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3 years ago

Graph the following lines and write the equation in slope-intercept form. With y intercept of −3 and an x intercept of −4.5.

Mathematics

1 answer:

makvit [3.9K]3 years ago

6 0

Answer:

$y=-\frac{2}{3}x-3$

Step-by-step explanation:

To write the equation of a line we need 2 points. We know:

If the y-intercept of the line is -3 then the point is (0,-3).

If the x-intercept of the line is -4.5 then the point is (-4.5,0).

Using these two point, we will find the slope and then substitute it into the point slope form $y-y_1=m(x-x_1)$ with a point.

Slope: $m=\frac{0--3}{-4.5-0}=\frac{0+3}{-4.5}=\frac{3}{-4.5}=-0.6667$

This decimal is -2/3. We will now substitute -2/3 and (0,-3) into the point slope form.

$y--3=-\frac{2}{3}(x-0)\\y+3=-\frac{2}{3}(x)\\y+3=-\frac{2}{3}x\\y=-\frac{2}{3}x-3$

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3 years ago

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3 years ago

Find the missing measure for a right circular cone given the following information. Find V if r = 2 and L.A. = 12. (16/3)√2 16√2

aksik [14]

Volume of cone is given by formula

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We are already given r =2, so we need to find h and then we can find volume

So missing meausre is height here ------------------------------------------------------------------------------

To find h we will use lateral area = $12\pi$ given

Formula for lateral area of cone is $\pi r\sqrt{r^{2}+ h^{2}}$

so we have $12 = \pi r\sqrt{r^{2}+ h^{2}}$

Now plug r as 2 in this equation

$12 \pi = \pi (2)\sqrt{2^{2}+ h^{2}}$

Now solve for h as shown and get h by itself

$\frac{12\pi}{2\pi} = \frac{2\pi\sqrt{4+h^{2}}}{2 \pi}$

$6 = \sqrt{4+h^{2}}$

$6^{2} = \sqrt{4+h^{2}} ^{2}$

$36} = 4+h^{2}$ $36 - 4 = 4+h^{2} -4$

$32 = h^{2}$ $\sqrt{32} = \sqrt{h^{2}}$

$\sqrt{16 \times 2} = h$ $\sqrt{16} \times \sqrt{2} = h$

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Now plug 2 in r place and $4\sqrt{2}$ in h place in volume formula given in (1)

$V = \frac{\pi r^{2}h}{3}$

$V = \frac{\pi (2)^{2}4\sqrt{2}}{3} [/tex][tex] V = \frac{\pi (4)4\sqrt{2}}{3}$

$V = \frac{16 \pi \sqrt{2}}{3}$

so choice (1) is right answer

$(1) \frac{16 \sqrt{2}\pi}{3}$

correct answer --------------------------------------------------------------------------------------------------

$(2) 16 \sqrt{2} \pi$

incorrect answer as correct volume answer we got as $\frac{16 \sqrt{2}\pi}{3}$ --------------------------------------------------------------------------------------------------

$(3) 4 \sqrt{38} \pi$

incorrect answer as correct volume answer we got as $\frac{16 \sqrt{2}\pi}{3}$ --------------------------------------------------------------------------------------------------------

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suter [353]

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