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2 years ago

The slope of the line below is 1 .write the point slope equation for the line using the coordinates of the labeled point. (5,7)

Mathematics

1 answer:

wariber [46]2 years ago

3 0

Answer:

y - 7 = 1 (x-5)

Step-by-step explanation:

The point slope equation of a line is expressed as;

y - y0 = m(x-x0)

m is the slope

(x0, y0) is the point on the line

Given the following

m = 1

(x0, y0) = (5, 7)

Substitute into the formula

y - 7 = 1 (x - 5)

y - 7 = x -5

y = x - 5 + 7

y = x + 2

Hence the point slope equation of the line is y - 7 = 1 (x-5)

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(4x - 1) + (-5x + 17)
=4x-1-5x+17
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3 years ago

Please help due in less than 3 hours!!!!!!!! When Anne biked down the canyon, she averaged 30 miles per hour. At this rate, how

bixtya [17]

Answer:

2 min.

Step-by-step explanation:

1h is 60 min so divide 60 by 30 and you get 2

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3 years ago

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<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B

riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

where we assume |r| < 1. Multiplying on both sides by r gives

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

As n → ∞, the exponential term will converge to 0, and the partial sums $S_n$ will converge to

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

2 years ago

Can someone please help me I really need help please please help me

Len [333]

Answer:

p= -3d-6

Step-by-step explanation:

I think this is right because he's eating 3 pieces each day after which would be -3d and d represents the amount of days, and the -6 represents the 6 pieces of candy he ate on his birthday. Hope this helps!

8 0

3 years ago

Read 2 more answers

HELP

uranmaximum [27]

20% of 60 is 12

60/300 = 20%

The friend is incorrect because that is 20% of 300 not 60

4 0

2 years ago

Read 2 more answers

The slope of the line below is 1 .write the point slope equation for the line using the coordinates of the labeled point. (5,7)​

The slope of the line below is 1 .write the point slope equation for the line using the coordinates of the labeled point. (5,7)