At Bob's binders, a set of 3 notebooks costs $4.20. At Pam's Paper Place a set of 4 notebooks costs $5.20. What is the unit price of the notebooks at each store? Which is the better buy?

5^4 /5

Use the exponent rule x^a/x^b = x^a-b

5^4/5 = 5^4-1 = 5^3

Answer as a positive exponent is 5^3

Answer:

x > 2

Step-by-step explanation:

Distribute and cross-simplify 1/2 with parenthesis

4x + x + 2 > 12

Solve left side

5x + 2 > 12

Subtract 2 from both sides

5x > 10

Divide both sides by 5

x > 2

Answer:

Factors of 15: 1, 3, 5 and 15.

Factors of 17: 1 and 17.

Factors of 26: 1, 2, 13 and 26

Factors of 80: 1, 2, 4, 8, 10, 20, 40, and 80.

Actually you can find all the answers in the Internet.

Patterns are set of rules that guide the creation of a dataset. The observation from the first three designs are as follows:

The pattern

The first three design show that, as the design number increases (i.e. 1, 2, 3), the number of tiles used also increases (i.e. 7, 12, 19)

The expressions for the number of tiles

The design number and the number of tiles is represented as follows

[tex]1 \to 7[/tex]

[tex]2 \to 12[/tex]

[tex]3 \to 19[/tex]

From the designs, we observe that some tiles are at the middle, while other tiles are at the sides.

Design 1 has 1 tile at the center and 6 tiles at either sides.

So, we have:

[tex]1 \to 1 + 6[/tex]

[tex]2 \to 4 + 8[/tex]

[tex]3 \to 9 + 10[/tex]

Expand

[tex]1 \to 1^2 + 6 \to 1^2 + 2 \times 3 \to 1^2 + 2 \times (1 + 2)[/tex]

[tex]2 \to 2^2 + 8 \to 2^2 + 2 \times 4 \to 2^2 + 2 \times (2 + 2)[/tex]

[tex]3 \to 3^2 + 10 \to 3^2 + 2 \times 5 \to 3^2 + 2 \times (3 + 2)[/tex]

Notice the pattern,

The number of tiles in design n will be:

[tex]Tiles = n^2 + 2 \times (n + 2)[/tex]

Open bracket

[tex]Tiles = n^2 + 2n + 4[/tex]

Hence, the expressions for number of tiles in design n are:

[tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex]

Technology to prove that both expressions are equivalent

To prove that [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] are equivalent using technology, the graphs of [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] can be plotted and then compared

The table and graph for the first 6 designs

The table entry for the first 6 designs is calculated as follows:

[tex]n = 1\ \ \ \ \ Tiles = 1^2 + 2 \times 1 + 4 = 7[/tex]        

[tex]n = 2\ \ \ \ \ Tiles = 2^2 + 2 \times 2 + 4 = 12[/tex]        

[tex]n = 3\ \ \ \ \ Tiles = 3^2 + 2 \times 3 + 4 = 19[/tex]        

[tex]n = 4\ \ \ \ \ Tiles = 4^2 + 2 \times 4 + 4 = 28[/tex]        

[tex]n = 5\ \ \ \ \ Tiles = 5^2 + 2 \times 5 + 4 = 39[/tex]        

[tex]n = 6\ \ \ \ \ Tiles = 6^2 + 2 \times 6 + 4 = 52[/tex]        

So, we have:

[tex]\begin{array}{cc}Design & {Tiles} & {1} & {7} & {2} & {12} & 3 & {19} & {4} & {28} & {5} & {39}& {6} & {52} \ \end{array}[/tex]

See attachment for the graph of the above table

All the points on the curve make sense in this scenario because all values are positive.

The pattern type

We have:

[tex]Tiles = n^2 + 2n + 4[/tex]

When an equation has a degree of 2, the equation is quadratic.

Hence, the pattern is quadratic.

The largest design that an empty sign of 10ft by 12ft can contain.

From the first three designs:

The number of tiles on a complete row and column are always the same.

Design 1 has 3 tiles in its complete row and column

Design 2 has 4 tiles in its complete row and column

Design 3 has 5 tiles in its complete row and column

The relationship between the design number (d) and the number of complete tiles (t) is:

[tex]d = t - 2[/tex]

For the 10ft by 12ft empty sign

[tex]t = 10[/tex] because [tex]10 < 12[/tex]

So, we have:

[tex]d = t - 2[/tex]

[tex]d = 10 - 2[/tex]

[tex]d = 8[/tex]

Hence, the largest design number is design 8

Read more about patterns at:

https://brainly.com/question/13382968

Answer:

[tex]f'(x)=1+\ln x[/tex]

Step-by-step explanation:

[tex]f'(x)[/tex] is notation for the first derivative of [tex]f(x)[/tex].

Recall the product rule:

[tex](f\cdot g)'=f'\cdot g+g'\cdot f[/tex]

Therefore, we have:

[tex]\displaystyle \frac{d}{dx}(x\ln x)=\frac{d}{dx}(x)\cdot \ln(x)+\frac{d}{dx}(\ln x)\cdot x[/tex]

Note that:

[tex]\displaystyle \frac{d}{dx}(x)=1,\\\\\frac{d}{dx}(\ln x)=\frac{1}{x}[/tex]

Simplify:

[tex]\displaystyle \frac{d}{dx}(x\ln x)=1\cdot \ln x+\frac{1}{x}\cdot x, \\\\\frac{d}{dx}(x\ln x)= \ln x+1=\boxed{1+\ln x}[/tex]

The derivative is:

[tex] \bold{f(x) \: = \: x \: \times \: (In(x))}[/tex]

[tex] \bold{f'(x) \: = \: \frac{d}{dx} (x \: \times \: In(x))}[/tex]

[tex] \bold{f'(x) \: = \: \frac{d}{dx} (x) \: \times \: In(x) \: + \: x \: \times \: \frac{d}{dx} (In(x))}[/tex]

[tex] \bold{f'(x) \: = \: 1In(x) \: + \: x \: \times \frac{1}{x} }[/tex]

[tex] \bold{f'(x) \: = \: In(x) \: + \: x \: \times \: \frac{1}{x} }[/tex]

[tex] \boxed{ \bold{f'(x) \: = \: In(x) \: + \: 1}}[/tex]

Answer:

2x-y= 5, x + 2y=5

Step-by-step explanation:

x = 3, y = 1

Answer:

Step-by-step explanation:

Answer:

Anything to a negative power is always the reciprocal. An example might be 2⁻² can be written as 1/4

Step-by-step explanation:

Answer:

You would shade the fourth quadrant (bottom right).

Step-by-step explanation:

Due to the domain and range sets, you're given the facts that x must be greater than or equal to 0, but y is less than or equal to zero. This gives you what quadrant the graph should be in. Since you're not given an equation to follow like y=ax+b, then I can not say that this will give you a line.

Answer:

The answer is 8.8

Step-by-step explanation:

4/5 x 20/20 = 80/100

80/100 = .8

Step-by-step explanation:

[tex]8 + \frac{4}{5} = \frac{40 + 4}{5} \\ = \frac{44}{5} = 8.8 \\ thank \: you[/tex]

Answer:

11. [tex]x^{5}[/tex]

12. 5*[tex]x^{2}[/tex]

13. x+21

14. 2x-8

Step-by-step explanation:

Answer:

Option 1 is the correct equation.

Step-by-step explanation:

x = price of the student ticket.

One half price of x + $8 = adult ticket price ($15)

Answer:

The correct answer is A

Because taking the student ticket to be x

one half of x + 8 =15

Answer:

since there is no value for the dimensions of the tennis ball. The tennis ball is a sphere with a Surface Area 4pir²

Answer:

4.43

Step-by-step explanation:

4 3/7

~Turn into an improper fraction

31/7

~Divide

4.42885714286...

~Round

4.43

Best of Luck!

Answer:

47

Step-by-step explanation:

8(4) + 2(6) + 3 = 47

32 + 12 + 3 = 47

Answer:

30%

Step-by-step explanation:

14+ 18+ 28 = 60

18/60 × 100 = 30%

Answer:

[tex] \frac{18}{60} = \frac{3}{10} = 30\%[/tex]

Step-by-step explanation:

Total token sample = 14 + 18 + 28 = 60

Frequency of blue:

[tex] = \frac{18}{60} \: [/tex]

[tex] = \frac{18}{60} \times 100\%[/tex]

[tex] = 30\%[/tex]

Answer:

True

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Step-by-step explanation:

6x-2+9y-3y-3x

6x-3x-2+9y-3y

3x-2+6y

Therefore its 3x-2+6y.

Answer:

[tex]b)8[/tex]

is the answer it's was helpful to you

Answer:

B ) 8

Is the answer have a great day

Step-by-step explanation:

if I understand the typed information here, we have

(-4 + 8x) + 3 > -4

so, I am looking at that :

-4 + 8x + 3 > -4

let's first add 4 on both sides

8x + 3 > 0

then subtract -3 on both sides

8x > -3

and finally divide both sides by 8

x > -3/8

since we never multiplied or divided by a negative number, the inequality sign stays the same.

so, this inequality is true for all x > -3/8

Answer:

-7

Step-by-step explanation:

The line (y-1)=(2/3)(x+1) contains point (a,-3)

=> (-3-1) = (⅔)(a+1)

-4 = (⅔)(a+1(

(a+1)= -4 ÷ ⅔

a + 1 = -4 × 3/2

a+ 1 = -6

a = -6-1

a = -7

The value of 'a' will be;

⇒ a = - 7.

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The equation of line is,

⇒ (y - 1) = (2/3) (x + 1)

And, The point on the line = (a, - 3)

Now,

Since, The point on the line = (a, - 3)

Hence, It satisfy the equation of line.

Substitute x = a and y = - 3, we get;

⇒ (y - 1) = (2/3) (x + 1)

⇒ (- 3 - 1) = (2/3) (a + 1)

⇒ - 4 × 3 = 2a + 2

⇒ - 12 - 2 = 2a

⇒ 2a = - 14

⇒ a = - 7

Thus, The value of a = - 7

Learn more about the substitution method visit:

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Answer:

1st box is "a 90°clockwise rotation about the origin

2nd box is "a 180° rotation about the origin

3rd box is "a 90° counterclockwise rotation about the origin

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{350 rounded to the nearest hundred is...}[/tex]

[tex]\huge\text{Rounding is basically is the}\\\huge\text{approximation of the given number.}[/tex]

[tex]\huge\bullet\huge\text{ So, when you are looking at 350, you are}\\\huge\text{asking yourself is it closer to 300 or 400.}\\\huge\text{If you are looking at the number correctly}\\\huge\text{you would see it is closer to \underline{\underline{400}} when you}\\\huge\text{rounded to NEAREST HUNDRED.}[/tex]

[tex]\huge\boxed{\textsf{Therefore, your ANSWER/RESULT is: \bf 400}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

Answer:

92% of Income is  Rs 18400

Step-by-step explanation:

I = 18400/.92 = Rs 20000

Answer:

3.2×10^-7 hope this will be of help

Step-by-step explanation:

3x²+1+8=27

3x²+9=2

3x²=27-9

3x²=19

x²=19/3

[tex]x = \frac{ \sqrt[]{19} }{ \sqrt{3} } [/tex]

Answer:

[tex]3^{2x} + 1 + 18 = 27\\ 3^{2x} = 18\\2x = log_{3} 18[/tex]

Step-by-step explanation: