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2 years ago

Write the slope-intercept form of the line that passes through the point (1, 0) and is parallel to x-y=7.

Mathematics

1 answer:

Mnenie [13.5K]2 years ago

8 0

We can rewrite the equation of the given line to be in slope-intercept form as follows.

$x-y=7\\x=y+7\\y=x-7$

Thus, the slope of the given line is 1.

Since parallel lines have equivalent slopes, the slope of the line we want to find is also 1.

Substituting into point-slope form,

$y-0=1(x-1)\\\\\boxed{y=x-1}$

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Hello!

The figure is made up of a cone and a hemisphere. To the nearest whole number, what is the approximate volume of this figure? Use 3.14 to approximate π . Enter your answer in the box. cm³

A 12 cm cone with a dome on top of it that has an 8 cm diameter

Data: (Cone)

h (height) = 12 cm

r (radius) = 4 cm (The diameter is 8 being twice the radius)

Adopting: $\pi \approx 3.14$

V (volume) = ?

Solving: (Cone volume)

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

$V = \dfrac{ 3.14 *4^2*\diagup\!\!\!\!\!12^4}{\diagup\!\!\!\!3}$

$V = 3.14*16*4$

$\boxed{V = 200.96\:cm^3}$

Note: Now, let's find the volume of a hemisphere.

Data: (hemisphere volume)

V (volume) = ?

r (radius) = 4 cm

Adopting: $\pi \approx 3.14$

If: We know that the volume of a sphere is $V = 4* \pi * \dfrac{r^3}{3}$ , but we have a hemisphere, so the formula will be half the volume of the hemisphere $V = \dfrac{1}{2}* 4* \pi * \dfrac{r^3}{3} \to \boxed{V = 2* \pi * \dfrac{r^3}{3}}$