Given that p=3i+j+2kand q=i-2j-4k are the position vectors
of points P and Q respectively, use the information to answer
Questions 2 and 3.
2.
Find an equation for the plane passing through Qand
perpendicular to liné PQ.

Answer:

x-2-10123

y0.1 0.3 0.9 2.7 8.1 24.3

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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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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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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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 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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Answer:

5 studs (3^3)

(3^3) = 5

Step-by-step explanation:

Answer:

use air math

Step-by-step explanation:

hope that helps

Answer:

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

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 cost of the car is $27,546

The sales tax is 7%

Jorge bought a ford mustang having a sales tax of $1,928.22

Therefore the cost of the car can be calculated as follows

1928.22÷ 7/100

= 1928.22/0.07

= 27,546

Hence the cost of the car is $27,546

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Answer:

To see if something is a function, just draw lines down the graph, if it touches the line twice, then that means it does not pass the vertical line test, meaning it is not a function
(By the line, I mean what you wrote on the paper,)
For example, a parabola is a function, because when you do the vertical line test, it only touches the line at one point, and not two,

Step-by-step explanation:

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!

(I included a picture that should help explain better)

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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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.

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:

4x + 27

Step-by-step explanation:

12x + 36 - 14 - 8x + 5 Combine like terms (36, -14, 5)

12x + 27 - 8x Combine like terms (12x, -8x)

Answer:

102.0625 square units

Step-by-step explanation:

First determine the length of each side using the distance formula  for two points. Then use Heron's formula to determine the area of a triangle given three sides

Distance Formula

The distance between two points is the length of the path connecting them

The distance between points (x₁, y₁) and (x₂, y₂) is given by the Pythagorean theorem:

[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

Let's compute the lengths of the sides FH, FG and HG

The three vertices are F(-2, 5)   G(7, -10) and H(-9, -6)  as indicated on the graph

So length FG between (-2,5) and (7,-10)

[tex]FG= \sqrt {(7 - (-2))^2 + (-10 - 5)^2}[/tex]

[tex]= \sqrt {(9)^2 + (-15)^2}[/tex]

[tex]= \sqrt {{81} + {225}}[/tex]

[tex]= \sqrt {306}[/tex]

FG [tex]= 17.492856[/tex]  (round to 17.5)

Length FH between(-2,5) and (-9, -6) is

[tex]FH = \sqrt {(-9 - (-2))^2 + (-6 - 5)^2}[/tex]

[tex]= \sqrt {(-7)^2 + (-11)^2}[/tex]

[tex]= \sqrt {{49} + {121}}[/tex]

[tex]= \sqrt {170}[/tex]

FH [tex]= 13.038405[/tex]  (can be rounded to 13.04

Length GH between (7, -10) and (-9, -6) is

[tex]GH = \sqrt {(-9 - 7)^2 + (-6 - (-10))^2}[/tex]

[tex]= \sqrt {(-16)^2 + (4)^2}[/tex]

[tex]= \sqrt {{256} + {16}}[/tex]

[tex]= \sqrt {272}[/tex]

GH [tex]= 16.492423[/tex]   (can be rounded to 16.5)

Determining the area of a triangle given 3 sides

Heron's formula allows us to find the area of a triangle given 3 sides If the sides are a, b and c the general form of Heron's formula is

[tex]Area = \sqrt {s(s-a)(s-b)(s-c)}[/tex]

where s is the semi-perimeter = [tex]\frac{a+b+c}{2}[/tex]

Substituting values we get

s = [tex]\frac{17.5+13.04+16.5}{2} = 23.52[/tex]

[tex]Area = \sqrt {23.52(23.52-17.5)(23.52-13.04)(23.52-16.5)}[/tex]

[tex]= \sqrt{23.52\cdot6.02\cdot10.48\cdot7.02}[/tex]

[tex]102.0625[/tex]  square units

The equation to the tangent line to [tex]y = e^{(x^2)}[/tex] at point (1,0) is given by:

y = 2e(x - 1).

Supposing that we have a function f(x) at a point [tex](x_0, y_0)[/tex], the equation of the tangent line to this function is given by:

[tex]y - y_0 = f^{\prime}(x_0, y_0)(x - x_0)[/tex]

In which f' is the derivative.

In this problem, the function is:

[tex]f(x) = e^{(x^2)}[/tex]

Applying the chain rule, the derivative is:

[tex]f^{\prime}(x) = 2xe^{(x^2)}[/tex]

At x = 1, the derivative is:

[tex]f^{\prime}(1) = 2(1)e^{((1)^2)} = 2e[/tex]

Hence the tangent line at point (1,0) is given by:

y = 2e(x - 1).

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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:

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:

230

Step-by-step explanation:

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:

450×6.75 = 2 956.5

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

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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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:

15

Step-by-step explanation:

[tex]3x-15=4x \\ \\ x-15=0 \\ \\ x=15[/tex]

The meaning of the terms and factors in the expression are

The expression is given as

180 + 15x

The above expression can be split as follows:

The meaning of the above terms and factors are

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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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