The number pi goes on forevermore with no repeating pattern therefore is it rational

Answer:

STEP 1

Step-by-step explanation:

Answer:

Option B JM is the right answer.

Step-by-step explanation:

The distance that represents the distance from point J to KL is JM.

The distance between any given point and a line is the shortest distance between a fixed point and any point on the line.

This implies that it is the length of the perpendicular line segment on the line and passes through the point.

Here, in the figure, JM is perpendicular to the line KL drawn from the point J.

So, the answer is JM.

perimeter = 2L +2W, divide total perimeter by 2 for total length of 1 side and 1 width

172/2 = 86 ( total for 1 side and 1 width)

86-24 = 62 (since length is 24 ft longer subtract 24 then divide by 2 for width)

62/2 = 31

width = 31 feet

length = 31 +24 = 55 feet

check: 31*2 = 62, 55*2 = 110,  110+62 = 172

The answers are 12x+8y≥1000, 12x+8y≤1000, x+y≤200, and x+y≥200,

The explanation behind the first equation is 12x signifies the regular tickets, being at $12 each. And 8y signifies the student tickets being $8 each. The symbol is "≥", because the manager wants $1000 or more from the ticket sale. While the second equation, just the same with the first but the symbols differ since the sale could be lesser than 1000.

The explanation behind the third equation is 200 is the number of seats at most. In the fourth equation, if many people came, they would lack seats so that’s why the greater sign is used.

linear means first degree

first degree means the hightest exponent of the variables is 1

so

equation 1:

[tex]y=2x^2+1[/tex]

highest exponent is 2, not 1

not leinear

equation 2: y^2=3x+1

highest exponent is 2, not 1

not linear

equaton 3 y=5x-1

y=5x^1-1, it is 1

it is linear

equaton 4

y=4x^4-1

highest is 4, not 1

not linear

answer is equation 3: y=5x-1

Answer:

equation 3

Step-by-step explanation:

Answer:

[tex]base=\frac{4x+16}{height}[/tex]   which is the required expression.

Step-by-step explanation:

We have been given the area of parallelogram which is (4x+16)

And the formula for area of parallelogram is [tex]base\cdot height[/tex]

Hence, when we substitute the value if area of parallelogram in the formula we get:

[tex]4x+16=base\cdot height[/tex]

Now, rearranging the terms so, as to get the expression for the base or value of base in terms of height and area we get:

[tex]base=\frac{4x+16}{height}[/tex]   which is the required expression.

Sound travels at different speeds depending on the medium, moving faster in more rigid and denser mediums, like stone, than in compressible and less dense mediums, like air. At sea level and room temperature, sound waves move at approximately 343 meters per second. Light travels much faster than sound, thereby reaching observers noticeably sooner than sound over larger distances.

The speed at which sound travels depends on the characteristics of the medium through which the sound is moving, specifically its rigidity and density. Sound waves move through a medium such as stone faster as it is more rigid (less compressible) and denser than a medium like air. This is why in your graph, sound travels 5971 meters in stone in one second, but only 346 meters in air in the same time period.

Sound waves are mechanical, pressure waves. In a vacuum where there are no molecules to oscillate, there are no sound waves. Variations in altitude, temperature, and the medium of transmission influence the speed of sound waves. For instance, at sea level and a temperature of 20° C, sound waves move in the air at approximately 343 meters per second.

Sound and light are both waves and travel at finite speeds. However, light travels significantly faster than sound, hence you see light from a fireworks display before hearing the sound. The speed difference between light and sound waves becomes noticeable over distances.

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The volume of the pyramid is 2520 cubic cm if the length is 24 cm, width is 18 cm, and height is 35 cm of the pyramid.

It is defined as a three-dimensional space enclosed by an object or thing.

As we know the volume of a pyramid is given by:

[tex]\rm Volume = \dfrac{1}{3} \times B\times H[/tex]

B is the base area of the pyramid.

We have L = 24 cm, W = 18 cm, and H = 35 cm

B = (24×18)/2 = 216 square cm

[tex]\rm Volume = \dfrac{1}{3} \times 216\times 35[/tex]

Volume = 2520 cubic cm

Thus, the volume of the pyramid is 2520 cubic cm if the length is 24 cm, width is 18 cm, and height is 35 cm of the pyramid.

Learn more about the volume here:

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point slope form is y=mx+ b

m is slope which is given as 1/2

 replace x & y into the equation to solve for b

b = 6

 so equation is y =1/2x+6

Since b = c, the angles B and C also equal

 so you get
180 - 45 = 135
135/2 = =67.5 for each angle

now we know 2 sides and all 3 angles, use the law of sines to find a

b/sin B = a/sin A

4/(sin 67.5) = a/(sin 45)

a = 4(sin 45)/(sin 67.5)

a^2 = (4(sin 45)/(sin 67.5))^2

a^2 = 9.37

 Answer is C

Given that the product of two numbers will be smallest when the two numbers are equal, the numbers closest to this rule given the condition of having a fixed difference of 44 are -22 and 22.

This problem falls under the branch of Mathematics called optimization problems in calculus. In this case, we are asked to find two numbers differing by 44 whose product is smallest. Remember that the product of two numbers that are a fixed difference apart will be smallest when the two numbers are equal. But since we can't have that according to the problem's conditions, we will have to get the closest possible which is making the two numbers as close to each other as possible.

Let's denote the smaller number as 'x'. Consequently, the larger number will be 'x + 44'. The product of these two numbers (which we want to minimize) is given by the function f(x) = x * (x + 44). To find the minimum, you would typically take the derivative of this function, set it equal to zero, and solve for 'x'. However, since we're dealing with a quadratic function, we know the graph is a parabola that opens upwards, and thus the minimum point is at the vertex. In a quadratic function given in the form of f(x) = a*(x - h)² + k, the vertex is at the point (h, k). Comparing this with our quadratic function, we can see by inspection that our 'h' is '-22'. Therefore, the two numbers are -22 and 22.

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The smallest product of two numbers differing by 44 is -484. These numbers are -22 and 22.

This problem is solvable using the principle of quadratic minimum. Let's denote the two numbers as x and x + 44. Their product equals x(x + 44) = x2 + 44x.

This is a quadratic function with a positive leading coefficient (x2), therefore, it will yield a minimum value. The x-value for this minimum can be found using the formula -b/2a for any quadratic ax2 + bx + c, where a = 1 and b = 44. Calculating, -b/2a = -44/2 = -22.

This means that the product will be smallest when x = -22. However, since we're looking for two numbers that differ by 44, the necessary pairs are -22 and 22. The product of these two numbers, (-22)(22), equals -484, which is indeed the smallest possible product for two numbers differing by 44.

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we know that

In a [tex]30-60-90[/tex] triangle

the ratio between the lengths of the two legs is equal to the tangent

so

[tex]tan(30\°)= \frac{1}{\sqrt{3}}= \frac{\sqrt{3}}{3}[/tex]

[tex]tan(60\°)= \sqrt{3}[/tex]

therefore

the answer is

Option B

[tex]\frac{1}{\sqrt{3}}[/tex] -------> could be the ratio

because is the value of the [tex]tan(30\°)[/tex]

Option C

[tex]\frac{\sqrt{3}}{3}[/tex] ------> could be the ratio

because is the value of the [tex]tan(30\°)[/tex]

Option E

[tex]\frac{3}{3\sqrt{3}}=\frac{1}{\sqrt{3}}[/tex] -------> could be the ratio

because is the value of the [tex]tan(30\°)[/tex]

19340 * (1-0.125)^10 =

19340 * 0.875^10 =

$5087.88  round to 5088

Answer:

[tex]b = \sqrt{csquare - a square[/tex]

Step-by-step explanation:

Answer:

The shape of that graph is a concave and strictly increasing curve, as shown in the attached graph.

Step-by-step explanation:

The natural logarithm, ln (x), is the inverse of the exponential function and defined in x only for positive real numbers, in addition, it is an irrational number.

From the analytical point of view, it can be defined that for any positive real number x> 0 as the area under the curve y = 1 / t between 1 and x. The natural logarithm is a function with domain of definition of positive real numbers.

Some of the properties of the natural logarithm are: it is a bijective, concave, strictly growing and continuous function

Answer:

b. Increasing x > 0; Decreasing x < 0

Step-by-step explanation:

We have been given graph of a function. We are asked to find the intervals on which our function is increasing and decreasing.

We know that when graph of function is going upwards from left to right then the graph is increasing.

When graph of function is going downwards from left to right then the graph is decreasing.

Upon looking at our given graph, we can see that for x values less than 0, the graph is going downwards from left to right, therefore, our function is decreasing on interval [tex]x<0[/tex].

We can see from our given graph that for x values greater than 0, the graph is going upwards from left to right, therefore, our function is increasing on interval [tex]x>0[/tex].