Ask question

Ask question

All categories

3 years ago

13

A map has a scale of 1 cm : 21 km. Two cities are 3.1 cm apart on the map. To the nearest tenth of a kilometer, what is the actu

al distance corresponding to the map distance?

1 answer:

MatroZZZ [7]3 years ago

8 0

For the answer to the question above,
use the concept of ratio and proportion. The ratio between 1 cm to 21 km should be the same as the ratio of 3.1 cm to the actual distance. Let x be the unknown actual distance and mathematically express the situation,

(1 cm/ 21 km) = (3.1 cm / x km)

This equation gives a value for x which is 65.1 km. Therefore, the answer is letter C.

You might be interested in

5^(2x-1)+5^(x+1)=250<br> how do you solve?<br> thank you

zepelin [54]

Answer:

<em>x = 2</em>

Step-by-step explanation:

<u>Exponential Equations</u>

Solve:

$5^{2x-1}+5^{x+1}=250$

Separate each exponential:

$5^{2x}5^{-1}+5^{x}5^{1}=250$

Operating:

$\displaystyle \frac{5^{2x}}{5}+5^{x}5=250$

Multiplying by 5:

$5^{2x}+25\cdot5^x=1250$

Rearranging:

$5^{2x}+25\cdot5^x-1250=0$

Recall that:

$5^{2x}=(5^{x})^2$

$(5^{x})^2+25\cdot5^x-1250=0$

Calling

$y=5^{x}:$

$y^2+25y-1250=0$

Factoring:

$(y-25)(y+50)=0$

There are two possible solutions:

y=25

y=-50

Since

$y=5^{x}$

y cannot be negative, thus:

$5^{x}=25=5^2$

The solution is:

x = 2

8 0

3 years ago

12 midnight ....... tell me

docker41 [41]

Answer:

I am not getting your question .

5 0

3 years ago

Read 2 more answers

There are 6 gallons in a tank that is 20% full. How many gallons are in a full tank? Use a double number line to show your work.

Alex17521 [72]

Answer: 30 gallons

Step-by-step explanation:

Let the number of gallons that are in a full tank be represented by x.

Since there are 6 gallons in a tank that is 20% full, this will be set up in an equation as:

20% × x = 6

20/100 × x = 6

0.2 × x = 6

0.2x = 6

x = 6/0.2

x = 30

There are 30 gallons in a full tank

3 0

3 years ago

What is the area of the circle? diameter= 15m

Natasha_Volkova [10]

Answer:

The answer is

A= 176.71 m2

8 0

3 years ago

Read 2 more answers

Now there is a square city of unknown size with a gate at the center of each side. There is a tree 20 b from the north gate. Tha

Brums [2.3K]

Answer:

The length of each side of the city is 250b

Step-by-step explanation:

Given

$a = 20$ --- tree distance from north gate

$b =14$ --- movement from south gate

$c = 1775$ --- movement in west direction from (b)

See attachment for illustration

Required

Find x

To do this, we have:

$\triangle ADE \sim \triangle ACB$ --- similar triangles

So, we have the following equivalent ratios

$AE:DE = AB:CB$

Where:

$AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775$

Substitute these in the above equation

$20:x/2 = 20 + x + 14: 1775$

$20:x/2 = x + 34: 1775$

Express as fraction

$\frac{20}{x/2} = \frac{x + 34}{1775}$

$\frac{40}{x} = \frac{x + 34}{1775}$

Cross multiply

$x *(x + 34) = 1775 * 40$

Open bracket

$x^2 + 34x = 71000$

Rewrite as:

$x^2 + 34x - 71000 = 0$

Expand

$x^2 + 284x -250x - 71000 = 0$

Factorize

$x(x + 284) -250(x + 284)= 0$

Factor out x + 284

$(x - 250)(x + 284)= 0$

Split

$x - 250 = 0 \ or\ x + 284= 0$

Solve for x

$x = 250 \ or\ x =- 284$

x can't be negative;

So:

$x = 250$

6 0

3 years ago