factorise fully 7x^3-35

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 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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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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Check the picture below, assuming counter-clockwise rotation.

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: 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:)

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).

Answer:

28 horses

Step-by-step explanation:

336/12=28

because every 12 miles they change the horse.

Answer:

-1°C

Step-by-step explanation:

-8+7=-1

Is your s key broken?

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

Step-by-step explanation:

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:

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

(Sorry if im wrong)

Step-by-step explanation:

Answer:

-14 + 23 = 9

Step-by-step explanation:

if you borrow 14 dollars and pay23 dollars you have a change of 9 dollars

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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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]

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:

2

Step-by-step explanation:

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: Choice B

Step-by-step explanation:

A doesn’t contain any variables

B is literal because you can solve for X

C doesn’t contain any numbers

D is an expression

- Your Welcome

Answer:

C.

Step-by-step explanation:

A literal equation consists of mainly variables.

A. has no variables

B. only has one variable

D. Is not an equation

Answer:

147 * 3/8

1176/3 = 392

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

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]

Answer:

be chill bro but which subject is this

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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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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Answer:

Step-by-step explanation:

3(3c + 1) = 21 is false

Answer:

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

Step-by-step explanation:

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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