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2 years ago

The speed of a sparrow is x km/h in still air. When the

Mathematics

1 answer:

Semmy [17]2 years ago

4 0

Answer:

x = 5m/s

Step-by-step explanation:

Distance flying out = 12 km (headwind)

Distance flying back = 12 km (tailwind)

total distance = 12 + 12 =24 km

wind speed = 1km/h

speed going out (with headwind) = (x - 1) km/h

speed coming back (with tailwind) = (x + 1) km/h

Time taken to go out = distance going out / speed going out

= 12 / (x-1)

Time taken to come back = distance coming back / speed coming back

= 12 / (x+1)

total time = time taken to go out + time taken to come back

5 =[ 12/(x-1) ] + [ 12/(x-1)]

expanding this, we will get

5x² - 24x - 5 = 0

solving quadratic equation, we will get

x = -1/5 (impossible because speed cannot be negative)

x = 5 (answer)

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What is the simplified form of this expression 3x+4+5x+3

Charra [1.4K]

Combine like terms such as 3x and 5x and combine 4 and 3
the answer would be 8x+7
mark me brainliest if the answer is correct, thank you in advance :)

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2 years ago

What is the simplified base of the function f(x) = One-fourth (Root Index 3 StartRoot 108 EndRoot) Superscript x?

son4ous [18]

Answer:

Simplified base would be 3∛4

Step-by-step explanation:

Given exponential function,

$f(x)=\frac{1}{4}(\sqrt[3]{108})^x$

Since, in an exponential function $f(x)=ab^x$

b is called base.

∵ 108 = 2 × 2 × 3 × 3 × 3,

Or 108 = 4 × 3³,

$\implies \sqrt[3]{108} = \sqrt[3]{4\times 3^3}$

$\sqrt[3]{108}=\sqrt[3]{4}\times \sqrt[3](3^3)$ ( Using $\sqrt[n]{ab}=\sqrt[n]{a}\times \sqrt[n]{b}$ )

$\sqrt[3]{108}=\sqrt[3]{4}\times (3^3)^\frac{1}{3}$

$\sqrt[3]{108}=\sqrt[3]{4}\times 3^{3\times \frac{1}{3}}$ ( Using power of power property of exponent )

$\sqrt[3]{108}=3\sqrt[3]{4}$

Hence, the required simplified base would be 3∛4

i.e. SECOND option is correct.

8 0

2 years ago

Read 2 more answers

Yuson used her calculator to solve the equation 4/5x - 8 = 3. She entered the following on her screen and got an incorrect answe

Firlakuza [10]

Answer:

55/4

Explanation:

Let's solve your equation step-by-step.

4 /5x−8=3

Step 1: Add 8 to both sides.

4 /5x−8+8=3+8

4 /5 x = 11

Step 2: Multiply both sides by 5/4.

( 5 /4 )*( 4 /5 x)=( 5 /4 )*(11)

x= 55/4

Answer:

55 /4

Hope that helps :)

4 0

2 years ago

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(05.02) What is the y-intercept of the line shown? 3 over 4. 2 3 4

Degger [83]

Hi there!

Looking at the graph, we can see exactly where the line crosses the y-axis (vertical line). The y-intercept is where the line goes through one point on the y-axis. The purple line goes perfectly through the point (0,4). Since the line goes through this point and the point is on the y-axis, the point (0,4), is the y-intercept.

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

5 0

2 years ago

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Which expression is equivalent to (x^6y^8)^3\x^2y^2

Damm [24]

Answer:

$\large\boxed{\dfrac{(x^6y^8)^3}{x^2y^2}=x^{16}y^{22}}$

Step-by-step explanation:

$\dfrac{(x^6y^8)^3}{x^2y^2}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=\dfrac{(x^6)^3(y^8)^3}{x^2y^2}=\dfrac{x^{(6)(3)}y^{(8)(3)}}{x^2y^2}=\dfrac{x^{18}y^{24}}{x^2y^2}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=x^{18-2}y^{24-2}=x^{16}y^{22}$

5 0

2 years ago

Read 2 more answers