Which expression is equivalent to the following complex fraction? startfraction 1 over x endfraction minus startfraction 1 over y endfraction divided by startfraction 1 over x endfraction + startfraction 1 over y endfraction startfraction y + x over y minus x endfraction startfraction (y minus x) (y + x) over x squared y squared endfraction startfraction x squared y squared over (y + x) (y + x) endfraction startfraction y minus x over y + x endfraction.

Answer:  A.( 2,10) B.(4,6) C(5,4)  D(6,2)

Step-by-step explanation:

An arithmetic sequence is a sequence where the difference between each consecutive term is the same.

The sum of an arithmetic sequence is given as,

S(n) = a + d(n - 1)

The total number of books sold over the first 18 months is 7600.

It is a sequence where the difference between each consecutive term is the same.

Example:

2, 4, 6, 8, 10 is an arithmetic sequence.

We have,

In the first month, the author sold 2500 books, but the sales were declining steadily at 12% each month.

This means,

a = 2500

12% of 2500

12/100 x 2500

= 12 x 25

= 300

d = 300

Now,

The sum of an arithmetic sequence is given as,

S(n) = a + d(n - 1)

Now,

n = 18

a = 2500

d = 300

S(23):

= 2500 + 300(18 - 1)

= 2500 + 300 x 17

= 2500 + 5100
= 7600

Thus,

The total number of books sold over the first 18 months is 7600.

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The product of the given irrational number  ∛5 × √2 is equal to

option b. [tex]\sqrt[6]{200}[/tex]

As given in the question,

Given irrational numbers are:

∛5 × √2

Take the least common multiple of 3 and 2

Least common multiple of 3 and 2 is 6.

∛5 = [tex]5^{2 \times\frac{1}{2}\times \frac{1}{3} }[/tex]

    = [tex]\sqrt[6]{5^2}[/tex]

    = [tex]\sqrt[6]{25}[/tex]

√2 = [tex]2^{3 \times\frac{1}{3}\times \frac{1}{2} }[/tex]

    =[tex]\sqrt[6]{2^3}[/tex]

    = [tex]\sqrt[6]{8}[/tex]

Product of ∛5 × √2 is given by:

∛5 × √2 = [tex]\sqrt[6]{25} \times \sqrt[6]{8}[/tex]

             = [tex]\sqrt[6]{25 \times 8}[/tex]

             = [tex]\sqrt[6]{200}[/tex]

Therefore, the product of the given irrational number is equal to [tex]\sqrt[6]{200}[/tex] .

The complete question is:

What is the following product?

∛5 × √2

a. [tex]\sqrt[6]{10}[/tex]

b. [tex]\sqrt[6]{200}[/tex]

c. [tex]\sqrt[6]{500}[/tex]

d. [tex]\sqrt[6]{10000}[/tex]

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The attached graph is defined by f(x) = x² + 5|x| + 6.

What is the graph function?

The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function is a special case of the graph of an equation.

We have,

y = x² + 5|x| + 6

we know,

|x|² = x² use this ,

y = |x|² + 5|x| + 6

Steps for drawing y = |x|² + 5|x| + 6

step1 :- first draw y = x² + 5x + 6, this graph is quadratic equation .

step2:- Leave the part of y=x² + 5x + 6 right side to the y-axis and also take its image with respect to the y-axis as a plane mirror.

step3 :- now remove the part of y = x² + 5x + 6 to left side from y - axis .

now your graph is ready

you can see in the figure attached.

Hence, the attached graph is defined by f(x) = x² + 5|x| + 6.

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Answer:

2.4 × 101

Step-by-step explanation:

that is 24 in scientific notation

Answer:

24 * 10^1

Step-by-step explanation:

Hope this helps. :)

The length of BD is 9 units when considering the idea of a line segment's midpoint.

A midpoint is a point that lies on a line connecting two other locations and is in the middle of the line. The midpoint is the point on the middle of the line that is equally distant from the two points if a line is drawn connecting the two points. The midpoint is the point B that lies halfway between any two points, let's say A and C. As a result, measuring the length of the line segment and dividing it by two will yield the midway.

According to the given information :

AE = 18, DE = 5

However, D is the middle of CE

CE = 2 × 5 = 10

The line CE will become 10

But AE is the total length of the line segment and it is equal to 18

AE = AC + CE

AC = AE - CE

AC = 8

If AC = 8 , BC = 1/2AC

BC = [tex]\frac{8}{2}[/tex]

BC = 4

The BD becomes BC + CD

BD = 9 units

The length of BD is 9 units when considering the idea of a line segment's midpoint.  

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Answer:

5 hours lifeguarding and two hours babysitting.

Step-by-step explanation:

5(20) = 100

10(2) = 20

100 + 20 = 120

You see from the graph that when x = 0, y = 2 so the y-intercept is ( 0 , 2).

you are given points (-6 , 3) and (6 , 1). Find slope:

slope = change in y / change in x

slope = (3 - 1) / (-6 - 6)

slope = 2/-12

slope = -1/6

slope-intercept form: y = mx + b where m = slope and b = y intercept.

y = -1/6x + 2

Answer:

How many ways can they fill the 4 positions?

The Answer is B. 210

Answer: b. 210

Step-by-step explanation:

it must be A because it's is going down word

Answer:

Slope is negative

Step-by-step explanation:

from one point to the next, it goes down 1 (-1) and over 4 (4)

or, from one point it goes left 4 (-4) and up 1 (1) just depending on how tou look at it.

The normal approximation to the binomial distribution is C ( n , r ) * p^r * q^n - r .

a )

the binomial distribution .

Null hypothesis H0: μ = 19.4

Alternative hypotheses H1: μ ≠ 19.4

19.4 with minus sign, we get

n = 20, x = 4 and n/2 = 10

Here x < n/2

Therefore, from table the computed P-Value is.

b )

the normal approximation to the binomial distribution ,

P = 2P(X ≤ 4 when θ = 1/2 )

= 2 (0.0059)

= 0.0118

Hence the P value, 0.0118, is less than 0.05, the null hypothesis must be rejected, and we conclude that the mean of the population is not 19.4 minutes.

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Step-by-step explanation:

These two angles are same side corresponding interior angles so they are equal to each other

[tex]5x + 20 = 120[/tex]

[tex]5x = 100[/tex]

[tex]x = 20[/tex]

Answer:

2x - 12

Hope this helps : )

Step-by-step explanation:

The equation for 12 less than twice a number is 2x-12. This is because "12 less than a number" means 12 is being subtracted from a number. The "number" is a variable which can be x. "Twice a number" is the variable being multiplied by 2. So the final equation would be 2x - 12.

Answer:

88 ft^2

Step-by-step explanation:

we can make this a full 10 by 10 rectangle and find the area

10x10

100

And now we subtract the 6 by 2 triangle area that we added

6x2

12

100-12

88 ft^2

Hopes this helps please mark brainliest

Answer:

Answer = 88 ft²

Step-by-step explanation:

Step 1: Divide the composite shape into two separate parrellagrams

    1. Dimensions of shape 1: Length is 10 ft, and width is 4 ft

    2. Dimensions of shape 2: Length is 8 ft, and width is 6 ft

Step 2: Multiply the length by the height of each shape

    Area = lw

    3. Area of shape 1: 10 ft ∙ 4 ft = 40 ft²

    4. Area of shape 2: 8 ft ∙ 6 ft = 48 ft²

Step 3: Add both areas together to get the total area of the composite shape

    5. 40 ft² + 48 ft² = 88 ft²

    Hence, the total area of this composite figure is 88 ft²

The diagram that models the ratio in the story is the first diagram.

Puppies = Seven green boxes.

Adults = Four violet boxes.

There are 66 dogs enrolled together.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of puppies = 7

Number of adult dogs = 4

This can be written as,

7 puppies = 4 adult dogs

Multiply 6 on both sides.

42 puppies = 24 adult dogs

Now,

The total number of enrolled dogs.

42 + 24 = 66 dogs

Thus,

The ratio that models the story is the first diagram.

The total number of enrolled dogs is 66.

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Answer:

the third onei

Step-by-step explanation:

it describes a quadratic equation/

Average velocity of the car as calculated from the given data is 6m/s.

The average velocity is calculated by dividing the total distance travelled by the whole time that has passed. Given the velocity as a function of time, you may integrate the velocity function from t = 4 to t = 8 to determine the total distance travelled.

The opposite of taking a derivative is to integrate; in other words, the function I get when I take a derivative is 2t1/2 + 1. Assuming you are aware of how to do that If not, you can input the aforementioned integral into your TI-84 to obtain the result.

The integral turns out to be

(4/3)t^3/2 + 4t so x(t)

= (4/3)t3/2 + 4t and x(8) - x(4)

= (4/3)(8)3/2 + 4(8) - [(4/3)(4)3/2 + 4(4)]

= 24 meters

The distance travelled in total was 24 meter and it took 4 seconds (8-4) to do it, so the average velocity is 24 /4 = 6 m/s.

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Answer:

The coordinates of the vertices of triangle ΔABC, A(0, -1), B(6, 5), and C(-4, 3), indicates that the triangle ΔABCD is a right triangle with all sides of different length.

Step-by-step explanation:

Using the equation of the plane and the provided point (1,2,3) with the unit values perpendicular to the plane .The answer is [tex]\frac{x-1}{3.14} + \frac{y-2}{3.14} + \frac{z-3}{3.14} = 1[/tex]

A plane is a doubly ruled surface in two dimensions that is spanned by two linearly independent vectors. A hyperplane is a generalization of the plane to higher dimensions. The dihedral angle is the angle formed by two intersecting planes.

A normal in geometry is a piece of geometry that is perpendicular to another piece of geometry, such as a line, ray, or vector. For instance, the (infinite) line perpendicular to the tangent line to the curve at the point is the normal line to a plane curve at the point.

x1=1

y1=2

z1=3

[tex]\frac{x-x1}{\sqrt{x1^{2}+y1^{2}+z1^{2}}} + \frac{y-2}{\sqrt{x1^{2}+y1^{2}+z1^{2}}} + \frac{z-3}{\sqrt{x1^{2}+y1^{2}+z1^{2}}} = 1[/tex]

[tex]\frac{x-1}{3.14} + \frac{y-2}{3.14} + \frac{z-3}{3.14} = 1[/tex]

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Answer:No, because you cant divide 20 balls into 3 equal groups.

Step-by-step explanation:

Answer: The discount is 25% * $20 = $5.

The sale price of the item is $20 - $5 = $15.

The value of f(-3) + g(-3) Or (f + g)(-3) is 11.

When the output of one function is given to the input of another function they are called composite functions. In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

Given, f(-3) is 9 and g(-3) is 2.

We know f(x) + g(x) = (f + g)(x).

∴ (f + g)(-3) = 9 + 2.

(f + g)(-3) = 11.

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Answer:

$560.30 & $60.30

Step-by-step explanation:

A = $560.30

A = P + I where

P (principal) = $500.00

I (interest) = $60.30

The required quotient is x² + x + 1 + (2/ x -1) which is determined by the synthetic division.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient.

Use the divisor and find x :

x - 1 = 0  add 1

x= 1

Now we'll divide with the number one:

Take the coefficients from the terms in front of them.

Make careful to include 0's for x² and x since all terms must be included.

set it up with a 1 in a box:

1|  1   0   0  1   bring the first number down

____________

    1                    multiply the boxed number by the first number and add it                                 to the second number

1|  1   0   0  1  

____+1_____       repeat with the rest of the terms

    1   1  

1|  1   0    0    1

 ___+1_+1_+1  

    1   1    1    2                              

When you're finished, use the new numbers to build an equation that begins with a term that has one fewer degree than the previous equation.

Because there is a remnant, divide it by the original divisor.

final answer:

x² + x + 1 + (2/ x -1)

Thus, the required quotient is x² + x + 1 + (2/ x -1) which is determined by the synthetic division.

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Answer: x + 2/3(x)

Step-by-step explanation:

x = distance F walks to school

2/3(x) = distance T walks to school

Felipe walks first to school, then walks to Tim's house, so total distance Felipe walks:  x + 2/3(x)

Answer:

Step-by-step explanation:

32

Answer:

there is a 25% increase from 24 to 30

Step-by-step explanation:

30-24/24 x 100

6/24x 100

0.25x100

25%

Answer:

[tex]\begin{align} \% \text{ Increase} &= \dfrac {\text{Final - Initial}}{\text{Initial}} \times 100 \\ \\ &= \dfrac {30 - 24}{24} \times 100 \\ \\ &= \dfrac {6}{24} \times 100 \\ \\ &= 0.25 \times 100 \\ \\ &= 25 \% \end{align} [/tex]

There is a 25 % increase from 24 to 30.