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4 years ago

What is equivalent to 3(y+4)+4(y-2)

Mathematics

1 answer:

amid [387]4 years ago

7 0

Answer:

7y+4

Step-by-step explanation:

combine liked terms

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What is the volume of the smaller sphere please help

Nata [24]

Answer:

32π is the volume of the larger sphere

Step-by-step explanation:

The volume of a sphere is V = 4/3πr³. The smaller sphere is V = 4π. This means r³ divided by 3 was 1. So r³ = 3. For the larger sphere, substitute r = 2r into the volume formula.

V = 4/3πr³

V = 4/3π(2r)³

V = 4/3π8r³

We know from the previous problem that r³ = 3.

So the volume formula simplifies to V = 4π(8) = 32π

3 0

3 years ago

Write an equation in slope-intercept form for the line that passes through (5,0) and is perpendicular to the line described by y

natta225 [31]

For this case we have to;

We have that an equation in slope-intercept form is given by:

$y = mx + b$

Where:

m is the slope

b is the cut point with the y axis

Also, by definition, two lines are perpendicular when the product of their slopes is -1. That is: $m_ {1} * m_ {2} = - 1$

We have the line as data: $y_ {1} = \frac {-5} {2} x + 6$

Then $m_ {1} = \frac {-5} {2}$

We found $m_ {2}$ :

$m_ {1} * m_ {2} = - 1$

$\frac {-5} {2} * m_ {2} = - 1$

$m_ {2} = \frac {-1} {(\frac {-5} {2})}$

$m_ {2} = \frac {(2) (- 1)} {(- 5) (1)}$

$m_ {2} = \frac {2} {5}$

Thus, $y_ {2} = \frac {2} {5} x_ {2} + b_ {2}$

We must find $b_ {2}$ :

We know that $y_ {2}$ passes through the point $(x_ {2}, y_ {2}) = (5,0)$

We substitute the point in the equation of $y_ {2}$ :

$0 = \frac {2} {5} (5) + b_ {2}\\0 = 2 + b_ {2}\\b_ {2} = - 2$

Thus, $y_ {2} = \frac {2} {5} x_ {2} -2$

Then the equation in slope-intercept for the line that passes through (5,0) and is perpendicular to the line described by $y_ {1} = \frac {-5} {2} x_{1} + 6$ is: $y_ {2} = \frac {2} {5} x_ {2} -2$