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2 years ago

Evaluate the following expression: 30 = 5(8 – 6 + 1) - (2^2 - 3)^3

Mathematics

1 answer:

grin007 [14]2 years ago

7 0

Answer:

30=15

Step-by-step explanation:

30=40-30+6-4-27

30=10+2-27

40=12-27

30=-15

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Which expression is equivalent to-6(-2/3+2x)<br> A.-4-12x<br> B.- 4+2x<br> C. 4-12x<br> D. 4 + 12x

irakobra [83]

Answer:

4-12x

Step-by-step explanation:

-6(-2/3 + 2x)

Expand the bracket

12/3 - 12x

4 - 12x

7 0

2 years ago

Read 2 more answers

Solve irrational equation pls

rusak2 [61]

$\hbox{Domain:}\\
x^2+x-2\geq0 \wedge x^2-4x+3\geq0 \wedge x^2-1\geq0\\
x^2-x+2x-2\geq0 \wedge x^2-x-3x+3\geq0 \wedge x^2\geq1\\
x(x-1)+2(x-1)\geq 0 \wedge x(x-1)-3(x-1)\geq0 \wedge (x\geq 1 \vee x\leq-1)\\
(x+2)(x-1)\geq0 \wedge (x-3)(x-1)\geq0\wedge x\in(-\infty,-1\rangle\cup\langle1,\infty)\\
x\in(-\infty,-2\rangle\cup\langle1,\infty) \wedge x\in(-\infty,1\rangle \cup\langle3,\infty) \wedge x\in(-\infty,-1\rangle\cup\langle1,\infty)\\
x\in(-\infty,-2\rangle\cup\langle3,\infty)$

$
\sqrt{x^2+x-2}+\sqrt{x^2-4x+3}=\sqrt{x^2-1}\\
x^2-1=x^2+x-2+2\sqrt{(x^2+x-2)(x^2-4x+3)}+x^2-4x+3\\
2\sqrt{(x^2+x-2)(x^2-4x+3)}=-x^2+3x-2\\
\sqrt{(x^2+x-2)(x^2-4x+3)}=\dfrac{-x^2+3x-2}{2}\\
(x^2+x-2)(x^2-4x+3)=\left(\dfrac{-x^2+3x-2}{2}\right)^2\\
(x+2)(x-1)(x-3)(x-1)=\left(\dfrac{-x^2+x+2x-2}{2}\right)^2\\
(x+2)(x-3)(x-1)^2=\left(\dfrac{-x(x-1)+2(x-1)}{2}\right)^2\\
(x+2)(x-3)(x-1)^2=\left(\dfrac{-(x-2)(x-1)}{2}\right)^2\\
(x+2)(x-3)(x-1)^2=\dfrac{(x-2)^2(x-1)^2}{4}\\
4(x+2)(x-3)(x-1)^2=(x-2)^2(x-1)^2\\$
$
4(x+2)(x-3)(x-1)^2-(x-2)^2(x-1)^2=0\\
(x-1)^2(4(x+2)(x-3)-(x-2)^2)=0\\
(x-1)^2(4(x^2-3x+2x-6)-(x^2-4x+4))=0\\
(x-1)^2(4x^2-4x-24-x^2+4x-4)=0\\
(x-1)^2(3x^2-28)=0\\
x-1=0 \vee 3x^2-28=0\\
x=1 \vee 3x^2=28\\
x=1 \vee x^2=\dfrac{28}{3}\\
x=1 \vee x=\sqrt{\dfrac{28}{3}} \vee x=-\sqrt{\dfrac{28}{3}}\\$

There's one more condition I forgot about
$-(x-2)(x-1)\geq0\\
x\in\langle1,2\rangle\\$

Finally
$x\in(-\infty,-2\rangle\cup\langle3,\infty) \wedge x\in\langle1,2\rangle \wedge x=\{1,\sqrt{\dfrac{28}{3}}, -\sqrt{\dfrac{28}{3}}\}\\
\boxed{\boxed{x=1}}$

3 0

2 years ago

In 2018, the population will grow over 700,000.The population of a city in 2010 was 450,000 and was growing at a rate of 5% per

Firlakuza [10]

Answer:

The year is 2020.

Step-by-step explanation:

Let the number of years passed since 2010 to reach population more than 7000000 be 'x'.

Given:

Initial population is, $P_0=450,000$

Growth rate is, $r=5\%=0.05$

Final population is, $P=700,000$

A population growth is an exponential growth and is modeled by the following function:

$P=P_0(1+r)^x$

Taking log on both sides, we get:

$\log(P)=\log(P_0(1+r)^x)\\\log P=\log P_0+x\log (1+r)\\x\log (1+r)=\log P-\log P_0\\x\log(1+r)=\log(\frac{P}{P_0})\\x=\frac{\log(\frac{P}{P_0})}{\log(1+r)}$

Plug in all the given values and solve for 'x'.

$x=\frac{\log(\frac{700,000}{450,000})}{\log(1+0.05)}\\x=\frac{0.192}{0.021}=9.13\approx 10$

So, for $x > 9.13$ , the population is over 700,000. Therefore, from the tenth year after 2010, the population will be over 700,000.

Therefore, the tenth year after 2010 is 2020.

8 0

2 years ago

Blueberries cost $4 per pound for each question explain how you show your reasoning music table to help you organize information

aleksley [76]

Answer:

1. Either none (if you have to buy a whole pound), or 1/4 of a pound

2. 3 whole pounds or 3 and 1/4 pounds

Step-by-step explanation:

If $4 = 1 pound, then we know that $1 (which is 1/4 of $4), will let you by 1/4 pound of blueberries. Knowing this, we can simply:

Add up the one fourths

do 1/4 times $$

See how many times 4 goes into the number of dollars you have

Please correct me if I'm wrong :)

5 0

2 years ago

Please help me quick im giving a lot for this!

Lady_Fox [76]

Answer:

The answer is D!!

Step-by-step explanation:

Hope this helps!! ;)

Here is a scary story for all!! Enjoy!!

The Ghost Man

Once upon a time there was a family, made up of two young ones and their parents. One day, the parents had to go out to do something important. They had to call someone to take care of their children, so they called a lady who was friends with them. Then the lady arrived and the parents left. She made sure the kids ate and then she put them on their bed to sleep. Their house had two floors and the kids were on the second floor upstairs. Then, she went to sit down on the couch and started to watch tv. She was watching tv when suddenly her phone rang, and she answered the phone. It was an unknown number. She answered it and a creepy voice said, “Have you gone to check on the kids?” When she heard that she automatically hung up. A few minutes later she heard it again, “Have you gone to check on the kids?”. She kept on hearing it for a few times until she started to be a little scared. She called the police as quickly as she could. She told the police that a man who was unknown kept calling her and threatening her. Then the police said that when that man calls again, he will try to locate the man that is calling her. Then the man called again and the police were able to locate the man. A few minutes later, the police called again and he said, “Get out of the house right now because the man that is calling you is on the second floor of your house”. Then the lady remembered that the kids were upstairs so she ran upstairs as fast as she could and it was too late, the kids were gone and there was blood all over their room. The kids were never seen again and lots of police men are still going to look out to find this mysterious man who is going out to get every person he sees. So be careful of what you do because you might hear their cries too.

Hope you like it!! ;)

5 0

2 years ago

Read 2 more answers