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3 years ago

A boy jogs 250 meters in 110 seconds. What is his average speed in m/s?

Mathematics

1 answer:

murzikaleks [220]3 years ago

6 0

250m/110s

25m/11s

25/11 m/s

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Select the three expressions that are equivalent to 6^{2}6 2 6, squared. a: (6^9/6^8)^2 b: 6 times 6 times 6 times 6 times 6 tim

Kamila [148]

Question:

Select the three expressions that are equivalent to $6^2$ :

a: $(\frac{6^9}{6^8})^2$

b: $\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 }$

c: $\frac{6^4}{6^2}$

d: $\frac{6^5 * 6^7}{6^{10}}$

Answer:

a: $(\frac{6^9}{6^8})^2$

c: $\frac{6^4}{6^2}$

d: $\frac{6^5 * 6^7}{6^{10}}$

Step-by-step explanation:

Given

$6^2$ :

Required

Find equivalent expressions

<em>To solve this question; we'll simplify options a to do, one after the other</em>

a: $(\frac{6^9}{6^8})^2$

From laws of indices;

$\frac{a^m}{a^n} = a^{m-n}$

This implies that;

$(\frac{6^9}{6^8})^2 = (6^{9-8})^2$

$(\frac{6^9}{6^8})^2 = (6^{1})^2$

From laws of indices;

${a^m}^n = a^{m*n} = a^{mn}$

This implies that

$(\frac{6^9}{6^8})^2 = (6^{1*2})$

$(\frac{6^9}{6^8})^2 = 6^{2}$

Hence, $(\frac{6^9}{6^8})^2$ is equivalent to $6^2$

b. $\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 }$

From laws of indices;

$a^m * a^n = a^{m+n}$

This implies that

$\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = \frac{6^{1+1+1+1+1+1}}{6^{1+1+1}}$

$\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = \frac{6^{6}}{6^{3}}$

From laws of indices;

$\frac{a^m}{a^n} = a^{m-n}$

This implies that

$\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = 6^{6-3}$

$\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = 6^{3}$

Hence; $\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 }$ is not equivalent to $6^2$

c. $\frac{6^4}{6^2}$

From laws of indices;

$\frac{a^m}{a^n} = a^{m-n}$

This implies that

$\frac{6^4}{6^2} = 6^{4-2}$

$\frac{6^4}{6^2} = 6^{2}$

Hence, $\frac{6^4}{6^2}$ is equivalent to $6^2$

d. $\frac{6^5 * 6^7}{6^{10}}$

From laws of indices;

$a^m * a^n = a^{m+n}$

This implies that

$\frac{6^5 * 6^7}{6^{10}} = \frac{6^{5+7}}{6^{10}}$

From laws of indices;

$\frac{a^m}{a^n} = a^{m-n}$

This implies that

$\frac{6^5 * 6^7}{6^{10}} = 6^{5+7-10}$

$\frac{6^5 * 6^7}{6^{10}} = 6^{2}$

Hence, $\frac{6^5 * 6^7}{6^{10}}$ is equivalent to $6^2$

3 0

3 years ago

Read 2 more answers

Hi everyone! I need help with this bonus question on this assignment does anyone know this?

Sindrei [870]

I'm pretty sure the answer would be D because one of the properties of a rectangle is that opposite sides are congruent, and statement D shows that.

4 0

4 years ago

Need help!!! A rocket scientist is designing a rocket to visit the planets in the solar system. The velocity that is needed to e

NeX [460]

Answer:

Mercury, Venus, Earth, Mars, and Uranus

Step-by-step explanation:

Calculate the escape velocity for each planet, using the equation v = √(2gR).

$\left[\begin{array}{cccc}Planet&R(m)&g(m/s^{2})&v(m/s)\\Mercury&2.43\times10^{6}&3.61&4190\\Venus&6.07\times10^{6}&8.83&10400\\Earth&6.37\times10^{6}&9.80&11200\\Mars&3.38\times10^{6}&3.75&5030\\Jupiter&6.98\times10^{7}&26.0&60200\\Saturn&5.82\times10^{7}&11.2&36100\\Uranus&2.35\times10^{7}&10.5&22200\\Neptune&2.27\times10^{7}&13.3&24600\end{array}\right]$

The rocket's maximum velocity is double the Earth's escape velocity, or 22,400 m/s. So the planets the rocket can escape from are Mercury, Venus, Earth, Mars, and Uranus.

7 0

3 years ago

Last questions for my last 15 pts.

klemol [59]

Step-by-step explanation:

${6}^{2} - 10 \\ = 36 - 10 \\ = 26 \\ so \: kurt \: forgot \: to \: write \: units \: place \: \\ number \: 6 \: after \: 2.$

8 0

3 years ago

Find the domain of (x,y) → (x + 7, y - 9) with R = {(-3, -14)

MA_775_DIABLO [31]

Answer:

Step-by-step explanation:

x+7=-3

x=-3-7=-10

x=-10

y-9=-14

y=-14+9

y=-5

Domain of (x,y)=(-10,-5)

4 0

3 years ago