1. (a) Find the greatest common divisor of the term 144x3y2and 81xy4
(b) Hence factorise completely this expression 144x3y2-81xy4​

Answers

Answer 1

Answer:

Step-by-step explanation:

a) 144x³y² = 2 *2*2*2* 3* 3* x³ * y² = 2⁴ * 3² * x³ * y²

 81xy⁴      = 3 * 3 * 3 * 3 * x * y⁴      =         3⁴ * x * y³

GCD is  that are in both term

Greatest common divisor = 3² * x * y² = 9xy²

b) 144x³y² - 81xy⁴ = 9xy² * 16x²y  - 9xy²*9y²

                             = 9xy²(16x²y - 9y²)


Related Questions

Find the length of the arc. A. 187π/12 ft B. 16π/3 ft C. 49π/6 ft D. 343π/12 ft

Answers

Answer:

[tex]\huge \boxed{\mathrm{Option \ C}}[/tex]

Step-by-step explanation:

Length of arc formula = θ/360 × 2[tex]\pi[/tex]r

The angle is 210 degrees.

The radius is 7 ft.

210/360 × 2[tex]\pi[/tex](7)

Simplify the expression.

210/360 × 14[tex]\pi[/tex]

2940/360[tex]\pi[/tex]

49/6[tex]\pi[/tex]

The length of the arc of circle having radius 7 feet is 49π/6 which is option C.

What is arc?

An arc is a part of circumference of a circle which is formed from two radius of the circle. The length of arc is equal to Θr in which r is radius and Θ is angle in radian form.

How to find length of arc?

We have been given the radius of the circle be 7 feet and angle be 210°.

The length of arc will be Θr in which r is the radius and Θ is the angle in radian form.

First we have to convert angle in radian form=210*π/180=7π/6.

Length of arc=7π/6*7

=49π/6

Hence the length of the arc of circle having radius 7 feet is 49π/6 which is option C.

Learn more about arc at https://brainly.com/question/2005046

#SPJ2

You are selling lemonade for $1.50, a bag of kettle corn for $3, and a hot dog for $2.50 at a fair. Write and simplify an expression for the amount of money you receive when p people buy one of each item

Answers

Answer:

1.5p + 3p + 2.5p

Step-by-step explanation:

This expression, 1.5p + 3p + 2.5p, will represent the amount of money received when p people buy one of each food item.

Since the price of each is the coefficient for p, this will represent how much money will be gained from each food item. All 3 terms will be added together to represent the total amount of money gained from selling all 3 items.

Help!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

x > - 8 or x < 2

Step-by-step explanation:

Given

- 8 < 2(x + 4) or - 3x + 4 > x - 4

Solve each part separately

- 8 < 2(x + 4) ← divide both sides by 2

- 4 < x + 4 ( subtract 4 from both sides )

- 8 < x , thus

x > - 8

OR

- 3x + 4 > x - 4 ( subtract x from both sides )

- 4x + 4 > - 4 ( subtract 4 from both sides )

- 4x > - 8

Divide both sides by - 4, reversing the symbol as a result of dividing by a negative quantity

x < 2

Solution is x > - 8 or x < 2

The marketing department at Quality Home Improvement Center (QHIC) uses simple linear regression analysis to predict home upkeep expenditure on the basis of home value. Predictions of home upkeep expenditures are used to help determine which homes should be sent advertising brochures promoting QHIC's products and services.

Answers

Full question :

The Tasty Sub Shop Case:

A business entrepreneur uses simple linear regression analysis to predict the yearly revenue for a potential restaurant site on the basis of the number of residents living near the site. The entrepreneur then uses the prediction to assess the profitability of the potential restaurant site.

And

The QHIC Case:

The marketing department at Quality Home Improvement Center (QHIC) uses simple linear regression analysis to predict home upkeep expenditure on the basis of home value. Predictions of home upkeep expenditures are used to help determine which homes should be sent advertising brochures promoting QHIC’s products and services.

Discuss the difference in the type of prediction in both cases and provide rational of the reasons that these predictions were used.

Answer and explanation:

In the first case, The Tasty Sub Shop Case, the entrepreneur aims to utlilize the predicted values from his regression analysis in ascertaining profit of his potential business. He does this using the values from number of residents in the area(independent variables) to predict the revenue for his business(dependent variables). His predictions using the number of residents in the area are largely because the residents in the area are his target consumers and are the ones to buy food from his restaurant and increase his revenue.

In the other case, the marketing department in QHIC utilizes the predicted values in determining their customers who need to be aware of their products. They get the predicted values(home upkeep expenditure and dependent variable) by plotting their relationship with home value(independent variable) and then use predicted values of home upkeep expenditures in determining their customers who they will market their products to. They do this because predicting home upkeep expenditures will enable them determine what homes can afford or will need their products and services.

one utilizes his predictions at ascertaining profit while the other uses his predictions in determining potential customer base to market products to. The first case is making a revenue/ profitability prediction while the other is making a market prediction

On the coordinate plane below, Point P is located at (2,-3), and point Q is located at (-4,4). Find the distance between points P and Q Round your answer to the nearest whole number.

Answers

Answer:

9

Step-by-step explanation:

When given two points (x₁, y₁) and (x₂, y₂) on a plane, the Formula for the distance between the points is calculated as:

D= √(x₂ - x₁)² +(y₂ - y₁)²

In the question, we are given Point P is located at (2,-3), and point Q is located at (-4,4).

P(2, -3) , Q(-4, 4)

D = √(-4 - 2)² +(4 -(-3))²

D = √(-6)² + (7)²

D =√36 + 49

D = √85

D = 9.2195444573

Approximately to the nearest whole number, the distance between points P and Q is 9

What are the answers to the following.​

Answers

Answer:

Step-by-step explanation:

[tex]8-11 =-3\\\\b. -8+10 = 2\\\\c. 13+(-6) = 13-6 \\= 7\\\\d. 7-(-3)\\= 7+3\\=10\\\\e.-5-(-2)\\=-5+2\\=-3\\\\f. -15-(-25)\\=-15+25\\=10\\\\g. -3+(-6)-(-9)\\= -3-6+9\\=-9+0\\=0\\\\h.-20-(-9)-(-8)\\=-20+9+8\\-20+17\\=-3\\\\[/tex]

[tex]-2+3-(-4)+(-5)\\-2+3+4-5\\= 1-1\\=0\\\\\\b. 18-(-10)+(-19)-8\\=18+10-19-8\\28-27\\=1\\\\c. 65+(-72)-(-45)\\= 65-72+45\\=-7+45\\=38[/tex]

solve for x 7(x+2) =6(x+5)

Answers

Answer:

16

Step-by-step explanation:

Distribute 7 into x and 2, which gets you 7x+14. Then distribute 6 into x and 5, which is 6x+30. 7x-6x= x, 30-14=16 so there’s your answer.

Answer:

Step-by-step explanation:

7x + 14 = 6x + 30

x + 14 = 30

x = 16

If BH = 108, find DE.

Answers

Answer:

BH= 108 --> 1st until 6th space

so, 108/6 = 18 for each space

DE...?

DE only use 1 space so the answers is 18 unit

I hope this helps^_^

the tripled product of 12 and a number is 102. what is the number​

Answers

Answer:

Step-by-step explanation:

Let

The known number = 12

The unknown number = x

Result = 102

Product of 12 and a number= 12*x

= 12x

Tripled product of 12x= 3(12x)

=36x

36x = 102

Divide both sides by 36

x = 102/36

= 2.833

x=2.833

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Answers

Answer:

See explanation

Step-by-step explanation:

a) 15:20 - 12:35 = 14:80 - 12:35 = 2 hours and 45 minutes

b) 13:05 - 10:15 = 12:65 - 10:15 = 2 hours and 50 minutes

c) 6:50 - 4:30 = 2 hours and 20 minutes

d) 1:15pm - 9:55am = 13:15 - 9:55 = 12:75 - 9:55 = 3 hours and 20 minutes

Answer:

a) 15:20 - 12:35 = 14:80 - 12:35 = 2 hours and 45 minutes

b) 13:05 - 10:15 = 12:65 - 10:15 = 2 hours and 50 minutes

c) 6:50 - 4:30 = 2 hours and 20 minutes

d) 1:15pm - 9:55am = 13:15 - 9:55 = 12:75 - 9:55 = 3 hours and 20 minutes

Step-by-step explanation:

nikhil has RS 80000 from this,he gives 30% to his wife and 20% to his father. Find the amount received by wife and father​

Answers

Answer:

Amount received by wife = RS 24000

Amount received by father = RS 16000

Step-by-step explanation:

His income is RS 80000

He gave 30% of his income to his wife

That's

[tex] \frac{30}{100} \times RS \: \: 80000[/tex]

Which is RS 24000

He gave 20% of his income to his father

That's

[tex] \frac{20}{100} \times RS \: \: 80000[/tex]

Which is RS 16000

Hope this helps you

Mother received 24000
Father received 16000

Plz thanks and mark me the branliest ans

Find the missing the side of the triangle A. 130−−−√ m B. 179−−−√ m C. 42–√ m D. 211−−−√ m

Answers

Answer:

The answer is option A

Step-by-step explanation:

Since the triangle is a right angled triangle we can use the Pythagoras theorem to find the missing side

Using the Pythagoras theorem

That's

[tex] {a}^{2} = {b}^{2} + {c}^{2} [/tex]

From the question

x is the hypotenuse or the longest side of the triangle

Substituting the values into the above formula we have

[tex] {x}^{2} = {9}^{2} + {7}^{2} [/tex]

[tex] {x}^{2} = 81 + 49[/tex]

[tex] {x}^{2} = 130[/tex]

Find the square root of both sides

We have the final answer as

x = √130 m

Hope this helps you

In circle O, AC and BD are diameters. Circle O is shown. Line segments B D and A C are diameters. A radius is drawn to cut angle C O C into 2 equal angle measures of x. Angles A O C and B O C also have angle measure x. What is mArc A B?

Answers

Answer:

120

Step-by-step explanation:

Got it right on the assigment

Answer:

c. 120

Step-by-step explanation:

distance between points on a coordinate plane=(y2−y1)2+(x2−x1)2−−−−−−−−−−−−−−−−−−√ Find the distance when y2=8, y1=4, x2=6, and x1=7. A. 6.95 B. 3.87 C. 4.12 D. 5.66

Answers

Answer:

C, 4.123

Step-by-step explanation:

√(17) which equals 4.12

The Ruiz family is exchanging euros for US dollars. The exchange rate is 1 euro equals 1.35261 USD. Since the Ruiz family knows that USD are stated to the nearest hundredth of a dollar, they used the conversion ratio. Will this give the Ruiz family the correct exchange?

Answers

Answer:

It will depend on how many euros they intend to convert. If they were only converting one euro they would get $1.35 whichever rate they used, but imagine it was a thousand euros - at the correct rate they would get $1352.61, at the proposed rate they would only get $1350.

Step-by-step explanation:

No, by rounding the conversion ratio, the Ruiz family will not be getting the most accurate answer. Using the more accurate conversion ratio will give an answer with more than 2 decimal places so the answer can accurately be rounded after the conversion.

Answer:

No, by rounding the conversion ratio, the Ruiz family will not be getting the most accurate answer. Using the more accurate conversion ratio will give an answer with more than 2 decimal places so the answer can accurately be rounded after the conversion.

Step-by-step explanation:

just copy/paste

For what real numbers x is x 2 − 10 x + 25 negative?

Answers

Answer:

no real numbers

Step-by-step explanation:

x^2 − 10 x + 25

Factor

What 2 numbers multiply to 25 and add to -10

-5*-5 = 25

-5+-5 = -10

( x-5) (x-5)

This touches the graph at x =5

The parabola is positive so there are no values where the graph is negative

Answer:

No real solutions

Step-by-step explanation:

Part 1: Factoring the quadratic

The equation is in quadratic form - ax² + bx + c = 0.

Therefore, we can use a factoring technique to solve for x. I will use the quadratic formula - [tex]x=\frac{-b \pm \sqrt{b^{2}-4ac} }{2a}[/tex].

[tex]x=\frac{-(-10)\pm \sqrt{(-10)^{2}-4(1)(25)} }{2(1)}\\\\x=\frac{10\pm\sqrt{100-4(25)} }{2}\\\\x=\frac{10\pm\sqrt{100-100}}{2}\\\\x=\frac{10\pm\sqrt{0}}{2}\\\\x=\frac{10\pm0}{2}\\\\x=\frac{10}{2}\\\\\boxed{x=5}[/tex]

Part 2: Using discriminant to determine roots

Because the discriminant (square root portion of formula) was equivalent to zero, this is the only solution that proves the equation correctly. Therefore, there is no possible negative value that can be substituted for x  without altering the final value that the equation is equal to.

Can someone help me? Thanks!

Answers

Answer:

question 11: A

question 12: B

Step-by-step explanation:

Thanks calculator :)

Answer:

11. less than

12.less than

hope this helps

Step-by-step explanation:

-2x-7+9-2= Please can i have an answer

Answers

Answer:

-2x

Step-by-step explanation:

-2x-7+9-2

Combine like terms

-2x +0

-2x

Answer:

-2x

Step-by-step explanation:

from the question

-2x-7+9-2=

step 1

collect the like terms

we have,

-2x-7+9-2

-2x + 2 -2

-2x + 0

-2x

therefore the answer to the question -2x-7+9-2 is equal to -2x

A group of students is arranging squares into layers to create a project. The first layer has 4 squares. The second layer has 8 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?

Answers

Answer:

answer is d

Step-by-step explanation:

For the function f(x) = x + 7, what is the ordered pair for the point on the graph where x = 2b? (2b, 2b + 7) (2b, x + 7) (x, x + 7) (x, 2b + 7)

Answers

Answer:

(2b, 2b + 7).

Step-by-step explanation:

y = x + 7 and x = 2b ,

therefore y = 2b + 7.

Answer:

(2b, 2b + 7)

Step-by-step explanation:

Please answer it now

Answers

Answer:

1306.90≅  1307 rounded to the nearest tens

Step-by-step explanation:

r= radius = 13 cm

l is the slant height =19 cm

surface area of the cone= area of the circle + area of the curved of the cone

SA=πrl +πr²

SA=π(13)(19) +169π

SA= 247π +169π= 416π=1306.90≅  1307 rounded to the nearest tens

Study the samples below to answer questions
26 and 27.
pls brainiest

Answers

Answer:

1 st pattern 48+122 = 170

2 nd pattern 8½+3½ = 5

so, 3rd pattern 41+13= 54 (B)

41+13=54 this is the ans

Solve for y.
y/-1 +-7=-11​

Answers

Answer:

y = 4

Step-by-step explanation:

Move all terms not containing  y  to the right side of the equation.

-y = -4

Multiply each term in  − y  =  − 4  by  − 1

y = 4

Hope this can help you

i need help on figuring this out and the answer plz!!

Answers

Answer:

$76

Step-by-step explanation:

The amount changed is the total amount of the whole entire thing.

Therefore, we use absolute value or simply find the difference.

21 - (-55) = 76

So the bank account changed $76 over the 2 days.

Someone please help me!! Tyy

Answers

Answer:

x² = 900

Step-by-step explanation:

ΔABC is an equilateral triangle because its sides are equal lengths

this means their angles are also equal.

180 / 3 = 60

∠BCA and ∠DCA are supplementary angles - add up to 180º

if ∠BCA = 60º, then ∠DCA = 120º

ΔACD is an isosceles triangle because two sides are equal lengths. this means their angles are equal.

∠CAD ≅ ∠CDA

180 - ∠DCA = 2(∠CAD)

180 - 120 = 60

60 / 2 = 30º

x = 30º

x² = 900

Simplify to create an equivalent expression. 8-4(-x+5)

Answers

Answer:= -12+4x

Step-by-step explanation:

Distribute -4 through the parentheses

8+4x=20

Calculate the difference

-12+4x

Two rectangles are joined together to form a single large area. The rectangles do not overlap. The first rectangle has side lengths of 333 meters and 555 meters. The second rectangle has side lengths of 777 meters and 444 meters. What is the combined area?

Answers

Answer:

Step-by-step explanation:

333 times 555=184815

777 times 444=344988

now add 184815+344988=529803

What is the value of the expression below when w = 3?
4w2 – 7w – 8​

Answers

Step-by-step explanation:

w=3

4w^2-7w-8

4*3^2-7*3-8

4*9-21-8

4*9-29

36-29

7

hope this helps

Answer:

7

Step-by-step explanation:

Two birds sit at the top of two different trees. The distance between the first bird and a birdwatcher on the ground is 32 feet. The distance between the birdwatcher and the second bird is 45 feet. A triangle is created from point Bird Watcher, point First Bird, and point Second Bird. Angle First Bird is a right angle, and angle Second Bird measures x degrees. What is the angle measure, or angle of depression, between this bird and the birdwatcher? Round your answer to the nearest tenth. 35.4° 44.7° 45.3° 54.6°

Answers

Answer:

Step-by-step explanation:

When you draw out that picture (and very good description, btw!) basically what you have is a right triangle that has a base of 32 and a hypotenuse of 45. The right angle is one of the base angles and x is the vertex angle. We need to find the vertex angle before we can find the angle of depression from the second bird to the watcher. The side of length 32 is opposite the angle x, and 45 is the hypotenuse, so the trig ratio we need is the only one that directly relates side opposite to hypotenuse, which is the sin ratio:

[tex]sin(x)=\frac{32}{45}[/tex] and

sin(x) = .711111111

Go to your calculator and hit the 2nd button then the sin button and on your screen you will see:

[tex]sin^{-1}([/tex]  

and after that open parenthesis enter in your decimal .711111111 and hit equals. You should get an angle of 45.325. That's angle x. But that's not the angle of depression. The angle of depression is the one complementary to angle x.

Angle of depression = 90 - angle x and

Angle of depression = 90 - 45.325 so

Angle of depression = 44.67 or 44.7 degrees.

Answer:

Its 45.3!!!

Step-by-step explanation:

PLEASE HELP! WILL GIVE BRAINLIEST!

Answers

Answer:

f(1) = 45

f(n) = f(n-1)*(4/5)

Step-by-step explanation:

f(1)

= 45(4/5)^(1-1)

= 45(4/5)^(0)          use law of exponents

= 45*1

= 45

f(1) = 45

f(n) = f(n-1)*(4/5)

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