 6.9 + 13.8 = 20.7m

D2 = 9.2 + 9.2 = 18.4m

Area =. 20.7 × 18.4

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

2

= 190.44m²

Answer:

-23

Step-by-step explanation:

15(-3)/9 + 4(-3)-6

-45/9 + (-12)-6

-5 + (-18)

-23

(missed the -6 sorry)

Answer:

-23

Step-by-step explanation:

15(-3)/9 +4(-3) -6 = -5 -12 -6 = -23

a) The only outcome that satisfies both events X and Y is the letter C.

b) The outcomes that satisfy either event X or event Y are {A, B, C, E, G}.

c) The complement of event X is {D, E, F, G}.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

The outcomes for each of the following events are:

(a) Event "X and Y": {C}

To satisfy both events X and Y, the letter selected must come before "D" (which includes the letters A, B, and C) and must be one of the letters in the word "CAGE" (which includes only the letter C). Therefore, the only outcome that satisfies both events X and Y is the letter C.

(b) Event "X or Y": {A, B, C, E, G}

The outcomes that satisfy event X are A, B, and C (since they come before "D"), and the outcomes that satisfy event Y are C, A, G, and E (since they are letters found in the word "CAGE"). Therefore, the outcomes that satisfy either event X or event Y are {A, B, C, E, G}.

(c) The complement of event X: {D, E, F, G}

The complement of event X is the set of outcomes that do not satisfy event X. The outcomes that do not satisfy event X are D, E, F, and G (since they come after or are equal to "D"). Therefore, the complement of event X is {D, E, F, G}.

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The answer of the given question based on the quadrilateral is , the line segment corresponding to EH⎯ is AD⎯.

A line segment is a part of a line that consists of two endpoints and all the points between those endpoints that are collinear (lying on the same straight line). In other words, a line segment is a straight line that is bounded by two distinct points. A line segment is usually denoted by drawing a line over the two endpoints and labeling it with a single letter representing the segment name or by labeling the endpoints with capital letters and drawing a bar over them to indicate the segment between them.

A line segment has a finite length and can be measured using a ruler or a measuring tape. The length of line segment is distance between its two endpoints.

In the pre-image, the line segment corresponding to EH⎯ is AD⎯.

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Answer:

Step-by-step explanation:

The base of the triangle is 3/2 feet or 1 1/2 feet

Triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

The area of triangle is expressed as ;

A = 1/2 bh

The area of the of the triangle is 2/15 and the height is 2/5.

2/15 = 1/2 b × 2/5

2/15 = 2b/10

20 = 30b

divide both sides by 30

b = 30/20

b = 3/2

there the base of the triangle is 3/2.

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The correct options are- B. x = –4 – √2 and D. x = –4 + √2 are the roots of the given quadratic equation.

When a square is complete, a quadratic is written in the shape of a squared bracket, and if necessary, a constant is added. Finding the function's highest or minimum value and the time it happens is one use for the square-root method.

Given quadratic equation:

x² – 8x + 16 = 2

This can be written as:

x² – 2*4x + 4² = 2

(x + 4)² = 2

Taking square root both sides:

√(x + 4)² = √2

(x + 4) = ±√2

x = ±√2  - 4

Or x = -4 + √2 and x = -4 - √2

Thus, the roots of the quadratic equation found by using the method of completing the square are - x = -4 + √2 and x = -4 - √2

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Complete question:

Use completing the square to solve this quadratic equation. Check all that apply. x² – 8x + 16 = 2

A. x = 4 –√2

B. x = –4 – √2

C. x = 4 + √2

D. x = –4 + √2

Answer:

36°

Step-by-step explanation:

angle a= 180-117

angle a=63°. because angles on straight line add to 180°

angle b= 180-81-63

angle b=36°. because angles in triangle add to 180°

Answer:  the ball reaches a maximum height of 76 ft, and it takes 2 seconds to reach the highest point.

Step-by-step explanation: The acceleration induced by gravity is estimated to be approximately -32 ft/s^2, with the negative value indicating its downward direction.

At the apogee of the ball's trajectory, its vertical velocity experiences a momentary cessation.

The duration required for the ball to attain its maximum height can be determined through employment of the equation t = Vf / a, in which Vf denotes the attained final velocity (which is zero in the present scenario) and a denotes the gravitational acceleration. Upon substitution of the given numerical values, the resulting value of t is determined to be equal to 2 seconds, achieved through the utilization of the equation t = 64 / 32.

The determination of the maximum height achieved by the ball can be achieved through utilization of the formula h = hi + Vit + 1/2at^2, with hi denoting the initial height (12 ft), Vi representing the initial velocity (64 ft/s), a signifying the acceleration due to gravity (-32 ft/s^2), and t representing the time it takes for the ball to reach the apex of its trajectory (2 seconds). Upon entering the provided numerical values into the formula, the resulting value for the height of the object can be determined as h = 12 + 64(2) + 1/2(-32)(2)^2, which equates to 76 feet.

Answer: C

Step-by-step explanation:

your typical equation for varies inversely is y=k/x

here E = k/d² from the wording of problem.  plug in numbers to solve for k.

120=k/20²

k=48000

plug k back in to get generic E equation.  

E=48000/d²

As a result, 1.554 g of sugar are included in the low-sugar yoghurt as if the low-sugar yoghurt has 26% less sugar.

A proportion is put up using a single unit when using a unitary method. For instance, the price of 1 apple is $2/3 if 3 bananas cost $2. The cost among one unit of something like the quantity "apples" is represented by this value of $2/3. In a similar vein, if a car can drive 300 km on 20 litres of gas, how far can it go on one litre of gas? The answer is 15 km (300/20). Finance, science, and engineering are just a few of the fields where the unitary technique can be applied to solve issues.

given

Regular yoghurt contains: If only 7% of the daily required amount of sugar is present in it:

7% of 30 g = [tex](7/100) * 30 g = 2.1 g[/tex]

This indicates that 2.1 g of sugar are present in ordinary yoghurt.

Hence, if the low-sugar yoghurt has 26% less sugar than the standard yoghurt, it contains:

[tex]1.554 g = 2.1 g - (26/100) x 2.1 g = 2.1 g - 0.546 g[/tex]

As a result, 1.554 g of sugar are included in the low-sugar yoghurt as if the low-sugar yoghurt has 26% less sugar.

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Answer:

Hey

So my brother posted this on Yahoo

Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth. A right-angled triangle is formed. Length of side to the water-surface is 5 cm, the hypot is 7 cm.

What you do now is the following:

Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7)

So θ is approx 44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8°

The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram.

Shaded area ≃ 88.8/360*area of circle - ½*7*7*sin88.8°

= 88.8/360*π*7² - 24.5*sin 88.8°

≃ 13.5 cm²

(using area of ∆ = ½.a.b.sin C for the triangle)

b)

volume of water = cross-sectional area * length

≃ 13.5 * 30 cm³

≃ 404 cm³

Hoped it Helped

Step-by-step explanation:

Hey

So my brother posted this on Yahoo

Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth. A right-angled triangle is formed. Length of side to the water-surface is 5 cm, the hypot is 7 cm.

What you do now is the following:

Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7)

So θ is approx 44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8°

The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram.

Shaded area ≃ 88.8/360*area of circle - ½*7*7*sin88.8°

= 88.8/360*π*7² - 24.5*sin 88.8°

≃ 13.5 cm²

(using area of ∆ = ½.a.b.sin C for the triangle)

b)

volume of water = cross-sectional area * length

≃ 13.5 * 30 cm³

≃ 404 cm³

Hoped it Helped

The equation of the line is

To find the equation of the line passing through the points (2,2) and (-2,0), we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where

m is the slope of the line, and

(x1, y1) are the coordinates of one of the points on the line.

First, we need to find the slope of the line. The slope is given by:

m = (0 - 2) / (-2 - 2) = -1/2

substituting the points

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

Expanding the right side and simplifying, we get:

y - 2 = (-1/2)x + 1

y = (-1/2)x + 3

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The height of the kite from the ground when the angle is 50 degrees is 232 feet.

The study of the correlations between triangles' sides and angles is the focus of the mathematic branch known as trigonometry. To link the angles of a right triangle to the lengths of its sides, it makes use of trigonometric functions like sine, cosine, and tangent.

Numerous industries, including physics, engineering, and navigation, use trigonometry. It can be used, for instance, to determine a building's height or the separation between two locations on a map, as well as to examine how waves and oscillations behave.

To find the height of the kite above the ground we use the trigonometric identity of tangent.

Thus, we have:

tan(50°) = h/200

Now, using cross multiplication:

h = 200 tan(50°) ≈ 232 feet

Hence, the height of the kite from the ground when the angle is 50 degrees is 232 feet.

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Therefore, the magnitude of the acceleration is instantaneously zero at t = 5/3 and t = 1. Therefore, the displacement of P from the origin when t = 2 is -8/3 meters.

A function is a mathematical concept that describes a relationship between two sets of values, called the domain and the range. It is a rule or a set of rules that assigns a unique output value for every input value in the domain. In other words, it is a process that takes one or more inputs and produces a corresponding output. Functions are commonly represented using equations, graphs, or tables. They are used in various branches of mathematics, science, engineering, and technology to model real-world phenomena, make predictions, and solve problems.

Here,

(a) To find the acceleration, we need to take the derivative of the velocity function with respect to time:

a = dv/dt

= d/dt (t³ - 4t² + 5t + 1)

= 3t² - 8t + 5

(b) To find the values of t for which the magnitude of the acceleration is instantaneously zero, we need to solve the equation:

|a| = |3t² - 8t + 5|

= 0

This occurs when 3t² - 8t + 5 = 0, which factors as (3t - 5)(t - 1) = 0. Therefore, the magnitude of the acceleration is instantaneously zero at t = 5/3 and t = 1.

(c) To find the displacement of P from the origin when t = 2, we need to integrate the velocity function from t = 0 to t = 2:

s = ∫(v dt)

= ∫(t³ - 4t² + 5t + 1 dt)

= (1/4)t⁴ - (4/3)t³ + (5/2)t² + t + C

We know that s(0) = 3, so we can solve for C:

3 = (1/4)(0)⁴ - (4/3)(0)³ + (5/2)(0)² + 0 + C

C = 3

Therefore, the displacement of P from the origin when t = 2 is:

s(2) = (1/4)(2)⁴ - (4/3)(2)³ + (5/2)(2)² + 2 + 3

= -8/3 meters

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The correct answer is option A: As x decreases in value, y increases in value. As x increases in value, y increases in value.

A mathematical object called a function accepts inputs (often represented by the symbol x) and creates outputs (typically represented by the symbol y or f(x)). An equation can be used to describe a function, although a function is not always defined by an equation.

It may incorporate one or more variables, but it does not always indicate how those variables are related.

For instance, even if the equation 2x + 3 = 7 involves the variable x, it does not define a function.

Given the function starts at (-3, 0) and extends upwards and to the right.

Thus, if x approaches negative infinity, the function cannot take on negative values, so the graph approaches the x-axis but never touches or goes below it.

Hence, the correct answer is option A: As x decreases in value, y increases in value. As x increases in value, y increases in value.

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Hence, the quotient is [tex]2x^2[/tex] in its simplest form as the numerator by the denominator to simplify the quotient.

In addition, ratios can be used to compare components of an ensemble, such as the ration of a circle's surface area to its circumference. As it is a linear correlation that cannot be reduced, the ratio in this instance is not simplified. In mathematics, science, economics, and many other disciplines, ratios are frequently employed to explain and study the quantitative relationships between various values.

given

The ratio is:

[tex]4x^5 / (2x^3)[/tex]

We can divide the numerator by the denominator to simplify the quotient.

By dividing 4x5 by 2x3, we obtain:

[tex](4x^5) / (2x^3) = 2x^(5-3) = 2x^2[/tex]

Hence, the quotient is [tex]2x^2[/tex] in its simplest form as the numerator by the denominator to simplify the quotient.

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Answer:

Step-by-step explanation: X=1

Answer:

To expand (x-y)³ using Pascal’s triangle, we can write:

    1

 1     1

1 2 1

1 3 3 1

Each row of the triangle represents the coefficients of the binomial expansion of (a+b)ⁿ, with the top row being n=0.

So for (x-y)³, we take the fourth row of the triangle (starting with n=0), and substitute x and y into the formula, alternating the signs of y:

1x³ + 3x²(-y) + 3x(-y)² + 1(-y)³

= x³ - 3x²y + 3xy² - y³

Thus, (x-y)³ = x³ - 3x²y + 3xy² - y³.

Answer:

10/3

Step-by-step explanation:

u = 2

v = 5

7 + 3(v - 2u)

= 7 + 3(5 - 2*2)

= 7 + 3(5 - 4)

= 7 + 3(1)

= 7 + 3

= 10

u + 1

= 2 + 1

= 3

7 + 3(v - 2u)/u + 1

= 10/3

The balance in this account has grown because of the interest earned on the account, which is compounded annually. Each year, the interest is calculated based on the beginning balance for the year, which includes the previous year's balance plus any new deposits made at the beginning of the year. The interest rate is then applied to this balance, and the resulting interest is added to the balance. This process is repeated each year, causing the balance to grow over time. Additionally, in this particular example, new deposits were made in the first year, which further increased the balance and contributed to its growth.

Answer:

addition and subtraction

The volume of the modelled Saturn is 2176.40 cm³.

Eliza made sphere-shaped models of the Earth and Saturn out of playdough for a science project. The model of Earth has a diameter of 4.8 cm and the model of Saturn has a diameter of 45.6 cm.

Therefore, the volume of the spherical Saturn can be found as follows:

volume of the Saturn = 4 / 3 πr³

where

r = radius

Therefore,

r = 45.6 / 2 = 22.8 cm

volume of the Saturn = 4 / 3 × 3.14 × 22.8²

volume of the Saturn = 4 / 3 × 3.14 × 519.84

volume of the Saturn = 6529.1904 / 3

volume of the Saturn = 2176.3968

volume of the Saturn = 2176.40 cm³

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Answer:

p = 1 or p = 7

So first number line is the answer we are looking for.

Step-by-step explanation:

|8-2p| = 6

To do that, we need to get rid of the brakes and rewrite equation in two forms:

8 - 2p = 6

or

8 - 2p = -6

For the first state:

8 - 2p = 6

- 2p = -2

2p = 2

p = 1

Now, the second state:

8 - 2p = -6

- 2p = -14

2p = 14

p= 7