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Leni [432]
3 years ago
9

write a system of equations for the problem, and then solve the system. if a plane can travel 340 miles per hour with the wind o

nly 260 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air. please show step by step
Mathematics
1 answer:
BlackZzzverrR [31]3 years ago
7 0

Answer:

w = 40 miles per hour

r = 300 miles per hour

Step-by-step explanation:

We add w with the wind and subtract w against the wind

r+w = 340 miles per hour

r - w = 260 miles per hour

Add the two equations together to eliminate w

r+w = 340 miles per hour

r - w = 260 miles per hour

----------------------------------------

2r = 600

Divide by 2

r = 300 miles per hour without the wind

Now find w

r+w = 340

300 + w = 340

Subtract 300

w = 340-300

w = 40 miles per hour

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9.6 miles per hour

Step-by-step explanation:

First find the unit rate.

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A researcher studying microorganisms has discovered a strain of bacteria that doubles every 2.8 days. How many bacteria will the
Luden [163]

Answer:

3960.4 bacteria

Step-by-step explanation:

The formula to solve the above question is given as:

P(t) = Po (2) ^t/k

P(t) = Population after time t = ?

Po = Initial population = 650 bacteria

t = Time in days = 7.3 days

k = doubling time = 2.8 days

P(t) = 650 × (2)^7.3/2.8

P(t) = 650 × 2^2.6071428571

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Therefore, the number of bacteria the researcher will have after 7.3 days if they started with 650 bacteria is 3960.4 bacteria.

4 0
3 years ago
The shorter leg of a right triangle is 7cm shorter than the longer leg. The hypotenuse is 7cm longer then the linger leg. What i
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The shorter leg is 21cm, longer leg is 28 cm and hypotenuse is 35cm.

Step-by-step explanation:

Let,

The longer leg = x

The shorter leg = x-7

Hypotenuse = x+7

Using Pythagoras theorem;

a^2+b^2=c^2\\(x-7)^2+(x)^2=(x+7)^2\\x^2-14x+49+x^2=x^2+14x+49\\2x^2-14x+49-x^2-14x-49=0\\x^2-28x=0\\x(x-28)=0\\

Either,

x= 0

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As length cannot be zero, therefore,

Longer side = 28cm

Shorter side = x-7 = 28-7 = 21cm

Hypotenuse = x+7 = 28+7 = 35cm

The shorter leg is 21cm, longer leg is 28 cm and hypotenuse is 35cm.

Keywords: triangle, pythagoras theorem

Learn more about triangles at:

  • brainly.com/question/9323337
  • brainly.com/question/9381080

#LearnwithBrainly

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3 years ago
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