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AnnyKZ [126]
3 years ago
6

David found and factored out the GCF of the polynomial 80b4 – 32b2c3 + 48b4c. His work is below.

Mathematics
2 answers:
Vikentia [17]3 years ago
8 0

Answer:

Given Polynomial:

80b^4-32b^2c^3+48b^4c

Factors of Coefficient of terms

80 = 5 × 16

32 = 2 × 16

48 = 3 × 16

Common factor of the coefficient of all term is 16.

Each term contain variable. So the Minimum power of b is common from all terms.

Common from all variable part comes b².

So, Common factor of the polynomial = 16b²

⇒ 16b² ( 5b² ) - 16b² ( 2c³ ) + 16b² ( 3b²c )

⇒ 16b² ( 5b² - 2c³ + 3b²c )

Therefore, Statements that are true about David's word are:

The GCF of the coefficients is correct.

The variable c is not common to all terms, so a power of c should not have been factored out.

In step 6, David applied the distributive property

Ad libitum [116K]3 years ago
8 0

Answer:

The GCF of the coefficients is correct.

The variable c is not common to all terms, so a power of c should not have been factored out.

The expression in step 5 is equivalent to the given polynomial.

In step 6, David applied the distributive property

Step-by-step explanation:

Only the above  four statements are true.

GFC of 80, 32, and 48: 16

We find that 16 is the highest number which divides 80, 32 and 48.  Hence 16 is GFC.

GCF of b4, b2, and b4: b2

Also we have taken the term of b in all three and found the least exponent as gCF hence correct.

Since c is not in the first term, no c term can be GCF hence iii is also true.

But the expression in step 5 is not equivalent to the given polynomial because I term in the step 5 = 80b^6c, but in the given no c term is there.

Yes. In step 6, he applied distributive property to take GCF outside the polynomial as a factor.

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Ann [662]

Answer:

248.96

Step-by-step explanation:

From this regression output we have the MS Residual or mean squared error to be equal to 61983.1

the question requires us to find the standard error of the estimate. The standard error of the estimate can be gotten by finding the square root of the MSE.

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6 0
3 years ago
F(x) = 3x + 6 please help quickly!!!!!!!
Georgia [21]

Given the function, <em>f(x) = 3x + 6,</em> we can solve for f(a), f(a + h) and \frac{(f(a + h) - f(a)) }{h} by substituting their values into f(x) = 3x + 6. We will have the following:

\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}

<em><u>Given:</u></em>

  • f(x) = 3x + 6

<em>We are told to find:</em>

  1. f(a)
  2. f(a + h), and
  3. \frac{(f(a + h) - f(a)) }{h}

1. <em><u>Find f(a):</u></em>

  • Substitute x = a into f(x) = 3x + 6

f(a) = 3(a) + 6

f(a) = 3a + 6

<em>2. Find f(a + h):</em>

  • Substitute x = a + h into f(x) = 3x + 6

f(a + h) = 3(a + h) + 6

f(a + h) = 3a + 3h + 6

<em>3. Find </em>\frac{(f(a + h) - f(a)) }{h}<em>:</em>

  • Plug in the values of f(a + h) and f(a) into \frac{(f(a + h) - f(a)) }{h}

Thus:

\frac{((3a + 3h + 6) - (3a + 6)) }{h}\\\\\frac{(3a + 3h + 6 - 3a - 6) }{h}\\\\

  • Add like terms

\frac{(3a - 3a + 3h + 6 - 6) }{h}\\\\= \frac{3h }{h}\\\\\mathbf{= 3}

Therefore, given the function, <em>f(x) = 3x + 6,</em> we can solve for f(a), f(a + h) and \frac{(f(a + h) - f(a)) }{h} by substituting their values into f(x) = 3x + 6. We will have the following:

\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}

Learn more here:

brainly.com/question/8161429

6 0
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tatyana61 [14]

Answer:

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Step-by-step explanation:

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How do you show work for<br> 3(2)(-5)^3
Trava [24]

Answer:

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Find the lengths of the legs. <br> (NO LINKS)
maks197457 [2]

Given:

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To find:

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Third angle = 180^\circ-45^\circ- 90^\circ

                   = 45^\circ

Base angles are equal it means the given triangle is an isosceles right triangle. So, the lengths of both legs are equal.

Let x be the lengths of both legs. Then by using Pythagoras theorem, we get

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(10)^2=x^2+x^2

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\dfrac{100}{2}=x^2

50=x^2

Taking square root on both sides, we get

\pm \sqrt{50}=x

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\pm 5\sqrt{2}=x

The side length cannot be negative. So, the only value of x is 5\sqrt{2}.

Therefore, the length of the both legs is 5\sqrt{2} units.

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3 years ago
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