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line j is perpendicular to lines m and n. if the products of the slope of all three lines is -8, what is the slope of line j?

jeka94

Answer:

the slope of line j is -1/8, the slope of lines m and n are both 8.

Explanation step by step:

Suppose j is the slope of line j, m the slope of line m and n the slope of line n. Since:

1. line j is perpendicular of line m, so j*m= -1

2. J is perpendicular of line n, so j*n=-1

3. m and n and parallel so m=n

As we want to know the slope of j we clear the equations presented to us in order to find it.

(1) m* n* j = -8, since n=m we have $n^{2}$ * j = -8.

we clear j; $n^{2} * j = -8 \\ j =\frac{-8}{n^{2} }$

replacing in the equation n*j = -1 we get

n*(-8/n^2) = -1. Thus n = 8. Since j = -1/n = -1/8.

7 0

2 years ago

A sphere has a radius of 3 centimeters. What is the volume of the sphere?

iris [78.8K]

Answer:

Volume = 113.1 cubic cm

Step-by-step explanation:

$Volume = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi 3^3 = 4 \pi \times 9 = 36 \pi=113.1 cm^3$

6 0

2 years ago

Read 2 more answers

Use x=5, equals, 5 to identify the value of each expression.

Lesechka [4]

Answer:

The answer to the first question is 625

The answer to the second question is 1

The answer to the third question is 1

4 0

2 years ago

Read 2 more answers

A circle has a radius of 20 centimeters and a central angle that measures 216 degrees. What is the length of the arc defined by

Bumek [7]

Answer:4320cm

Step-by-step explanation:

(length of the arc)/(length of the radius)=central angle

lengthof the arc/20=216

lengthof the arc=216×20

length of the arc=4320cm

8 0

2 years ago

What is the equation of the quadratic graph with a focus of (1, 1) and a directrix of y = −1? PLs HELP!!

Delicious77 [7]

ANSWER
$f(x)= \frac{1}{4} {(x - 1)}^{2}$

EXPLANATION

Since the directrix is
$y = - 1$

the axis of symmetry of the parabola is parallel to the y-axis.

Again, the focus being,

$(1,1)$

also means that the parabola will open upwards.

The equation of parabola with such properties is given by,

${(x - h)}^{2} = 4p(y - k)$
where
$(h,k)$

is the vertex of the parabola.

The directrix and the axis of symmetry of the parabola will intersect at
$(1, - 1)$

The vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix.

This implies that,
$h = \frac{1 + 1}{2} = 1$

and
$k = \frac{ - 1 + 1}{2} = 0$

The equation of the parabola now becomes,

$(x - 1) ^{2} = 4p(y - 0)$

$|p| = 1$

Thus, the distance between the vertex and the directrix.

This means that,

$p = - 1 \: or \: 1$

Since the parabola opens up, we choose
$p = 1$
Our equation now becomes,

${(x - 1)}^{2} = 4(1)(y - 0)$

This simplifies to
${(x - 1)}^{2} = 4y$

or

$y = \frac{1}{4} {(x - 1)}^{2}$

This is the same as,

$f(x)= \frac{1}{4} {(x - 1)}^{2}$

The correct answer is D .

4 0

3 years ago