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Deffense [45]
3 years ago
6

Determine the intercepts of the line that correspond to the following table of values

Mathematics
1 answer:
almond37 [142]3 years ago
7 0
Find the equation

alrighty, the slope is rise/run

from (21,-3) to (28,-1)
rise is from -3 to -1 or a rise of 2
run is form 21 to 28 or a run of 7


so slope is 2/7

y=2/7x+b
find b which is the y intercept
alirhgty
use (21,-3)
x=21 and y=-3
-3=(2/7)(21)+b
-3=42/7+b
-3=6+b
-9=b

y=2/7x-9

the y intercept is (0,-9
the x intercept is where y=0

0=2/7x-9
9=2/7x
63/2=x

x intercept is (63/2,0) or (31.5,0)
y intercept is (0,-9)
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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 ...

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This can be rearranged to ...

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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 ...

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3 0
3 years ago
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What are the zeros of the function y=2x^2 +7x+3
enyata [817]
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1. Isosceles Triangle The two equal sides of an isosceles triangle are each 42
gavmur [86]

Answer:

1. H = 29 cm

2. θ = 44°

Step-by-step explanation:

1. We can find the height of the triangle by considering the isosceles triangle as two right triangles. The height can be found by using Pitagoras:

L^{2} = H^{2} + B^{2}

Where:

L: is the sides of the isosceles triangle = 42 cm

B: is the base = 30 cm

H: is the height =?

Then, the height is:

H = \sqrt{L^{2} - B^{2}} = \sqrt{(42 cm)^{2} - (30 cm)^{2}} = 29.4 cm = 29 cm

2. The two equal angles (θ) can be found using the following trigonometric identity:          

cos(\theta) = \frac{B}{L}

\theta = cos^{-1}(\frac{30 cm}{42 cm}) = 44.4^{\circ} = 44^{\circ}

Hence, the two equal angles are 44°.

I hope it helps you!  

3 0
2 years ago
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NNADVOKAT [17]

Answer:

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3 years ago
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Answer:

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