Enter the value of (-3)(2)(3).

Hey there! :-)

-8+r>-8

r>-8+8

r>0

Hope it helps!

~Just a joyful teen

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\(GraceRosalia\)

Hey there!

-8 + r > -8

= r > -8 + 8

= r > 0.

Steps :-

Hope it helps ya!

The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

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To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer: \(m\angle DE F=90^{\circ}\)

Step-by-step explanation:

The slope of \(DE\) is \(\frac{7-3}{5-4}=4\).

The slope of \(EF\) is \(\frac{3-2}{4-8}=-\frac{1}{4}\).

Thus, \(DE \perp EF\), meaning \(m\angle DE F=90^{\circ}\).

Answer:

Step-by-step explanation:

Let's just say this circle has value x.

x increases by 5%, or 0.05 of x.

x + 0.05x = 1.05x

1.05x now increases by 5% again:

1.05x + 0.05(1.05x) = 1.1025x

The total increase is equal to (1.1025-1)*100 = 10.25%

Hope this helps!

Answer:

The answer is 10.

Step-by-step explanation:

f(x) = 6* x^2 + 5

f(0) = 6*0^2 + 5 = 5

g(x) = 3x - 5

g(f(x)) = 3 * (f(x)) - 5

g(f(0)) = 3 * 5 - 5 = 10

It is important to note that this equation assumes a constant density of seawater, which is not always the case in the deep ocean. In addition, the pressure at a given depth can vary depending on factors such as temperature and salinity. This equation should be used with caution and in conjunction with other measurements and data analysis techniques.

The given equation for pressure in pounds per square foot at a depth of d feet is P = 14 + 4d/9. We are given that the pressure measured by the scientific team is 306 pounds per square foot. To find the depth at which this pressure is measured, we need to solve the equation for d.

Substituting P = 306 in the equation, we get:

306 = 14 + 4d/9

Multiplying both sides by 9, we get:

2754 = 126 + 4d

Subtracting 126 from both sides, we get:

2628 = 4d

Dividing both sides by 4, we get:

d = 657 feet

The scientific team is measuring the pressure at a depth of 657 feet below the surface of the ocean.

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The number 2/5 is both a ratio and a fraction.

The number 2/5 is both a ratio and a fraction. Fractions are meant to signify the numerator and denominator in an expression. in the above expression, we have the denominator as 5 and the numerator as 2.

The expression is also a ratio because it indicates the quantitative relationship between the figures.

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On solving the given equation, we have - 125 adult tickets and 179= children tickets.

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."

301= 104

6.40 =2.25

4.00=1.75

Suppose the number of adult ticket bought =x

And number of children tickets bought =  (301-x).

equation is

6.40(x) + 4(301-x) = 1504

6.40x + 1204 - 4x = 1504

2.40x = 300

x= 125

125 adult tickets and 179= children tickets.

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Answer:

From the given figure we can see that :---

MN||PO, MN=PO and MP=NO

Therefore, angle M=angle N (adjacent sides of the trapezoid)

\((8x - 16) = (6x + 20) \\ 2x = 36 \\ \boxed{x = 18}\)

angle M=angle N= (6×18)+20=108+20 =128°

angle O =(180°-128°)=52°

====================================

\( \large \sf \underline{Problems:}\)

====================================

\( \large \sf \underline{Answers:}\)

\( \large \qquad \qquad \bold{ \#1. \: x \: = \: 4}\)

\( \large \qquad \qquad \bold{ \#2. \: x \: = \: \frac{7}{2} }\)

\( \large \qquad \qquad \bold{ \#3. \: x \: = \: 6}\)

====================================

\( \large \sf \underline{Solutions:}\)

\( \therefore\) The answer of you're problem is x = 4.

====================================

\( \therefore\) The answer of you're problem is 7/2.

====================================

\( \therefore\) The answer of you're problem is x = 6.

====================================

Hope this helps!

Answer: Step-by-step explanation:

To find the average rate of change of a function over an interval, we can use the following formula:

average rate of change = (y2 - y1)/(x2 - x1)

Where x1 and x2 are the values of x at the beginning and end of the interval, and y1 and y2 are the corresponding values of the function at those points.

In this case, we are asked to compare the average rate of change of the functions g(x) and f(x) over the interval where -1≤x≤3.

For the function g(x) = x²+6x, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:

average rate of change = (g(3) - g(-1))/(3 - (-1))

= (9 + 18 - (1 - 6))/(4)

= 27/4

= 6.75

For the function f(x) = 2, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:

average rate of change = (f(3) - f(-1))/(3 - (-1))

= (2 - 2)/(4)

= 0

Since the average rate of change of the function g(x) is greater than the average rate of change of the function f(x), the function g(x) has a greater average rate of change over the interval where -1≤x≤3.

I hope this helps clarify the comparison of the average rate of change for these two functions. Do you have any other questions?

Answer:

table D

Step-by-step explanation: I got it right on edge

Answer:

table D

Step-by-step explanation:

Step-by-step explanation:

Let's solve the given questions step by step:

1. Determine the equation of f:

From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:

f(x) = a(x + p)^2 + q

Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:

4 = a(1 + p)^2 + q

This gives us one equation involving a, p, and q.

2. Determine the equation of g:

The equation of g is given as g(x) = 0.3x + p1.

3. Determine the coordinates of the x-intercept of g:

The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.

Setting g(x) = 0, we can solve for x:

0 = 0.3x + p1

-0.3x = p1

x = -p1/0.3

Therefore, the x-intercept of g is (-p1/0.3, 0).

4. For which values of x will f(x) ≥ g(x)?

To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.

f(x) = a(x + p)^2 + q

g(x) = 0.3x + p1

We need to find the values of x for which f(x) ≥ g(x):

a(x + p)^2 + q ≥ 0.3x + p1

Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.

To summarize:

We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).

The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

\(-x^2 + 7 = 2x + 4\)

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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The derivative of a composite function is given by the chain rule: the fifth derivative of fog(x) depends only on the second and fourth derivatives of f.

d(fog(x))/dx = df/d(g(x)) * d(g(x))/dx

The fifth derivative of fog(x) can be calculated by taking the derivative five times:

d^5(fog(x))/dx^5 = d^5f/d(g(x))^5 * (dg(x)/dx)^5 + 5 * d^4f/d(g(x))^4 * d^2g(x)/dx^2 * (dg(x)/dx)^3 + 10 * d^3f/d(g(x))^3 * (dg(x)/dx)^2 * (d^2g(x)/dx^2)^2 + 10 * d^2f/d(g(x))^2 * (dg(x)/dx) * (d^3g(x)/dx^3) + 5 * df/d(g(x)) * (d^4g(x)/dx^4)

Since g'(x) is constant, dg(x)/dx is also constant, and its derivative is 0. Therefore, all the terms with derivatives of g(x) higher than 1 are 0, leaving us with:

d^5(fog(x))/dx^5 = 5 * d^2f/d(g(x))^2 * (dg(x)/dx)^2 * d^2g(x)/dx^2 + 5 * df/d(g(x)) * d^4g(x)/dx^4

Since g'(x) is constant, dg(x)/dx and d^2g(x)/dx^2 are also constant, and can be replaced by their values. Therefore, the fifth derivative of fog(x) depends only on the second and fourth derivatives of f.

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A population of bacteria growing exponentially can be modeled as P(t)= P0e kt, where is the time in hours and P0 is the initial population. if the population has a doubling time of 3 hours, the growth constant  is k = ln(2) / 3 = 0.231049.

The growth constant (k) can be calculated by taking the natural log of 2 (ln(2)) and dividing it by the doubling time (3 hours). Therefore, the growth constant is 0.231049.  This equation models exponential growth, which is a type of growth where the rate of increase is proportional to the population size. In this case, the population doubles every 3 hours.

This exponential growth is modeled using the equation P(t)= P0e^kt, where P(t) is the population size at a given time, P0 is the initial population size, and k is the growth constant.  By finding the growth constant, we can predict the population size at any given time. The growth constant is found by taking the natural log of 2 (ln(2)) and dividing it by the doubling time (3 hours).

This equation is used to find the amount of growth per unit time and is the same regardless of the population size. This equation can be used to predict the population size at any given time, allowing us to estimate the population size in the future.

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Solution : \(F(n)= (320) 1.25^{n-1}\)

In Maths, Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern. Also, learn arithmetic progression here. The common ratio multiplied here to each term to get a next term is a non-zero number. An example of a Geometric sequence is 2, 4, 8, 16, 32, 64, …, where the common ratio is 2.

A geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio. The next term of the sequence is produced when we multiply a constant (which is non-zero) by the preceding term. It is represented by:

a, ar, ar2, ar3, ar4, and so on.

Where a is the first term and r is the common ratio.

Note: It is to be noted that when we divide any succeeding term from its preceding term, then we get the value equal to the common ratio.

Suppose we divide the 3rd term by the 2nd term we get:

ar2/ar = r

In the same way:

ar3/ar2 = r

ar4/ar3 = r

General Form of Geometric Progression

The general form of Geometric Progression is:

a, ar, ar2, ar3, ar4,…, arn-1

Where,

a = First term

r = common ratio

ar^(n-1) = nth term

On the first day, the video was viewed = 320 times.

the number of views was 25% more than the day before which means increasing 1.25 per day.

G.P.

Where common ratio r = 1.25

First term = f(1) = 320

The formula of nth term in G.P. =

\(F(n)= f(1) r^{n-1}\)

So, nth term of the given situation :

\(F(n)= (320) 1.25^{n-1}\)

Where f(n) denotes the number of views on an nth day.

\(F(n)= (320) 1.25^{n-1}\)

So, the number of views Vera's video got on an nth day =

\(F(n)= (320) 1.25^{n-1}\)

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Answer:

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Step-by-step explanation:

Answer:

imma go with the answer A

Step-by-step explanation:

hope this helps

Answer:

depends on the ammount

Step-by-step explanation:

The common ratio of a geometric sequence will be;

⇒ r = 5 / 10

What is Geometric sequence?

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

In a geometric sequence,

The third term is 100 and the eighth term is 3.125.

Now,

We know that;

The nth term of geometric sequence is,

⇒ \(T_{n} = a r^{n - 1}\)

Hence, The third term is;

⇒ \(T_{3} = a r^{3 - 1} = 100\)

⇒ \(a r^{2} = 100\)   ..(i)

And, The eighth term is,

⇒ \(T_{8} = a r^{8 - 1} = 3.125\)

⇒ \(a r^{7} = 3.125\)   ..(ii)

Divide equation (ii) by (i), we get;

⇒ ar⁷ / ar² = 3.125/100

⇒ r⁷ / r² = 3125 / 100000

⇒ r⁷⁻² = 3125 / 100000

⇒ r⁵ = 3125 / 100000

⇒ r = 5/10

Thus, The common ratio of a geometric sequence will be;

⇒ r = 5 / 10

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Answer:

equilateral for the first one scalene for the second one scalene for the third one equilateral for the fourth one

Step-by-step explanation:

The domain of function A and function B are compared by the statement of Option A: The domain of Function A is the set of real numbers greater than 0. The domain of Function B is the set of real numbers greater than or equal to 1.

What is a function?

A function is a fundamental concept in mathematics that relates a set of inputs (also known as the domain) to a corresponding set of outputs (sometimes referred to as the codomain). For each input, there exists exactly one output, and the output can be linked to its corresponding input in a unique manner.

The domain of a function refers to the set of all possible input values for which the function can produce an output.

In Function A, the domain consists of all real numbers greater than 0, since it is a logarithmic function that can take any positive number as an input.

In contrast, the domain of Function B includes all real numbers greater than or equal to 1, since it is a square root function that begins at (1,0) and continues to infinity.

This means that any number greater than or equal to 1 can be used as an input to produce a corresponding output.

It is essential to define the domain of a function accurately to ensure that the function is well-defined and to avoid potential errors or ambiguities in mathematical computations.

Therefore, the correct statement is A.

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The expression for the perimeter is P = 12x - 16

The given parameters are

Length = 3x + 1

Width = 3x - 9

The perimeter is calculated as

P = 2 * (Width + Length)

So, we have

P = 2 * (3x + 1 + 3x - 9)

Evaluate

P = 2* (6x - 8)

Expand

P = 12x - 16

Hence, the expression for the perimeter is P = 12x - 16

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The surface area of the given shape is 285.01 ft²

From the question, we are to calculate the surface area of the given shape.

The given shape in the diagram is a cone.

The surface area of a cone is given by the formula,

\(S = \pi r(r+l)\)

Where S is the surface area

r is the radius

and \(l\) is the slant height

First, we will calculate the slant height of the cone

\(l^{2}=9^{2} +5.6^{2}\) (Pythagorean theorem)

\(l^{2}=81+31.36\)

\(l^{2}=112.36\)

\(l}=\sqrt{112.36}\)

\(l=10.6 \ ft\)

∴ The slant height is 10.6 ft

Now, for the surface area

\(S = \pi \times 5.6(5.6+10.6)\)
\(S = \pi \times 5.6(16.2)\)

\(S = 90.72\pi \ ft^{2}\)

\(S = 285.0053 \ ft^{2}\)

S ≅ 285.01 ft²

Hence, the surface area of the given shape is 285.01 ft²

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Step-by-step explanation:

\(\frac{3x+5}{2x-1} +\frac{7x+3}{1-2x}=\frac{3x+5}{2x-1}-\frac{7x+3}{2x-1} =\frac{-4x+2}{2x-1}=-2.\)

this experssion does not depend on x, then for its domain: x∈(-∞;+∞).

The diagram shows the quantity x is 13.

A tape diagram, also known as a bar model or a strip diagram, is a visual representation of a problem or situation that helps students to organize and solve mathematical problems. It involves drawing a rectangular strip or bar to represent a quantity or a value, and then dividing or labeling the strip to represent different parts of the problem.

The full completed question is related to an equation as shown in the below diagram (Check it).

Given equation is x+4 = 17

If we select part 'a' the diagram is shown in the below diagram, see it.

For part 'b' the quantity x can be represent by:

x+4 = 17

x = 17 - 4

x = 13

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