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patriot [66]
2 years ago
6

Combine like terms. y + 7 + 4(y + 3) =

Mathematics
1 answer:
bearhunter [10]2 years ago
8 0

Answer:

5y+19

Step-by-step explanation:

should be the answer

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Lines s and t are perpendicular if the slope of line s is 5 what is the slope of line t
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The slope of line T is -1/5, because perpendicular lines have opposite reciprocal slopes, meaning the opposite sign (positive or negative) and flipped (whole number becomes a fraction).

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What are the zeros of (x-2)(x^2-9)
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(x-2)(x^2-9)=0\iff x-2=0\ or\ x^2-9=0\\\\x-2=0\ \ \ \ |add\ 2\ to\ both\ sides\\\\\boxed{x=2}\\\\x^2-9=0\ \ \ \ |add\ 9\ to\ both\ sides\\\\x^2=9\iff x=\pm\sqrt9\to \boxed{x=-3\ or\ x=3}\\\\Answer:\boxed{x=-3\ or\ x=2\ or\ x=3}
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3 years ago
P and W are twice-differentiable functions with P(7)=2(W(7)). The line y=9+2.5(x-7) is tangent to the graph of P at x=7. The lin
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Using the product rule, we have

m(x) = x W(x) \implies m'(x) = xW'(x) + W(x)

so that

m'(7) = 7W'(7) + W(7)

The equation of the tangent line to <em>W(x)</em> at <em>x</em> = 7 has all the information we need to determine <em>m'</em> (7).

When <em>x</em> = 7, the tangent line intersects with the graph of <em>W(x)</em>, and

<em>y</em> = 4.5 + 2 (7 - 7)   ==>   <em>y</em> = 4.5

means that this intersection occurs at the point (7, 4.5), and this in turn means <em>W</em> (7) = 4.5.

The slope of this tangent line is 2, so <em>W'</em> (7) = 2.

Then

m'(7) = 7\cdot2 + 4.5 = \boxed{18.5}

4 0
3 years ago
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Check the picture below.

so the rhombus has the diagonals of AC and BD, now keeping in mind that the diagonals bisect each, namely they cut each other in two equal halves, let's find the length of each.

\bf ~~~~~~~~~~~~\textit{distance between 2 points}&#10;\\\\&#10;A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-2})\qquad &#10;C(\stackrel{x_2}{6}~,~\stackrel{y_2}{8})\qquad \qquad &#10;%  distance value&#10;d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}&#10;\\\\\\&#10;AC=\sqrt{[6-(-4)]^2+[8-(-2)]^2}\implies AC=\sqrt{(6+4)^2+(8+2)^2}&#10;\\\\\\&#10;AC=\sqrt{10^2+10^2}\implies AC=\sqrt{10^2(2)}\implies \boxed{AC=10\sqrt{2}}\\\\&#10;-------------------------------

\bf ~~~~~~~~~~~~\textit{distance between 2 points}&#10;\\\\&#10;B(\stackrel{x_1}{-2}~,~\stackrel{y_1}{6})\qquad &#10;D(\stackrel{x_2}{4}~,~\stackrel{y_2}{0})\qquad \qquad BD=\sqrt{[4-(-2)]^2+[0-6]^2}&#10;\\\\\\&#10;BD=\sqrt{(4+2)^2+(-6)^2}\implies BD=\sqrt{6^2+6^2}&#10;\\\\\\&#10;BD=\sqrt{6^2(2)}\implies \boxed{BD=6\sqrt{2}}

that simply means that each triangle has a side that is half of 10√2 and another side that's half of 6√2.

namely, each triangle has a "base" of 3√2, and a "height" of 5√2, keeping in mind that all triangles are congruent, then their area is,

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Answer:

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