One endpoint of a line segment is at (4, 2). The line is bisected by placing the midpoint of the line segment at (−2, −1). What are the coordinates of the other endpoint?

A) (−4, −6)
B)(−8, −4)
C)(10, 5)
D)(−8, 4)

The given points are

[tex] P(4,1) , Q(3,-5) [/tex]

First we find the slope using slope formula which is

[tex] m= \frac{y_{2} - y_{1}}{x_{2}- x_{1}} [/tex]

Substituting the values of x1,y1 and x2, y2, we will get

[tex] m = \frac{-5-1}{3-4} = 6 [/tex]

Now we use slope point form, which is

[tex] y-y_{1} = m (x-x_{1}) [/tex]

Using the values of m,x1 and y1, we will get

[tex] y-1=6(x-4) \\
y-1=6x-24 \\
y = 6x-23 [/tex]

Answer: 3x^3-7x^2+5=7x^4+2x Is correct on edg

Step-by-step explanation:

The above answer will be calculated as -

The seating capacity of the class that follows an AP is 5180.

An arithmetic progression(AP) is a sequence or series of numbers such that the difference of any two successive members is a constant. The first term is a, the common difference is d, n is number of terms.

For the given situation,

There are 10 seats in the first row, 13 seats in the second row, 16 seats in the third row and so on. There are 56 rows.

This statement follows as Arithmetic Progression.

The series is 10,13,16,.....

Here [tex]a=10, d= 3[/tex]

Number of rows, [tex]n = 56[/tex]

The formula of sum of n terms of an AP is

[tex]S_{n} =\frac{n}{2} [2a+(n-1)d][/tex]

On substituting the above values,

⇒ [tex]S_{56} =\frac{56}{2} [2(10)+(56-1)3][/tex]

⇒ [tex]S_{56} =28 [20+(55)3][/tex]

⇒ [tex]S_{56} =28 [185][/tex]

⇒ [tex]S_{56} =5180[/tex]

Hence we can conclude that the seating capacity of the class that follows an AP is 5180.

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Answer:

a

Step-by-step explanation:

its a

Answer:C

Step-by-step explanation:

Original size of the picture

Answer:

Step-by-step explanation:

tour answer would me a or 1:2

1) The precise difference is 158.268.

2) The difference when rounded to the nearest whole number is 159.

3) the difference using front-end rounding is 150.

1) To find the difference, subtract the smaller number from the larger number:

[tex]217.64 - 59.372 = 158.268[/tex]

2) First, let's round each of the numbers to the nearest whole number.

217.64 rounds to 218.

59.372 rounds to 59.

Now, subtract these rounded numbers:

[tex]218 - 59 = 159[/tex]

3) Front-end rounding means rounding the numbers based on the left-most digit (or most significant digit). For simplicity, we will keep the first digit and change the others to zeros.

217.64 can be rounded to 200.

59.372 can be rounded to 50.

Now, subtract these rounded numbers:

[tex]200 - 50 = 150[/tex]

Final answer:

The factors of the number 211 are only 1 and 211 itself, indicating that it is a prime number. Thus, the correct answer is option a (1 and 211).

Explanation:

To find all the factors of 211, you need to determine all whole numbers that can divide 211 without leaving a remainder. Starting with the smallest factor, which is always 1, and ending with the number itself, because any number is divisible by itself, we iterate through the numbers between 1 and 211 to check if they are factors.

Through inspection or a process of trial and error, we find that there are no numbers other than 1 and 211 that can divide 211 evenly, indicating that 211 is a prime number. Therefore, the correct answer to the question 'Find all the factors of 211.' is option a. 1 and 211 are the only factors of 211

Answer:7.20

Step-by-step explanation:

The correct cost function for Vanessa’s clothing store per month is,

C = 7.20n + 825

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Vanessa is opening a clothing store. She plans to start by selling gym shorts.

Here, It costs her $4 for each pair of shorts, $3 for ink per shorts, and $0.20 a bag.

And, Vanessa also spends $750 on rent, $50 on electricity, and $25 on advertising each month.

Now, Let us assume that, n represent the number of things he sell.

Hence, We can formulate;

The correct cost function for Vanessa’s clothing store per month is,

C = (4 + 3 +  0.20)n + (750 + 50 + 25)

C = 7.20n + 825

Thus, The correct cost function for Vanessa’s clothing store per month is,

C = 7.20n + 825

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A regular  quadrilateral prism has 12 edges. It is given perimeter of the base 32 cm. Length of each edge of base will be 32÷4=8 cm. The 4 edges at the top will also have the same number of edges that is 4 with measure 8cm each.

Given: The height of the prism is 2 times greater than the length of the base edge.Height of prism = 2(8)= 16cm. Number of edges  with measure 16 cm is 4.

Sum of all the 12 edges= 8+8+8+8+16+16+16+16+8+8+8+8=128 cm.

[tex] |\Omega|=10\\ [/tex]

3a

[tex] |A|=4\\\\P(A)=\dfrac{4}{10}=\dfrac{2}{5}=40\% [/tex]

3b

[tex] |A|=3\\\\P(A)=\dfrac{3}{10}=30\% [/tex]

In year 2000, the population was 15,000.

In year 2001, the population was 16,250.

In year 2002, the population was 17,500.

The population growth from year 2000 to year 2001 was (16,250-15,000) = 1,250.

The population growth from year 2001 to year 2002 was (17,500-16,250) = 1,250.

So the slope of the line would be m = 1250.

And y-intercept would be the initial population i.e. b = 15,000.

So the equation of line is y = 1250x + 15000.

Hence, n years after 2000, the population would be P = 1250n + 15000.

True , Therefore, there are only three polygons with regular tessellations.

A semi-regular tessellation is a tiling of the plane by two or more regular polygons in such a way that every vertex has the same configuration of polygons in the same order. In other words, at every vertex, the same set of regular polygons meet in the same order.

Unlike regular tessellations, where only one type of regular polygon is used, semi-regular tessellations can use different regular polygons. However, the regular polygons used must have the same number of sides meeting at each vertex. For example, a semi-regular tessellation might use triangles and squares, with three triangles and one square meeting at each vertex.

Given data ,

There are actually infinitely many regular polygons that can make a regular tessellation. In fact, any regular polygon can be used to create a regular tessellation of the plane.

The number of polygons meeting at each vertex depends on the angle of the polygon, which is determined by the number of sides.

Only three regular polygons(shapes with all sides and angles equal) can form a tessellation by themselves—triangles, squares, and hexagons.

Hence , Equilateral triangles, squares and regular hexagons are the only regular polygons that will tessellate.

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Answer:  0.04

Step-by-step explanation:

Given : Sample size : n= 150

No. of females in the sample  : x= 90

Proportion of females = [tex]\hat{p}=\dfrac{x}{n}=\dfrac{90}{150}=0.6[/tex]

Standard error of proportions :

[tex]SE=\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex] , where [tex]\hat{p}[/tex] = sample proportion and n= sample size .

Substitute the corresponding values , we get

[tex]SE=\sqrt{\dfrac{0.6(1-0.6)}{150}}[/tex]

[tex]SE=\sqrt{\dfrac{0.6 (0.4)}{150}}[/tex]

[tex]SE=\sqrt{0.0016}=0.04[/tex]

Hence, the standard error of the proportion is 0.04 .

The standard error of the proportion is 0.04

Since the random sample is 150 people and the number of female in the sample is 90 people

First step is to determine the sample proportion (p)

[tex]Sample proportion (p) =90/150[/tex]

[tex]Sample proportion (p) =0.6[/tex]

Now let determine the standard error of the proportion  using this formula

[tex]Standard error= \sqrt{p(-p)/n}[/tex]

Where:

[tex]p=Sample proportion (p)=0.6[/tex]

[tex]p=(1-0.6)= 0.4[/tex]

[tex]n=150[/tex]

Let plug in the formula

Standard error=\sqrt{(0.6) (0.4)/150}[tex]Standard error=\sqrt{(0.6) (0.4)/150}[/tex]

[tex]Standard error= \sqrt{0.24/150}[/tex]

[tex]Standard error= \sqrt{0.0016}[/tex]

[tex]Standard error= 0.04[/tex]

Inconclusion The standard error of the proportion is 0.04

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