What is the square root of 180x^9y^16 in simplest form?

Answers

Answer 1

Answer: $\sqrt{180x ^{9y ^(16) } }$

Apply radical rule :

$\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}$

$√(180) \sqrt{x ^{9y^(16) } }$

Break the number to its primes : $180 : 2^2*3^2*5$

$√(2^2*3^2*5)$

Apply radical rule :

$\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}$

$√(5) √(2^2) √(3^2)$

Apply radical rule :

$\sqrt[n]{a^n} =a$

$√(2^2) =2$

$2* √(5) √(3^2)$

Apply radical rule :

$\sqrt[n]{a^n} =a$

$√(3^2) =3$

$= 2*3* √(5)$

Refine:

$√(5) *6$

$√(5) *6 \sqrt{x ^{9y ^(16) } }$

Apply radical rule :

$\sqrt[n]{a^m} = a (m)/(n)$

$\sqrt{x ^{9y ^(16) } } = x (9y ^(16) )/(2)$

$= √(5) *6x (9y ^(16) )/(2)$

hope this helps!

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2x- 3y=9

5x+3y=12

How would i solve this? I dont understand this and i really need help with it!Also I have to graph the anwsers afterward on a graph, so i really need the help. I appreciate it:)

Answers

$\begin{cases} 2x- 3y=9 \n5x+3y=12 \end{cases}\n + \ \ ------- \n 7x=21 \ \ /: 7\n \nx=(21)/(3)\n \n x=3 \n \n2x- 3y=9$

$2*3-3y=9\n \n6-3y =9\n \n-3y=9-6\n \n-3y=3 \ \ / :(-3)\n \nx=-1\n \n \begin{cases} x=3\ny= -1 \end{cases}$

$graph\n \n\begin{cases} 2x- 3y=9 \n5x+3y=12 \end{cases}\n \n \begin{cases} - 3y=-2x+9\ \ /:(-3) \n 3y=-5x+12 \ \ /:3 \end{cases}\n \n \begin{cases} y= (2)/(3)x-3 \n y=-(5)/(3)x+4 \end{cases}$

What is the area of this triangle?Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

Answers

Answer:

28.46

Step-by-step explanation:

Use a^2+b^2=c^2 to find height

Then use the area formula bh/2 to find area :))

Answer: 44.1

Step-by-step explanation:

What is the area of a square with a perimeter of 64 mm

Answers

Answer:

A =256 mm^2

Step-by-step explanation:

The perimeter of a square is given by the formula

P = 4s where s is the length of a side

64 = 4s

Divide each side by 4

64/4 =4s/4

16 = s

To find the area of a square, use the formula

A =s^2

A = 16^2

A =256 mm^2

Mrs. Smith decides to buy three sweaters and a pair of jeans. she had $120 in her wallet. if the price of jeans is $45,what is the highest possible price (p) of a sweater, if each sweater, if each sweater is the same price? write, solve, and graph the inequality.

Answers

Answer:

$3s+2j\leq $120$ . The sweaters cost $10 or less each. We graph it on a number line at 10 and use a filled in dot pointing towards zero for less than.

Step-by-step explanation:

Mrs. Smith buys 3 sweaters (represented by 3s) and 2 jeans (represented by 2j) for a total of at most $120. We don't know the total but we do know she couldn't spend more than $120.

We write $3s+2j\leq $120$ .

We know the jeans cost $45 each, so j=45. We substitute,

$3s+2(45)\leq $120\n3s+90\leq $120$