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bonufazy [111]
3 years ago
15

2. The sum of the reciprocals of two consecutive positive integers is 17/72. Write an equation that can be used to find the two

integers. What are the integers?
Steve helped me yesterday and gave me the hint 8+9=17. Then I thought about it and saw 8*9=72, but I am confused about how to put it into an equation.
Mathematics
1 answer:
Lena [83]3 years ago
8 0
To answer this item, we let x be the first positive integer. Then, the second would be x+1. Their reciprocals would be 1/x and 1/(x+1). Then, the equation that would best represent the scenario above is,
                            1/x + 1/(x+1) = 17/72
Solving the equation above,
                           ((x+1) + x) / (x)(x+1) = 17/72
If we take the numerators of both sides of the equation,
                              (x+1) + x = 17
The value of x from the equation is 8 and x+1 would be 9. Thus, the answer would be 8 and 9. 
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32x - 4 = 4x2 + 60 For the equation shown, choose the description of the solutions.
Furkat [3]
All to one side:

4x^2-32x+64 = 0,

divide by 4:

x^2 -8x + 16 = 0

apply formula or see that it is (x-4)^2!, so only x =4 is a root and it is double.
3 0
3 years ago
Read 2 more answers
FASTEST WITH EXPLAINATION ANSWER GETS BRAINLIEST
castortr0y [4]

Answer:

explanation to what

Step-by-step explanation:

6 0
3 years ago
A boat costs 16,000 and decreases in value by 14% per year. How much will the boat be worth after 11 years?
elixir [45]

<u>Answer</u>

    = 3,045.10

<u>Explanation</u>

A = P(1 - 14/100)ⁿ

A = 16,000(1-0.14)¹¹

    = 16,000 × 0.86¹¹

    = 16,000 × 0.190319

<em>     = 3,045.109725</em>

4 0
3 years ago
HELP PLS Given a polynomial function f(x), describe the effects on the Y-intercept, regions where the graph is increasing and de
Mashcka [7]
1. Remarks:

f(x) to f(x)-3 is the whole graph of f(x), shifted 3 units down. 

f(x) to -2f(x): 

The effect of "multiplication by -" is that the whole graph is reflected with respect to the x axis, so it is turned upside down.
 
The effect of "multiplication by 2" is that every point is "stretched vertically by a factor of 2" . So for example the point (-1, -4) in the original function, becomes (-1, -8) in the second one. Or (2, 5) would become (2, 10). 

The only points that do not change (are not streched vertically) are the roots. For example if (4,0) is an x-intercept (a root) in the original function, (4,0) is still a root in the second one because  2 times 0 is still 0.


2. Consider the polynomial function of degree n: 

f(x)= a_{n} x^{n} +a_{n-1} x^{n-1}+....+a_{2} x^{2}+a_{1} x^{1}+a_{0}

a. Y-intercept

The y - intercept is the value of the polynomial function at x=0. 
So it is f(0)=a_{0}, that is, the constant term of f(x)

in f(x)-3 the y intercept is shifted 3 units down as any other point, so it becomes  a_{0}-3

In -2f(x), the y-intercept a_{0} becomes -2a_{0}

b. Regions of f decreasing or increasing

f(x)-3 is f(x) just shifted down 3 units, so they are both increasing and decreasing in the same intervals of x

-2f(x) is f(x) turned upside down, so -2f(x) is increasing in all intervals f(x) is decreasing and it is decreasing in all intervals f(x) is increasing.

c. End behaviors

By now it is clear that end behaviors of f(x) and f(x)-3 are same, and f(x) with -2f(x) are opposite

d. Evenness, oddness

If f(x) is even, then f(x)=f(-x)

Let g(x)=f(x)-3

g(x)=f(x)-3=f(-x)-3=g(-3), so in this case f(x)-3 is even

If f(x) is odd, then f(-x)=-f(x)

g(x)=f(x)-3=-f(-x)-3,

so -g(x)=f(-x)+3

g(-x)=f(-x)-3,  

so g(-x) is not equal to -g(x). Which means f(x)-3 is not odd if f(x) is


Consider f(x)=-2f(x)

If f(x) is even, f(x)=f(-x)

g(x)=-2f(x)=-2f(-x)
g(-x)=-2f(-x)

So g(x)=g(-x), which means -2f(x) is even if f(x) is even

If f(x) is odd, f(x)=-f(-x)

let g(x)=-2f(x)=-2(-f(-x))=2f(-x)

g(-x)=-2f(-x)=-2(-f(x))=2f(x)

so g(-x) is not equal to -g(x), thus -2f(x) is not odd if f(x) is odd.

The conclusions about oddness and evenness can be also derived from the discussions about the graphs.
 

6 0
3 years ago
Helpppppopoppoppppppppp
notka56 [123]

Answer:

0.19

Step-by-step explanation:

i am not so sure but it's my opinion

8[14-(7+4×4)]

__________

1-121-1-8

8[14-[44]

_______

-120-1-8

8[-30]

_____

119-8

8-30

____

111

-22

___

111

✓ 0.19

don't blame me if it is wrong lol

6 0
3 years ago
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