At a local department store, pants have been reduced to $26. this price is at 68.4% of the original price for pants. given this, what was the original price of the pants?

y = x^2 - 10x + 25 - 25

 y = (x-5)^2 - 25

 y+25 = (x-5)^2

 x-5 = +/-sqrt(y+25)

 And you get TWO inverses:

 x = 5 + sqrt(y+25), for x>=5

 x = 5 - sqrt(y+25), for x<=5

Answer:

[tex]y=5\pm \sqrt{(25+x)}[/tex]

Step-by-step explanation:

We are asked to find the inverse for the function [tex]y=x^2-10x[/tex].

We know that to find inverse, we interchange x and y values and then solve for y.

After interchanging x and y values, we will get:

[tex]x=y^2-10y[/tex]

Switch sides:

[tex]y^2-10y=x[/tex]

[tex]y^2-10y-x=x-x[/tex]

[tex]y^2-10y-x=0[/tex]

Now, we will use quadratic formula to solve for y.

[tex]y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]y=\frac{-(-10)\pm \sqrt{(-10)^2-4(1)(-x)}}{2(1)}[/tex]

[tex]y=\frac{10\pm \sqrt{100+4x}}{2}[/tex]

[tex]y=\frac{10\pm \sqrt{4*25+4x}}{2}[/tex]

[tex]y=\frac{10\pm \sqrt{4(25+x)}}{2}[/tex]

[tex]y=\frac{10\pm 2\sqrt{(25+x)}}{2}[/tex]

[tex]y=5\pm \sqrt{(25+x)}[/tex]

Therefore, the inverse function for our given function would be [tex]y=5\pm \sqrt{(25+x)}[/tex].

Answer:

This is true!

Step-by-step explanation:

P.S: keep in mind that the opposite is not true! If f is continuous at x = c, then f is NOT differentiable at x = c.

:)))

If f is differentiable at x = c, then f is continuous at x = c is not true.

Any point inside the range of a function's purview has a derivative, making it a computable function of one real variable. In these other phrases, each interior site in the domain of an invertible method's graph does indeed have a non-vertical line segment.

F is NOT differentiable at x = c if it is continuous at x = c.

When working with units, this quality is highly helpful since, if a curve is discrete, we automatically infer that it is indeed continuous.

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Answer:

  b.  –2x^5 + x^3/2 + x/4 + 1

Step-by-step explanation:

In the given expression, the degrees of the terms, in the order given, are ...

  1, 5, 3, 0

When the terms are properly arranged in standard form, they will be ...

  5, 3, 1, 0 . . . . descending order

The standard form of this expression is ...

  -2x^5 +x^3/2 +x/4 +1 . . . . . . matches choice B

Answer: b.–2x^5 + x^3/2 + x/4 + 1

Step-by-step explanation:

Answer:

1. C) Inverse Property of Multiplication

2. None of these. The answer is Associative property of Addition

3. C) Inverse Property of Multiplication

4. None of these. The answer is Associative property of Multiplication

Step-by-step explanation:

1.

Given a number a , the inverse property of multiplication states that

a * 1/a = 1  

and 1/a is called the multiplicative inverse of a.

So 8 * 1/8 = 1 features the inverse property of multiplication where a = 8.

2.

Given three numbers a,b,c , the associative property of addition states that a + (b + c) = (a + b) + c

In this case, a = -5, b = 8 and c = 10

3.

-4 x -1/4 = 1 features the inverse property of multiplication where a = -4.

4.

Given three numbers a,b,c , the associative property of multiplication states that  (a * b) * c = a * (b * c)

In this case, a = a, b = b and c = 3

The total number of rectangles and triangles used for the net of this solid is 4.

To find the total number of rectangles and triangles used for the net of a solid, we need to examine the shape of the solid. If the given solid has 4 faces, like a regular tetrahedron or a pyramid, then it will have 3 triangles and 1 rectangle. Hence, the total number of rectangles and triangles used for the net of this solid is 4, so the answer is option b.

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Answer: 16 signs

Step-by-step explanation: i not saying this cause the other person said it i am saying it because i tookthe question

[tex]\sum^5_{j=1} (5j-12)[/tex] represents the series in sigma notation.

The symbol Σ (sigma) is generally used to denote a sum of multiple terms. This symbol is generally accompanied by an index that varies to encompass all terms that must be considered in the sum.

Given is a series (-7 + (-2) + 3 + 8 + 13), we need to define it in sigma notation,

Therefore,

For j = 1 up to j = 5

j = 1

(5j - 12) = (5(1) - 12) = 5 - 12 = - 7

j = 2

(5j - 12) = (5(2) - 12) = 10 - 12 = - 2

j = 3

(5j - 12) = (5(3) - 12) = 15 - 12 = 3

j = 4

(5j - 12) = (5(4) - 12) = 20 - 12 = 8

j = 5

(5j - 12) = (5(5) - 12) = 25 - 12 = 13

This gives us the given series,

(-7 + (-2) + 3 + 8 + 13)

Hence, [tex]\sum^5_{j=1} (5j-12)[/tex] represents the series in sigma notation.

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Answer:

Option B is correct.

Obtuse triangle.

Step-by-step explanation:

Acute triangle:

In acute triangle, all angles are less than 90 degree.

Obtuse triangle:

In obtuse triangle, the triangle has an angle more than 90 degree.

Right triangle.

In right triangle, it has a right angle 90 degree.

Isosceles triangle.

In isosceles triangle, it can be acute, right or obtuse depends only on the apex angle.

Therefore, the triangle whose angles are all more that 90 degree is, Obtuse triangle.

Answer:

k = 22.5; xy = 22.5

your welcome

XD

Area of circle is 345.4 cm²

Given that;

Angle of sector = 45°

Area of sector = 13.75π cm²

Find:

Area of the circle

Computation:

Area of sector = [tex]\frac{\theta}{360}[/tex][Area of circle]

13.75π = [tex]\frac{\theta}{360}[/tex][Area of circle]

13.75(3.14) = [tex]\frac{45}{360}[/tex][Area of circle]

13.75(3.14) = [tex]\frac{45}{360}[/tex][Area of circle]

43.175 = 0.125[Area of circle]

Area of circle = 345.4 cm²

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Answer:

Option A is correct

Step-by-step explanation:

Given is a table which shows data from a survey about the amount of time students spend doing homework each week.

          College    HS

High    50            16

Low     5                0

Q1       7.5             9.5

Q3      15              14.5

 IQR    7.5             5

Median  11             13

Mean     13.8         10.7

Std dev 6.4            5.3

1.5IQR         11.25         7.5

Q1-1.5IQR     -9.38      -12

Q3+1.5IQR    37.5       29.5

WE find that there is only one outlier in college with 50 as high.

Except that all others are well within IQR range.  Hence outliers are minimum

So option A is right.

Final answer:

To determine the spread of data on student homework hours, IQR and standard deviation are used. The college data's spread is best described by IQR, while the high school data's spread is best described by standard deviation, making Option C the most suitable choice.

Explanation:

To measure the spread of the data for the amount of time students spend doing homework each week, we have two primary measures: the Interquartile Range (IQR) and the standard deviation (σ). IQR represents the difference between the third quartile (Q3) and the first quartile (Q1) and describes the spread of the middle 50% of the data. The standard deviation indicates how much the values in the dataset deviate from the mean, which can help in understanding the overall spread including potential outliers.

When dealing with outliers, it's important to consider that potential outliers are typically identified as values that are more than 1.5 × IQR above Q3 or below Q1. We would use the minimum (Low) and maximum (High) values provided alongside the IQR to check for outliers. For the college data, with a High of 50 and a Low of 5, the range is 45. For high school, the range is 16. Outliers could potentially affect the standard deviation significantly, making IQR a better measure for the middle spread of data.

Based on this, the college data with a wider range may be more affected by outliers, whereas the high school data with a smaller range may not. Therefore, the spread for the college data can be better described by the IQR, while the standard deviation can be a good measure for the high school data. This suggests that Option C: "The college spread is best described by the IQR. The high school spread is best described by the standard deviation." is the most suitable choice.