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DaniilM [7]
2 years ago
13

Find the missing side, please

Mathematics
1 answer:
AVprozaik [17]2 years ago
4 0

Answer:

a. √442, b. √540, c. 8

Step-by-step explanation:

remember that a^2 + b^2 = c^2

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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
If you are good at sequences in math please help I am giving more points
vodka [1.7K]

Answer:

C. 101 - 5(n - 1)

Step-by-step explanation:

d = (26 - 71)/(16 - 7)

d = -45/9

d = -5

a7 = a1 + (7-1)(-5)

71 = a1 - 30

a1 = 101

an = 101 + (n - 1)(-5)

an = 101 - 5(n - 1)

4 0
3 years ago
Read 2 more answers
Please help me <br>solve 3x+1/2=3/8+x​
gavmur [86]

Answer:

x= -\frac{1}{32}

Step-by-step explanation:

First move the x on the right side the the left side. Now your equation is

2x+\frac{1}{2}=\frac{3}{8} Next move 1/2 to the right side. Now your equation is 4x=\frac{-1}{8}. Next divide both sides by 4 to isolate "x." Now your equation is x= -\frac{1}{32}

Hope this helped and have a great day.

(brainliest please)

6 0
2 years ago
If f(x)=x-2 which of the following is the inverse of f(x) brainly
Lostsunrise [7]

Answer:

The inverse of f(x) is  f ^ {- 1}(x) = x + 2

Step-by-step explanation:

To find the inverse of the function f (x) = x-2, perform the following steps:

1) do y = f (x)

y = x-2

2) Solve the equation for the variable x.

y + 2 = x -2 +2

y + 2 = x

3) exchange the variable x with the variable y

y + 2 = x ----> x + 2 = y

4) Change the variable y by f ^{- 1}(x)

Finally the inverse function is:

 f ^ {- 1} (x) = x + 2

4 0
3 years ago
Explain why this means that 251/2=5
8_murik_8 [283]
It’s 251 divided by 2 equals 5
7 0
2 years ago
Read 2 more answers
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