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notka56 [123]
3 years ago
8

*GET 30 POINTS IF YOU ANSWER* NEED ASAP! Three students were given the expression shown to simplify. Use the drop-down menus to

complete the statements about whether each student's answer is an equivalent expression. Then choose an expression that is equivalent.

Mathematics
1 answer:
Bas_tet [7]3 years ago
4 0

Answer:

The equivalent equation would be 6-2+4x, which could be simplified down to 4+4x

Sophia´s expression is wrong because she did not distribute correctly.

Ursula´s expression is incorrect because she tried adding -4x with 2. This is incorrect because the 2 does not a variable or 2 does not have an x beside it, so you can not add them both together to try to get to the answer.

Step-by-step explanation:

6⁻(2-4x) Given

6(-2+4x) Distributive Property, this is when you multiply everything in the parenthesis that is outside which would be -1 multiplied by -2 and -1 multiplied by -4x.

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Answer:

Average rate of change: -3

Step-by-step explanation:

<u>Remember:</u>

The average rate of change of a function over an interval [a,b] is \frac{f(b)-f(a)}{b-a}

<u>Given:</u>

[a,b]=[1,7]

f(b)=f(7)

f(a)=f(1)

<u>Calculation:</u>

f(b)=f(7)=-(7)^2+5(7)+14=-49+35+14=-49+49=0

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\frac{f(b)-f(a)}{b-a}=\frac{0-18}{7-1}=\frac{-18}{6}=-3

Therefore, the average rate of change of the function g(x)=-x^2+5x+14 over the interval 1\leq x\leq7 is -3.

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Answer:

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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

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