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2 years ago

Solve. Log8 (6x) = Log8 2 + Log8 (x-4)

Mathematics

1 answer:

Romashka-Z-Leto [24]2 years ago

7 0

Write both sides as powers of 8, then simplify:

$8^{\log_86x}=8^{\log_82+\log_8(x-4)}=8^{\log_82}8^{\log_8(x-4)}$

$\implies6x=2(x-4)$

$\implies6x=2x-8$

$\implies4x=-8$

$\implies x=-2$

However, on the left hand side, this would mean we'd have, $\log_8-12$ , which is undefined (assuming the real-valued logarithm), so this equation has no real solution.

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Factorize 2a^2+7a-15

loris [4]

$\huge\bf \pink {\underline{Solution :-}}$

$2 {a}^{2} + 7a - 15$

$= 2 {a}^{2} + 10a - 3a - 15$

$= 2a(a + 5) - 3(a + 5)$

$= (a + 5)(2a - 3)$

$\sf \red{Hence, Answer \: is \: (a + 5)(2a - 3).}$

$\\$

$\bf \purple{ \underline{ Important \: Formulas \: for \: Factorization :-}}$

$• \: {a}^{2} + 2ab + {b}^{2} = {(a + b)}^{2}$

$• \: (a + b)(a - b) = {a}^{2} - {b}^{2}$

$• \: {a}^{2} - 2 ab + {b}^{2} = {(a - b)}^{2}$

$• \: {a}^{3} + 3 {a}^{2} b + 3a {b}^{2} + {b}^{3} = {(a + b)}^{3}$

$• \: {a}^{3} - 3 {a}^{2} b + 3a {b}^{2} - {b}^{3} = {(a - b)}^{3}$

$• \: {(a + b)}^{2} + {(a - b)}^{2} = 2( {a}^{2} + {b}^{2} )$

$• \: {(a + b)}^{2} - {(a - b)}^{2} = 4ab$

$• \: (a + b)( {a}^{2} -ab + {b}^{2} ) = {a}^{3} + {b}^{3}$

$• \: (a - b)( {a}^{2} + ab + {b}^{2} ) = {a}^{3} - {b}^{3}$

$• \: {( \frac{a + b}{2} )}^{2} - ( {\frac{a - b}{2} } )^{2} = ab$

5 0

3 years ago

Read 2 more answers

4. A very scared penguin has decided to go downhill skiing. When he is nervous he likes to do math. The ski lift starts at 100 f

Ainat [17]

Answer: is -100 +1500-200

Step-by-step explanation:

5 0

2 years ago

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The class average on a math test was an 82 with a standard deviation of 5. If the

Alex787 [66]

Answer:

Option 3 and 4.

Step-by-step explanation:

The z score shows by how many standard deviations the raw score is above or below the mean. The z score is given by:

$z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean, \ \sigma=standard\ deviation$

Given that mean (μ) = 82, standard deviation (σ) = 5

1) For x = 74:

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{74-82}{5} =-1.6$

Option 1 is incorrect

2) For x < 87

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{87-82}{5} =1$

From the normal distribution table, P(x < 87) = P(z < 1) = 0.8413 = 84.13%

Option 2 is incorrect

3) For x = 95:

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{95-82}{5} =2.6$

Option 3 is correct

4) For x < 77

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{77-82}{5} =-1$

From the normal distribution table, P(x < 77) = P(z < -1) = 0.16 = 16%

Option 4 is correct

5) For x > 92

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{92-82}{5} =2$

From the normal distribution table, P(x > 92) = P(z > 2) = 1 - P(z < -2) = 1 - 0.9772 = 0.0228 = 2.28%

Option 5 is incorrect

8 0

2 years ago

It takes a softball team 2 hours to complete a game. How long will it take them to complete 3/4 of the game?

kolezko [41]

1 hour and a half. Every half hour is a quarter. So 3 half hours = 1 hours and a half. Hope this helps!

4 0

3 years ago

Read 2 more answers

Which equation could be used to solve the problem? Joan picked 4 bushels of apples in one hour. At that rate, how many bushels w

jeka94

Hello!

Unit rates can be written as ratios. In this case, we have 4 bushels in one hour, or 4:1. In eight hours, we can multiply like a fraction, multiplying both by eight to get eight hours.

Our final answer is B) 8·4.

I hope this helps!

3 0

2 years ago