Expand the function.
f(x) = (3x - 1)3

All answer choices are equivalent

All the expressions given in option is equivalent to the expression

([tex]10^{t^{2}+2t-3 }[/tex])

An expression in maths, a sentence with a minimum of two numbers or variables and at least one maths operation. This maths operation can be addition, subtraction, multiplication, or division.

Given is an expression, ([tex]10^{t^{2}+2t-3 }[/tex])

We know, when equal base get multiplied with different powers, the power get added and in case of division they get subtracted,

([tex]10^{t^{2}+2t-3 }[/tex]) = [tex]10^{t^{2} }[/tex]x[tex]10^{2t}[/tex]x[tex]10^{-3}[/tex]

[tex]10^{t^{2} }[/tex]x[tex]10^{2t}[/tex]x[tex]10^{-3}[/tex] = [tex]\frac{10^{t^{2} +2t } }{1000}[/tex]

When we factorize, t²+2t-3, we get,

t²+2t-3 = (t+3)(t-1)

Therefore, ([tex]10^{t^{2}+2t-3 }[/tex]) = [tex]10^{t^{2} }[/tex]x[tex]10^{2t}[/tex]x[tex]10^{-3}[/tex] = [tex]\frac{10^{t^{2} +2t } }{1000}[/tex] = [tex]10^{(t+3)(t-1)}[/tex]

Hence, we can say that, All the expressions given in option is equivalent to the expression ([tex]10^{t^{2}+2t-3 }[/tex])

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Answer: X=6  Y=4

x+y= 10

6+4=10

 x-y=2

6-4=2

Answer:

x=6

y=4

Step-by-step explanation:

Use an elimination method:

add equation 1 and 2 together.

2x = 12

divide both side by 2

x = 12/2

x = 6

use equal 1,

x + y = 10

y = 10 - x

y = 10 - 6

y = 4

Answer:

[tex]gross \ pay = 4200\\\\federal \ deduction = \frac{16.05}{100} \times 4200 = 674.10\\\\Net \ pay = 4200 - 674.10 -321.30= 3204.60[/tex]

Answer:

C

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

the real answer would be 54.25 but you have to round

Step-by-step explanation:

434/8= 54.25

We can't have a decimal of a box, so,

55 boxes

You add half of the coefficient of x and square it.

What you do on one side,you must do it on the other.

The number of personal trips for leisure travel will be equal to 1.5 billion.

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that out of 2 billion person trips, 75 per cent were leisure travel.

The number of the person trips will be calculated as,

N = ( 2 x 75 ) / 100

N = 150 / 100

N  = 1.5 Billion

Therefore, the number of personal trips for leisure travel will be equal to 1.5 billion.

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Answer:

5.7 feet i think

Step-by-step explanation:

Answer:

4.15+1.12x

Step-by-step explanation:

So lets go over what we know.

The cost of a pickup is 4.15 dollars.

The cost of the pickup fee increases by 1.12 dollars per mile.

So when we start off, it will orginate as 4.15 dollars.

We know that this price is going to be increased by the other value, so we can write it as:

4.15+

We know that for each mile, this price goes up by 1.12.

If we went 10 miles, for instance, it would be 1.12 10 times, or 11.2 dollars.

So we know that thr 4.15 will be increased by 1.12 times the amount of miles.

Or:

4.15+1.12*m

=

4.15+1.12m.

Hope this helps!

Answer:

-11,8 or 11,8........both are correct

Answer:

just plot the coordinates down on graph and then u'll have them graphed

Step-by-step explanation:

I don't know I'm too lazy 2 put an explanation

Answer:

(-1,-1)

Step-by-step explanation:

From the diagram you can see that the two equation crossed each other at this point

Answer:

48

Step-by-step explanation:

The blank would be 48 because 3 times 4 is 12. 12 times 4 is 48. And 48 times 4 would be 192

Answer:

NO = 10

Step-by-step explanation:

Given a segment joining the midpoints of 2 sides of a triangle, then it is half the length of the third side, that is

18 - 2x = [tex]\frac{1}{2}[/tex] (9x - 16) ( multiply both sides by 2 to clear the fraction )

36 - 4x = 9x - 16 ( add 4x to both sides )

36 = 13x - 16 ( add 16 to both sides )

52 = 13x ( divide both sides by 13 )

4 = x

Then

NO = 18 - 2x = 18 - 2(4) = 18 - 8 = 10

Given :

A shopkeeper earns a profit of Rs. 1 by selling a pencil and a loss of 20 paisa by selling an eraser.

To Find :

In a given day he had a loss of Rs. 10. On this day, he sold 35 pencils. How many erasers were sold on this day.

Solution :

Money earned by selling 35 pencils.

P = 35 × 1 = Rs 35 .

Now, it is given that he had a loss of Rs 10 .

Therefore, amount of loss done by money is :

E = 35 + 10

E = Rs 45

Now, number of erase sold :

[tex]n = \dfrac{E}{0.2}\\\\n = \dfrac{45}{0.2}\\\\n = 225\ erasers[/tex]

Hence, this is the required solution.

Answer:

[tex]3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n[/tex]

[tex]4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n[/tex]

[tex]2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n[/tex]

[tex]3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n[/tex]

Step-by-step explanation:

Given

See attachment for complete question

Required

Match equivalent expressions

Solving (a):

[tex]3 + 12 + 48 + 192 + 768[/tex]

The expression can be written as:

[tex]3 \to 3*4^{0[/tex] --- 0

[tex]12 \to 3 * 4^{1[/tex] ---- 1

[tex]48 \to 3 * 4^{2[/tex] --- 2

[tex]192 \to 3 * 4^{3[/tex] ---- 3

[tex]768 \to 3 * 4^{4[/tex] ---- 4

For the nth term, the expression is:

[tex]Term = 3 * 4^{n[/tex] ---- n

So, the summation is:

[tex]3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n[/tex]

Solving (b):

[tex]4 + 32 + 256 + 2048 + 16384[/tex]

The expression can be written as:

[tex]4 \to 4 * 8^0[/tex] --- 0

[tex]32 \to 4 * 8^1[/tex] ---- 1

[tex]256 \to 4 * 8^2[/tex] --- 2

[tex]2048 \to 4 * 8^3[/tex] ---- 3

[tex]16384 \to 4 * 8^4[/tex] ---- 4

For the nth term, the expression is:

[tex]Term \to 4 * 8^n[/tex] ---- n

So, the summation is:

[tex]4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n[/tex]

Solving (c):

[tex]2 + 6 + 18 + 54 + 162[/tex]

The expression can be written as:

[tex]2 \to 2 * 3^0[/tex] --- 0

[tex]6 \to 2 * 3^1[/tex] ---- 1

[tex]18 \to 2 * 3^2[/tex] --- 2

[tex]54 \to 2 * 3^3[/tex] ---- 3

[tex]162 \to 2 * 3^4[/tex] ---- 4

For the nth term, the expression is:

[tex]Term \to 2 * 3^n[/tex] ---- n

So, the summation is:

[tex]2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n[/tex]

Solving (d):

[tex]3 + 15 + 75 + 375 + 1875[/tex]

The expression can be written as:

[tex]3 \to 3 * 5^0[/tex] --- 0

[tex]15 \to 3 * 5^1[/tex] ---- 1

[tex]75 \to 3 * 5^2[/tex] --- 2

[tex]375 \to 3 * 5^3[/tex] ---- 3

[tex]1875 \to 3 * 5^4[/tex] ---- 4

For the nth term, the expression is:

[tex]Term \to 3 * 5^n[/tex] ---- n

So, the summation is:

[tex]3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n[/tex]

Answer:

Hello There!!

Step-by-step explanation:

Combine like terms:

•5t+8t-12t

•5t+8t=13t

•13t-12t=1t

•1t=t

hope this helps,have a great day!!

~Pinky~

Answer:

T

Step-by-step explanation:

See the steps below:)

Answer:

4pi or 12.57

Step-by-step explanation:

Area = pi * radius^2

Area = pi * 2^2

Area = pi * 4

Area = 4pi or 12.57

Answer:

2.) 56

Step-by-step explanation:

(5 x 4) ÷ 2 = 10

10 x 4 = 40

4 x 4 = 16

40 + 16 = 56

========================================================

Explanation:

When we divide two fractions like this, we flip the second fraction and multiply like so...

[tex]\frac{5}{7} \div \frac{8}{9}\\\\\frac{5}{7} \times \frac{9}{8}\\\\\frac{5 \times 9}{7 \times 8}\\\\\frac{45}{56}\\\\[/tex]

which points us to choice B as the answer.

The fraction 45/56 cannot be reduced further because 45 and 56 do not have any factors in common other than 1.

Answer:

45/56

Step-by-step explanation:

5/7 ÷ 8/9

Copy dot flip

5/7 * 9/8

5*9 =45

7*8 = 56

45/56

Answer:

See explanation

Step-by-step explanation:

The question is incomplete; So, I will solve the question generally.

Assume the following;

[tex]l \to length[/tex]

[tex]w \to width[/tex]

[tex]h \to height[/tex]

Since the water level must be 2 inches below the tank height, the water height is:

[tex]H \to h - 2[/tex]

So, the water volume is:

[tex]Volume = l * w * H[/tex]

[tex]Volume = l * w * (h - 2)[/tex]

Hence, the expression is:

[tex]Volume = l * w * (h - 2)[/tex]

Assume that:

[tex]l = 5; w = 10; h = 8[/tex]

The volume becomes:

[tex]Volume = 5 * 10 * (8 - 2)[/tex]

[tex]Volume = 5 * 10 * 6[/tex]

[tex]Volume = 300[/tex] cubic units

Answer: $18.75

Step-by-step explanation: Each bag cost $3.75 individually.

Answer:

y = 3/4x + 2

Step-by-step explanation:

By looking at the graph, we can easily see that the y-intercept (where the line passes through y) is 2. In the equation y = mx + b. B is the y-intercept. So at the moment, we have, y = mx + 2. Now to find the slope which will take place over "m" all we need is the rise over run. To get this we will look at the points provided, count up the amount to get to the next point above then count to left/right to the point. For this we count up 3 points and 4 points to the right. So we finally get y = 3/4x + 2.

(3/4 = 0.75 if decimal is needed)

Answer:

Amount A get = 2,575

Total amount = 5,150

Step-by-step explanation:

Given:

Ratio between A,B and C = 10:6:4

Assume;

Common ration is 'a'

So,

Amount A get = 10a

Amount B get = 6a

Amount C get = 4a

So,

Amount B get - Amount C get = 515

6a - 4a = 515

2a = 515

a = 257.5

Total amount = 10a + 6a + 4a

Total amount = 20a

Total amount = 20(257.5)

Total amount = 5,150

Amount A get = 10a

Amount A get = 10(257.5)

Amount A get = 2,575

Answer:420

Step-by-step explanation:

600 x 0.70 is 420. so 600 minus 420 is 180

Answer:

7 hours

Step-by-step explanation:

Rental cost :

Fixed pay = $20

Hourly cost = 2.65

To obtain the minimum rental hour, we work with the least amount that can be spent ;

For tourist that can spend more than $37 but less than $65

Total cost of rental :

20 + 2.65h ; h = number of hours

When total cost > 37

20 + 2.65h > 37

2.65h > 37 - 20

2.65h > 17

h > 6.415

Hence, the minimum whole hour of bicycke rental is 7 hours