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Elenna [48]
3 years ago
8

smiddle" class="latex-formula">
Mathematics
2 answers:
spayn [35]3 years ago
7 0

Answer:

v = 2

Step-by-step explanation:

Given

6(5 - 8v) + 12 = - 54 ← distribute and simplify left side

30 - 48v + 12 = - 54

42 - 48v = - 54 ( subtract 42 from both sides )

- 48v = - 96 ( divide both sides by - 48 )

v = 2

Lena [83]3 years ago
3 0

Answer:

v = 2

Step-by-step explanation:

6(5-8v)+12=-54 \\ 30 - 48v + 12 =  - 54 \\ 42 - 48v =  - 54 \\  - 48v =  - 54  - 42 \\  - 48v =  - 96 \\  \\ v =  \frac{( - 96)}{( - 48)}  \\  \\ v =  \frac{96}{48}  \\  \\ v = 2

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sineoko [7]

Answer:

Step-by-step explanation:

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We can rotate counterclockwise 90° but we cannot do it about the origin (0,0) because the red point (5, 1) will end up at ( -1, 5) .

We see that the point (5, 1)  ends up at ( -2, 4) so the center of rotation is lower than the origin.

The transformation is rotation of 90° about the point (0,-1)

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3 years ago
What is the measure of each exterior angle of a decagon?
NemiM [27]
The sum of all of the exterior angles of any regular polygon is 360  (I'm assuming by decagon you mean a regular dodecagon).

Because the total has to be 360, and a decagon has 10 sides, you divide 360 by 10 to get each exterior angle.

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3 years ago
M..................................find the value of x ...y and z..​
My name is Ann [436]
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angle BCA = 80

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5 0
2 years ago
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8 0
3 years ago
Find the derivative of f(x) = 12x^2 + 8x at x = 9.
zvonat [6]

Answer:

224

Step-by-step explanation:

We will need the following rules for derivative:

(f+g)'=f'+g' Sum rule.

(cf)'=cf' Constant multiple rule.

(x^n)'=nx^{n-1} Power rule.

(x)'=1 Slope of y=x is 1.

f(x)=12x^2+8x

f'(x)=(12x^2+8x)'

f'(x)=(12x^2)'+(8x)' by sum rule.

f'(x)=12(x^2)+8(x)' by constant multiple rule.

f'(x)=12(2x)+8(1) by power rule.

f'(x)=24x+8

Now we need to find the derivative function evaluated at x=9.

f'(9)=24(9)+8

f'(9)=216+8

f'(9)=224

In case you wanted to use the formal definition of derivative:

f'(x)=\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}

Or the formal definition evaluated at x=a:

f'(a)=\lim_{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}

Let's use that a=9.

f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}

We need to find f(9+h) and f(9):

f(9+h)=12(9+h)^2+8(9+h)

f(9+h)=12(9+h)(9+h)+72+8h

f(9+h)=12(81+18h+h^2)+72+8h

(used foil or the formula  (x+a)(x+a)=x^2+2ax+a^2)

f(9+h)=972+216h+12h^2+72+8h

Combine like terms:

f(9+h)=1044+224h+12h^2

f(9)=12(9)^2+8(9)

f(9)=12(81)+72

f(9)=972+72

f(9)=1044

Ok now back to our definition:

f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}

f'(9)=\lim_{h \rightarrow 0} \frac{1044+224h+12h^2-1044}{h}

Simplify by doing 1044-1044:

f'(9)=\lim_{h \rightarrow 0} \frac{224h+12h^2}{h}

Each term has a factor of h so divide top and bottom by h:

f'(9)=\lim_{h \rightarrow 0} \frac{224+12h}{1}

f'(9)=\lim_{h \rightarrow 0}(224+12h)

f'(9)=224+12(0)

f'(9)=224+0

f'(9)=224

8 0
3 years ago
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