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3 years ago

Complete The Square: (Z^2)-19z=66

1 answer:

8 0

To solve the equation using complete square method we proceed:
z^2-19z=66
but
c=(-b/2a)^2
c=(-19/2)^2
c=361/4
thus:
z^2-19z+361/4=66+361/4
factoring the LHS we get:
1/4(2z-19)^2=625/4

(2z-19)^2=625
getting the square root of both sides we get:
2z-19=+/-25
2z=+/-25+19
2z=44 or -6
z=22 or -3
Answer: z=22 or z=-3

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Please help! asap! thank you so much! I have photos attached!

schepotkina [342]

Answer:

Step-by-step explanation:

Given problems are absolute value problems, So we need to plug the values of given parameters and get the final result.

We have given here,

a =-2 , b = 3 , c = -4 and d = -6

Now we know that An absolute function always gives a positive value.

Let's apply this strategy in the given problems.

1. ║a+b║

Plug a= -2 and b = 3

We get, ║-2+3║=║1║= 1

2. 5║c+b║

Plug c= -4 and b=3

i.e. 5║-4 + 3║= 5║-1║=5×1 = 5

3. a+b║c║

Plug values a= -2 , b=3 and c=-4

i.e -2 +3║-4║ = -2 + 3×4 = -2 + 12 = 10

4. ║a+c║÷(-d)

i.e ║-2 + (-4)║÷(-6) = ║-6║÷(-6) = 6÷(-6) = -1

5. 3║a+d║+b

i.e 3║-2+(-6)║+3 = 3║-8║+3 = 3×8 +3 = 27

4 0

3 years ago

Mr. Zelman wants to give 50% of his comic book collection to his nephew Alex. If Mr. Zelman has 800 comic books, then how many w

BARSIC [14]

Mr. Zelman gave 400 books to his nephew

<em><u>Solution:</u></em>

Given that, Mr. Zelman wants to give 50% of his comic book collection to his nephew Alex

Mr. Zelman has 800 comic books

Number of books with Zelman = 800

Mr. Zelman wants to give 50% of books to Alex

Number of books given to nephew = 50 % of books of Zelman

Therefore, we have to find 50 % of 800

$\rightarrow 50 \% \text{ of } 800$

$\rightarrow 50 \% \times 800\\\\\rightarrow \frac{50}{100} \times 800 = 400$

Thus he gave 400 books to his nephew

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3 years ago

Amelia pays $24 to rent a boat at the lake for up to six hours she constructs the inequality and number line below to represent

liubo4ka [24]

Money= how many hours
$4= 1h
$8=2h
$12=3h
$16=4h
$20=5h
$24=6h
l hope that helps :)

5 0

3 years ago

Im turning percents into fractions and im not sure how to do this one please help

slava [35]

4 1/7 = (4*100) +(1/7 of 100)= (400+ 14.28)= 414.28

The answer is 414.28

3 0

3 years ago

Which system of equation should you use to solve this problem

Alex17521 [72]

Last option is the correct answer.

Step-by-step explanation:

Given that

Let x stand for the solution a and y stand for the solution B

So,

According to statement that

30 gallons have to be made

$x+y=30$

Solution A contains 29 percent bromine => 0.29x

Solution B contains 53 percent =>0.53y

And the mixture of 30 gallons contains 45% bromine

$0.29x+0.53y=30*0.45\\0.29x+0.53y=13.5$

Following equations will be used for solving the problem

$x+y = 30\\0.29x+0.53y=13.5$

Hence,

Last option is the correct answer.

Keywords: Equations, Variables

Learn more about linear equations at:

#LearnwithBrainly

4 0

3 years ago