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dsp73
3 years ago
5

What is y=x^2+74, translated 2 units up and 5 units left

Mathematics
2 answers:
Sonja [21]3 years ago
5 0
There’s an answer
y=(x+5)^2+76
OlgaM077 [116]3 years ago
4 0

Answer:

y = x² + 10x + 101

Step-by-step explanation:

Start with the basic function: y = x² + 74.

To shift the parabola up two units, you add two units to the value of y. The equation becomes

y = x² + 76

To shift the parabola five units to the left, you must add five units to the value of x. The equation for the parabola becomes

y = (x + 5)² + 76

y = x² + 10x + 25 + 76

y = x² + 10x + 101

The figure below shows the graphs of

y = x² (red)

y = x² + 76 (blue) (shifted up two units)

y = x² + 10x + 101 (green) (shifted left five units)

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Solve the equation. dy dx = ay + b cy + d , where a, b, c, and d are constants. (assume a ≠ 0 and ay + b ≠ 0.)
Reil [10]

 

It solves it in x. the solution for y includes heavy use of the product log function.

dy/dx                                = ay + b/cy +d

(cy +d/ ay + b) dy            = dx

∫ (cy +d/ ay + b) dy          = x (t) + C

 

Into solving the integral, integration by parts followed by u substitution and another integration by parts.

 

∫ (cy +d/ ay + b) dy

u            = cy + d dv          = dy/ay + b

du          = c dy v               = ln I ay + b l / a

 

Then, use u substitution for the new integral

 

u            = ay + b

du          = a dy

∫ ln l ay + b I dy                = ∫ ln IuI /a du    = 1/a ∫ ln luI du

 

Integrating the natural log includes thus far another integration by parts

r             = ln IuI ds            = du

dr          = du / u (s)           = du

∫ ln IuI / du                         = u ln IuI - ∫ du   = u ln IuI - ∫ a dy                                                                                   = (ay + b) ln Iay +bl – ay

 

The original integral of expression

∫ (cy +d/ ay + b) dy             = cy + d/a ln lay+bl – c/a² [(ay+b) ln lay+bl – ay]

Then simplify

∫ (cy +d/ ay + b) dy             = cy + d/a ln lay+bl – c/a²[(ay+b) ln lay+bl – ay]

                                           = a (cy + d)/a² ln lay+bl – c (ay+b)/ a²ln lay+bl +                                                               c/a² ay

                                           = cay + ad – cay – cb/ a² ln lay+bl + cay/a²

                                           = ad – cb/a²ln lay+bl + cy/a

 The final answer will be

x(t) + C                               = ad – cb/a² ln lay+bl + cy/a

x(t)                                     = ad – cb/a² ln lay+bl + cy/a + k

 

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3 0
3 years ago
(-3+7i)(1-2i) can you help me with the answer to this
lozanna [386]

Answer:

11 + 13i

Step-by-step explanation:

A must know is that

\sqrt{i}  =  - 1

Complex numbers

1st: foil the equations

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2nd Combine like terms and substitute

i ^{2} for \:  - 1

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11  +  13i

4 0
2 years ago
maxwell borrows 1,000 to repair his car at 9% interest if he pays the loan back over the next 1.5 years how much does he pay bac
worty [1.4K]

is interest per 1 year? if so:

interest per year=9%×1000

=90

interest for .5 years=90÷2

=45

1000+90+45=1135

Ans: 1135

6 0
3 years ago
Read 2 more answers
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Bezzdna [24]

Answer:

Step-by-step explanation:

It's a perfect square.

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Make sure it is correctly factored.

3g*3g = 9g^2

3g * - 5h  = - 15gh

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These four terms add to 9g^2 - 15gh - 15gh + 25h^2 = 9g^2 - 30gh + 25h^2 which is exactly what you started with.

7 0
3 years ago
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Anastaziya [24]

Answer:

The only possible answer that is correct is the first one, x = -4.

Step-by-step explanation:

Simplify the given inequality as much as possible, and then substitute each of the given x values one by one to determine which is in the solution set.

9(2x + 1) < 9x - 18 becomes 18x + 9 < 9x - 18, which, if reduced by dividing all four terms by 9, becomes 2x + 1 < x - 2.

Simplifying further, we get x < - 3.  The only possible answer that is correct is the first one, x = -4.  -4 < -3 is true.

8 0
2 years ago
Read 2 more answers
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