can someone please check my work! question: simplify the expression and rationalize the denominator. 16x^4y^8 / 5

if it’s wrong can you please explain step by step and what i did wrong please :) and thank you.

Step-by-step explanation:

[tex] = { (- 12)}^{ - 2} [/tex]

[tex] = \frac{1}{ {( - 12)}^{2} } [/tex]

[tex] = \frac{1}{ {12}^{2} } \: or \: \frac{1}{144} [/tex]

Answer:

-3

Step-by-step explanation:

Answer: $14

Step-by-step explanation:

We know that Ruben spends $5 on candy, and saves $7 for college. If we add these together we get 12. Remaining: $2, which he donates to a children’s hospital. So 7+5+2=14, so Ruben has a weekly allowance of $14.

Thisbis a general geometric progression

So iterative formula

Answer:

[tex]a_n=9 \cdot \left(\frac{2}{3}\right)^{n-1}[/tex]

Step-by-step explanation:

Given:

[tex]\begin{cases}a_1=9\\a_n=\frac{2}{3}(a_n-1)\end{cases}[/tex]

General form of a geometric sequence:

[tex]a_n=ar^{n-1}[/tex]

where:

Therefore:

Substitute the given values into the general formula:

[tex]\implies a_n=9 \cdot \left(\frac{2}{3}\right)^{n-1}[/tex]

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the answer is 3,000

4% × 25 = 100%

$120 × 25 = $3000

Answer:

The Answer is Option C. 24

Explanation:

Red Marbles = [tex] \frac{2}{6} \times 24 = 8[/tex]

Blue Marble = (Red Marbles [tex] + 8[/tex])

Total Marbles = (Red Marbles+Blue Marbles) =[tex](8 + 16)[/tex] [tex] = 24[/tex]

Answer:

[tex]\displaystyle \frac{d}{dx}\Big|_{x=3} & = \frac{9(3)-6}{\sqrt{(3(3)-2)^2-4}} = \frac{7\sqrt{5}}{5}[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]\displaystyle f(x) = \sqrt{x^2 -4} \text{ and } g(x) = 3x-2[/tex]

And we want to find:

[tex]\displaystyle \frac{d}{dx}\left[f(g(x))\right] \text{ at } x = 3[/tex]

Recall that from the chain rule:

[tex]\displaystyle \frac{d}{dx}\left[ f(g(x))\right] = f'(g(x)) \cdot g'(x)[/tex]

Hence, find both f'(x) and g'(x).

The derivative of f(x) can be determined using the chain rule:

[tex]\displaystyle \begin{aligned} f'(x) &= \frac{d}{dx}\left[ \sqrt{x^2-4}\right]\\ \\ & = \frac{1}{2\sqrt{(x^2-4)}}\cdot \frac{d}{dx}\left[x^2-4\right] \\ \\ & = \frac{x}{\sqrt{x^2-4}} \end{aligned}[/tex]

Because g(x) is simply a linear function, its derivative will be the slope of the linear function at any point. That is:

[tex]\displaystyle g'(x) = 3[/tex]

Hence:

[tex]\displaystyle \begin{aligned} \frac{d}{dx}\left[f(g(x))\right] & = \frac{(g(x))}{\sqrt{(g(x))^2-4}} \cdot (3) \\ \\ & = \frac{9x-6}{\sqrt{(3x-2)^2-4}} \end{aligned}[/tex]

Then at the point x = 3, the derivative is:

[tex]\displaystyle \frac{d}{dx}\Big|_{x=3} & = \frac{9(3)-6}{\sqrt{(3(3)-2)^2-4}} = \frac{7\sqrt{5}}{5}[/tex]

Answer: it should be -27

Step-by-step explanation:

-7.21 < - 7.18 < -7.09 < 6.99 < 7.15

Step-by-step explanation:

-7.21

-7.18

-7.09

6.99

7.15

Parenthesis

Exponent

Multiplication

Division

Addition

Subtraction

(left to right)

4²-(3.1+6.4)+4.5

According to PEMDAS, we will do what is inside the parenthesis.

3.1+6.4 = 9.5

4²-9.5+4.5

Then we do figure out the exponent.

4² =  (4)(4) = 16

16-9.5+4.5

Then we do subtraction then addition because PEMDAS also tells us we should do adding and subtracting from left to right. In this expression, subtracting is on the left side so we should do that first.

16-9.5 = 6.5

6.5 + 4.5 = 11

11 is your answer :)

Answer:

3

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

x = 16

y = 70.4

Step-by-step explanation:

Two triangles are similar, so we can use the similarity ratio to so find the variables

(2.8)/(22.4) = (8.8)/y cross multiply expressions

197.12 = (2.8)*y divide both sides by 2.8

70.4 = y

use same operation to find x

(2.8)/(22.4) = x/128 cross multiply expressions

358.4 = (22.4)*x divide both sides by 22.4

16 = x

option B is correct, the money Luna left with is $20.00-(3×2.25+3.85)

An expression is combination of variables, numbers and operators.

Given that Luna goes to the convenience store with $20.00.

Luna buys 3 frozen drinks for $2.25 each and a snack for $3.85.

The cost for 3 frozen drinks will be 3×$2.25

The cost of snacks is $3.85.

To find the money left we have to subtract the amount spend for drinks and snack.

$20.00-(3×2.25+3.85)

Hence, option B is correct, the money Luna left with is $20.00-(3×2.25+3.85)

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Step-by-step explanation:

U need to make a graph

than plot the points they give u

than find the rise over run

rise/run = slope

Answer:

6.3

Step-by-step explanation:

1.48 * 2.5= 3.7

10-3.7= 6.3

9514 1404 393

Answer:

  $6.30

Step-by-step explanation:

The cost of the grapes is ...

  (2.5 lb)×($1.48 /lb) = $3.70

After that amount is subtracted from the gift card, the remaining balance is ...

  $10.00 -3.70 = $6.30

$6.30 remains on the gift card.

The length of the floor is obtained as 14 feet.

A rectangle is a type of parallelogram having equal diagonals.

All the interior angles of a rectangle are equal to the right angle.

The diagonals of a rectangle do not bisect each other.

The kitchen floor can be considered as a rectangle.

The width is given as 7 feet.

Suppose the length of floor be x feet.

Since, the area of a rectangle is the product of length and width, the following equation can be written for the given case,

7x = 98

=> x = 98/7

       = 14

Hence, the length of the kitchen's floor is found to be 14 feet.

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By applying the exponential and logarithmic functions, we have

[tex]x^{\sin(x)} = \exp \left(\ln \left(x^{\sin(x)}\right)\right)[/tex]

Then in the limit,

[tex]\displaystyle \lim_{x\to0} x^{\sin(x)} = \lim_{x\to0} \exp \left(\ln \left(x^{\sin(x)}\right)\right)[/tex]

[tex]\displaystyle \lim_{x\to0} x^{\sin(x)} = \exp \left( \lim_{x\to0} \ln \left(x^{\sin(x)}\right)\right)[/tex]

[tex]\displaystyle \lim_{x\to0} x^{\sin(x)} = \exp \left( \lim_{x\to0} \sin(x) \ln(x) \right)[/tex]

[tex]\displaystyle \lim_{x\to0} x^{\sin(x)} = \exp \left( \lim_{x\to0} \frac{\ln(x)}{\csc(x)} \right)[/tex]

As x approaches 0 (from the right), both ln(x) and csc(x) approach infinity (ignoring sign). Applying L'Hopitâl's rule gives

[tex]\displaystyle \lim_{x\to0} x^{\sin(x)} = \exp \left( \lim_{x\to0} \frac{\frac1x}{-\csc(x)\cot(x)} \right) = \exp \left( -\lim_{x\to0} \frac{\sin^2(x)}{x\cos(x)} \right)[/tex]

Recall that

[tex]\displaystyle \lim_{x\to0} \frac{\sin(x)}{x} = 1[/tex]

Then

[tex]\displaystyle \lim_{x\to0} \frac{\sin^2(x)}{x\cos(x)} = \lim_{x\to0} \frac{\sin(x)}{\cos(x)} = \lim_{x\to0} \tan(x) = 0[/tex]

So, our limit is

[tex]\displaystyle \lim_{x\to0} x^{\sin(x)} = \exp(0) = \boxed{1}[/tex]

Answer:

100

Step-by-step explanation:

you  see im very smart

Answer:

0.3

Step-by-step explanation:

Answer:

Step-by-step explanation:

what is 10/7 divided by 4

10/7 : 4 =

10/7 * 1/4 =

5/14

Answer:

Step-by-step explanation:

So how u do it is

you take 28 and 2.10 and you add it.

you add it with the bigger number at the bottom and the smaller number at the top. You then add it and that’s how many nickels and dimes are in the jar.

Hope this helped. Hehe

Answer:

14.88 kilometers per liter.

Step-by-step explanation:

^

Answer:

its c and e

Step-by-step explanation:

Answer:

8 is the correct answer ...

Answer:

[tex]\displaystyle m = \frac{2}{3}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify.

Point (-4, 1)

Point (2, 5)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m.

Answer:

D

Step-by-step explanation:

0.6x17.5 which is 10.5

Answer:

59/3

Explanation:

8 5/12 + 11 1/4 in simplest form is 59/3.

Step-by-step explanation:

[tex] d = \frac{m}{V}[/tex]

[tex] V \times d = m[/tex]

[tex] V = \frac{m}{d}[/tex]