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3 years ago

(12) Which equation has irrational solutions? Group of answer choices

Mathematics

1 answer:

Drupady [299]3 years ago

8 0

Answer:

9(x+3)²=27

Step-by-step explanation:

hello :

9(x+3)²=27 means : (x+3)²=27/9

(x+3)²=3 because 3 is not the perfect square

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A girl ran from her home to a store at the rate of 6 mph, and she walked back home at the rate of 4 mph. if it took 15 minutes f

viva [34]

Home is 0.6 miles away from the store

How to solve such time related questions?

The key concept for solving such questions is the relationship between speed, distance and time.

The relationship between them is Distance = Speed x Time

Given:-

Total time taken by girl to complete the trip = 15 minutes = $\frac{1}{4}$ hours

Speed while riding going = 6 miles per hour

Speed while coming back = 4 miles per hour

Total time taken by girl =

Time taken while going + Time taken while coming back - (1)

Let x be distance from home to store

$\frac{x}{6}$ = Time taken while going

$\frac{x}{4}$ = Time taken while coming back

Substituting in (1) we get

$\frac{1}{4} = \frac{x}{6} + \frac{x}{4}$

$\frac{1}{4} = \frac{2x + 3x}{12}$

$\frac{1}{4} = \frac{5x}{12}$

$x= \frac{12}{20}$

x = 0.6 miles

Thus home is 0.6 miles away from the store

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brainly.com/question/12759408

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2 years ago

Translate into an expression the sum of 4 and m

jek_recluse [69]

Answer:

Step-by-step explanation:

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3 years ago

Log(x-2)+log2=2logy<br>log(x-3y+3)=0

In-s [12.5K]

Answer:

Step-by-step explanation:

$\left\{\begin{array}{ccc}\log(x-2)+\log2=2\log y&(1)\\\log(x-3y+3)=0&(2)\end{array}\right$

$===========================\\\text{DOMAIN:}\\\\x-2>0\to x>2\\y>0\\x-3y+3>0\to x-3y>-3\\=====================\\\\\text{We know:}\ \log_ab=c\iff a^c=b,\\\\\text{therefore}\ \log_ab=0\iff a^0=b\to b=1\\\\\text{From this we have}\\\\\log(x-3y+3)=0\iff x-3y+3=1\qquad\text{add}\ 3y\ \text{to both sides}\\\\x+3=3y+1\qquad\text{subtract 3 from both isdes}\\\\\boxed{x=3y-2}\qquad(*)\\\\\text{Substitute it to (1)}$

$\log(3y-2-2)+\log2=2\log(y)\qquad\text{use}\ \log_ab^n=n\log_ab\\\\\log(3y-4)+\log2=\log(y^2)\qquad\text{subtract}\ \log(y^2)\ \text{from both sides}\\\\\log(3y-4)+\log2-\log(y^2)=0\\\\\text{Use}\ \log_ab+\log_ac=\log_a(bc)\ \text{and}\ \log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\\log\dfrac{(3y-4)(2)}{y^2}=0\qquad\text{use}\ \log_ab=0\Rightarrow b=1\\\\\dfrac{(3y-4)(2)}{y^2}=1\iff y^2=(3y-4)(2)\\\\\text{Use the distributive property}\ a(b+c)=ab+ac$

$y^2=(3y)(2)+(-4)(2)\\\\y^2=6y-8\qquad\text{subtract}\ 6y\ \text{from both sides}\\\\y^2-6y=-8\qquad\text{add 8 to both sides}\\\\y^2-6y+8=0\\\\y^2-2y-4y+8=0\\\\y(y-2)-4(y-2)=0\\\\(y-2)(y-4)=0\iff y-2=0\ \vee\ y-4=0\\\\\boxed{y=2\ \vee\ y=4}\in D$

$\text{Put the values of}\ y\ \text{to }\ (*):\\\\\text{for}\ y=2:\\\\x=3(2)-2\\\\x=6-2\\\\\boxed{x=4}\in D\\\\\text{for}\ y=4:\\\\x=3(4)-2\\\\x=12-2\\\\\boxed{x=10}\in D$

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3 years ago

In the Pacific, Allied forces began to take Japanese territory by _[blank].

Tomtit [17]

Beach invasions beach invasions

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3 years ago

a file that is 278 megabytes is being downloaded. If downloaded is 14.1% complete, how many megabytes been downloaded? To round

Gekata [30.6K]

14.1% of 278 is 39.2. So 39.2 megabytes have been downloaded.

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3 years ago

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