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1 year ago

Find the cube root of 27d3 + 54a2b + 36ab2 + 8b3

Mathematics

1 answer:

enot [183]1 year ago

8 0

Answer:

(3a + 2b)3

Step-by-step explanation:

STEP 1 :

Equation at the end of step 1

(((27•(a3))+((54•(a2))•b))+(36a•(b2)))+23b3

Step 2:

(((27•(a3))+((54•(a2))•b))+(22•32ab2))+23b3

Step 3:

(((27•(a3))+((2•33a2)•b))+(22•32ab2))+23b3

Step 4:

((33a3 + (2•33a2b)) + (22•32ab2)) + 23b3

Step 5:

Factoring: 27a3+54a2b+36ab2+8b3

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Fabio and carlos play on a basketball team together. in the last game, fabio had 777 points less than 222 times as many points a

jasenka [17]

For this case, the first thing we must do is define variables.

We have then:

f: number of points that fabio scored.

c: number of points that Carlos scored.

We now write the equation that models the problem:

$f = 2c - 7$

Then, for f = 31 we have:

$2c - 7 = 31$

From here, we clear the number of points:

$2c = 31 + 7$

$2c = 38$

$c = \frac{38}{2}$

$c = 19$

Answer:

The equation to find the number of carlos points is:

$2c - 7 = 31$

Then, Carlos scored:

$c = 19$

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2 years ago

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Sadie simplified the expression StartRoot 54 a Superscript 7 b cubed EndRoot, where a greater-than-or-equal-to 0, as shown colon

Nadusha1986 [10]

Answer:

Sadie's error is " she made error in step 2 $=\sqrt{3^2\times 6\times a^2\times a^5\times b^2\times b}$ where $a\geqslant 0$ "

Because she made error in splitting the powers to simplify the square root

<h3>Therefore the correct answer for Sadie's expression is $3ab\sqrt{6ab}$ where $a\geqslant 0$ </h3>

Step-by-step explanation:

Given that " Sadie simplified the expression StartRoot 54 a Superscript 7 b cubed EndRoot, where a greater-than-or-equal-to 0, "

It can be written as $\sqrt{54a^7b^3}$ where $a\geqslant 0$

The given expression is $\sqrt{54a^7b^3}$ where $a\geqslant 0$

To find Sadie's error and explain the correct answer :

Sadie's steps are

$\sqrt{54a^7b^3}$ where $a\geqslant 0$

$=\sqrt{3^2\times 6\times a^2\times a^5\times b^2\times b}$

$=3ab\sqrt{6a^5b}$

<h3> $\sqrt{54a^7b^3}=3ab\sqrt{6a^5b}$ where $a\geqslant 0$ </h3><h3><u>Now corrected steps are</u></h3>

$\sqrt{54a^7b^3}$ where $a≥0$

$=\sqrt{(9\times 6)(a^{6+1})(b^{2+1})$

$=\sqrt{(3^2\times 6)(a^6.a^1)(b^2.b^1)$ (by using the identity $a^{m+n}=a^m.a^n$

$=\sqrt{3^2\times 6\times ((a^3)^2.a)(b^2.b)$ (by using the identity $a^{mn}=(a^m)^n$ )

$=3ab\sqrt{6ab}$

Therefore $\sqrt{54a^7b^3}=3ab\sqrt{6ab}$ where $a\geqslant 0$

<h3>The correct answer is $3ab\sqrt{6ab}$ where $a\geqslant 0$ </h3>

Sadie's error is " she made error in step 2 $=\sqrt{3^2\times 6\times a^2\times a^5\times b^2\times b}$ " where $a\geqslant 0$

Because she made error in splitting the powers to simplify the square root

<h3>Therefore the correct answer for Sadie's expression is $3ab\sqrt{6ab}$ where $a\geqslant 0$ </h3>

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1 year ago

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If the measure of angle 5 equals 102 degrees, then the measure of angle 8 equals what?

kiruha [24]

I hope this helps you

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1 year ago

2.314 divided by 1.3

kirza4 [7]

1.78 is the correct answer.

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2 years ago

The Boeing 757-200 ER airliner carries 200 passengers and has doors with a height of 72 inches. Heights of men are normally dist

Maksim231197 [3]

Answer:b)0.8577

Step-by-step explanation:

Since the heights of men are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - u)/s

Where

x = heights of men

u = mean height

s = standard deviation

From the information given,

u = 69 inches

s = 2.8 inches

We want to find the probability that the mean height of the 100 men is less than 72 inches.. It is expressed as

P(x < 72)

For x = 72

z = (72 - 69)/2.8 = 1.07

Looking at the normal distribution table, the probability corresponding to the z score is 0.8577

P(x < 72) = 0.8577

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1 year ago

Find the cube root of 27d3 + 54a2b + 36ab2 + 8b3​

Find the cube root of 27d3 + 54a2b + 36ab2 + 8b3