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a_sh-v [17]
3 years ago
6

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

Mathematics
2 answers:
lara31 [8.8K]3 years ago
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  <span>slope of -5 and a y-intercept of -1, the equation of the line should be:

y = -5x - 1</span>
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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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
Sladkaya [172]

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!}

and when you do its derivative:

1) the constant term renders zero,

2) the following term (term of order 1, the linear term) renders: g'(-1)\,(1) since the derivative of (x+1) is one,

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

6 0
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
Ipatiy [6.2K]

<em>Question:</em>

<em>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.</em>

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

If

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 <em>in the world</em>

<em>Substitute 195 for Countries</em>

195 \geq 50 + 5y

<em>Collect Like Terms</em>

195 - 50 \geq 5y

145 \geq 5y

<em>Divide through by 5</em>

145/5 \geq y

29 \geq y

<em>Reorder</em>

y \leq 29

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

3 0
3 years ago
What integer is closet to n​
11Alexandr11 [23.1K]

Answer:

Rounding to the Nearest Integer

The most common type of rounding is to round to the nearest integer. The rule for rounding is simple: look at the digits in the tenth's place (the first digit to the right of the decimal point).

7 0
3 years ago
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