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3 years ago

Write the equation of the line in slope-intercept form with a slope of -5 and a y-intercept of -1.

2 answers:

7 0

First, we need to know what is the general equation of the slope-intercept form. It is expressed as follows:

y = mx + b

where m is the slope and b is the y-intercept. Therefore, having a slope of -5 and a y-intercept of -1, the equation of the line should be:

y = -5x - 1

Ghella [55]3 years ago

6 0

Slope intercept form : y = mx + b

the slope is represented by m....so m = -5
the y intercept is represented by b....so b = -1

now we sub
y = mx + b
y = -5x + (-1) or y = -5x - 1 <===

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2 years ago

I need help with part b. I feel like there’s a catch, I want to do the first derivative test, however, I feel like there is a be

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Answer:

The fifth degree Taylor polynomial of g(x) is increasing around x=-1

Step-by-step explanation:

Yes, you can do the derivative of the fifth degree Taylor polynomial, but notice that its derivative evaluated at x =-1 will give zero for all its terms except for the one of first order, so the calculation becomes simple:

$P_5(x)=g(-1)+g'(-1)\,(x+1)+g"(-1)\, \frac{(x+1)^2}{2!} +g^{(3)}(-1)\, \frac{(x+1)^3}{3!} + g^{(4)}(-1)\, \frac{(x+1)^4}{4!} +g^{(5)}(-1)\, \frac{(x+1)^5}{5!}$

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3) all other terms will keep at least one factor (x+1) in their derivative, and this evaluated at x = -1 will render zero

Therefore, the only term that would give you something different from zero once evaluated at x = -1 is the derivative of that linear term. and that only non-zero term is: $g'(-1)= 7$ as per the information given. Therefore, the function has derivative larger than zero, then it is increasing in the vicinity of x = -1

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3 years ago

Abraham has visited country somebody he has a cold or visiting at least 50 countries he plans to choose a school by visiting fiv

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Question:

Abraham has visited at least 50 countries; he plans to visit five new countries per year (Y) for the next several years. Which inequality and solution shows the amount of years they will take for Abraham to meet his goal.

Answer:

$Countries \geq 50 + 5y$

$y \leq 29$

Step-by-step explanation:

Given

$Countries = 50$ ------ at least

$Yearly =5$

Required

Represent as an inequality

"at least" means $\geq$

So the countries he has visited can be represented as thus;

$Countries \geq 50$

1 year = 5 countries

y years would be 5y countries

So, in y years; he'd have visited

$Countries \geq 50 + 5y$

To determine the value of y.

We have that

$Countries = 195$ in the world

Substitute 195 for Countries

$195 \geq 50 + 5y$

Collect Like Terms

$195 - 50 \geq 5y$

$145 \geq 5y$

Divide through by 5

$145/5 \geq y$

$29 \geq y$

Reorder

$y \leq 29$

This means that; he'll visit all countries in at most 29 years' time

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3 years ago

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