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pantera1 [17]
3 years ago
5

Ndicate the equation of the line through (2, -4) and having slope of 3/5.

Mathematics
2 answers:
lord [1]3 years ago
7 0

\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})~\hspace{10em} slope = m\implies \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-4)=\cfrac{3}{5}(x-2) \implies y+4=\cfrac{3}{5}x-\cfrac{6}{5} \\\\\\ y=\cfrac{3}{5}x-\cfrac{6}{5}-4\implies \implies y=\cfrac{3}{5}x-\cfrac{26}{5}

shusha [124]3 years ago
3 0

Answer:

Point-slope form: y+4=\frac{3}{5}(x-2)

Slope-intercept form: y=\frac{3}{5}x-\frac{26}{5}

Standard form: 3x-5y=26

Step-by-step explanation:

The easiest form to use here if you know it is point-slope form.  I say this because you are given a point and the slope of the equation.

The point-slope form is y-y_1=m(x-x_1).

Plug in your information.

Again you are given (x_1,y_1)=(2,-4) and m=\frac{3}{5}.

y-y1=m(x-x_1) with the line before this one gives us:

y-(-4)=\frac{3}{5}(x-2)

y+4=\frac{3}{5}(x-2) This is point-slope form.

We can rearrange it for different form.

Another form is the slope-intercept form which is y=mx+b where m is the slope and b is the y-intercept.

So to put y+4=\frac{3}{5}(x-2) into y=mx+b we will need to distribute and isolate y.

I will first distribute. 3/5(x-2)=3/4 x -6/5.

So now we have y+4=\frac{3}{5}x-\frac{6}{5}

Subtract 4 on both sides:

y=\frac{3}{5}x-\frac{6}{5}-4[tex]Combined the like terms:[tex]y=\frac{3}{5}x-\frac{26}{5} This is slope-intercept form.

We can also do standard form which is ax+by=c. Usually people want a,b, and c to be integers.

So first thing I will do is get rid of the fractions by multiplying both sides by 5.

This gives me

5y=5\cdot \frac{3}{5}x-5 \cdot 26/5

5y=3x-26

Now subtract 3x on both sides

-3x+5y=-26

You could also multiply both sides by -1 giving you:

3x-5y=26

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Answer:

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Step-by-step explanation:

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  • \implies y\:\alpha\: \frac{1}{\sqrt z}......(2)

  • Combining (1) & (2), we find:

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  • Now, when y = 2, x = 3 and z = 4, we find the value of k i.e. constant.

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1) Let f(x)=ax2+bx+c for some value of a, b and c. f intersects the x-axis when x=−2 or x=3, and f( 1 3 )=−25. Find the values o
antiseptic1488 [7]

Answer:

1) a = -⅙, b = ⅙, c = 1

2) 6 units

Step-by-step explanation:

1) f(x) = ax² + bx + c

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f(x) = a (x + 2) (x − 3)

We know that f(13) = -25, so we can plug this in to find a:

-25 = a (13 + 2) (13 − 3)

-25 = 150a

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Distributing:

f(x) = -⅙ (x² − x − 6)

f(x) = -⅙ x² + ⅙ x + 1

Graph: desmos.com/calculator/6m6tjoodvb

2) Volume of a right prism is area of the base times the height.

V = Ah

The base is an equilateral triangle.  Area of a triangle is one half the base times height.

V = ½ ab h

The height of the triangle is the same as the height of the prism.

V = ½ bh²

In an equilateral triangle, the height is equal to half the base times the square root of 3.

V = ½ b (½√3 b)²

V = ⅜ b³

Given that V = 81, solve for b.

81 = ⅜ b³

216 = b³

b = 6

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