Which situation has a unit rate of $7?

If right I’ll mark brainiest

RUDIKE [14]

Answer: See explanation

Step-by-step explanation:

Population- Every student...

Sample- 10 students sitting together at a table in the cafeteria

Random Sample- 10 Students whose names...

5 0

2 years ago

200 centimeters = how many meters

melomori [17]

2 meters is your answer

7 0

2 years ago

What is a correlation

posledela

Answer: a relationship/connection between two variables, there are negative and positive correlations.

7 0

2 years ago

A is 2 times older than B. Identify the appropriate expression.

-Dominant- [34]

Answer:

C. 2x

Step-by-step explanation:

Let

B's age = x years

A's age = 2 times older than B

= 2 * x

= 2x years

A's age = 2x years

For instance, if B's age is 17 years

Then,

A's age = 2x

= 2(17)

= 34 years old

6 0

2 years ago

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

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