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3 years ago

A map has a scale of 1 cm: 5 km. Determine how far apart two cities are if they are 8 cm apart on the map.

Mathematics

2 answers:

german3 years ago

6 0

Answer:

Step-by-step explanation:

Let's set up two ratios...

1 cm : 5km

8 cm : x km

Therefore the answer is A

andrey2020 [161]3 years ago

6 0

Yes A is correct because the 8 cm turns into the same amount of kilometers

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jose's family is traveling 345 miles to an aquarium. They have already traveled 131 miles. How many more miles must you travel t

Luden [163]

Answer:

214 more miles

Step-by-step explanation:

345-131= 214

6 0

3 years ago

Read 2 more answers

An elliptical culvert is 3.5 feet tall and 6 feet wide. It is filled with water to a depth of 0.95 feet. Find the width of the s

maks197457 [2]

Answer:

$W_s \approx5.3$

Step-by-step explanation:

From the question we are told that

Height $H=3.5ft$

Weight $W= 6ft$

Depth $D=0.95ft$

Generally the equation for ellipses is given as

$\frac{x^2}{a^2} +\frac{y^2}{b^2} =1$

Where

$b=H/2\\b=3.5/2\\Therefore\\b=1.75\\a=W/2\\a=6/2\\Therefore\\a=3\\$

$\frac{x^2}{3^2} +\frac{y^2}{1.75^2} =1$

Generally to find y in the equation $\frac{x^2}{a^2} +\frac{y^2}{b^2} =1$

$y=-b+d$

$y=-1.75+0.95$

$y=-0.8$

Therefore

$\frac{x^2}{3^2} +\frac{(0.8)^2}{1.75^2} =1$

$\frac{x^2}{3^2} =1-\frac{(0.8)^2}{1.75^2}$

$\frac{x^2}{3^2} =1-0.2089795918$

$X^2 =3^2(1-0.2089795918)$

$X^2 =7.119183674$

$X =\sqrt{7.119183674}$

$X =2.66817984$

Therefore the width of the given stream is

$W_s=2.66817984*2$

$W_s=5.33635968$

$W_s \approx5.3$

3 0

3 years ago

Help me please and thank you!

lorasvet [3.4K]

Answer:

-4/3

Step-by-step explanation:

-2 - 1 is -3

6-2 is 4

6 0

3 years ago

Emanuel has 12 trading cards and then buys some more cards at the store. His aunt joan him a package of six cards for his birthd

sveta [45]

A) the equation accuretly models this scenario because Emanuel has a total of 48 cards. He bought some (X) and his aunt gave him 18. In order to find the number of cards he bought you set the number of cards he bought and the number of cards he got from his aunt equal to the number of cards he has. B) 48= X + 18 Subtract 18 over 30=X He bought 30 cards from the store. 48+ 30+18

7 0

3 years ago

Use the tangent identity to

Lunna [17]

Answer:

$tan(x)=\frac{44\sqrt{89}}{89}$

Step-by-step explanation:

tan is defined as: $tan(x)=\frac{opposite}{adjacent}$

sin is defined as: $sin(x)=\frac{opposite}{hypotenuse}$

cos is defined as: $cos(x)=\frac{adjacent}{hypotenuse}$

We can also define tan as: $tan(x)=\frac{sin(x)}{cos(x)}$

because plugging in the definitions of sin and cos in we get: $tan(x)=\frac{(\frac{opposite}{hypotenuse})}{(\frac{adjacent}{hypotenuse})}\\\\tan(x)=\frac{opposite}{hypotenuse}*\frac{hypotenuse}{adjacent}\\\\tan(x)=\frac{opposite}{adjacent}$

which you'll notice is the original definition of tan(x)

So using this definition of tan(x) we can use the givens sin(x) and cos(x) to find tan(x)

$sin(x)=\frac{44}{45}\\\\cos(x)=\frac{\sqrt{89}}{45}\\\\tan(x)=\frac{sin(x)}{cos(x)}$

plugging in sin(x) and cos(x) we get:

$tan(x)=\frac{\frac{44}{45}}{\frac{\sqrt{89}}{45}}\\\\tan(x)=\frac{44}{45}*\frac{45}{\sqrt{89}}\\\\tan(x)=\frac{44}{\sqrt{89}}$

We usually don't like square roots in the denominator, and from here we want to rationalize the denominator which we do by removing the square root from the denominator.

We can do this by multiplying the fraction by: $\frac{\sqrt{89}}{\sqrt{89}}$ which doesn't change the value of the fraction since it simplifies to 1, but it gets rid of the square root in the denominator

$tan(x)=\frac{44}{\sqrt{89}}*\frac{\sqrt{89}}{\sqrt{89}}\\\\tan(x)=\frac{44\sqrt{89}}{89}$

5 0

1 year ago