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11111nata11111 [884]
3 years ago
14

Someone please help 4(x-2)-3>-3(-2+6)+2

Mathematics
1 answer:
NNADVOKAT [17]3 years ago
5 0

Answer:

Fraction form: x > 1/4

Decimal form: x > 0.25

Step-by-step explanation:

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Write the equation of the line, in general form, that has a slope of 2 and a y-intercept of -5 .
quester [9]

Answer:

Y=2x-5

Step-by-step explanation:

The prblem is y=mx+b. You have to then repace your symbols with your slope (m) and your y - Intercept (B)

4 0
3 years ago
Find the generating function for the sequence 1,-2,4,-8, 16, ...
kirill [66]

Answer:

  a(x)=\dfrac{1}{1+2x}

Step-by-step explanation:

The generating function a(x) produces a power series ...

  a(x)=a_0+a_1x+a_2x^2+a_3x^3+\dots

where the coefficients are the elements of the given sequence.

We observe that the given sequence has the recurrence relation ...

  a_0=1;a_n=-2a_{n-1} \quad\text{for n $>$ 0}

This can be rearranged to ...

  a_n+2a_{n-1}=0

We can formulate this in terms of a(x) as follows, then solve for a(x).

\sum\limits^{\infty}_{n=1} {a_{n}x^n} =a(x)-a_0 \quad\text{and}\\\\\sum\limits^{\infty}_{n=1} {2a_{n-1}x^n} =(2x)a(x) \quad\text{so}\\\\\sum\limits^{\infty}_{n=1} {(a_n+2a_{n-1})x^n}=0=a(x)-a_0+2xa(x)\\\\a(x)=\dfrac{a_0}{1+2x}=\dfrac{1}{1+2x}

The generating function is ...

  a(x) = 1/(1+2x)

3 0
2 years ago
Read 2 more answers
You owe 12% interest each year on a $500 loan. If you make no payments and take no additional loans, what will the loan balance
Yakvenalex [24]
20000000000099999000
3 0
3 years ago
Fundamental theorem of calculus<br> <img src="https://tex.z-dn.net/?f=g%28s%29%3D%5Cint%5Climits%5Es_6%20%7B%28t-t%5E4%29%5E6%7D
mr_godi [17]

Answer:

\displaystyle g'(s) = (s-s^4)^6

Step-by-step explanation:

The Fundamental Theorem of Calculus states that:
\displaystyle \frac{d}{dx}\left[ \int_a^x f(t)\, dt  \right] = f(x)

Where <em>a</em> is some constant.

We can let:
\displaystyle g(t) = (t-t^4)^6

By substitution:

\displaystyle g(s) = \int_6^s g(t)\, dt

Taking the derivative of both sides results in:
\displaystyle g'(s) = \frac{d}{ds}\left[ \int_6^s g(t)\, dt\right]

Hence, by the Fundamental Theorem:

\displaystyle \begin{aligned} g'(s) & = g(s) \\ \\  & = (s-s^4)^6\end{aligned}

3 0
2 years ago
What is the equation of the quadratic graph with a focus of (1 ,3) and a directrix of y=1?
zimovet [89]
Check the picture below.

now, we know the directrix is at y = 1, and the focus point is at 1,3, well, notice the picture, the distance between those fellows is just 2 units.

the vertex is half-way between those fellows, therefore, the vertex will be at 1,2.

the distance "p", from the vertex to either the directrix or focus, is really just 1 unit.  Since the focus point is above the directrix, is a vertical parabola, and it opens upwards, like in the picture, and since it opens up, the "p" value is positive, or +1.

\bf \textit{parabola vertex form with focus point distance}\\\\&#10;\begin{array}{llll}&#10;4p(x- h)=(y- k)^2&#10;\\\\&#10;\boxed{4p(y- k)=(x- h)^2}&#10;\end{array}&#10;\qquad &#10;\begin{array}{llll}&#10;vertex\ ( h, k)\\\\&#10; p=\textit{distance from vertex to }\\&#10;\qquad \textit{ focus or directrix}&#10;\end{array}\\\\&#10;-------------------------------\\\\&#10;\begin{cases}&#10;h=1\\&#10;k=2\\&#10;p=1&#10;\end{cases}\implies 4(1)(y-2)=(x-1)^2\implies 4(y-2)=(x-1)^2&#10;\\\\\\&#10;y-2=\cfrac{1}{4}(x-1)^2\implies y=\cfrac{1}{4}(x-1)^2+2

4 0
3 years ago
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