what is 63 as the product of prime factors in ascending order?

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:

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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19340 * (1-0.125)^10 =

19340 * 0.875^10 =

$5087.88  round to 5088

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.

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.

Jesse’s annual premium would be $175.50. The correct option is A.

An annual premium is the amount of money paid by an insurance policyholder each year in order to keep their coverage.

It is usually paid all at once, but it can also be paid in installments throughout the year.

The amount of the premium is determined by factors such as the type of insurance, the level of coverage, and the policyholder's risk profile.

The face value of the policy is $75,000. Since the annual premium rate is $2.34 per $1000 of face value, the annual premium Jesse would have to pay is:

$75,000 / $1000 = 75

75 x $2.34 = $175.50

Therefore, Jesse’s annual premium would be $175.50. The correct option is a.

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Answer:

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

Step-by-step explanation:

11. y - y₁ = m(x - x₁)

y - 4 = ²/₃(x - 3)

y - 4 = ²/₃x - 2

y = ²/₃x + 2

12. y - y₁ = m(x - x₁)

y - 0 = ⁻¹/₅(x - 5)

y - 0 = ⁻¹/₅x + 1

y = ⁻¹/₅x + 1

Answer:

7.

Step-by-step explanation:

2/5x -3

If we plug in 25, we get:

2/5(25) - 3 =

50/5 - 3 =  

10 - 3

7

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

The correct equation for the given scenario is 38m + 150 = 3,000. Solving this equation, we find that it will take Paula approximately 75 minutes to finish her essay.

The question involves calculating how much time Paula needs to complete her essay based on her typing speed and desired essay length. Paula needs to write 3,000 words, but she already has 150 written. Therefore, she needs to write 3,000 - 150 = 2,850 more words. If she types at a rate of 38 words per minute, the number of minutes, represented as m, can be found using the equation 38m = 2,850. Therefore, the correct equation from the options is 38m + 150 = 3,000. Solving this equation for m gives m = 2,850 / 38 ≈ 75 minutes. Thus, option c) 38m + 150 = 3,000; m = 75 minutes is the correct answer.

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Reflexive Property of Congruence justifies the following statement ∠AOB ≅ ∠AOB. Option B is correct.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
∠AOB ≅ ∠BOB
It can be obtained, only by when the angle gets reflected.
So by the reflexive Property of Congruence justified.

Thus, the reflexive Property of Congruence justifies the following statement ∠AOB ≅ ∠AOB. Option B is correct.

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Answer:

100

Step-by-step explanation:

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].

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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