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Arlecino [84]
3 years ago
8

There is $500 in Holly's bank account. She takes out $50 from her account each month but doesn't put money back in. What is the

slope/rate? *
Mathematics
1 answer:
galina1969 [7]3 years ago
3 0

Answer:

The rate of change or slope m  = -50

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

  • m is the rate of change or slope
  • b is the y-intercept

Given that there is $500 in Holly's bank account.

Thus, the y-intercept b = 500

It is stated that she takes out $50 from her account each month but doesn't put money back in.

It means the rate of change or slope is decreasing.

Thus, the rate of change or slope m  = -50

<u>EXTRA BONUS!</u>

We can also determine the line equation by substituting m = -50 and b = 500 in the slope-intercept form

y = mx+b

y = -50x + 500

Here:

The slope m = -50

The y-intercept = 500

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<h2>Answer:</h2>

2\vec{v}-6\vec{u}=(-52,48) \\ \\ ||2\vec{v}-6\vec{u}||=75.28}

<h2>Step-by-step explanation:</h2>

In this problem we have two vectors:

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So we need to find two things:

2\vec{v}-6\vec{u}

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FIRST:

In this case we have the multiplication of vectors by scalars. A scalar is a simple number, so:

2\vec{v}-6\vec{u} \\ \\ Replace \ \vec{v} \ and \ \vec{u} \ by \ the \ given \ vectors: \\ \\ 2(-11,3)-6(5,-7) \\ \\ Multiply \ each \ component \ by \ the \ corresponding \ scalar:\\ \\ (2\times (-11),2\times 3)+(-6\times 5,-6\times (-7)) \\ \\ (-22,6)+(-30,42) \\ \\ Sum \ of \ vectors: \\ \\ (-22-30,6+42) \\ \\ \therefore \boxed{(-52,48)}

SECOND:

If we name:

\vec{w}=2\vec{v}-6\vec{u}

Then, ||2\vec{v}-6\vec{u}|| is the magnitude of the vector \vec{w}. Therefore:

||\vec{w}||=||2\vec{v}-6\vec{u}|| \\ \\ ||\vec{w}||=||(-52,48)|| \\ \\ ||\vec{w}||=\sqrt{(-58)^2+48^2} \\ \\ ||\vec{w}||=\sqrt{3364+2304} \\ \\ ||\vec{w}||=\sqrt{5668} \\ \\ \boxed{||\vec{w}||=75.28}

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