A parabola has the equation –5x^2 + 30x – y – 34 = 0. Which equation is that of the parabola in vertex form? ...?

Answer:

Salesman's commission 4% of total monthly sales.

Step-by-step explanation:

A sneaker store salesman had $4,125 in total monthly sales last month.

He made $165 in commission from those sales.

Suppose, it is x% of the total sale.

So, x% of $4125 will be,

[tex]=4125\times \dfrac{x}{100}[/tex]

According to the question it is equal to $165, so

[tex]\Rightarrow 4125\times \dfrac{x}{100}=165[/tex]

[tex]\Rightarrow x=\dfrac{165\times 100}{4125}[/tex]

[tex]\Rightarrow x=\dfrac{16500}{4125}[/tex]

[tex]\Rightarrow x=4\%[/tex]

Therefore, salesman's commission 4% of total monthly sales.

Answer: 4%

Step-by-step explanation:

Due to the fact that the salesman had $4,125 in total monthly sales the previous month, the answer would be 4%

Final answer:

9.7814 rounded to the nearest whole number is 10, as the first digit after the decimal point is 7, which requires rounding up.

Explanation:

To find the nearest whole number to 9.7814, we need to look at the first digit after the decimal point. Since this digit is 7 (which is equal to or greater than 5), we round up the number. Rounding up changes 9.7814 to the next whole number, which is 10.

The general rule for rounding to the nearest whole number is:

Therefore, 9.7814 rounded to the nearest whole number is 10.

we know that

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so

Let

a,b,c------> the length sides of a triangle

The theorem states that three conditions must be met

case 1)

[tex] a+b > c [/tex]

case 2)

[tex] a+c > b [/tex]

case3)

[tex] c+b > a [/tex]

therefore

the answer is the option

B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

To find the indicated function values of the inverse of a function, substitute the given values into the original function and solve for x.

To find the indicated function values of the inverse of the function f(x)=x^3+4x-1, without solving for the inverse function, we substitute the given values into the original function and solve for x.

(a) To find f^-1(-1), we substitute -1 into the function: f(-1)=(-1)^3+4(-1)-1 = -1+(-4)-1 = -6.

(b) To find f^-1(4), we substitute 4 into the function: f(4)=(4)^3+4(4)-1 = 64+16-1 = 79.

The given sequence involves a two-part pattern. One part is halving the previous number and the other part alternates between 4 and 6. Considering the pattern, the next number should be 0.5.

The sequence 8,4,2,6,3,2,4 appears to have a pattern. It seems to be a two-part pattern that alternates. The first part, observed in the numbers 8, 2, and 2, is halving (8 divided by 2 is 4, and 2 divided by 2 is 1, and 1 by 2 is 0.5). Then, the second part, observed in 4,6,4, seems to alternate between 4 and 6. So, if the pattern continues, the next number after 4 should be 0.5 from the first part of the pattern.

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The sequence could actually be representing two series - one series is halving the number (8 to 4 to 2) and the other is multiplying each number by 2 (3 to 2 to 4 to 8). Thus, the next number could either be 1 (if we continue the halving series) or 12 (if we continue the multiplying by 2 series).

The number sequence provided seems to be made of two different series interwoven. One series is halving each number (8 to 4 to 2), and the other series is multiplying each number by 2 (2 to 4 to 6 to 12).

Therefore, the next number after 8, 4, 2, 6, 3, 2, 4 should be 1 (half of 2) whereas the next number in the second series after 6, 3, 2, 4 should be 12 (four times 3). So, depending on which pattern the sequence is following, the next number could be either 1 or 12.

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The equation of line WX in slope-intercept form is,

⇒ y = 1/2x + 3

And, Lines WX and Kl are not parallel lines because its slopes are not equal to each other.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation of line KL is,

⇒ y = - 1/2x - 6.

And, The equation line WX is,

⇒ 7x - 14y = - 42

Now,

The equation of line WX in slope-intercept form is,

⇒ 7x - 14y = - 42

⇒ 7x + 42 = 14y

⇒ 14y = 7x + 42

⇒ y = 7x/14 + 42/14

⇒ y = 1/2x + 3

Hence, Slope of equation of line WX is,

⇒ y = 1/2x + 3

⇒ dy/dx = 1/2

⇒ m = 1/2

And, Slope of equation of line KL is,

⇒ y = - 1/2x - 6

⇒ dy/dx = - 1/2

⇒ m = - 1/2

We know that;

Slopes of parallel lines are equal.

Hence, Lines WX and Kl are not parallel lines because its slopes are not equal to each other.

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Answer:

It includes points in Quadrant II.

It does not include points in Quadrant I.

Step-by-step explanation:

Given : If f(x) is an odd function and the graph of f(x) includes points in Quadrant IV.

To find :  which statement about the graph of f(x) must be true.

Solution : We have given that f(x) is an odd function is lies in Quadrant IV.

Definition of an odd function: the y-value of the function at negative x is always opposite sign as the y-value of function at opposite x.

Like  (x ,-y) or (x , -y)

In odd function x and y values are in opposite sign that mean odd function always lies in Quadrant II and  Quadrant IV.

It does not include points in Quadrant I

Therefore, It includes points in Quadrant II.

It does not include points in Quadrant I.

Answer:

includes quad 2

Step-by-step explanation:

The prime factorization of the number 126 is 2,3,3, and 7.

Any number can be represented as a sum of prime numbers by prime factorization. A number with exactly two factors, 1 and the number itself, is said to be a prime number. As an illustration, the prime factorization of 18 is 2,3, and 3.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the number is 126. The prime factorization of the number 126 will be calculated as:-

126 = 2 x 3 x 3 x 7

Hence, the prime factorization of the number 126 is 2,3,3, and 7.

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Final answer:

The translation rules in geometry involve moving every point in a figure the same distance and direction. For a horizontal translation, add or subtract the same value from the x-coordinate of each point. For a vertical translation, add or subtract the same value from the y-coordinate of each point.

Explanation:

In geometry, translation is a transformation that moves every point in a figure the same distance and direction. The translation rules involve determining the new coordinates of the translated figure.

The translation rules in geometry can be summarized as:

For example, if you have a point with coordinates (2, 3) and you want to translate it 3 units to the right and 2 units up, you would add 3 to the x-coordinate and 2 to the y-coordinate to get the new coordinates of the translated point: (5, 5).