the area of a circle is 78.5 square centimeters, and a subtending arc on the circle has an arc length of 6 pie. what is he measure of the angle subtended by the arc?

When graphed, a function and its inverse function become symmetrical across the line y = x.  

A function that is symmetric is a function whose variables remain constant regardless of the ways in which the variables are permutated.

Hence When graphed, a function and its inverse function become symmetrical across the line y = x.

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The reasoning is because you are subtracting 2. If you were to be adding 2, then it would be -6.

Since you are subtracting 2 it = 10.

Glad to help a Senior mod out.

Thanks, Plip.

Answer: Options Third, Second , Fourth are correct.

Step-by-step explanation:

Since we have given that

[tex]6x^2\\\\9x^8\\\\16x^9\\\\25x^{12}\\\\36x^{16}[/tex]

Since we know that

9, 16, 25, 36 are perfect squares.

So, we get that

[tex]9x^8=(3x^4)^2\\\\25x^{12}=(5x^6)^2\\\\36x^{16}=(6x^8)^2[/tex]

Hence, Options Third, Second , Fourth are correct.

Answer:

Option C is the answer.

Step-by-step explanation:

The given expression is [tex]\frac{(5-3x)}{5}[/tex]

We solve it further to get the simplified form.

[tex]\frac{(5-3x)}{5}[/tex] = [tex]\frac{5}{5}-\frac{3x}{5}[/tex]

= [tex](1-\frac{3x}{5})[/tex] [Since [tex]\frac{a-b}{a}=\frac{a}{a}-\frac{b}{a}][/tex]

Therefore, option C matches the simplified form of the expression.

The side lengths of the triangle are 8 cm, 12 cm, and 16 cm

To solve for the side lengths of the right triangle, we can use the Pythagorean Theorem, which states that for any right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, this is written as a^2 + b^2 = c^2.

Let's denote the shorter leg of the triangle as x. Then, according to the problem, the longer leg is x + 4 cm and the hypotenuse is x + 8 cm. Plugging these expressions into the Pythagorean Theorem, we have:

x^2 + (x + 4)^2 = (x + 8)^2

Expanding and simplifying the equation:

x2 + x2 + 8x + 16 = x2 + 16x + 64

2x2 + 8x + 16 = x2 + 16x + 64

x2 - 8x - 48 = 0

Solving this quadratic equation for x, we find:

x = 8 cm (shorter leg)

x + 4 = 12 cm (longer leg)

x + 8 = 16 cm (hypotenuse)

Therefore, the side lengths of the triangle are 8 cm, 12 cm, and 16 cm

Parabola is a plane curve with a U shape.

The parabola equation is given as:

y = a (x – h)² + k

The equation of a parabola that has a vertex (-3, 7) and passes through the point (-2, 11) is y = 11.

Parabola is a plane curve with a U shape.

The parabola equation is given as:

y = a (x – h)² + k

(h, k) is the vertex.

We have,

Parabola:

Vertex = (-3, 7)

Passes through the point = (-2, 11)

The equation of the parabola is y = a (x - h)² + k

(-3, 7) = (h, k)

Since the parabola passes through the point (-2, 11) we get,

11 = a (-2 - (-3))² + 11

11 = a (-2 + 3)² + 11

11 = a x 1 + 11

11 = a + 11

Subtract 11 on both sides.

0 = a

a = 0

Now,

y = 0 (x + 3)² + 11

y = 0 + 11

y = 11

Thus,

The equation of a parabola that has a vertex (-3, 7) and passes through the point (-2, 11) is y = 11.

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The equation representing the number of people, y, at the fair x hours after the gates open:

y = 68 * 1.5^(x-1)

Initial number of people: 68 (given)

Growth factor per hour: 1.5 (given)

Number of hours since gates opened: x

The equation uses the following logic:

Start with the initial number of people (68).

Multiply by the growth factor (1.5) to account for the increase after the first hour.

Since the growth factor applies after each hour, raise it to the power of (x-1) to account for the total number of times it's applied after x hours. This is because the first hour's growth is already accounted for in the initial number.

Therefore, the equation y = 68 * 1.5^(x-1) accurately represents the number of people at the fair x hours after opening.

Complete question:

When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. If this pattern continues, write the equation representing the number of people, y, at the fair x hours after the gates open.

The function f(x)=300-25x represents the decline of population in a fishing lake that was initially stocked with 300 bass. Each year, the population reduces by 25. For instance, after 4 years, the number of bass left in the lake would be 200.

The question is about a fishing lake that was initially stocked with 300 bass. As per the information given, the population of bass in the lake decreases by 25 each year. Therefore, if we let x represent the number of years, then every year, the number of bass decreases by 25x. This relationship is represented by the algebraic function f(x)=300-25x.

To provide a practical understanding, suppose you want to calculate the number of bass remaining after 4 years. You just substitute '4' in place of x in the equation. Hence, f(4) = 300 - 25 * 4 = 300 - 100 = 200. So, after 4 years, there would be 200 bass remaining in the lake.

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Jim Shu made two mistakes in simplifying radicals: they missed the initial steps and included an irrelevant step of checking the answer's reasonability.

The instructions provided to Jim Shu involve simplifying radicals, but there is an omission of the initial steps in the process.

The student proceeds with step 6 without detailing the necessary earlier steps in simplifying the algebraic expression.

This misstep results in an incomplete representation of the solution process.

Furthermore, step 7 introduces an unrelated directive, advising the student to check the answer for reasonability.

This step is incongruent with the task at hand, which is the simplification of radicals.

To address this error, Jim Shu should incorporate the essential preliminary steps for simplifying radicals, ensuring a comprehensive presentation.

Additionally, the extraneous step of checking reasonability should be omitted, aligning the solution process with the given directions.

The given sequence is 25, 10, 4.

Notice that this is a geometric sequence because here we have equal common ratio.

So, common ratio : r = [tex] \frac{a_{2}}{a_{1}} [/tex]

= [tex] \frac{10}{25} [/tex]

= 0.4

So, each term is 0.4 times of it's previous term.

Hence, to get the next term of this sequence, multiply 0.4 with the third term 4.

So, fourth / next term = 4* 0.4 =1.6

Hence, next term of this sequence is 1.6.

Hope this helps you!

Answer:

Step-by-step explanation:

the answer is 8/5 i just did it on my quiz and got it right.

John can make a profit by selling ice cream from the cylindrical jar. After calculating the volume, he would earn approximately $15.70 in revenue, and by deducting the initial cost ($7), he makes a profit of around $8.70.

To determine if John will make a profit by selling the entire ice-cream cylindrical jar, we first need to calculate the volume of the jar to find out how many cones he can fill. The jar has a diagonal of 20 cm and a height that is three times its width. Assuming the width is 'w' and height is '3w', we can use the Pythagorean theorem with the jar's diagonal to find 'w', since the diagonal forms a right triangle with the width and height of the cylinder.

The formula for the Pythagorean theorem is diagonal^2 = width^2 + height^2, which gives us 20^2 = w^2 + (3w)^2. Solving for 'w', we get w = 4 cm and height = 12 cm. The volume 'V' of the cylinder is given by V = π * radius^2 * height, which gives us V = π * 2^2 * 12, therefore, V = 48π cm^3. Then, we divide the jar's volume by the volume of each ice cream cone to find the number of cones, 48π cm^3 / 30 cm^3/cone ≈ 5π cones.

Given that John sells each cone for $1, the total revenue from selling all the ice-cream cones would be approximately $5π. Since π is approximately 3.14, his total revenue would be about $15.70. Subtracting the initial cost of the jar ($7), we find that John would make a profit of approximately $8.70.

Therefore, John will indeed make a profit out of selling the jar of ice cream.

it is a translation.

The given information is not clear enough to determine the measure of angle G p//r.

To find m<G p//r, we need to understand the given diagram. However, the provided information is not clear enough to determine the measure of angle G p//r. More information or a clear diagram is needed to find the angle accurately. Please provide additional details or a clear diagram for further assistance.

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Answer:

0.005377 people/m²

Step-by-step explanation:

5377 people/km² can written as

5377 × [tex]\frac{people}{km^2}[/tex]

Now we have to find the value in [tex]\frac{people}{meter^2}[/tex]

Since 1 km = 1000 meter.

So 5377 × [tex]\frac{people}{km^2}[/tex] = 5377 × [tex]\frac{people}{(1000)^2met^2}[/tex]

= [tex]\frac{5377}{(1000)^2}[/tex] people per met²

=  [tex]\frac{5377}{(1000000)}[/tex]

= 0.005377 people/m²