What is the next fraction
in this sequence?
Simplify your answer

5/14, 3/7, 1/2, 4/7 …

Step-by-step explanation:

1. gradient=y2-y1/x2-x1

=21-9/-7-(-12)

=21-9/-7+12

=12/5

2.consider any two coordinates:

(13,32),(7,33)

gradient:

=33-32/7-13

=1/-5

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x-\cfrac{4}{5}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is 2/3 and that it passes through (-3 , 2) in standard form

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{2}{3}}(x-\stackrel{x_1}{(-3)}) \implies y -2= \cfrac{2}{3} (x +3)[/tex]

[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-2)=3\left( \cfrac{2}{3} (x +3) \right)}\implies 3y-6=2(x+3)\implies 3y-6=2x+6 \\\\\\ 3y=2x+12\implies -2x+3y=12\implies {\Large \begin{array}{llll} 2x-3y=-12 \end{array}}[/tex]

To get 1 four, probability is 1/6

To get 2 fours, probability is (1/6)^2

So

To get 5 fours, probability is (1/6)^5 = 0.0001286

The smallest amount that can be charged per box of seeds to make a profit of $409 is $20.125

A profit is the financial gain from a business transaction when the revenue from the transaction exceeds the expenses and taxes.

The function for the profit from the fund raiser is; p = -0.5·x² + 36·x - 113

When the profit is $409, we have;

p = 409 = -0.5·x² + 36·x - 113

-0.5·x² + 36·x - 113 = 409

-0.5·x² + 36·x - 522 = 0

The solutions of the above quadratic function, found using the quadratic formula are as follows;

x = (-36 ± √(36² - 4×(-0.5)×(-522)))/(2×(-0.5))

From which we have;

x = (-36 + √(36² - 4×(-0.5)×(-522)))/(2×(-0.5)) ≈ 20.125

x = (-36 - √(36² - 4×(-0.5)×(-522)))/(2×(-0.5)) ≈ 51.875

Therefore, when the profit is $409, the amount charged are x ≈ 51.875 or x ≈ 20.125

The smallest amount charged when the profit is $409 is therefore;

x ≈ $20.125

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The required value of the function x is 41.6

This relationship is typically represented as y = f(x), or "f of x," where y and x are coupled such that for each value of x, there is a specific value of y. This means that f(x) can only have one value for a given x. In set theory jargon, a function connects an element x to an element f(x) in another set.

Given : f (x ) = 3x - 121

to find ; value of f ( x ) when f (x) = 4

Since two values of f(x ) are given

we can simply equate these two values

and the answer which we will get is the final answer

thus we get

3x - 121 = 4

3x = 121 + 4

3x = 125

x = 125/ 3

x = 41.6

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Answer:

length × width

5×9=45cm²

45cm²×2=90cm²

Tthe total area of the shape is 85 cm².

Rectangle 1:

Length = 9 cm

Width = 5 cm

Area of Rectangle 1 = Length * Width

= 9 cm * 5 cm

= 45 cm²

Rectangle 2:

Length = 8 cm

Width = 5 cm

Area of Rectangle 2 = Length * Width = 8 cm * 5 cm = 40 cm²

Total area of the shape

= Area of Rectangle 1 + Area of Rectangle 2 = 45 cm² + 40 cm²

= 85 cm²

Therefore, the total area of the shape is 85 cm².

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The probability that it is a blue ball is 5/12 ≈ 0.416.

Given:

A bag contains 5 blue balls 4 red balls 3 orange balls.

Total balls = 5 + 4 + 3

= 12

Number of possible outcomes = 12

Number of favorable outcomes =  number of blue balls = 5

Probability = Number of favorable outcomes / Number of possible outcomes.

= 5/12.

= 0.416

Therefore the probability that it is a blue ball is 5/12 ≈ 0.416.

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Answer:

be chill bro but which subject is this

Answer:

pretty sure its the 2nd, 3rd, and 5th one

(Sorry if im wrong)

Step-by-step explanation:

Error free in finding the sum of 2 is 9/30

we need to correct the error and find the sum of 2

= [tex]\frac{5}{6}[/tex]  + ([tex]\frac{-8}{15}[/tex])  

let's find the l.c.m  of both

LCM stands for 'Least Common Multiple'. The least common multiple (LCM) of two numbers is the lowest possible number that can be divisible by both numbers. It can be calculated for two or more numbers as well. There are different methods to find the LCM of a given set of numbers. One of the quickest ways to find the LCM of two numbers is to use the prime factorization of each number and then the product of the highest powers of the common prime factors will be the LCM of those numbers.

= 25 -16 / 30

= 9/30

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3(3c + 1) = 21 is false

Answer:

3(3c + 1) = 21 is false.

Step-by-step explanation:

Answer:

Step-by-step explanation:

With corners as

A

(

−

2

,

−

1

)

,

B

(

1

,

2

)

,

C

(

5

,

2

)

and

D

(

2

,

−

1

)

, let us find slopes of each side of the parallelogram

A

B

C

D

.

Slope of

A

B

is

2

−

(

−

1

)

1

−

(

−

2

)

=

3

3

=

1

Slope of

B

C

is

2

−

2

5

−

1

=

0

4

=

0

Slope of

C

D

is

(

−

1

−

2

2

−

5

=

−

3

−

3

=

1

Slope of

D

A

is

−

1

−

(

−

1

)

2

−

(

−

2

)

=

0

4

=

0

As slopes of alternate sides of quadrilateral are equal, alternate sides are parallel to each other

and

A

B

C

D

is a parallelogram.

Answer:

  C  1/2

Step-by-step explanation:

You have differentiable functions f and g that are inverses of each other with ...

and you want to know g'(-4).

Consider the composition ...

  f(g(x)) = x . . . . . . the functions are inverses of each other.

Differentiating with respect to x, we get ...

  f'(g(x))·g'(x) = 1

  g'(x) = 1/f'(g(x)) . . . . . . divide by the coefficient of g'(x)

For x = -4, this is ...

  g'(-4) = 1/f'(g(-4)) = 1/f'(7) . . . . . use the given values

  g'(-4) = 1/2

__

Additional comment

In the attachment, you can consider the red line to be the tangent to f(x) at x=7, and the blue line to be tangent to g(x) at x=-4. The slope of the tangent, g'(-4), is 1/2, the reciprocal of the slope at f(7)=-4.

A function and its inverse are reflections of each other in the line y=x. That line is shown as dashed orange, and the points of interest are marked: (7, -4) and its inverse, (-4, 7).

The coordinates on the x-axis (the x-intercepts) and y-axis (the y-intercepts) are;

(a) (i) The point, A = (6, 0)

(ii) The point B = (0, 6)

(b) The point A = (4, 0)

The point B = (0, 3)

The x and y-intercepts are the points at which the graph intersects the x-axis and the y-axis respectively. The coordinates of the points are (x, 0) and (0, y) respectively.

(a) (i) The equation of the line of the graph is; x + y = 6

The x-intercept of the line is at point A

The y-intercept of the line is at point B

At the x-intercept, the y-coordinate is 0, from the equation, x + y = 6, when y = 0, we get;

x + y = 6

x + 0 = 6

x = 6

The coordinate of the x-intercept, A = (6, 0)

(ii) The y-coordinate of the y-intercept is the value c of the equation of the line y = m·x + c

The x-coordinate at the y-intercept is 0

Rearranging the equation, x + y = 6, we get;

y = -x + 6

The y-coordinate at the y-intercept is therefore, c = 6

The point B is therefore; (0, 6)

(b) (i) The equation of the line is 4·y + 3·x = 12

The equation can be rearranged so that we get;

4·y + 3·x = 12

4·y = 12 - 3·x

y = (12 - 3·x) ÷ 4 = 3 - (3/4)·x

y = 3 - (3/4)·x

At the x-intercept, the value of y is 0. Plugging in y = 0 in the equation, y = 3 - (3/4)·x, we get;

0 = 3 - (3/4)·x

3 = (3/4)·x

x = 3 ÷ (3/4) = 4

x = 4,

y = 0 and x = 4, therefore the coordinate of the point A is (4, 0)

(ii) The y-intercept is point B

The x-value at the y-intercept is 0

Plugging the value x = 0 in the equation y = 3 - (3/4)·x, we get;

y = 3 - (3/4)× 0 = 3

x = 0 and y = 3

The coordinate of the point B is (0, 3)

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The true statement for the function p(x) is p(-2) and p(0) cannot be compared because p(0) is undefined. Option D is correct.

The given function is a logarithmic function and it is undefined at x = 0.

First, let us understand the logarithmic function:

A logarithmic function is a function of the form which is read as “ y equals the log of x, base b” or “ y equals the log, base b, of x.” In both forms, x > 0 and b > 0, b ≠ 1.

We are given:

p(x) = log 5x

substitute x = 0 in the above equation, we will get;

p(0) = log 5 * 0

p(0) = log 0

p(0) = undefined

Thus, the true statement for the function p(x) is p(-2) and p(0) cannot be compared because p(0) is undefined. Option D is correct.

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Answer:

Step-by-step explanation:

As per the concept of right angled triangle, the set of side measurements that could be used to form a right triangle is √15, 6, and √51

Right-angle triangle:

Right angle triangle means a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

Given,

√19, √35, 54

√15, 6, √51

5, 8, 30

5, 6, 7

Now, we have to determine which set of side measurements could be used to form a right triangle.

Here we  know that, according to the Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

So, by using Pythagoras' theorem:

Option (2) √15, 6, √51

Makes the right angle triangle,

Because when we verify these by using the Pythagoras theorem,

(√15)² + (6)² = (√51)²

15 + 36 = 51

51 = 51

Therefore, the set of side measurements that could be used to form a right triangle is √15, 6, and √51  option (2) is correct.

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Answer:

28 horses

Step-by-step explanation:

336/12=28

because every 12 miles they change the horse.

The solutions of -1 + 3x ≥ 14 are 5 and 8.        

A linear inequality is a Mathematical expression that represents that both sides are not equal. In simple words, we can say that If the relationship makes a non-equal comparison between any two numbers or expressions, then it is known as Linear inequality.

Here we have      

-1 + 3x ≥ 14        

To determine the solutions of a given linear inequality substitute each value of x and check if the value satisfies the given expression

At x = 5 ⇒ -1 + 3(5) ≥ 14  

⇒ -1 + 15 ≥ 14  

⇒ 14 ≥ 14      

∴ x = 5 is a solution to -1 + 3x ≥ 14        

At x = 8 ⇒ -1 + 3(8) ≥ 14  

⇒ -1 + 24 ≥ 14  

⇒ 23 ≥ 14      

∴ x = 8 is a solution to -1 + 3x ≥ 14        

At x = -4 ⇒ -1 + 3(-4) ≥ 14  

⇒ -1 - 12 ≥ 14  

⇒ - 13 ≥ 14   [ which is not true ]  

∴ x = - 4 is not a solution to -1 + 3x ≥ 14        

At x = 2 ⇒ -1 + 3(2) ≥ 14  

⇒ -1 + 6 ≥ 14  

⇒ 5 ≥ 14   [ which is not true ]

∴ x = 2 is a solution to -1 + 3x ≥ 14        

Therefore,

The solutions of -1 + 3x ≥ 14 are 5 and 8    

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Answer:

90 - 2x

Step-by-step explanation:

Angle A and B are both equal as both connect to the middle of the circle

ABO = [tex]x[/tex]

BAO = [tex]x[/tex]

Look at the diagram I attached

Angle ABC is = [tex]x+90[/tex]

Angle BAC = [tex]x[/tex]

Total Angle in a Triangle = 180

[tex]x + 90 + x + ACB = 180[/tex]

[tex]180 - 90 - 2x = ACB[/tex]

[tex]ACB = 90 - 2x[/tex]

Kareem Abdul-Jabbar scored a total of 38387 point in his career

In math, to multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem. In the multiplication problem, 6 × 9 = 54, the numbers 6 and 9 are the factors, while the number 54 is the product.

To find the number of points he had in his total career, we just need to multiply his points per season with the total number of years he spent play game.

This becomes 1919.35 * 20 = 38387 points

He had a total of 38387 points all time in his career

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Check the picture below, assuming counter-clockwise rotation.

Answer:

147 * 3/8

1176/3 = 392

Answer: well about 3

Step-by-step explanation:

father(youngest)mom(middle child)oldest

oldest(youngest)mom(middle child)father

father(middle child)mom(youngest)oldest

hope this helps:)

Function for which x -intercepts is at 4 and -6 is given by

y = k (x - 4)( x + 6).

As given in the question,

Let us consider f(x) be the required function.

y = f(x)

Standard form of a function whose x- intercepts is defined as x = a and

x = b is given by ;

f(x) = k (x - a ) ( x -b)

⇒ y =  k (x - a ) ( x -b)

Where 'k' is constant which can be evaluate when quadratic function  passes through point ( x₁ , y₁).

Here x - intercept is  at 4 and -6

a = 4 and b = -6

Function for which x -intercepts is at 4 and -6 is given by :

y = k (x - 4) ( x -(-6))

⇒ y = k ( x - 4 ) ( x+ 6 )

Therefore, function for which x -intercepts is at 4 and -6 is given by

y = k (x - 4)( x + 6).

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The correct option is option (d).

Using Combination,

Total 120, different samples of size 3 (without replacement) can be taken from a finite population of size 10.

Population size: The population is the entire group of guesses. A sample is a specific group for which you collect data. It is denoted by N.

Sample Size: The sample size is always smaller than the total size of the population. A sample is a subset of the population set. It is denoted by n.

we have given that , n = 3 and N = 10

Using the following formula for calculating the possible number of different samples of size 3 (without replacement) can be taken from a finite population of size 10.

Number of possible different samples of size n from Population size N = NCn = N!/n! (N-n)!

then we have, 10C3 = 10!/3! × 7!

=> 10×9×8/3×2 = 15×8 = 120

Hence, 120 different samples of size 3 (without replacement) is possible from Population of size 10.

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Answer:

2

Step-by-step explanation:

Answer:move one part on the right-side of zero

Step-by-step explanation:

The percentage of flowers she did not pay for is 25% (option A)

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

For instance, 25% means 25/100. This means that 25% of a 50mangoes is 25/100× 50 =12.5mangoes

Similarly, the discount when she paid $60 instead of $80 is $80-$60= $20

therefore %discount = 20/80 ×100= 2000/80= 25%

therefore the percentage she did not pay for is 25%

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