What must be true for line EF to not intersect plane L?

The expression that represents the number of reams of paper produced in the second year is 4.704 x [tex]10^{10}[/tex] (option d)

The quantity of paper produced in the first year is written in scientific notation. Scientific notation is used to compress larger numbers into smaller numbers.  

In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

For example, The number 5 x 10³ is equivalent to 500

Paper produced in the second year = paper produced in the first year x 5.6

(8.4 x [tex]10^{9}[/tex] ) x 5.6 = 47.04 x [tex]10^{9}[/tex]

4.704 x [tex]10^{9 + 1}[/tex]

= 4.704 x [tex]10^{10}[/tex]

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Answer:

16

Step-by-step explanation:

Mean is same as average. To find the average, add all items and divide the sum by the number of items in the list.

Avg = (13 + 7 + 8 + 4) / 2 = 32 / 2 = 16

Hi there,

please see below for solution steps :

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To find the mean you first need to add all numbers and divide by how many there are :

  [tex]\sf{\dfrac{13+7+8+4}{4}}[/tex]

⨠ simplify

[tex]\sf{\dfrac{32}{4}}[/tex]

[tex]\boxed{\sf 8}[/tex]                                                                                              [tex]\tiny\pmb{\sf{Frozen \ melody}}[/tex]

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Answer:

C

Step-by-step explanation:

The red dotted line we see is the asymptote, which is a line that the functions will never cross.

The asymptotes we see currently is:

x = -3

and

x = 2

We can find the vertical asymptotes using the denominator of the function since the x value that makes the denominator 0 is the asymptote. Since -3 and 2 is the asymptote, the denominator of the function will be:

(x-2) (x+3)

If we look at the answer choices, we can see that C is the only option with a denominator of (x-2)(x+3), so that is our answer.

Answer:

C

Step-by-step explanation:

there are 2 vertical asymptotes at x = - 3 and x = 2

then the factors on the denominator will be (x + 3) and (x - 2)

then

f(x) = [tex]\frac{1}{(x-2)(x+3)}[/tex]

The value of x in A is 7 and the value of y in B is -15

Functions are represented as a function of variable. Given the following sets of numbers.

A = [3 x 6 1 -8 5] and;

-5A = [-15 35 -30 -5 40 y]

Equate the individual values to have:

-5A= -15

Divide both sides by -5

-5A/-5 = -15/-5
A = 3

Determine the value of y

-5A = y

-5(3) = y

y = -15

Similarly;

5x = 35

x = 35/5

x = 7

Hence the value of x in A is 7 and the value of y in B is -15

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Answer:

The value of x in A is -7

The value of y in B is -25

Step-by-step explanation:

Everything in the first matrix can be multiplied by -5 to equal everything in the second matrix, since we are dealing with x and y, only the first and third rows matter.

In the first row, we know that 3 times -5 equals -15 and x times -5 equals 35

therefore, -5x=35, with basic algebra we find that X = -7

In the third row, we know that 8 times -5 is 40 and 5 times -5 equals y.

This takes just basic multiplication to find that Y = -25

Answer:

x > -10

Step-by-step explanation:

2 + x > -8

x > -8 - 2

x > -10

Answer:

x>-10

Step-by-step explanation:

2+x-2>-8-2

x>-10

Step-by-step explanation:

we have a rectangle, that is then cut in half diagonally into 2 right-angled triangles.

in our problem it does not matter which side is the larger and which is the shorter one, because the distance calculation for both cases involve one short and one long side. the sequence does not matter.

Mary walks one short and one large side to get to the opposite corner (from D to F) :

264 + 900 = 1,164 ft

Kate walks diagonally. and that diagonal is the Hypotenuse of the right-angled triangle with a short and a long side of the rectangle.

so, Pythagoras applies :

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle), and a and b are the legs.

in our case that means

diagonal² = 264² + 900² = 69,696 + 810,000 =

= 879,696

diagonal = sqrt(879,696) = 937.9211054... ft ≈ 938 ft

so, Kate walked

1,164 - 938 = 226 ft

less than Mary.

Answer:

0

Step-by-step explanation:

hi

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haha

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are doing

dog food

0 answer

(scroll to bottom for answer)The equation you want to be using is A(n)+1=(A(n))r because this is a exponential sequence

r represents the ratio, which you said was 25, so basically you said

A(n)

____     = 25

A(n)-1

rthe sum of the first 2 terms are 16, the first two terms being A1 and A2, they need to follow the equation:

A2

__  = 25

A1

lets give them variables to make this a bit easier-

A1 will be x and A2 will be y

x+y=16(1st equation)

y/x=25, 25x=y(2nd equation)

(if you multiply y/x=25 by x you will get that 25x=y, which is where that other equation came from)

going back to x+y=16

subtract y from both sides

x=16-y

use substitution and solve for the second equation

25(16-y)=y

distribute

400-25y=y

add 25y to both sides to get rid of the -25y on the left side while keeping the equation equal

400=26y

divide both sides by 26 and you get 400/26 which simplifies to 200/13

after all that you need to multiply 200/13 by 25, 3 separate times

200                              1875000

___ x 25 x 25 x 25= _________

13                                      13

pull it into a calculator and you get something like

142846.153846

Answer:

-4

Step-by-step explanation:

Given vertex, the axis of symmetry is x = h.

Answer:

9

Step-by-step explanation:

6 ÷ 2/3   =    6 /  (2/3 )   =  (6/1) / (2/3)  = 6/1  x  3/2 = 18/2 = 9

Answer:

what is the question show the pic

The true statements are:

The median number of pages of the sixth graders is 76.

One-fourth of the students have read less than 72 pages.

One-half of the students have read between 72 and 86 pages.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers.

The end of the first line represents the minimum number and the end of the second line represents the maximum number. The difference between the minimum number and the maximum number is the range.

Range = 92 - 61 = 31

On the box, the first line to the left represents the lower (first) quartile. 1/4 of the score represents the lower quartile. The next line on the box represents the median. 1/2 of the score represents the median. The third line on the box represents the upper (third) quartile. 3/4 of the scores represents the upper quartile.

First quartile = 72

Third quartile = 86

Median = 76

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Based on the number of years that Peter and Blair have till retirement, the total amount that they need to save to completely fund their income shortfall is $65,545.72.

First, find the income shortfall:

= 75,017 - 54,000

= $21,017

The amount they need to save to cover this shortfall is the future value of this amount at retirement. The rate will be the real rate which is:

= 6% - 2% inflation

= 4%

The future value is:

= Income shortfall x future value interest factor, 4%, 29 years

= 21,017 x 3.1187

= $65,545.72

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Answer: 15/2 or 7.5

Step-by-step explanation:

2/3x = 5

5 divided by 2/3 or 5 x 3/2

= 15/2 or 7.5

Answer: 15/2

Step-by-step explanation:

[tex]\frac{2}{3} x-1=4\\\\\frac{2}{3}x=5\\ \\x=5(\frac{3}{2})\\\\x=\frac{15}{2}[/tex]

Answer:

7.88 x 10^5 is 788,000 is scientific notation

The difference between the total number of wholesalers and those that supply on 30-day credit, gives the number that require cash on delivery as 2

The number of wholesalers Sue has sourced = 4

Terms of two suppliers = 30 days credit

Amount of stock Sue has = $15000

Amount of stock on credit = $10000

Operating cash reserve of the business = $20000

Required:

The number of wholesalers that require terms of cash on delivery

Solution:

Given that the number of wholesalers = 4

The number number of suppliers (wholesalers) that supply on 30-day credit = 2

Therefore;

The number of wholesalers that require terms of cash on delivery = 4 - 2 = 2

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Answer:

  D.  x = -7/3

Step-by-step explanation:

A graphical solution is often easier when the problem is written in the form f(x) = 0. That way, the x-intercept(s) of the function f(x) will be the solution.

The desired form can be found by subtracting 16 from both sides of the equation:

  [tex]\left(\dfrac{1}{64}\right)^{-x-3}=16\qquad\text{given}\\\\\left(\dfrac{1}{64}\right)^{-x-3}-16=0\quad\Longrightarrow\quad f(x)=\left(\dfrac{1}{64}\right)^{-x-3}-16[/tex]

A graph is attached, showing x=-7/3 is the solution.

Using powers of 4, the equation can be rewritten ...

  [tex]\left(\dfrac{1}{4^3}\right)^{-x-3}=4^2\qquad\text{given}\\\\4^{3(x+3)}=4^2\\\\3(x+3)=2\qquad\text{equating exponents, or taking base-4 logs}\\\\x=\dfrac{2}{3}-3=\boxed{-\dfrac{7}{3}}\qquad\text{divide by 3, subtract 3}[/tex]

Answer:-2,0 & 1,0

Step-by-step explanation:

Substitute them in with zero product property

Answer:

42km/h

Step-by-step explanation:

70km=100 minutes

7km= 10min

42km=60min

42km/h

Answer:

The value of C will be -1.

Step-by-step explanation:

Greetings !

[tex]f(1) = - 6 \\ thus \: substitute \: in \: the \: equation \: \\ f(x) = 3x {}^{2} - 8x + c \\ - 6 = 3(1) {}^{2} - 8(1) + c \\ - 6 = 3 - 8 + c \\ - 6 = - 5 + c \\ - 1 = c \\ c = - 1 \\ therefore \: f(x) = 3x {}^{2} - 8x - 1 \\ f(1) = 3(1) {}^{2} - 8(1) - 1 \\ f(1) = 3 - 8 - 1 \\ f(1) =3 - 9 \\ f(1) = - 6[/tex]

The surface area of the given two rectangular prism is given as follows:

498 cm².

The surface area of a rectangular prism of length l, width w and height h is given as follows:

S = 2(lw + wh + hl).

For this problem, there are two prisms, with dimensions given as follows:

Hence the surface area of the figure is the combined surface area of each figure, hence:

S = 2(7 x 7 + 12 x 7 + 12 x 7) + 2(2 x 7 + 2 x 2 + 7 x 2) = 498 cm².

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Answer:

1.46m or 14600cm are left over

Step-by-step explanation:

Assuming you mean that there were 4m of string and 254cm were used/removed.

Let z=a+bi, w=c+di

[tex]|z+w|^2 -|z-w|^2 \\ \\ = |(a+c)+i(b+d)|^2 -|(a-c)^2 +i(b-d)|^2\\\\=(a+c)^2 +(b+d)^2-(a-c)^2 -(b-d)^2\\\\=a^2 +2ac+c^2 +b^2 +2bd+d^2 -a^2 +2ac-c^2 -b^2+2bd-d^2\\\\=4ac+4bd\\\\=4Re(z)Re(w)+4Im(z)Im(w)[/tex]

Answer:

The increase is $18.

(In case you are asked about the percent increase,

percent increase = 20%)

Step-by-step explanation:

To find an increase, subtract.

$108 - $90 = $18

The increase is $18.

Answer: The increase is $18.

If you are asked about the percent increase, then use this formula:

percent change = (new number - old number)/(old number) × 100%

Here, the new number is $108. The old number is $90.

percent change = ($108 - $90)/($90) × 100%

percent change = $18/$90 × 100%

percent change = 0.2 × 100%

percent change = 20%

Since the percent change is a positive number, it is a percent increase.

Answer: percent increase = 20%

Answer:

10 m/s

Step-by-step explanation:

Let x = speed of fish and y = speed of current. When swimming with current, the fish's speed is x + y. When swimming against it, the speed is x - y. Therefore, we can set up a system of linear equations to solve for x, the speed of fish.

x + y = 14

x - y = 6

2y = 8

y = 4

x - 4 = 6

x = 10

The speed of fish in still water is 10 m/s, and the speed of current is 4 m/s.

Answer:

Speed of fish in still water = 10 m/s

Speed of current = 4 m/s

Step-by-step explanation:

Let the speed of the fish in still water = x m\s

Let the speed of the current  = y m/s

Speed of the fish with the current = x + y

 x +y = 14 m/s ------------------(I)

Speed of the fish against current = x -y

 x - y = 6 m/s ----(II) &

Add the equations (I) & (II) and 'y' will be eliminated and we can find the value of 'x'.

     x + y = 14

     x - y =  6      {Now, add)

     2x    = 20

           x = 20/2

          x = 10

[tex]\sf \boxed{\text{\bf Speed of fish in still water = 10 \ m / s}}[/tex]

Plugin x = 10 in equation (I)

    10 + y = 14

            y = 14 - 10

           y = 4

[tex]\sf \boxed{\text{\bf Speed of the current = 4 \ m/s}}[/tex]

Answer:

b = 2a

Step-by-step explanation:

a = [tex]\frac{1}{2}[/tex] b ( multiply both sides by 2 to clear the fraction )

2a = b

Answer: b = 2a

Step-by-step explanation:

Original equation

a = (1/2) b

Multiply 2 on both sides

a * 2 = (1/2) b * 2

[tex]\Large\boxed{b=2a}[/tex]

Hope this helps!! :)

Please let me know if you have any quesitons

The proof that the line AE bisects the segment can be seen below.

Let us have

Γ1  and 2 are the two intersecting circles. to be the circumcircle of the shape ADE. Then we can see that  Γ1 is tangent to the line DB.

A common tangent would have to touch T1 at A and also touch T2 at B

Such that what we would have would be

<ADB = 180◦ − 2<ABD = <ABC = <AEC

This would then tell us that the line is tangent to the segment.

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The coordinates of C - (2n, 0) and the coordinates of D - (n, -p). The diagonals of a rhombus are perpendicular and bisect each other.

The properties of a rhombus are:

The given rhombus BCDE has B(n, p) and E(0, 0).

Since the diagonals of a rhombus are perpendicular bisectors,

EO = OC or BO = OD

Where O is the midpoint of EC and BD.

In the given diagram, points B and D are opposite each other. They are reflecting each other over the x-axis.

So, if B has coordinates (n, p) then its reflection over the x-axis is (x, -y) i.e., (n, -p).

Thus, we have B(n, p), D(n, -p), and E(0, 0)

Consider the coordinates of C as (x, y).

The midpoint of BD = ([tex]\frac{n+n}{2}[/tex], [tex]\frac{p-p}{2}[/tex])

⇒ coordinates of O = (n, 0)

So,

The midpoint of EC = ([tex]\frac{0+x}{2}[/tex], [tex]\frac{0+y}{2}[/tex])

⇒ coordinates of O = (x/2, y/2)

⇒ (n, 0) = (x/2, y/2)

∴ x = 2n and y = 0

Then, the coordinates of C are (2n, o)

Therefore, the required coordinates of the given rhombus are C(2n, 0) and D(n, -p).

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Answer: [tex]\Large\boxed{2a^3+4ab^2-3a^2b-6b^3}[/tex]

Step-by-step explanation:

Given expression

(2a - 3b) (a² + 2b²)

Apply the FOIL method (First Outer Inner Last)

Please refer to the attachment below for a graphical understanding

= 2a · a² + 2a · 2b² - 3b · a² - 3b · 2b²

Simplify by multiplication

=2 (a · a²) + 4 (a · b²) - 3 (b · a²) - 6 (b · b²)

[tex]\Large\boxed{=2a^3+4ab^2-3a^2b-6b^3}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Your answer is 2a³ + 4ab² - 3a²b - 6b³.

Step-by-step explanation:

(2a - 3b) (a² + 2b²)

=2a (a² + 2b²) -3b (a² + 2b²)

=2a.a² + 2a.2b² - 3b.a² - 3b.2b²

=2a³ + 4ab² - 3a²b - 6b³        ans.

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