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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:

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

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:

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:

-181

Step-by-step explanation:

According to the arithmetic calculator, it should be this.

Answer:

5.7 feet i think

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Answer:

A. We cannot calculate this value.

Step-by-step explanation:

Had it on my test c:

We cannot calculate this value because the width is not given so we cannot find the area of the region option (A) is correct.

It is defined as the ratio of the population to the total area. The population density represents the average number of people living on each square unit.

We have:

If you live in a rectangular city that is 1 mile along the southern border and contains 1000 people,

As we know,

population density = number of people/area of the region

As we have a rectangular city,

The area of the city = length×width

Width is not given so we cannot find the area of the region.

Thus, we cannot calculate this value because the width is not given so we cannot find the area of the region option (A) is correct.

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Answer:

(-1,-1)

Step-by-step explanation:

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

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]

=> 4(7)–2(7+a)=8

Answer and Step-by-step explanation:

To find out how long each side is, divide 60 by 5 (since there are 5 sides in a pentagon).

60 divided by 5 = 12.

Each side is 12 meters long.

#teamtrees #PAW (Plant And Water)

Answer:

1

Step-by-step explanation:

Because 1.38185 is below 1.5 so it rounds to 1

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: $18.75

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

Answer: D) Groundwater collects only where the soil and geological features allow water to seep down into underground chambers.

In other words, as long as there are gaps to allow water through, then that would lead to underground aquifers. Another important component is the amount of rain water that happens. Sources such as rivers, lakes and streams are also a contributing factor.

Stuff like earthquakes, volcanic activity, and continental movement doesn't really have much an effect on where or how aquifers form. It's really all about the soil type and how the landscape is formed, and of course the other factors mentioned in the previous paragraph.

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:

x = 0   or   x = - 16

Step-by-step explanation:

16+x^2=0

x ( x + 16 ) = 0

using the algebra rule a . b = a = 0 and b = 0

x = 0    or   x = - 16

so the answer is  x = 0 and x = -1 6

Mark brainliest plsssssssssss

Answer:

true.

Step-by-step explanation:

hope this helps, i looked it up :)

Answer:

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

Answer: C. How many mountain ranges are in the U.S.

Step-by-step explanation:

A statistical question first of all has to have a quantitative response i.e., answers should be in numbers.

The only two questions here that would yield a numeric answer are options C and D.

Furthermore, a statistical question has variability in it which means that the answer is based on multiple observations not just one. The observations in option C are mountain ranges and as the question requires finding out details about multiple mountain ranges, this is a statistical question.

This is opposed to option D which addresses issues surrounding just one mountain.

Answer:

Step-by-step explanation:

use formula

x^3+y^3=(x+y)^3-3*x*y(x+y)

=12^3-3*27(12)

=1728-972

=756

Answer:

x^3 + y^3 = 756

Step-by-step explanation:

Given that,  x+y=12 and xy=27

We know that,

[tex]( x + y )^3 = x^3 + y^3 + 3xy(x + y)[/tex]

∴ [tex]12^3 = x^3 + y^3 + 3 * 27 * 12[/tex]

[tex]=> 1728 = x^3 + y^3 + 972[/tex]

[tex]x^3 + y^3 = 1728 - 972[/tex]

[tex]==> x^3 + y^3 = 756[/tex]

Answer:

Hello! answer: 78.5 in2

Step-by-step explanation:

IMPORTANT ATTENTION: Im using 3.14 for pi so answers might vary if you are using say 22/7 for pi so please know that since this problem doesn't tell to use a certain method I will use 3.14

area can be found by doing radius × radius × 3.14 so... diameter is just twice the radius so... 10 ÷ 2 = 5 5 × 5 = 25

25 × 3.14 = 78.5 therefore 78.5 is the answer HOPE THAT HELPS!

The approximate area of a circle with a diameter of 10 in is,

⇒ Area of circle = 78.5 in²

Given that;

Diameter of circle = 10 in.

Now, We know that;

⇒ Area of circle = πr²

Where, 'r' is radius of circle.

Here, Diameter of circle = 10 in.

Hence, Radius = 10 / 2 = 5 in

Thus, We get;

⇒ Area of circle = πr²

⇒ Area of circle = 3.14 x (5)²

⇒ Area of circle = 78.5 in²

Thus, The approximate area of a circle with a diameter of 10 in is,

⇒ Area of circle = 78.5 in²

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Answer:

C

Step-by-step explanation:

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

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:

1/2 = 0.5

Step-by-step explanation:

Given that the game company gave each customer a single game for testing

There is definitely just two outcomes, i.e. the customer will either recommend the game or Not recommend the game.

since we do not have additional information regarding what might influence the decision of the customer, hence the probability of either recommending the tested game or not recommending the game will be equal

∴P ( recommending tested game ) = 1 - 0.5 = 0.5

Answer:420

Step-by-step explanation:

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