1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tema [17]
2 years ago
6

Simplify the following expression: 7472

Mathematics
2 answers:
Rainbow [258]2 years ago
7 0

Answer:

7^2

Step-by-step explanation:

i hope this helps :)

Alex787 [66]2 years ago
7 0

Answer:

49

Step-by-step explanation:

Exponent properties state that when two like bases are being divided, the exponents can be subtracted. So the first step in simplifying is to subtract the two exponents, 4-2=2. This leaves the fraction as \frac{7^{2} }{7^{0} }, since anything to the power of 0 is just 1, the simplified expression is 7^{2}. Then, because they are both constants, 7 can just be squared. This equals 49.

You might be interested in
Which of these systems of equations would be best solved using the subtraction​ method?
Lynna [10]

Answer:

Step-by-step explanation:

1. x+2y=6 or x=6-2y

3x-2y=2

3(6-2y)-2y=2

18-6y-2y=2

18-8y=2

-8y=-18+2

-8y=-16

y=-16/-8

y=2 ans.

x+2*2=6

x+4=6

x=6-4=2 ans.

Proof:

3*2-2*2=2

6-4=2

2=2

I leave the rest for you to practice with.

3. 4x+y=7

2x+5y=-1

 

5. 3x+2y=-2

6x-y=6

Solve the system using the elimination method. Show all your steps.

7. -3x+3y=3

3x+y=9 add.

---------------------------------

4y=12

y=12/4

y=3 ans.

3x+3=9

3x=9-3

3x=6

x=6/3

x=2 ans.

Proof:

-3*2+3*3=3

-6+9=3

3=3

I'll leave the rest for practice.

9. -5x+12y=20

x-2y=-6

11. 3x+2y=1

4x+ 6y= 7

4 0
2 years ago
The graph of an exponential function is given. Which of the following is the correct equation of the function?
katen-ka-za [31]

Answer:

If one of the data points has the form  

(

0

,

a

)

, then a is the initial value. Using a, substitute the second point into the equation  

f

(

x

)

=

a

(

b

)

x

, and solve for b.

If neither of the data points have the form  

(

0

,

a

)

, substitute both points into two equations with the form  

f

(

x

)

=

a

(

b

)

x

. Solve the resulting system of two equations in two unknowns to find a and b.

Using the a and b found in the steps above, write the exponential function in the form  

f

(

x

)

=

a

(

b

)

x

.

EXAMPLE 3: WRITING AN EXPONENTIAL MODEL WHEN THE INITIAL VALUE IS KNOWN

In 2006, 80 deer were introduced into a wildlife refuge. By 2012, the population had grown to 180 deer. The population was growing exponentially. Write an algebraic function N(t) representing the population N of deer over time t.

SOLUTION

We let our independent variable t be the number of years after 2006. Thus, the information given in the problem can be written as input-output pairs: (0, 80) and (6, 180). Notice that by choosing our input variable to be measured as years after 2006, we have given ourselves the initial value for the function, a = 80. We can now substitute the second point into the equation  

N

(

t

)

=

80

b

t

to find b:

⎧

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎩

N

(

t

)

=

80

b

t

180

=

80

b

6

Substitute using point  

(

6

,

180

)

.

9

4

=

b

6

Divide and write in lowest terms

.

b

=

(

9

4

)

1

6

Isolate  

b

using properties of exponents

.

b

≈

1.1447

Round to 4 decimal places

.

NOTE: Unless otherwise stated, do not round any intermediate calculations. Then round the final answer to four places for the remainder of this section.

The exponential model for the population of deer is  

N

(

t

)

=

80

(

1.1447

)

t

. (Note that this exponential function models short-term growth. As the inputs gets large, the output will get increasingly larger, so much so that the model may not be useful in the long term.)

We can graph our model to observe the population growth of deer in the refuge over time. Notice that the graph below passes through the initial points given in the problem,  

(

0

,

8

0

)

and  

(

6

,

18

0

)

. We can also see that the domain for the function is  

[

0

,

∞

)

, and the range for the function is  

[

80

,

∞

)

.

Graph of the exponential function, N(t) = 80(1.1447)^t, with labeled points at (0, 80) and (6, 180).If one of the data points has the form  

(

0

,

a

)

, then a is the initial value. Using a, substitute the second point into the equation  

f

(

x

)

=

a

(

b

)

x

, and solve for b.

If neither of the data points have the form  

(

0

,

a

)

, substitute both points into two equations with the form  

f

(

x

)

=

a

(

b

)

x

. Solve the resulting system of two equations in two unknowns to find a and b.

Using the a and b found in the steps above, write the exponential function in the form  

f

(

x

)

=

a

(

b

)

x

.

EXAMPLE 3: WRITING AN EXPONENTIAL MODEL WHEN THE INITIAL VALUE IS KNOWN

In 2006, 80 deer were introduced into a wildlife refuge. By 2012, the population had grown to 180 deer. The population was growing exponentially. Write an algebraic function N(t) representing the population N of deer over time t.

SOLUTION

We let our independent variable t be the number of years after 2006. Thus, the information given in the problem can be written as input-output pairs: (0, 80) and (6, 180). Notice that by choosing our input variable to be measured as years after 2006, we have given ourselves the initial value for the function, a = 80. We can now substitute the second point into the equation  

N

(

t

)

=

80

b

t

to find b:

⎧

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎩

N

(

t

)

=

80

b

t

180

=

80

b

6

Substitute using point  

(

6

,

180

)

.

9

4

=

b

6

Divide and write in lowest terms

.

b

=

(

9

4

)

1

6

Isolate  

b

using properties of exponents

.

b

≈

1.1447

Round to 4 decimal places

.

NOTE: Unless otherwise stated, do not round any intermediate calculations. Then round the final answer to four places for the remainder of this section.

The exponential model for the population of deer is  

N

(

t

)

=

80

(

1.1447

)

t

. (Note that this exponential function models short-term growth. As the inputs gets large, the output will get increasingly larger, so much so that the model may not be useful in the long term.)

We can graph our model to observe the population growth of deer in the refuge over time. Notice that the graph below passes through the initial points given in the problem,  

(

0

,

8

0

)

and  

(

6

,

18

0

)

. We can also see that the domain for the function is  

[

0

,

∞

)

, and the range for the function is  

[

80

,

∞

)

.

Graph of the exponential function, N(t) = 80(1.1447)^t, with labeled points at (0, 80) and (6, 180).

Step-by-step explanation:

4 0
2 years ago
What is the area of the parallelogram 4cm 5cm 9cm
Alenkasestr [34]

Answer:

Step-by-step explanation:

180

6 0
3 years ago
Read 2 more answers
Right answer gets brainliest, again..
Alecsey [184]

Answer:

Answer number c (0.3 liters per hour is the average rate)

Step-by-step explanation:

5 0
2 years ago
If you had carried out the algebra using variables before plugging numbers into your expressions, you would have found that (vf)
SashulF [63]

Answer:

Step-by-step explanation:

Volt is energy per electric charge

1V=1J/C

and the energy units in terms of meters, seconds and kilograms are:

1J= 1kg\frac{m^{2}}{s^{2}}

So the unit of volt is

1V= kg \frac{m^{2}}{Cs^{2}}

So the velocity expression (it can not be read completly) but i guess that it could be as follows

vf_{a} = -2\sqrt{\frac{q_{a}\Delta V}{m_{a}}}

So the unit analysis would be

vf_{a} = \sqrt{\frac{C kg\frac{m^{2}}{Cs^{2}}}{kg}}}

note that the coulomb unit of numerator is cancelled from the denominator. The same occurs for kg unit.

vf_{a} = \sqrt{\frac{m^{2}}{s^{2}}}

Applying square root

vf_{a} = \frac{m}{s}

7 0
3 years ago
Other questions:
  • How to subtract an integer
    14·2 answers
  • Two factory plants are making TV panels. Yesterday, Plant A produced 3 times as many panels as Plant B. Three percent of the pan
    12·1 answer
  • At a restaurant, four people ordered fried crab cakes and four people ordered a cup of gumbo, with a total of $31. If only two p
    13·1 answer
  • Solve the equation <br> -13/4 -x= 1/2x -1
    9·2 answers
  • 15 -points helppppppppppppppppppppppppp
    8·1 answer
  • Evaluate the function at the given value,
    9·1 answer
  • The function f is defined by f(x) = 4x + 1. What is the value of f(3)?
    9·2 answers
  • Which is the domain of the function f(x) = -
    5·1 answer
  • What is the main idea or topic of a story called?
    7·2 answers
  • Help me it’s due at 12 I’ve been doing this for 3 days now
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!