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3 years ago

Someone please help!

Mathematics

1 answer:

USPshnik [31]3 years ago

6 0

Here are the log properties you need:
$log(ab) = log(a) +log(b) \\ \\ log(\frac{a}{b}) = log(a) - log(b) \\ \\ log(a^n) = n log(a)$

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The distance between the towns of Averton and Brackston is 10km. On map the distance is 5cm. What is the scale of the map in its

strojnjashka [21]

Answer: The scale of the map in its simplest form is 1:200,000

Step-by-step explanation: From the question,

The distance between the two towns is 10km which is a distance of 5cm on the map.

This means, 5cm represents 10km. Now we will determine what 1cm represents.

If 5cm represents 10km

Then 1cm will represent (10÷5) km

Hence, 1 cm will represent 2km

Now, convert 2km to cm

2km = 2000m = 200,000cm

Hence, 1cm represents 200,000cm

This means on the map 1cm represents 200,000cm.

The scale of the map is therefore

1:200,000

3 0

3 years ago

Calculate the total cost of an item bought at a negotiated price of $15,640 and a $2,500 trade-in allowance. The sales tax is 7.

mylen [45]

Answer:

B. $14352.08

Step-by-step explanation:

Let us find cost of item after 7.2% of sales tax. The cost of item after 7.2% of sales tax will be equal to 15640 plus 7.2% of 15640.

$\text{The cost of item after sales tax}=15640+(\frac{7.2}{100}\times 15640)$

$\text{The cost of item after sales tax}=15640+(0.072\times 15640)$

$\text{The cost of item after sales tax}=15640+1126.08$

$\text{The cost of item after sales tax}=16766.08$

Therefore the cost of item after 7.2% of sales tax will be $16766.08.

Now let us add registration fee to the cost of item.

$\text{The cost of item after registration fee}=16766.08+86$

$\text{The cost of item after registration fee}=16852.08$

Now let us subtract $2500 trade allowance to find the total cost of the item.

$\text{The total cost of item}=16852.08-2500$

$\text{The total cost of item}=14352.08$

Therefore, the total cost of item will be $14352.08 and option B is the correct choice.

6 0

3 years ago

kumpel [21]

I think 4ft 2in or 50in but im not 100% sure

4 0

3 years ago

find the absolute maximum absolute minimum of the function F(x)=(x^2-12x+32)^(1/3) on the interval [3,10]

jeka94

9514 1404 393

Answer:

minimum: -∛4 ≈ -1.58740
maximum: ∛12 ≈ 2.28943

Step-by-step explanation:

The expression under the radical can be written in vertex form as ...

x^2 -12x +32 = (x -6)^2 -4

The function will be symmetrical about x=6. The minimum is at x=6 where we have ...

F(6) = ∛(-4)

The maximum is at the end of the interval farthest from the vertex, so is ...

F(10) = ∛((10 -6)² -4) = ∛12

The minimum is -∛4 ≈ -1.587; the maximum is ∛12 ≈ 2.289.

5 0

3 years ago

A triangle has a perimeter of 280 cm, and its side lengths are a, b and c respectively. If

Irina-Kira [14]

Answer:

The length of the sides are 64 cm, 96 cm and 120 cm.

Step-by-step explanation:

Perimeter of a triangle:

The perimeter of a triangle is the sum of it's sides.

A triangle has a perimeter of 280 cm, and its side lengths are a, b and c respectively.

This means that:

$a + b + c = 280$

a:b= 2:3

This means that:

$\frac{a}{b} = \frac{2}{3}$

$2b = 3a$

$b = \frac{3a}{2}$

b:c=4:5

This means that:

$\frac{b}{c} = \frac{4}{5}$

$4c = 5b$

$c = \frac{5b}{4}$

$c = \frac{5*3*a}{4*2} = \frac{15a}{8}$

At the original equation:

We replace b and c in function of a. So

$a + b + c = 280$

$a + \frac{3a}{2} + \frac{15a}{8} = 280$

Multiplying everything by 8

$8a + 12a + 15a = 280*8$

$35a = 280*8$

$a = \frac{280*8}{35}$

$a = 64$

Sides b and c:

Since we have a, we can find sides b and c:

$b = \frac{3a}{2} = \frac{3*64}{2} = 3*32 = 96$

$c = \frac{15a}{8} = \frac{15*64}{8} = 15*8 = 120$

The length of the sides are 64 cm, 96 cm and 120 cm.

3 0

3 years ago