HELP ASAP!!!
Determine the direction in which the graph of the function f(x)=x^2+x-2 opens.
A.upward
B.downward
C.to the left
D.to the right

The data set that has the same standard deviation with the given data set is: B. {2, 2, 4, 6, 9}.

Given the data set, {1, 1, 3, 5, 8}, the standard deviation (σ) is calculated as shown below:

Standard deviation (σ) = √(SS/n)

Count (n) = 5

Mean (μ) = 3.6

Sum of Squares (SS) = 35.2

Standard deviation (σ) = (√35.2/5)

Standard deviation (σ)  = √7.04

Standard deviation (σ) ≈ 2.7

Also, the standard deviation of {2, 2, 4, 6, 9} is calculated as shown below:

Count (n) = 5

Mean (μ) = 4.6

Sum of Squares (SS) = 35.2

Standard deviation (σ) = (√35.2/5)

Standard deviation (σ)  = √7.04

Standard deviation (σ) ≈ 2.7

Therefore, the data set that has the same standard deviation with the given data set is: B. {2, 2, 4, 6, 9}.

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The line segment that is skew line to line segment BF is CD.

Skew line:

Skewed lines are two lines that are not parallel to one another, and neither do they intersect. Only dimensions greater than two-dimensional space can have skew lines. They must be non-coplanar, which means that they must exist on several planes. Two lines in two-dimensional space can either intersect or run parallel to one another. Therefore, skew lines are impossible in 2D space.

The line segment AB is perpendicular to the line segment BF which means it is not the skew line to line segment BF

The line segment CD is not parallel and not perpendicular to the given line segment BF which means it is a skew line to the given line segment BF.

Therefore, The line segment that is skew line to line segment BF is CD.

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Answer:

explicit formula is a mix of different upgraded formulas

Step-by-step explanation:

Answer:

  220

Step-by-step explanation:

You want to use differences to find the pattern and the next term in the sequence 3, 8, 15, 28, 51, 88, 143.

Subtracting each term from the next, we find the sequence of first differences to be ...

  5, 7, 13, 23, 37, 55

The first differences are not constant, so we know the sequence is not linear. They are not in an arithmetic progression, so we know the sequence is not quadratic. They do not have a common ratio, so we know the sequence is not exponential.

The second differences are the differences of the sequence of first differences. They are ...

  2, 6, 10, 14, 18

The differences of the terms of the 2nd-difference sequence are constant: 4.

  4, 4, 4, 4, 4

Constant 3rd differences mean the original sequence can be described by a 3rd degree polynomial. The coefficients found by a calculator are shown in the attachment.

Since we know the third differences are constant, we can work our way back up the chain of differences to find the next term of the original sequence.

  next 2nd difference = 18 +4 = 22

  next 1st difference = 55 +22 = 77

  next sequence term = 143 +77 = 220

The eighth term should be 220.

__

Additional comment

The n-th term is ...

  f(n) = 2/3n^3 -3n^2 +28/3n -4

Answer:

10 and 28

Step-by-step explanation:

let x be one number then the other is x + 18 ( 18 more than the other ), then

x + x + 18 = 38

2x + 18 = 38 ( subtract 18 from both sides )

2x = 20 ( divide both sides by 2 )

x = 10

and x + 18 = 10 + 18 = 28

the 2 numbers which divide 38 into the 2 parts are 10 and 18

Answer:

literature most commonly refers to works of the creative imagination, including poetry, drama, fiction, nonfiction, and in some instances, journalism, and song.

The homeowners pay a $25 monthly usage fee and $3 per hundred cubic feet for water number line is- 75,100

Given:

In Town A

$25 monthly usage fee

$3 per hundred cubic feet for water.

In Town B,

homeowners pay $2.00 per hundred cubic feet and a $50 monthly

For town A=25×3=75

For town B=50×2=100

When we write numbers on a number line, we can easily compare them and execute simple arithmetic operations on them. A number line's origin is defined as zero (0). The numbers to the left of 0 are all negative, whereas the numbers to the right of 0 are all positive. So, as we walk towards the right on a number line, the value of numbers increases.

A number line includes both positive and negative numbers. A negative number line is formed by the segment of the number line to the left of zero.

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The salaries of each will be 127975 and 182875.

Lat the salaries of B = b

Let the salary of A = b + 54900

Therefore, we will add them together to get the value:

b + b + 54900 = 310850

2b + 54900 = 310850

2b = 310850 - 54900

2b = 255950

b = 255950/2

b = 127975

a = b + 54900 = 127975 + 54900 = 182875

Therefore, the salaries of each will be 127975 and 182875.

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0.0030  is the probability that you will​ win .

In statistics, what does a probability mean?

Here order of selection is important, so we will use permutation.

Total number of ways to choose 3 horses out of 8 = 8P3 = 8! / (8 - 3)! = 336

P(win) = 1/336 = 0.0030

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The the coordinates of Q and T in terms of a and b is -

Q [(3a + b)/4] and T [(5a + 3b)/4].

The mid-point of a line segment is a point on the line segment which divides it into two equal parts.

Given is a line segment AB whose mid-point is M with a and b being the coordinates of A and B respectively. Further, Q is the midpoint of AM and T is the midpoint of QM.

[Refer to the image attached for clear explanation]

Since M is the mid-point of AB, therefore the coordinates of point M will be = M [(a + b)/2]

Now, Q is the mid-point of AM. Therefore, the coordinates of Q will be =

[(a + b)/2 + a]/2 = Q [(3a + b)/4]

and

T is the mid-point of QM. Therefore, its coordinates will be =

(a + b)/2 + (3a + b)/4 = T [(5a + 3b)/4]

Hence, the the coordinates of Q and T in terms of a and b is -

Q [(3a + b)/4] and T [(5a + 3b)/4]

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Answer:

Step-by-step explanation:

y = x^3 + 3
y = (-1)^3 + 3
y = -1 + 3
y = 2

The interval on a number line (-∞, -6)​ using set-builder notation is;

{ x | x ∈ R, x ≤ -6 }

Set-builder notation is a mathematical notation for describing a set by representing its elements or explaining the properties that its members must satisfy.

Real numbers (R) include all rational and irrational numbers. Thus, If we need to write the interval on a number line (-∞, -6)​ using set-builder notation, we will write as:

{ x | x ∈ R, x ≤ -6 }

In words : "x such that x belongs to R, x is less than or equal to -6"

This shows that x is any real number less than or equal to -6

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Answer:

5(x+3) = 7

Step-by-step explanation:

5(x+3) = 7

Answer: N * (n+7) = n^2 + 7n

Step-by-step explanation:

This equation would be the number, n, times n+7 because n+7 is 7 more than n. To do this, you have an equation like this:

N * (N+7). You would then do distributive property, and n*n would be n squared, and n*7 would be 7n. This would give you a combined answer of n squared + 7n, or n^2 +7n.

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{((243 {)}^{2n/5} ) \sdot( {3}^{2n + 1}) }{ ({9}^{n + 1}) \sdot( {3}^{2(n - 2)} )}[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{(3{)}^{5(2n/5)} ) \sdot( {3}^{2n + 1}) }{ ({3 }^{2(n + 1)}) \sdot( {3}^{2(n - 2)} )}[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{(3{)}^{2n} \sdot( {3}^{2n + 1}) }{ ({3 }^{(2n + 2)}) \sdot( {3}^{(2n - 4)} )}[/tex]

let's break it up :

now let's take [tex]{ \sf {3}^{(2n-4)}} [/tex] common here ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{(3{)}^{(2n - 4)} (3 {}^{4} \sdot{3}^{5}) }{ {(3 )}^{(2n - 4)}(3 {}^{6} \sdot1)}[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{{} (3 {}^{4} \sdot{3}^{5}) }{ (3 {}^{6} \sdot1)}[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{{} 3 {}^{9} }{ 3 {}^{6} }[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 {}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 27[/tex]

Answer:

Step-by-step explanation:

[tex]\sf \cfrac{243^{\frac{2n}{5}}\cdot \:3^{2n+1}}{9^{n+1}\cdot \:3^{2\left(n-2\right)}}[/tex]

[tex]\sf 9^{n+1}\cdot \:3^{2\left(n-2\right)}[/tex]

Simplify:-

[tex]\sf \cfrac{3^{2n}\cdot \:3^{2n+1}}{\boxed{\bf 3^{4n-2}}}[/tex]

Now, Factor:-

[tex]\sf \cfrac{3^{2n}\cdot \:3^{2n+1}}{3^{4n-2}}[/tex]

Now, let's simplify:-

Simplify:-

Apply the exponent rule:-

Therefore, your answer is 27.

______________________

Hope this helps!

Have a great day!

Answer:

B

Step-by-step explanation:

because it most reasonable

also you times the number as much as the exponents

Answer:

A. (5^8)/(5^9)

Step-by-step explanation:

Using the properties of exponents, in this case case the Power of Quotient Rule, can be changed into the one in A.

Answer:

  93 square units  (the figure is not a rhombus)

Step-by-step explanation:

You want the area of the figure whose vertex coordinates are A(0,-5), B(9,2), C(12,13), and D(2,7).

The formula for the area of a polygon based on its coordinates might be written ...

  [tex]\displaystyle A=\frac{1}{2}\left|\sum_{k=1}^n{x_k(y_{k+1}-y_{k-1})}\right|[/tex]

where coordinate indices wrap around from the end to the beginning.

Using this formula, we find the area to be ...

  A = 1/2|0(2-7) +9(13-(-5)) +12(7-2) +2(-5-13)|

  A = (1/2)|0 +162 +60 -36| = 1/2(186) = 93

The area of the figure is 93 square units.

The area of a rhombus could be calculated as half the product of the lengths of the diagonals. This is only true because the diagonals of a rhombus cross at right angles.

Here, the differences between diagonally opposite coordinates are ...

  AC = (12, 18) . . . . slope = 18/12 = 3/2

  BD = (-7, 5) . . . . slope = 5/-7 = -5/7

If the diagonals are perpendicular, their slopes have a product of -1. Here, the product is ...

  (3/2)(-5/7) = (-15/14) ≠ -1

The given figure is not a rhombus.

If we assume the diagonals are perpendicular, then the area would be ...

  A = 1/2√(12²+18²)√((-5)²+7²) = 1/2√34632 ≈ 93.048

Rounded to the nearest tenth, this area would be 93.0 square units.

The diagonals actually cross at an angle of about 88.152°, so the area is actually ...

  93.048·sin(88.152°) = 93 square units (exactly)

(Development of this formula is beyond the scope of this answer.)

The expression involving fractions that have a quotient less than 1 is: 2. 3 ⅛ ÷ 2 ⅖

To solve each of the expressions involving fractions, convert mixed fractions into improper fractions before finding the quotient of each.

1. 4 ⅔ ÷ 5 ¼

Convert to improper fractions

14/3 ÷ 21/4

14/3 × 4/21

= 56/63 (less than 1)

2. 3 ⅛ ÷ 2 ⅖

Convert to improper fractions

25/8 ÷ 12/5

25/8 × 5/12

125/96 (greater than 1)

3. 1 6/7 ÷ 2 1/3

13/7 ÷ 7/3

13/7 × 3/7

= 39/49 (less than 1)

4. 5 3/4 ÷ 7 ⅜

23/4 ÷ 59/8

23/4 × 8/59

= 184/236 (less than 1)

Therefore, the expression involving fractions that have a quotient less than 1 is: 2. 3 ⅛ ÷ 2 ⅖

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Answer:

x-2-10123

y0.1 0.3 0.9 2.7 8.1 24.3

The inequality will be:

x ≥ $9

Which says that x can be equal to or larger than $9.

An inequality is a mathematical statement that relates two or more mathematical elements (variables, expressions, etc.) in such a way that there is not a equality like in an equation (an equality can be a solution, but not necessarily)

For example, if x represnts what you bring for dinner, we know that x needs to be at least $9.

So x = $9 is a solution.

But if x is a larger value than $9, it also is a solution.

This situation is represented by the inequality:

x ≥ $9

Which says that x can be equal to or larger than $9.

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6.7×10 8 is your correct answer

Answer:

the scientific notation is: [tex]6.7 ~x~10^{8}[/tex]

Step-by-step explanation:

The proper format for scientific notation is;

where a is a number or decimal number such that the absolute value of a is greater than or equal to one.

Given:

Thus, the scientific notation is:

Answer:

use air math

Step-by-step explanation:

hope that helps

The values of A, B, and C are  mathematically given as

This is further explained below.

Generally, the equation for the statement is  mathematically given as

AB + C = 52

AB+ (C x 10) = 97....1

Using the substitution technique we have

AB = 52- C ....2

Subbing 2 in 1

AB+ (C x 10) = 97

Therefore

52- C +  10C = 97

9C=97-52

9C=45

C=5

In conclusion,

AB = 52- C

AB = 52- 5

AB=48

A=48/B

Hence

B=48/A

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Answer:

54=12+r

Step-by-step explanation:

'Sum' means to add.

54 = 12 + rhonda's height

54 = 12 + r

The equation that could be used to determine, m, is 4m = 18.2 - 5

The average number of miles (m) is 3.3 miles to ride each day to meet her goal.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Total distance of ride Alisha wants by her bicycle (d) = 18.2 miles.

And, She has already ridden 5 miles.

She rides for 4 more days.

Now, Let the average number of miles = m

She has already ridden 5 miles.

And, She rides for 4 more days.

The number of miles she needs to ride more is

18.2 miles  - 5 miles

= 13.2 miles

If m is the average number of miles she must cycle in 4 days to reach her objective,

Hence, we can formulate;

4m = 13.2

Divide both side by 4,

m = 3.3 miles

So, The equation that could be used to determine, m, is 4m = 18.2 - 5

The average number of miles is 3.3 to ride each day to meet her goal.

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Answer:

450×6.75 = 2 956.5

So the serviceman will get 2 956.5 after 6.75 hours of doing the job

Using basic derivative rules the value of y' (2) is 19.6 .

We have given a function of t y(t) = 450-4.9t².

On differentiating with respect t , we get

         y'(t) = 2 × 4.9t

          y'(t)  = 9.8 t              ......(1)

Putting t = 2 in equation (1) , we get

      y'(2)  = 9.8 × 2

               = 19.6

Hence , value of y'(2) is 19.6

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Answer:

its 1/3

Step-by-step explanation:

see picture for referance

Time taken in hours from home to college is; 5 hours 20 minutes

We are given;

Going home DATA:

Speed rate = 61.5 mph

Distance = x miles

Time taken = distance/speed = x/61.5 hrs

Going to college DATA:

Speed rate = 65.2 mph

Distance = x miles

Time taken = x/65.2 hrs

Thus, the equation set up is:

x/61.5 + x/65.2 = 11

Multiply through by (61.5 * 65.2) to get;

65.2x + 61.5x = 11 * (61.5 * 65.2)

126.7x = 44107.8

x = 44107.8/126.7

x = 348.1279 miles

Thus;

Time in hours from home to college = 348.1279/65.2

Time in hours from home to college = 5.34 hours = 5 hours 20 minutes

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Answer:

23,716 ft

Step-by-step explanation:

Let the side length of each of the four smaller lots be s.

Then, Fritz will use 12s feet, which is equal to 924.

This means s=77.

This means the area of each smaller square is 77²=5929, and thus the total area is 23,716 ft.