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3 years ago

Find the value of x so that the line passing through (-2, 7) and (x, 2) has a slope of -1/3

1 answer:

3 0

Slope between (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)
we are given the points (-2,7) and (x,2)
slope is -1/3
so
(x,y)
(-2,7) and (x,2)
x1=-2
y1=7
x2=x
y2=2

slope=(2-7)/(x-(-2))=-1/3
slope=(-5)/(x+2)=-1/3
multiply both sides by (-3)(x+2) (basically cross multiply)
15=x+2
minus 2 both sides
13=x
x=13
the value of x is 13

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Brenda has $30. She gets $5 every time she takes out the trash. Which inequality can be used to find x, the number of times Bren

kobusy [5.1K]

Brenda has to take out the trash more than 4 times to have more than $50.

Step-by-step explanation:

Given,

Amount Brenda already have = $30

Amount she gets each time for throwing trash = $5

Amount she wants to have = More than $50

Let,

x be the number of times she throws trash.

Amount for throwing trash * Number of times trash thrown + Amount already have > Amount she wants to have

$5*x+30>50\\5x>50-30\\5x>20$

Dividing both sides by 5

$\frac{5x}{5}>\frac{20}{5}\\x>4$

Brenda has to take out the trash more than 4 times to have more than $50.

Keywords: variable, inequality

Learn more about variables at:

#LearnwithBrainly

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3 years ago

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AVprozaik [17]

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3 years ago

Jace invested $380 in an account paying an interest rate of 6.2% compounded continuously. Assuming no deposits or withdrawals ar

SOVA2 [1]

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Step-by-step explanation:

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3 years ago

Question 2 of 5

AlekseyPX

Given:

The different recursive formulae.

To find:

The explicit formulae for the given recursive formulae.

Solution:

The recursive formula of an arithmetic sequence is $f(n)=f(n-1)+d, f(1)=a,n\geq 2$ and the explicit formula is $f(n)=a+(n-1)d$ , where a is the first term and d is the common difference.

The recursive formula of a geometric sequence is $f(n)=rf(n-1), f(1)=a,n\geq 2$ and the explicit formula is $f(n)=ar^{n-1}$ , where a is the first term and r is the common ratio.

The first recursive formula is:

$f(1)=5$

$f(n)=f(n-1)+5$ for $n\geq 2$ .

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 5. So, the explicit formula for this recursive formula is:

$f(n)=5+(n-1)(5)$

$f(n)=5+5(n-1)$

Therefore, the correct option is A, i.e., $f(n)=5+5(n-1)$ .

The second recursive formula is:

$f(1)=5$

$f(n)=3f(n-1)$ for $n\geq 2$ .

It is the recursive formula of a geometric sequence with first term 5 and common ratio 3. So, the explicit formula for this recursive formula is:

$f(n)=5(3)^{n-1}$

Therefore, the correct option is F, i.e., $f(n)=5(3)^{n-1}$ .

The third recursive formula is:

$f(1)=5$

$f(n)=f(n-1)+3$ for $n\geq 2$ .

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 3. So, the explicit formula for this recursive formula is:

$f(n)=5+(n-1)(3)$