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3 years ago

find an equation for the line that passes through (-4, 8) and (3, -7). what is the slope? where does the line intersect the x-ax

is and the y-axis?

Mathematics

1 answer:

leonid [27]3 years ago

7 0

$(x_1;\ y_1);\ (x_2;\ y_2)\\\\the\ slope:m=\dfrac{y_2-y_1}{x_2-x_1}\\\\the\ slope\ form\ of\ the\ line:y=mx+b\\the\ point-slope\ form:y-y_1=m(x-x_1)\\-------------------\\\\(-4;\ 8)\to x_1=-4;\ y_1=8\\(3;-7)\to x_2=3;\ y_2=-7\\\\m=\dfrac{-7-8}{3-(-4)}=\dfrac{-15}{3+4}=-\dfrac{15}{7}\\\\\\y-8=-\dfrac{15}{7}(x-(-4))\\\\y-8=-\dfrac{15}{7}x-\dfrac{60}{7}\\\\y=-\dfrac{15}{7}x-\dfrac{4}{7}\\\\x-intercept\ when\ y=0\\-\dfrac{15}{7}x-\dfrac{4}{7}=0\ \ \ |\cdot7\\\\-15x-4=0\ \ \ |+4\\\\-15x=4\ \ \ |:(-15)$

$x=-\dfrac{4}{15}\to\left(-\dfrac{4}{15};\ 0\right)\\\\y-intrcept\ when\ x=0\\\\y=-\dfrac{15}{7}\cdot0-\dfrac{4}{7}\\\\y=-\dfrac{4}{7}\to\left(0;-\dfrac{4}{7}\right)$

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Plz help if u can 20 pt please just don't take the points..

sergey [27]

Answer:

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Step-by-step explanation:

you need to distribute the -2 to all the numbers inside parentheses and then combine like terms.

-2*3x= -6x

-2*12y= -24y

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-2*-16y=32y

-2*4= -8

Now combine like terms

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32y-24y=8y

10-8=2

Write the expression: 28x + 8y +2

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3 years ago

A special liquid is held in a tank described as (x 2 + y 2 ) ≤ z ≤ 1 in a Cartesian coordinate system. Assume that the density o

vivado [14]

Since $\rho=\dfrac mV$ (density = mass/volume), we can get the mass/weight of the liquid by integrating the density $\rho(x,y,z)$ over the interior of the tank. This is done with the integral

$\displaystyle\int_{-1}^1\int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\int_{x^2+y^2}^1(2-z^2)\,\mathrm dz\,\mathrm dy\,\mathrm dx$

which is more readily computed in cylindrical coordinates as

$\displaystyle\int_0^{2\pi}\int_0^1\int_{r^2}^1(2-z^2)r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=\boxed{\frac{3\pi}4}$

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3 years ago

How do i prove 2sec^2x-2sec^2xsin^2-sin^2x-cos^2x=1

kramer

$2\sec^2x-2\sec^2x\sin^2x-\sin^2x-\cos^2x=2\sec^2x(1-\sin^2x)-(\sin^2x+\cos^2x)$

Since $\sin^2x+\cos^2x=1$ , you have

$2\sec^2x(1-\sin^2x)-(\sin^2x+\cos^2x)=2\sec^2x\cos^2x-1$

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3 years ago

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sineoko [7]

Step-by-step explanation:

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4 years ago

Pattern: 0, 1, 3, 6, 10, 15, __<br> Explain the pattern of these numbers.

chubhunter [2.5K]

Answer:

Step-by-step explanation:

0 + 1 = 1

1 + 2 = 3

3 + 3 = 6

6 + 4 = 10

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Each number is added to an increase of 1 - first add 1, then add 2, then add 3,etc

Not listed but next would be 21 + 7 = 28

so it would be 0, 1, 3, 6, 10, 15, 21, 28

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3 years ago