What is 2√54+5√24 in simplified radical form?

Answers

Answer 1

Answer:

Answer:

Simplified radical form is $16√(6)$

Step-by-step explanation:

In this problem we have the sum of two radical expressions. First step is to rewrite the radical using factorization process. Numbers 54 and 24 can be written as the products of square and non-square numbers.

$54 = 9 * 6 = 3^(2) *6\n24 = 4* 6 = 2^(2) *6$

After that, we can replace the numbers in the radical expression, and we can simplify them. Square numbers can be simplified with the radical. Then, we can expand the products.

$2√(54) + 5√(24)\n2√(6*9) + 5√(4*6)\n2\sqrt{3^(2) * 6} + 5\sqrt{2^(2)*6}\n2\sqrt{3^(2)}*√(6) + 5\sqrt{2^(2)}*√(6)\n2*3*√(6) + 5*2*√(6)\n6√(6) + 10√(6)$

Now, we can take the radical as common term and add the numbers.

$6√(6) + 10√(6)\n√(6)* (6+10)\n16√(6)$

Finally, Simplified radical form is $16√(6)$

Answer 2

Answer:

The simplified radical form of 2√54 + 5√24 is 16√6.

How to find the simplified radical form

To simplify the expression 2√54 + 5√24, we can first simplify the square roots of the numbers under the radicals.

√54 can be simplified as follows:

√54 = √(9 * 6) = √9 * √6 = 3√6.

Similarly, √24 can be simplified as:

√24 = √(4 * 6) = √4 * √6 = 2√6.

Now, we can substitute these simplified forms back into the original expression:

2√54 + 5√24 = 2(3√6) + 5(2√6).

Applying the distributive property, we have:

2(3√6) + 5(2√6) = 6√6 + 10√6.

Combining like terms, we get:

6√6 + 10√6 = (6 + 10)√6 = 16√6.

Therefore, the simplified radical form of 2√54 + 5√24 is 16√6.

Learn more about radical form at

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There are several, however one is 6.
The other answers are 4 and 8.

4) Arnold ate breakfast at a restaurant. His total came to $76.75. There is an 8% sales tax and 15% tip. What is Arnold's total cost? Show all your work and label all your answers.all your answers.

Answers

Answer:

The total cost is $95.32.

Step-by-step explanation:

Given:

Total came to $76.75. There is an 8% sales tax and 15% tip.

Now, to find the total cost.

8% sales tax is there so we calculate the amount after adding sales tax:

$76.75 + 8% of $76.75

$76.75+(8)/(100)* 76.75$

$76.75+0.08* 76.75$

$76.75+6.14$

$82.89$

The cost after sales tax is $82.89.

Now, the cost after 15% tip:

$82.89 + 15% of $82.89

$82.89+(15)/(100)* 82.89$

$82.89+0.15* 82.89$

$82.89+12.43$

$95.32$

The cost after the tip is $95.32.

Therefore, the total cost is $95.32.

Rachel made a mosaic from different color rectangle tiles 3 tiles measured three and a half inches x 3 inches 6 tiles measures 4 inches x 3 1/4 inches what is the area of the whole mosaic in square inches

Answers

so assuming that the only had 3+6=9 tiles
what we have to do it find teh area total
area=legnth times width

3 tiles are 3 and 1/2 times 3
3 times 3 and 1/2=10 and 1/2
times 3 tiles
10 and 1/2 times 3=31 and 1/2 squar inches

6 tiles are 4 by 3 and 1/4
4 times 3 and 1/4=13
6 tiles times 13 inchessquare=78

so we add
31 and 1/2+78=109 and 1/2 square inches

109 ¹/₂ in²

Further explanation

Given:

Rachel made a mosaic from different color rectangle tiles.
Three tiles measured 3 ¹/₂ inches x 3 inches.
Six tiles measured 4 inches x 3 ¹/₄ inches.

Question:

What is the area of the whole mosaic in square inches?

The Process:

Let's use the formula of a rectangular area.

$\boxed{\boxed{ \ Area = length * width \ }}$

Part-1: three tiles measured 3 ¹/₂ inches x 3 inches.

The area of the three tiles is as follows:

$\boxed{ \ Area = 3 * length * width \ }$

$\boxed{ \ Area = 3 * 3 * 3(1)/(2) \ }$

$\boxed{ \ Area = 3 * 3 * (7)/(2) \ }$

$\boxed{ \ Area = 9 * (7)/(2) \ }$

$\boxed{\boxed{ \ Area = (63)/(2) \ in^2\ }}$

Part-2: six tiles measures 4 inches x 3 ¹/₄ inches.

The area of the six tiles is as follows:

$\boxed{ \ Area = 6 * length * width \ }$

$\boxed{ \ Area = 6 * 4 * 3(1)/(4) \ }$

$\boxed{ \ Area = 6 * 4 * (13)/(4) \ }$

$\boxed{ \ Area = 24 * (13)/(4) \ }$

Both 24 and 4 are divided by 4.

$\boxed{ \ Area = 6 * 13 \ }$

$\boxed{\boxed{ \ Area = 78 \ in^2 \ }}$

Finally, let's add up the two areas above to get the area of the whole mosaic.

$\boxed{ \ = (63)/(2) + 78 \ }$

$\boxed{ \ = 31(1)/(2) + 78 \ }$

$\boxed{ \ = 109(1)/(2) \ }$

Thus, the area of the whole mosaic is $\boxed{\boxed{ \ = 109(1)/(2) \ in^2 \ }}$

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Keywords: Rachel made a mosaic, different color, rectangle, three tiles, measured, 3 1/2 inches, 3 inches, six tiles, 4 inches x 3 1/4 inches, what is the area, the whole mosaic, in square inches

Some one help me please

Answers

For this case we have that by power properties it is fulfilled:

$(a ^ n) ^ m = a ^ {n * m}$

Now, we can rewrite the expression as:

$\frac {64g ^ 9 * h ^ 6 * k ^ {12}} {8g ^ 3 * h ^ 2} -h ^ {25} k ^ {15} =$

We also have by definition of properties of powers that:

$\frac {a ^ m} {a ^ n} = a ^ {m-n}$

So:

$8g ^ {9-3} * h ^ {6-2} * k ^ {12} -h ^ {25} k ^ {15} =\n8g ^ 6 * h ^ 4 * k^(12) -h^(25) * k^(15)$

Answer:

Option D

F(x) = 3x+2
What is f(5)?

Answers

Answer:

f(5) = 17

Step-by-step explanation:

f(x) = 3x+2

Let x =5

f(5) = 3(5) +2

f(5) = 15+2

f(5) = 17

Tina is making rectangular signs. Each poster has an area of 1800 square inches and the length is 30 inches more than the width. Find the length and width of her sign. If x represents the width of each sign, select all of the equations that could be used to solve this problem. 2(x)+2(x+30)=1800 (x+30)(x)=1800 x(30x)=1800 x(x+30)=1800 Part 2 Find the dimensions of each rectangular sign. width = inches length = inches

Answers

Let the width be x. Since the length is 30inches longer than the width, the length is 30 + x.
Area = length x width = (30 + x)(x)
i.e. (30 + x)(x) = 1800 square inches.

$30x + x^(2) =1800 \n x^(2) +30x-1800=0 \n x^(2) -30x+60x-1800=0 \n ( x^(2) -30x)+(60x-1800)=0 \n x(x-30)+60(x-30)=0 \n (x+60)(x-30)=0$
x + 60 = 0 or x - 30 = 0
x = -60 or x = 30
but the width cannot be a negative number, hence x = 30inches
i.e. width = 30 inches
length = 30 + 30 = 60 inches.

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