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3 years ago

Evaluate [(51 + 3) − 32] ÷ 9 ⋅ 2.

Mathematics

2 answers:

marin [14]3 years ago

4 0

51+3 = 54

54 - 32 = 22

22/9 = 2.444

2.444 times 2 = 4.888

8090 [49]3 years ago

4 0

[(51 + 3) − 32] ÷ 9 ⋅ 2

[(54) − 32] ÷ 9 ⋅ 2

(22)÷ 9 ⋅ 2

44/9

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This is algebra 2. Would like an answer ASAP. Thanks! Between the two chunks of numbers, thats a division sign, not an addition

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Answer:

Simplified form of $\frac{x+1}{x^2+x-6}\div \frac{x^2+5x+4}{x-2}$ is $\mathbf{\frac{1}{(x+3)(x+4)} }$

Option A is correct answer.

Step-by-step explanation:

We need to find simplified form of $\frac{x+1}{x^2+x-6}\div \frac{x^2+5x+4}{x-2}$

Solving the given expression:

$\frac{x+1}{x^2+x-6}\div \frac{x^2+5x+4}{x-2}$

First we find factors of $x^2+x-6$

$x^2+x-6 \\= x^2+3x-2x-6\\= x(x+3)-2(x+3)\\=(x-2)(x+3)$

So, factors of $x^2+x-6$ are $(x-2)(x+3)$

Now, fining the factors of $x^2+5x+4$

$x^2+5x+4\\=x^2+4x+x+4\\=x(x+4)+1(x+4)\\=(x+1)(x+4)$

So, factors of $x^2+5x+4$ are $(x+1)(x+4)\\$

Now the given expression will become:

$\frac{x+1}{(x-2)(x+3)}\div \frac{(x+1)(x+4)}{x-2}$

Now, converting division sign into multiplication sign:

$=\frac{x+1}{(x-2)(x+3)}\times \frac{x-2} {(x+1)(x+4)}\\Cancelling, \:common\:terms\\=\frac{1}{(x+3)(x+4)}$

So, simplified form of $\frac{x+1}{x^2+x-6}\div \frac{x^2+5x+4}{x-2}$ is $\mathbf{\frac{1}{(x+3)(x+4)} }$

Option A is correct answer.

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Varvara68 [4.7K]

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3 years ago

There are some nickels, dimes, and quarters in a large piggy bank. For every 2 nickels there are 3 dimes. For every 2 dimes ther

rodikova [14]

Answer: a) Number of nickels, dimes, and quarters are 80, 120, 300 respectively.

b) The coins are worth of 91 dollars i.e. $91 in the piggy bank.

Explanation:

Since we have given that

For every 2 nickels there are 3 dimes ,

So, their ratio will be 2:3

and for every 2 dimes there are 5 quarters.\,

So, their ratio will be 2:5

Now, we'll first find the ratio of nickles to dimes to quarters i.e.

Nickle Dimes Quarters

2 3

2 5

So, it becomes ,

Nickle : Dimes : Quarters

2×2 : 3×2 : 3×5

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Now, let the number of nickle be 4x

Let the number of dimes be 6x

Let the number of quarters be 15x

According to question,

$4x+6x+15x=500\\\\25x=500\\\\x=\frac{500}{25}=20$

So, number of nickels is given by

$4x=4\times 20=80$

Number of dimes is given by

$6x=4\times 20=120$

Number of quarters is given by

$15x=4\times 20=300$

As we know that

$1\ nickel=5\ cents\\\\1\ dime=10\ cents\\\\1\ quarter=25\ cents$

So, According to our question, we get

$80\times 5+120\times 10+300\times 25=400+1200+7500=9100\ cents\\\\1\ cent=0.01\ dollar\\\\9100\ cents=9100\times 0.01\ dollars=91\ dollars.$

Hence,

a) Number of nickels, dimes, and quarters are 80, 120, 300 respectively.

b) the coins are worth of 91 dollars i.e. $91 in the piggy bank.

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3 years ago

Please hellppp ......

katovenus [111]

Answer:

Step-by-step explanation:

To solve for BC we use sine

sin ∅ = opposite / hypotenuse

From the question

AC is the hypotenuse

BC is the opposite

So we have

sin 58 = BC / AC

sin 58 = BC / 14

BC = 14 sin 58

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BC = 11.9 to one decimal place

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4 years ago

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