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3 years ago

the formula y-y1 =m(x-x1) is the pot slope form of the equation of a line where m is the slope of the line and(x,y) and (x1,y1)

are points of the line. Solve the equation for m, and e slope of a line that6 includes the poits (4,-2) and (5,0).

Mathematics

1 answer:

oksano4ka [1.4K]3 years ago

6 0

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~{{ 4}} &,&{{ -2}}~) 
% (c,d)
&&(~{{ 5}} &,&{{ 0}}~)
\end{array}
\\\\\\
% slope = m
slope = {{ m}}\implies 
\cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{5-(-2)}{0-4}\implies \cfrac{5+2}{0-4}\implies -\cfrac{7}{4}$

$\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-2)=-\cfrac{7}{4}(x-4)
\\\\\\
y+2=-\cfrac{7}{4}(x-4)\implies y+2=-\cfrac{7}{4}x+7\implies y=-\cfrac{7}{4}x+9$

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Answer:

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Step-by-step explanation:

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(write equation) Cos 27 (cos 27 = 0.89) = $\frac{x}{20}$

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(write equation) tan 40 (tan 40 = 0.84) = $\frac{32}{x}$

(new equation) 0.84 = $\frac{32}{x}$

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(write equation) cos 55 (cos 55 = 0.57) = $\frac{16}{x}$

(new equation) 0.57 = $\frac{16}{x}$

(multiply 16 on both sides) 0.57 x 16 = $\frac{16}{x}$ x 16

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4th pic: $tan = \frac{adjacentx}{hypothenuse}$

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3 years ago

1-What is the sum of the series? ∑j=152j Enter your answer in the box.

tangare [24]

Answer:

Please see the Step-by-step explanation for the answers

Step-by-step explanation:

∑ $\left \ {{5} \atop {j=1}} \right.$ 2j

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∑ = 2(1) + 2(2) + 2(3) + 2(4) + 2(5)

= 2 + 4 + 6 + 8 + 10

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This question is not given clearly so i assume the following series that will give you an idea how to solve this:

∑ $\left \ {{4} \atop {k=1}} \right.$ 2k²

The sum of series from k=1 to j=4 is:

∑ = 2(1)² + 2(2)² + 2(3)² + 2(4)²

= 2(1) + 2(4) + 2(9) + 2(16)

= 2 + 8 + 18 + 32

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∑ = (2*1)² + (2*2)² + (2*3)² + (2*4)²

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∑ = (2*1)²-4 + (2*2)²-4 + (2*3)²-4 + (2*4)²-4

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= (4-4) + (16-4) + (36-4) + (64-4)

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∑ = 2(1)²-4 + 2(2)²-4 + 2(3)²-4 + 2(4)²-4

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Hence the common ratio is r = 1/2

So n-th term is:

$ar^{n-1}$ = $1(\frac{1}{2})^{n-1}$

So the answer that represents the series in sigma notation is:

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This is an arithmetic sequence where the first term is -3 and the common difference is 2. So

a = 1

This can be derived as

-1 - (-3) = -1 + 3 = 2

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Hence the common difference d = 2

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marusya05 [52]

Answer:

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3 years ago

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