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3 years ago

13

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

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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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

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3 years ago

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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>

$0=7x-4y+18$

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