The roof of a factory rises vertically 7 ft through a horizontal run of 42 ft. What is the pitch of the roof?

Answer:

2600

Step-by-step explanation:

The answer to your question is B :)

The total number of animals in a shelter is 50 and number of cats in the shelter is 34.

Given that, a animal shelter has 16 puppies. If the puppies are 32% of the total dogs and cats population.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Let x be the total number of dogs and cats are in the animal shelter.

So, 32% of x=16

⇒ 32/100 ×x=16

⇒ 0.32x=16

⇒ x=16/0.32

⇒ x=50

So, number of cats =50-16

= 34

Therefore, the total number of animals in a shelter is 50 and number of cats in the shelter is 34.

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The general form of the equation of a circle with centre at [tex]\((a, b)\)[/tex] and radius [tex]\(m\)[/tex] is: [tex]\[ x^2 + y^2 - 2ax - 2by + (a^2 + b^2 - m^2) = 0 \][/tex].

The general form of the equation of a circle is [tex]\( (x - h)^2 + (y - k)^2 = r^2 \)[/tex], where [tex]\((h, k)\)[/tex] represents the centre of the circle and [tex]\(r\)[/tex] represents the radius.

If we expand and rearrange this equation, we get [tex]\( x^2 + y^2 - 2hx - 2ky + (h^2 + k^2 - r^2) = 0 \)[/tex].

Comparing this with the given options, we see that [tex]\( h = a \), \( k = b \), and \( r = m \)[/tex].

Substituting these values into the general form, we get [tex]\( x^2 + y^2 - 2ax - 2by + (a^2 + b^2 - m^2) = 0 \)[/tex], which matches the correct option.

Complete Correct Question:

What is the general form of the equation of a circle with center at (a, b) and radius of length m?

a. x2 + y2 - 2ax - 2by + (a2 + b2 - m2) = 0.

b. x2 + y2 + 2ax + 2by + (a2 + b2 - m2) = 0.

c. x2 + y2 - 2ax - 2by + (a2 + b2 + m2) = 0.

d. x2 + y2 + 2ax + 2by + a2 + b2 = -m2.

The function [tex]f[/tex] in terms of the radius [tex]r[/tex] that represents the area of the shaded region is [tex]f(r) = 2\pi\cdot r^{2}[/tex].

The area of the shaded region is the sum of the areas of the two circles of same radius, each of them represented by the following formula:

[tex]A_{r} = \pi\cdot r^{2}[/tex] (1)

Where:

Then, the formula for the shaded area is:

[tex]f(r) = 2\cdot A_{r}[/tex]

[tex]f(r) = 2\pi\cdot r^{2}[/tex] (2)

The function [tex]f[/tex] in terms of the radius [tex]r[/tex] that represents the area of the shaded region is [tex]f(r) = 2\pi\cdot r^{2}[/tex]. [tex]\blacksquare[/tex]

The figure is missing and the statement present mistakes. Correct statement is shown below:

Two circle are inscribed inside squares. Write a function [tex]f[/tex] in terms of the radius [tex]r[/tex] that represents the area of the shaded region. Leave your answer in terms of π.

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The length of rectangular outdoor patio is 17 feet and the width is 13 feet.

Given that, the perimeter of a rectangular outdoor patio is 60 ft.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Let the width of the rectangular outdoor patio be x.

Then, the length is 4 ft greater than the width = x+4

Now, perimeter = 2(x+x+4)

⇒ 2(2x+4) = 60

⇒ 4x+8=60

⇒ 4x=52

⇒ x=13

Length = x+4 = 17

Therefore, the length of rectangular outdoor patio is 17 feet and the width is 13 feet.

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Answer:

[tex]\frac{2\sqrt a}{a}[/tex]

Step-by-step explanation:

The given equation is  [tex]2a^{-1/2}[/tex]

The exponent rule: [tex]x^{-a}=\frac{1}{x^a}[/tex]

Using this rule, we get

[tex]2a^{-1/2}\\\\=\frac{2}{a^1/2}[/tex]

We can rewrite this in radical form as

[tex]\frac{2}{\sqrt a}[/tex]

Rationalize the denominator by multiplying numerator and denominator by [tex]\sqrt a[/tex]

[tex]\frac{2}{\sqrt a}\cdot \frac{\sqrt a}{\sqrt a}[/tex]

On simplifying

[tex]\frac{2\sqrt a}{a}[/tex]

Answer:

B. 43

Step-by-step explanation:

The measure of one angle in an octagon is 135.625 degrees.

Let's denote the measure of one angle as x.

Since there are eight angles in an octagon,

the sum of all the angles in the octagon is 180(x) + 7(2x) = 180x + 14x = 194x.

We know that the sum of the angles in any polygon is equal to (n-2) times 180 degrees, where n is the number of sides of the polygon.

Therefore, 194x = (8-2) × 180. Solving this equation,

we find that x = 135.625. So, the measure of each angle is 135.625 degrees.

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By using the tangent function and the angles of depression given, we can calculate the distances from the boat to the lighthouse when it was first spotted and when it stopped. Subtracting the second distance from the first gives us the distance the boat traveled.

This is a question about Trigonometry, involving the concepts of angles of depression and distances. In the situation presented, we are given the height of the lighthouse (200 feet), and two angles of depression - 17°31' when the boat was first noticed and 46°41' when the boat stopped. We can use the tangent function to calculate the distance from the lighthouse to the boat at these two points, then subtract these distances to find how far the boat traveled.

The tangent of an angle in a right triangle is equal to the opposite side divided by the adjacent side. Therefore, when the angle of depression was 17°31', we can use the equation tan(17°31') = 200/distance1 to solve for the first distance. Similarly, for the angle of depression 46°41', we use the equation tan(46°41') = 200/distance2.

Solving these two equations separately will give us the distances from the boat to the lighthouse at these two moments. Then we subtract distance2 from distance1 to get the distance the boat traveled.

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Final answer:

To find the slope of the line given by 3x + 4y = -11, the equation is rearranged into the slope-intercept form, yielding a slope (m) of -3/4.

Explanation:

The question asks: What is the slope of the line 3x + 4y = -11?

To find the slope of the line, we first need to rearrange the equation into the slope-intercept form, which is y = mx + b, where m is the slope, and b is the y-intercept. Starting with the given equation

We isolate y on one side by first moving 3x to the right side of the equation, and then dividing everything by 4:

Now, in the form of y = mx + b, it's clear that the slope (m) of the line is -3/4.

After 8 years, there will be approximately 10,260 owls remaining in the wild. This calculation is based on an initial population of 20,000 owls decreasing by 8% annually, yielding a final population using the formula for exponential decay.

To find out how many owls will remain after 8 years, we can use the formula for exponential decay:

[tex]\[ \text{Final population} = \text{Initial population} \times (1 - \text{Rate of decrease})^{\text{Number of years}} \][/tex]

Given:

Initial population (P) = 20,000 owls

Rate of decrease (r) = 8% = 0.08

Number of years (t) = 8

Plugging in the values:

[tex]\[ \text{Final population} = 20,000 \times (1 - 0.08)^8 \][/tex]

[tex]\[ \text{Final population} = 20,000 \times (0.92)^8 \][/tex]

[tex]\[ \text{Final population} \approx 20,000 \times 0.513 \][/tex]

[tex]\[ \text{Final population} \approx 10,260 \][/tex]

So, after 8 years, there will be approximately 10,260 owls remaining in the wild.