(b) Factorise fully 2 a²b + 6ab2

Answer:16

explanation:

=64⅔

=(4)3×⅔(there is 3 and 3 will be cancel)

=(4)²(4²=4×4)

=16 Ans

The length of the rectangular solid delivery box is 6 inches.

Volume of a rectangular solid, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units

It is given that, the volume of the delivery box is 540 cubic inches, the width of the delivery box is 3 inches longer than the length and the height is 4 inch longer than the length.

Width of the rectangular solid delivery box = (length + 3) inches

Height of the rectangular solid delivery box = (length + 4) inches

Now,

let us assume that the length of the rectangular solid delivery box is X.

So, Width = (X+3) inches and Height = (X+4) inches.

Volume of rectangular solid delivery box = Length × Width × Height

=> Length × Width × Height = 540 cubic inches.

After putting all the values in the above equation,

=> X × (X+3) × (X+4) = 540

=> X=6 inches

Therefore, the length of the rectangular solid delivery box is 6 inches.

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The values of the functions are h(0) = 1, h(10) = 3, h(-3) = 7 and h(3) = 4

The piecewise function is given as:

h(x) = {7, when x<0

         {x+1, when 0 ≤x ≤4

          {√x-1, when x>4

Next, we solve the function values

1. Function h(0)

This means that x = 0

To do this, we make use of h(x) = x + 1 because x= 0 is in its domain

So, we have

h(0) = 0 + 1

h(0) = 1

2. Function h(10)

This means that x = 10

To do this, we make use of h(x) = √x - 1 because x= 10 is in its domain

So, we have

h(10) = √10 - 1

h(10) = √9

h(10) = 3

3. Function h(-3)

This means that x = -3

To do this, we make use of h(x) = 7 because x= -3 is in its domain

So, we have

h(-3) = 7

4. Function h(3)

This means that x = 3

To do this, we make use of h(x) = x + 1 because x= 3 is in its domain

So, we have

h(3) = 3 + 1

h(3) = 4

Hence, the values of the functions are h(0) = 1, h(10) = 3, h(-3) = 7 and h(3) = 4

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

Using Trigonometric ratios :

[tex]\qquad \sf  \dashrightarrow \: \cos(45 \degree) = \dfrac{b}{ 4 } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{1}{ \sqrt{2} } = \dfrac{b}{4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: b = \dfrac{4}{ \sqrt{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: b = 2 \sqrt{2} [/tex]

The images of points are

From the question, we have the coordinate of point A to be

A = (-4, 3)

The sequence of transformations is given as:

180 degrees rotation around the origin

The rule of the above transformation is

(x, y)= (-x, -y)

So, we have

A' = (4, -3)

This means that

B = (4, -3)

Hence, the image of point B after the transformation of the point A is (4,- 3)

From the question, we have the coordinate of point A to be

A = (-4, 3)

The sequence of transformations is given as:

The rules of the above transformations are

Translation two units to the right

(x, y)= (x + 2 , y)

So, we have

A' = (-2, 3)

Reflection across the x-axis

(x, y)= (x, -y)

So, we have

A'' = (2, -3)

This means that

C = (2, -3)

Hence, the image of point C after the transformation of the point A is (2, -3)

From the question, we have the coordinate of point A to be

A = (-4, 3)

The sequence of transformations is given as:

The rules of the above transformations are

Reflection across the y-axis

(x, y)= (-x, y)

So, we have

A' = (4, 3)

Translation two units to the right

(x, y)= (x + 2 , y)

So, we have

A'' = (6, 3)

This means that

D = (6,3)

Hence, the image of point D after the transformation of the point A is (6,3)

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The number of bills worth $20 is found to be 18 and the  number of bills worth $5 is 12.

A linear equation in two variables is one that is written in the form;

ax + by + c=0, where a, b, and c are real numbers and also the coefficients of x and y, i.e. a and b, are not equal to zero.

Now, as per the given question;

Let 'X' be the number of bills worth $20.

Let 'Y' be the number of bills worth $5.

Then, the total cost of the bills $330 is written as;

330 = 20X + 5Y

Now, if 6 more $5 bills is added to than $20 bills.

Y = X + 6, as there are 6 more $5 bills than $20 bills.

Substitute the value of Y in original equation.

330 = 20X + 5(X+6)

330 = 20X + 5X + 30

Further solving the equation.

300 = 25X

X = 300/25

X = 12 (number of bills worth $20)

Substitute the value in Y to find the number of bills worth $5.

Since, there are 6 more $5 bills than $20 bills, Y = 12+6 = 18

Thus, there are 18 number of bills worth $20.

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[tex]increasing ( \infty \: to \: 1) and \: increasing(3 \: to \: 4) \\ \\ decreasing(1 \: to \: 3) \: and \: (4 \: to - \infty )[/tex]

Step-by-step explanation:

by increasing it means the gradient is positive, so coming positive infinity gradient is positive but once it reaches (1;0) it becomes 0 (=0). from (1;0) it starts to decrease approaching the asymptote of 3

Answer:

B: <

Step-by-step explanation:

2 1/4 is smaller than 3 1/4 because first of all, 2 is smaller than 3. Also, when you make both an improper fraction, than 2 1/4 will be 9/4 and 3 1/4 would be 13/4. 9/4 is smaller than 13/4.

Answer:

Step-by-step explanation:

The coplanar points in plane U are

Point P

Point W

Point S

Point L

Coplanar points are three or more points which all lie in the same plane

Collinear points are the points that lie on the same straight line or in a single line.

In the image attached, points A, B, C, and D are coplanar points. This is because they all lie on the same plane.

Now,

In the given image, points P, W, and S all lie on the same straight line. Thus, they are collinear.

and

Points P, W, S, and L all lie on plane U. This means the points are coplanar.

Hence, the coplanar points in plane U are

Point P

Point W

Point S

Point L

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Using the concepts of similarity and congruence, the correct statement is given by:

a. Q and W are similar but not congruent.

For this problem, we have that:

Hence the correct statement is given as follows:

a. Q and W are similar but not congruent.

From the two bullet points, we justify we the other statements are not correct.

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Answer:2.35

Step-by-step explanation:

The value of the expression is 2.35.

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,

9.4 ÷ 4

= 9.4/4

= 94/(10 x 4)

= 94/40

= 2.35

Thus,

The value of the expression is 2.35.

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Answer:9

Step-by-step explanation:

I'm assuming the equation is : [tex]9^{6}[/tex]=[tex]x^{3}[/tex]*[tex]9^{3}[/tex]

1) [tex]9^{6}[/tex]=531441

  [tex]9^{3}[/tex]    =729

2) 531441=729  [tex]x^{3}[/tex]

3) [tex]\frac{531441}{729}[/tex]= [tex]x^{3}[/tex]

4)729=[tex]x^{3}[/tex]

5) [tex]\sqrt[3]{729}[/tex] =[tex]\sqrt{x}[/tex]^3    

6) 9=x

Answer:

56 packs of seeds

Step-by-step explanation:

To find the area of Chang's backyard, we can use the formula for an area of a rectangle.

Area = length·width or A = lw

32·21 = 672 sq ft.

To find how many packets of seed he will need to cover the backyard, we can take the area of Chang's yard and divide it by how many square feet each pack of seed covers.

672/12 =  56

Chang will need 56 packs of seeds to cover the backyard.

2 times 1 is 2 so the equation becomes x/2 and x is 10 so 10/2 is same as 10÷2 which is 5

Answer:

1.5(x+4) is the answer of this question.

Answer:

the answer is B

Step-by-step explanation:

Answer:

The number of $5 bills is 6

The number of $1 bills is 8

Step-by-step explanation:

Given the number of $1 bills is x, and of $5 bills is y

Then x + y = 14 or x = 14 - y

And 1(x) + 5(y) = 38

then 1(14 - y) + 5y = 38

14 - y + 5y = 38

4y = 38 - 14

4y =24

y = 6

if the number of $5 bills is 6

then the number of $1 bills is 14 - 6 = 8

Answer:

x>−10

Step-by-step explanation:

x = 100/9  ............

Answer:

72% go twice a month

60% prefer comedies

Step-by-step explanation:

45+63=108

108/150=0.72 ---> 72%

63+27=90

90/150=0.6 ---> 60%

Answer:

Step-by-step explanation:

2 1/3 because I learned this exact question at school

Velocity is 5m/s.

In the given statement is :

You walk down a hill for 45 meters. You accomplish this in 9 seconds. What is your velocity? ______m/s.

Firstly, Let's know the:

What is Velocity?

Velocity refers to the rate of change in displacement with respect to time.

Furthermore, distance and displacement are the key points of the velocity.

Now, Calculate the velocity, by using formula of Velocity

Velocity = Displacement/ time

And, Velocity = 45/9 = 5m/s.

Therefore Velocity is 5m/s

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The location of the x value of R' after using the translation rule is 28

The translation rule is given as:

(x + 4, y - 7)

The pre-image of R is located at (24, -13)

Rewrite as

R = (24, -13)

When the translation rule is applied, we have:

R' = (24 + 4, -13 - 7)

Evaluate

R' = (28, -20)

Remove the y coordinate

R'x = 28

Hence, the location of the x value of R' after using the translation rule is 28

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Answer:

x^2y^2(x^2 − 2xy) ..............

The rewritten polynomial of x⁴y² - 2x³y³ is x²y²(x²-2xy).

The greatest number that can divide the numbers in equal parts.

It is called as greatest common factor.

We have a polynomial,

x⁴y² - 2x³y³.

Factor out the common terms,

x⁴y² - 2x³y³,

= x²y²(x²-2xy)

Therefore, x²y²(x²-2xy) is the required expression.

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At least 16 more herb gardens must be sold in order to meet the fundraising goal

It is given that the environmental club is selling indoor herb gardens for $8 each for Earth Day.

The goal for the club is to raise at least $500 during the fundraiser.

So far the club has raised $256 toward the goal.

Let the number of herb gardens yet to be sold be 'x'

Thus total amount raised by 'x' herb garden sold= 8x

Thus, the equation for fundraising will be

8x+256=500

8x=500-256

8x=244

x= 244/8=31/2=15.5

Hence at least 16 more herb gardens must be sold in order to meet the fundraising goal

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Main Answer :16

Concept and definitions should be there:

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.

a ≠ b says that a is not equal to b

a < b says that a is less than b

a > b says that a is greater than b

(those two are known as strict inequality)

a ≤ b means that a is less than or equal to b

a ≥ b means that a is greater than or equal to b.

Given that:

It is given that the environmental club is selling indoor herb gardens for $8 each for Earth Day.

The goal for the club is to raise at least $500 during the fundraiser.

So far the club has raised $256 toward the goal.

Solving Part:

Let the number of herb gardens yet to be sold be 'x'

Thus total amount raised by 'x' herb garden sold= 8x

I can match an inequality to a situation it represents, solve it, and then explain what the solution means in the situation.

If I have a situation and an inequality that represents it, I can explain what the parts of the inequality mean in the situation.

We know that

$256≥ $500 → inequality that represent the situation

Thus, the equation for fundraising will be

8x+256=500

8x=500-256

8x=244

x= 244/8=31/2=15.5

Hence at least 16 more herb gardens must be sold in order to meet the fundraising goal.

Final Answer: 16

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The area of the cardboard in Pedro's model is 190 sq inches.

The only difference between lateral surface area and total surface area is in lateral surface area we only consider the side views and neglect the top and bottom on the other hand for total surface area we consider all sides.

As a sphere has no side it has only total surface area which is 4πr².

According to the given question Pedro uses cardboard to make a model of a square pyramid.

Also given that the edges of the of the model is 5 in. long and the height of the triangular face is 4 in.

As to make the base of the pyramid with is square we need to form a cube which has sides = height = 5 inches.

We know the total surface area of a cube is 6(side)² which is

= 6(5)² sq inches.

= 6(25) sq inches.

= 150 sq inches.

Now for the upper triangular part we need 4 triangles with height 4 inches and as the base of the cube is 5 inches therefore the base of the triangle will also be of 5 inches.

We know area of a triangles with given height and base is

= (1/2)×base×height.

So for four such triangles the area will be 4 times of this.

= 4[(1/2)×5×4] sq inches.

= 4[10] sq inches.

= 40 sq inches.

So, the total area of the square pyramid model will be (150 + 40) = 190 sq inches.

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Answer:

4.5 lb of coffee

Step-by-step explanation:

4.5/20.25