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oksian1 [2.3K]
3 years ago
13

If f​(x​)=x+11 and g(x)=3x^2​, find ​(f+​g)(x​) and ​(f+​g)(5​).

Mathematics
1 answer:
Stella [2.4K]3 years ago
8 0
(f+g)(x) = f(x) + g(x) = x + 11 + 3x^2
(f+g)(5) = f(5) + g(5) = 5 + 11 +3(5^2) = 91
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Assume that y varies inversely with x. If y=1/3 when x=1/2, find y when x=1/4.
LenKa [72]

Answer:

y = \frac{2}{3}

Step-by-step explanation:

Given that y varies inversely with x then the equation relating them is

y = \frac{k}{x} ← k is the constant of variation

To find k use the condition y = \frac{1}{3} when x = \frac{1}{2} , thus

\frac{1}{3} = \frac{k}{\frac{1}{2} } = 2k ( divide both sides by 2 )

k = \frac{1}{6}

y = \frac{1}{6x} ← equation of variation

When x = \frac{1}{4} , then

y = \frac{1}{6(\frac{1}{4}) } = \frac{1}{\frac{3}{2} } = \frac{2}{3}

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What is 10.04 rounded to nearest tenth?
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*<br> Simplify the expression:<br> (-6p+7). -4
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Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Passing through (-2,1 ) and perpendicular to<br> 4x + 7y + 3 = 0.
Lunna [17]

Answer:

<h2>7x - 4y + 18 = 0</h2>

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y=mx+b

m - slope

b - y-intercept

========================================

Let

k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2

========================================

We have the equation of a line in a general form (Ax + By + C = 0)

Convert it to the slope-intercept form:

4x+7y+3=0             <em>subtract 7y from both sides</em>

4x+3=-7y         <em>divide both sides by (-7)</em>

-\dfrac{4}{7}x-\dfrac{3}{7}=y\to m_1=-\dfrac{4}{7}

Therefore

m_2=-\dfrac{1}{-\frac{4}{7}}=\dfrac{7}{4}

We have the equation:

y=\dfrac{7}{4}x+b

Put the coordinates of the point (-2, 1) to the equation, and solve for <em>b</em> :

1=\dfrac{7}{4}(-2)+b

1=-\dfrac{7}{2}+b     <em>multiply both sides by 2</em>

2=-7+2b           <em>add 7 to both sides</em>

9=2b            <em>divide both sides by 2</em>

[te]x\dfrac{9}{2}=b\to b=\dfrac{9}{2}[/tex]

Finally:

y=\dfrac{7}{4}x+\dfrac{9}{2} - <em>slope-intercept form</em>

Convert to the general form:

y=\dfrac{7}{4}x+\dfrac{9}{2}         <em>multiply both sides by 4</em>

4y=7x+18      <em>subtract 4y from both sides</em>

0=7x-4y+18

6 0
3 years ago
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