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
Nezavi [6.7K]
3 years ago
8

Fill in the blanks to make each of the following a true statement. Also name the property exhibited by each statement.

Mathematics
1 answer:
Ludmilka [50]3 years ago
4 0
1. 522
2. 1
3. 108
4. 0
5. 1
53*99+53 = 5300
53*(99+1) = 5300

Hope it helped!
You might be interested in
Please help! Its for my big test tomorrow!
Travka [436]

Answer:

# The solution x = -5

# The solution is x = 1

# The solution is x = 6.4

# The solution is x = 4

# The solution is 1.7427

# The solution is 0.190757

Step-by-step explanation:

* Lets revise some rules of the exponents and the logarithmic equation

# Exponent rules:

1- b^m  ×  b^n  =  b^(m + n) ⇒ in multiplication if they have same base

  we add  the power

2- b^m  ÷  b^n =  b^(m – n) ⇒  in division if they have same base we

   subtract  the power

3- (b^m)^n = b^(mn) ⇒ if we have power over power we multiply

   them

4- a^m × b^m = (ab)^m ⇒ if we multiply different bases with same  

   power then we multiply them ad put over the answer the power

5- b^(-m) = 1/(b^m)  (for all nonzero real numbers b) ⇒ If we have

   negative power we reciprocal the base to get positive power

6- If  a^m  =  a^n  ,  then  m  =  n ⇒ equal bases get equal powers

7- If  a^m  =  b^m  ,  then  a  =  b    or    m  =  0

# Logarithmic rules:

1- log_{a}b=n-----a^{n}=b

2- loga_{1}=0---log_{a}a=1---ln(e)=1

3- log_{a}q+log_{a}p=log_{a}qp

4- log_{a}q-log_{a}p=log_{a}\frac{q}{p}

5- log_{a}q^{n}=nlog_{a}q

* Now lets solve the problems

# 3^{x+1}=9^{x+3}

- Change the base 9 to 3²

∴ 9^{x+3}=3^{2(x+3)}=3^{2x+6}

∴ 3^{x+1}=3^{2x+6}

- Same bases have equal powers

∴ x + 1 = 2x + 6 ⇒ subtract x and 6 from both sides

∴ 1 - 6 = 2x - x

∴ -5 = x

* The solution x = -5

# ㏒(9x - 2) = ㏒(4x + 3)

- If ㏒(a) = ㏒(b), then a = b

∴ 9x - 2 = 4x + 3 ⇒ subtract 4x from both sides and add 2 to both sides

∴ 5x = 5 ⇒ divide both sides by 5

∴ x = 1

* The solution is x = 1

# log_{6}(5x+4)=2

- Use the 1st rule in the logarithmic equation

∴ 6² = 5x + 4

∴ 36 = 5x + 4 ⇒ subtract 4 from both sides

∴ 32 = 5x ⇒ divide both sides by 5

∴ 6.4 = x

* The solution is x = 6.4

# log_{2}x+log_{2}(x-3)=2

- Use the rule 3 in the logarithmic equation

∴ log_{2}x(x-3)=2

- Use the 1st rule in the logarithmic equation

∴ 2² = x(x - 3) ⇒ simplify

∴ 4 = x² - 3x ⇒ subtract 4 from both sides

∴ x² - 3x - 4 = 0 ⇒ factorize it into two brackets

∴ (x - 4)(x + 1) = 0 ⇒ equate each bract by 0

∴ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

OR

∵ x + 1 = 0 ⇒ subtract 1 from both sides

∴ x = -1

- We will reject this answer because when we substitute the value

 of x in the given equation we will find log_{2}(-1) and this

 value is undefined, there is no logarithm for negative number

* The solution is x = 4

# log_{4}11.2=x

- You can use the calculator directly to find x

∴ x = 1.7427

* The solution is 1.7427

# 2e^{8x}=9.2 ⇒ divide the both sides by 2

∴ e^{8x}=4.6

- Insert ln for both sides

∴ lne^{8x}=ln(4.6)

- Use the rule ln(e^{n})=nln(e) ⇒ ln(e) = 1

∴ 8x = ln(4.6) ⇒ divide both sides by 8

∴ x = ln(4.6)/8 = 0.190757

* The solution is 0.190757

7 0
3 years ago
Read 2 more answers
Which point would map onto itself after a reflection across the line y= -x
lutik1710 [3]
I need help on that too

5 0
3 years ago
Read 2 more answers
What is the median for this data set?
Sever21 [200]
The meridian for this set is 3.005 (option C)

Note ➡The word Median is lime the "average" for all of the values of the particular problem
8 0
3 years ago
Line segment MN is graphed in the first and second quadrants of a coordinate plane. The segment is translated 2 units up, then r
Ksju [112]

Answer:

Step-by-step explanation:

Since the line segment is only being translated and reflected it would still maintain its length. This is pretty much the only characteristic that would remain the same as te original line segment. It would not maintain the same x-axis positions for both endpoints of the line segment. This is because when it is translated 2 units up it is only moving on the y-axis and not the x-axis. But when it is reflected over the y-axis the endpoints flip and become the opposite values.

6 0
3 years ago
What is m∠KNL?<br> Cough coufh coufh I need to add words
horsena [70]
The measure of angle KNL is 102.
5 0
3 years ago
Other questions:
  • The surface area of a triangular pyramid is 305 square inches. The area of the base is 35 square inches. Each face has a base of
    10·1 answer
  • Write the eqWrite the equation of the line, in point-slope form. Identify the point (-2, -2) as (x1, y1). Use the box provided o
    9·1 answer
  • Please help sorry it’s hard to read
    12·2 answers
  • A paintER painted about half a room in half a day. Coley estimated the painter would paint 7 Rooms in 7 days. Is coley estimate
    5·1 answer
  • Fencing costs $3.25 per foot. A certain
    6·1 answer
  • NEED HELLP ASAP !!!
    8·1 answer
  • What is 720° converted to radians?<br> 1/4<br> pi/4<br> 4/pi<br> 4pi
    9·2 answers
  • Salvador sold hats during a weekend sporting event. On Saturday, Salvador sold 47 of the total number of hats. On Sunday, he sol
    13·1 answer
  • I need help please help me
    15·2 answers
  • THE SUM 10 INFINITY OF A GEOMETRIC SERIES IS 100. FIND THE TERM IF THE COMMON FIRST RATIO IS - 1/2​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!