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3 years ago

How to do this and the answers.

Mathematics

1 answer:

ANEK [815]3 years ago

8 0

Answer:

I'm gonna estimate about 240 miles one way

Explanation:

You have a guide on the bottom right-hand corner of the map that tells you how many miles per that amount of distance. As you can see it is split off into tiles incremented by 30. What you do is take a ruler and measure that guide. For example, let's say the map is 9.5cm and the guide is 2cm per 60 miles. The next thing I would do is to measure the distance in centimeters of the physical map between point a and point b which is 8cm. Finally, I convert the centimeters into miles which is (8/2)*60 = 240.

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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

∵ 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

I will give brainliest Given ⊙N, what is mABC ?

Ulleksa [173]

A circle with center point N and three points A, B, C on its circumference. A line is drawn connecting the points A, N and C and the angle ANC is given as 138 degree.

B. 138°

3 0

2 years ago

Read 2 more answers

PLEASE HELP ME !! WILL GIVE BRAINLIEST!!

PolarNik [594]

B is a times b
C is also a times b

sorry im stuck on the rest

6 0

3 years ago

An auto dealership sells minivans and sedans. In January, they sold 10 minivans and 20 sedans. In February, they sold 7 minivans

zaharov [31]

Answer:

january = 10/20 = 1/2

februry = 7/14 = 1/2

so, we conclude that the auto dealership didn't have a lower ratio, since the ratio is equal in both months.

hope it helps :)

8 0

3 years ago

Which algebraic rule describes the translation of ADEF to AD'E'F?

Marrrta [24]

Answer:

B: (x, y) --> (x + 4, y - 3)

Step-by-step explanation:

the shape DEF went to the right along the x axis wich increased x and then went down the y axis or decreased y to make D'E'F'

some good way to remember these translations and orders are...
- x is first when plotting points, then y (x, y)
- x increases going right, and decreases going left, as well as y increasing going up, then decreasing going down

BONUS FACT:
the symbol ( ' ) is called a prime when refering to transformations and geometry ((as in D' is pronounced D prime))

4 0

2 years ago