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3 years ago

Find an equation of the line that goes through the points (7,-42) and (10,-57). Write your answer in the form

Mathematics

2 answers:

aksik [14]3 years ago

4 0

Answer:

y = -5x - 7

Step-by-step explanation:

What's the slope of this line? Going from (7,-42) to (10,-57), we see x increasing by 3 and y decreasing by 15. Thus, the slope is m = rise / run = -15/3, or m = -5.

Now subst. -42 for y in y = mx + b, -5 for m and 7 for x:

-42 = -5(7) + b. Thus, b = -42 + 35, or b = -7. and the equation of this line is thus y = -5x - 7.

Check: if x = 10, does this equation yield y = -57? Yes

tatuchka [14]3 years ago

3 0

Y=-5x-7. I'm almost certain but you never know

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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

Whats the mean of the data set <br>86,90,93,85,79,92

k0ka [10]

Answer:

87.5

you need to add all the numbers and the divide it by the sum of values

4 0

3 years ago

Jack the kangaroo hopped 50 yards in the same time that a young kangaroo hopped 10 feet. How many more feet did Jack hop? ft

nasty-shy [4]

Ack hopped a total of 150 feet, that is 140 over what the young kangaroo hopped

4 0

3 years ago

Read 2 more answers

Willa says the slope of the graph is - 3. What error did

Yuri [45]

Answer:B

Step-by-step explanation: “she counted the squares instead of using the scale” by looking at the graph the first coordinates are (4,24) and instead of doing that Willa counted the squares.

5 0

4 years ago

The spread of a flu virus on a college campus is modeled by y= 5000/(1+4999e^-0.8t), where y is the number of students infected

Darina [25.2K]

Answer:

537 students

11 days

Step-by-step explanation:

5000

y= -----------------

(1+4999e^-0.8t)

a) after 8 days means t =8

5000

y= -----------------

(1+4999e^-0.8*8)

5000

y= -----------------

(1+4999e^-6.4)

5000

y= -----------------

(1+8.306)

5000

y= -----------------

(9.306)

y =537.28

Rounding to the nearest student

y = 537 students

b) 1/2 the student population means y =2500 (The 5000 is the student population)

5000

2500= -----------------

(1+4999e^-0.8t)

Multiply each side by (1+4999e^-0.8t)

2500 (1+4999e^-0.8t) = 5000

Divide each side by 2500

(1+4999e^-0.8t) = 5000/2500

(1+4999e^-0.8t) = 2

Subtract 1

(4999e^-0.8t) = 2-1

(4999e^-0.8t)=1

Divide by 4999

(4999/4999e^-0.8t)=1/4999

e^-0.8t=1/4999

Take the natural log of each side

ln(e^-0.8t)=ln(1/4999)

-.8t = ln(1/4999)

Divide by -.8

-.8/-8t = -1/.8 *ln(1/4999)

t = -1/.8 *ln(1/4999)

t≈10.6462

Rounding, it will take 11 days

7 0

3 years ago

Read 2 more answers