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1. (ab + bc) (ab – bc) + (bc + ca) (bc – ca) + (ca + ab) (ca – ab) = 0

We know that (a+b)(a-b) = a²-b²

(ab + bc)(ab -bc) can be written as a²b² - b²c²

(bc + ca)(bc -ca) can be written as b²c² - c²a²

(ca + ab)(ca - ab) can be written as c²a² - a²b²

→ a²b² - b²c² + b²c² - c²a² + c²a² - a²b²

→ a²b² - a²b² - b²c² + b²c² - c²a² + c²a²

→ 0

2. (a + b + c) (a² + b² + c² – ab – bc – ca) = a³ + b³+ c³ – 3abc

→ a³ + ab² + ac² -a²b - abc -ca² + a²b + b³ + bc² - ab² - b²c - abc + a²c + b²c + c³ - abc - bc² - c²a

→ a³ + b³+ c³ + (- abc - abc - abc) + (ab² - ab² )+ (ac² - ca² ) -(a²b + a²b )+ (bc² - bc² )+ (a²c - c²a) + (b²c - b²c)

→ a³+b³+c³ - 3 abc .

3. (p – q) (p² + pq + q²) = p³ – q³.

→ p³ + p²q + pq² - p²q - pq² - q³

→ p³ - q³ +(p²q - p²q) + (pq² - pq²)

→ p³ - q³

Answer:

Step-by-step explanation:

[tex] \mathsf{ 12 {p}^{2} q - 9 {q}^{2} }[/tex]

In such an expression, the factor which is present in all terms of the expression is taken out as common and each term of the expression should be divided by the common factor to get another factor.

Factor out 3q from the expression

[tex] \mathsf{ = 3q(4 {p}^{2} - 3q)}[/tex]

Hope I helped!

Best regards!

Factorization of 12p²q-9q² is  3q(4p²-3q).

Factorization is defined as breaking an entity into a product of another entity, or factors, which when multiplied together give the original number.

Here, given expression is,   12p²q-9q²

Now, by factorizing this we get,

3q(4p²-3q)

Hence, required factorization is 3q(4p²-3q)

To learn more on factorization click:

https://brainly.com/question/14549998

#SPJ2

Answer:

Ok, our function is:

f(x) = 3*(x - 1)^2 + 2.

First, domain:

We should assume that the domain is all the set of real numbers, and then we see if for some value we have a problem.

In this case we do not see any problem (we can not have a zero in the denominator, and there is no function that has problems with some values of x)

Then the domain is the set of all real numers.

Vertex:

Let's expand our function:

f(x) = 3*x^2 - 3*2*x + 1 + 2

f(x) = 3*x^2 -6*x + 2

The vertex of a quadratic function:

a*x^2 + b*x + c is at:

x = -b/2a

here we have:

a = 3 and b = -6

x = 6/2*3 = 6/6 = 1.

And the value of y at that point is:

f(1) = 3*(1 - 1)^2 + 2 = 2

Then the vertex is at: (1, 2)

Range:

The range is the set of all the possible values of y.

Ok, we can see that the leading coefficient is positive, this means that the arms of our quadratic function will go up.

Then the minimal value of our quadratic function is the value at the vertex, y = 2.

This means that the range can be written as:

R = y ≥ 2

So the range is the set of all real numbers that are larger or equal than 2.

Answer:

6 sqrt(3) = y

Step-by-step explanation:

We can use the leg rule to find y

hyp      leg

----- = -------

leg        part

9+3      y

----- = -------

y       9

Using cross products

12*9 = y^2

108 = y^2

Taking the square root of each side

sqrt(108) = sqrt(y^2)

sqrt(36 *3) = y

6 sqrt(3) = y

Answer: B) 6/3 units

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=2/5x-12 it is a linear equation in the form of y=mx+b

the best way to know is to graph the function

Answer:

its z y and x

Step-by-step explanation:

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Answer:

The properties and characteristics of the sum of two cubes

1) In the sum of two cubes, the middle sign of the binomial factor on the right hand side of the equation is positive

2) The trinomial factor has a middle sign that is opposite to the middle sign in the question on the sum of two cubes

The properties and characteristics of the difference of two cubes

1) In the difference of two cubes, the middle sign of the binomial factor on the right hand side of the equation is always negative

2) The trinomial factor has a middle sign that is opposite to the middle sign in the question on the difference of two cubes

Step-by-step explanation:

The sum and difference of two cubes are;

a³ + b³, and a³ - b³

Factorizing the expressions for the sum and difference of two cubes can be shown as follows;

Sum of two cubes; a³ + b³ = (a + b) × (a² - a·b + b²)

Difference of two cubes; a³ - b³ = (a - b) × (a² + a·b + b²).

The other answer is correct, its both !<3

Answer:

Both

Step-by-step explanation:

Both Tori and Gavin are correct, the two methods work. Completed this in Khan Academy, it's correct.

Answer:

I’m not entirely sure what the question is asking but...

The spinner has a 1/4 chance of landing on green

with this, being a 12 section game wheel, it means that 3 of the sections are green.

Answer:

h=6.003 cm

Step-by-step explanation:

[tex] \frac{1}{3} \pi {r}^{2} h \: \: is \: the \: volume \: of \: cone[/tex]

1/3×22/7×7×7×h=308

h=308/51.3

Answer:

h = 6 cm

Step-by-step explanation:

r = 7 cm

Volume of cone = 308 cm³

[tex]\frac{1}{3}\pi r^{2}h=308\\\\\\\frac{1}{3}*\frac{22}{7}*7*7*h=308\\\\\\h=\frac{308*3*7}{22*7*7}\\\\\\h=2*3[/tex]

h = 6 cm

Answer:

x=6

Step-by-step explanation:

13(x-3) = 39

Divide each side by 13

13/13(x-3) = 39/13

x-3 = 3

Add 3 to each side

x-3+3 = 3+3

x = 6

Answer:

x=6 ,is right.

6-3=3&multiply 13=39

so answer is x=6

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Answer:

[tex]\huge \boxed{x < 3}[/tex]

Step-by-step explanation:

4x - 1 < 11

Add 1 on both sides.

4x - 1 + 1 < 11 + 1

4x < 12

Divide both sides by 4.

(4x)/4 < 12/4

x < 3

Answer:

Step-by-step explanation:

3x² + 7x - 6 = 3x² + 9x - 2x - 2*3

                  = 3x (x + 3) - 2(x +3)

                  = (3x - 2)(x + 3)

Area of the rectangle = 3x² + 7x - 6

length * width = 3x² + 7x - 6

length * (x + 3) = (3x -2)(x +3)

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

          length = (3x - 2)

Answer:32

Step-by-step explanation:

if selling is 28 and she is 4 years greater than Drake then that is 28-4 which is 32 so Drake is 32 years old

Answer:

The answer is 32.

Step-by-step explanation:

If Celine is 28 and Drake is four years older than her, we do 28+4.

[tex]9-i+(-5-i)=9-i-5-i=4-2i[/tex]

Answer:

Slope = -1

Step-by-step explanation:

To find the slope of the line between two points, we simply need to take the difference of the y-coordinates over the difference of the x-coordinates.

(-2, 1) and (3, -4)

Slope = (-4 - 1) / (3 - (-2) )

Slope = -5 / ( 5 )

Slope = - 1

Cheers.

Answer:

x = 2

Step-by-step explanation:

3x - 5 = 1

Adding 5 to both sides gives us:

3x - 5 + 5 = 1 + 5

3x = 6

Dividing the equation by 3 gives us:

3x / 3 = 6 / 3

x = 2

Answer:

x = 2 Hfizfifsits96eotst9s

Answer:

Step-by-step explanation:

=-5 +4

= -1

put a dot on -1 and go from -5 to -1 and then from -1 to -5

Answer:

x= 36 km

Step-by-step explanation:

Vince went on a 3 day hiking trip. Each day, he walked 3/4 the distance that he walked the day before. He walked 83.25 kilometers total in the trip. How far did Vince walk on the 1st day of the trip?

Assume vince walked x km on the first day .

The following equation can be formed

x + 3/4 x + (3/4)^2 x = 83.25

x + 0.75x + 0.5625x = 83.25

Add the like terms

2.3125x = 83.25

Divide both sides by 2.3125

x = 36 km.

Answer:

36

Step-by-step explanation:

Answer:

The remaining dimensions of the triangle are [tex]A \approx 31.7368^{\circ}[/tex], [tex]C \approx 18.2632^{\circ}[/tex] and [tex]a \approx 45.3201[/tex].

Step-by-step explanation:

As angle B is an obtuse angle, Angle C can be obtained by means of the Law of Sine:

[tex]\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]

[tex]\sin C = \frac{b}{c}\cdot \sin B[/tex]

[tex]C = \sin^{-1}\left(\frac{b}{c}\cdot \sin B \right)[/tex]

Where:

[tex]b[/tex], [tex]c[/tex] - Measures of triangle sides, dimensionless.

[tex]B[/tex], [tex]C[/tex] - Measures of angles, measured in degrees.

If [tex]b = 27[/tex], [tex]c = 66[/tex] and [tex]B =130^{\circ}[/tex], then:

[tex]C = \sin^{-1}\left(\frac{27}{66}\cdot \sin 130^{\circ} \right)[/tex]

[tex]C \approx 18.2632^{\circ}[/tex]

Given that sum of internal angles in triangles equals to 180º, the angle A is now determined:

[tex]A = 180^{\circ}-B-C[/tex]

[tex]A = 180^{\circ}-130^{\circ}-18.2632^{\circ}[/tex]

[tex]A \approx 31.7368^{\circ}[/tex]

Lastly, the length of the side [tex]a[/tex] is calculated by Law of Cosine:

[tex]a = \sqrt{b^{2}+c^{2}-2\cdot b\cdot c\cdot \cos A}[/tex]

[tex]a =\sqrt{27^{2}+66^{2}-2\cdot (27)\cdot (66)\cdot \cos 31.7368^{\circ}}[/tex]

[tex]a \approx 45.3201[/tex]

The remaining dimensions of the triangle are [tex]A \approx 31.7368^{\circ}[/tex], [tex]C \approx 18.2632^{\circ}[/tex] and [tex]a \approx 45.3201[/tex].

Answer:

23×x

=23x

Hope it helps

Answer:

23x

Step-by-step explanation:

"The product of" indicates that we will be multiplying the two quantities. 23 multiplied by x can be written as 23 * x which simplifies to 23x.

Answer:

2c^3(c+11)^2

Step-by-step explanation:

2c^5 + 44c^4 + 242c^3

Factor out the greatest common factor

2c^3(c^2+22c+121)

Recognizing inside the parentheses is (a+b) ^2 where a =c and b = 11

2c^3(c+11)^2

Answer:

4x+3=0 or x=-3/4

Step-by-step explanation:

9x+26+7x-17=2x-3x+5x

arrange all numbers with coefficient x at one side let's say the left hand side and constant or real numbers at the right hand side in doing that we get

9x+7x-2x+3x-5x=17-26

12x=-9

(12x)/3=-9/3

4x=-3

x=-3/4

Answer: Infinitely many solutions

Step-by-step explanation:

The lines is on top of each other so this makes it many solution.

It can't be NO solution because the lines are not parallel  to each, which means  they will not intersect.

It  can't be one solution because the lines doesn't intersect.

It can't be two solutions because the lines never intersect and they never intersect twice either.

Answer:

3

Step-by-step explanation:

Here, by reading the histogram, we will provide answer for the question asked.

We want to know how many more festivals had 18 to 23 countries represented than 0 to 5 countries.

Checking the histogram, we can see the 0-5 countries having a value of 1, while the 18-23 has a value of 4.

So, the number of more countries will be simply 4-1 = 3

Answer:

3

Step-by-step explanation:

Answer:

3x^2

Step-by-step explanation:

Given:

(3x) * {(1/x)^-4 }* (x^-3)

=(3x) * {1 ÷ (1/x)^4} * {1/x^3}

=(3x) * {1(x/1)^4} * (1/x^3)

=(3x) * (x^4) * (1/x^3)

=(3x) (x^4) (1) / x^3

Multiply the denominators

=3x^5 / x^3

Can also be written as

=3*x*x*x*x*x / x*x*x

Divide the x

= 3*x*x / 1

=3x^2

Answer:

[tex]\boxed{3^5}[/tex]

Step-by-step explanation:

Hey there!

Look at the image below↓

By looking at the image we can tell the PR expression is [tex]3^5[/tex].

Hope this helps :)

Answer:

Below in bold.

Step-by-step explanation:

Dividing  by primes:

3 ) 243

3 )  81

3 )  27

3)     9

        3.

So the prime factors of 243 are 3 * 3 * 3 * 3 * 3  or  3^5.

Answer:

Weight of wastage=179.775kg

weight of rice cultivated= 585.225 kg

percentage of rice cultivated=76.5%

Step-by-step explanation:

Area of land=100 square meters

Cultivated rice=765kg

Wastage=23.5%

1) Weight of the wastage=23.5% of 765kg

=23.5/100 × 765

=17977.5 / 100

=179.775 kg

2) Weight and percentage of rice cultivated.

weight of rice cultivated = 765 kg - 179. 775 kg

= 585.225 kg

percentage of rice cultivated = 100 - 23.5

= 76.5%

3) if area is increased 40 times in size

New area=1000 square meters × 40

=40,000 square meters

Cultivated rice= 765kg × 40

=30,600 kg

Cultivated rice excluding wastage=585.225 kg × 40

=23,409 kg

Answer:

TRUE

Step-by-step explanation:

Length of other leg [tex]= \sqrt {12^2 - 8^2} \\

= \sqrt {144 -64} \\

= \sqrt {80} \\

= 4\sqrt {5} \\[/tex]

Since, [tex] \sqrt 5[/tex] is an irrational number, hence Perimeter of triangle will also be irrational.

TRUE

Answer:

True.

Step-by-step explanation:

The length of the other side = sqrt ( 12^2 - 8^2)

= sqrt (144 - 64)

= sqrt ( 80) which is irrational so the perimeter is also irrational.

(The sum of a rational number and an irrational is irrational).

Answer:

Kindly check explanation

Step-by-step explanation:

SMALL SIZE :

AMOUNT OF LIQUID = 250 milliliters

Sales price = $4.50

Cost per milliliter :

Sales price / amount of liquid

$4.50 / 250 = $0.018

MEDIUM SIZE :

AMOUNT OF LIQUID = 500 milliliters

Sales price = $9.95

Cost per milliliter :

Sales price / amount of liquid

$9.95 / 500 = $0.0199

= $0.020 ( 3 decimal places)

LARGE SIZE :

AMOUNT OF LIQUID = 1 LITRE = 1000 milliliters

Sales price = $16.95

Cost per milliliter :

Sales price / amount of liquid

$16.95 / 500 = $0.0199

= $0.01695

= $0.017 ( 3 decimal places)

A) LARGE < SMALL < MEDIUM

B) LEAST EXPENSIVE WAY TO BUY 1500 milliliters of green cleaner :

1 large size + 2 small sizes

$16.95 + 2($4.50)

$16.95 + $9.00

= $25.95

C.) MOST EXPENSIVE WAY TO BUY 1500 milliliters of green cleaner :

3 medium sizes

3 * ($9.95)

$29.85