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2 years ago

Find the equation, in standard form, of the line passing through the points (3,-4) and (5,1)

1 answer:

4 0

(3,-4)(5,1)
slope = (1 - (-4) / (5 - 3) = (1 + 4) / 2 = 5/2

y = mx + b
slope(m) = 5/2
use either of ur points (5,1)...x = 5 and y = 1
now we sub and find b, the y int
1 = 5/2(5) + b
1 = 25/2 + b
1 - 25/2 = b
2/2 - 25/2 = b
-23/2 = b

so ur equation is y = 5/2x - 23/2...but we need it in standard form

y = 5/2x - 23/2...subtract 5/2x from both sides
-5/2x + y = -23/2....multiply everything by -2
5x - 2y = 23 <== standard form

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c) If an initial investment of $ 35,000 grows to $257,000 in 15 years, what annual interest rate, continuously compounded, was e

castortr0y [4]

Answer: 13.29%

Step-by-step explanation:

The formula to calculate the compound amount (compounded continuously) is given by :-

$A=Pe^{rt}$ , where P is the principal amount , r is the rate of interest ( in decimal) and t is the time period.

Given : P= $ 35,000 , A= $257,000 and t=15 years

To find : r , we substitute all the values in the above formula , we get

$257000=(35000)e^{15r}\\\\\Rightarrow\ e^{15r}=\dfrac{257000}{35000}\\\\\Rightarrow\ e^{15r}=7.3428$

Taking natural log on both the sides , we get

$15r=\ln(7.3428)\\\\\Rightarrow\ 15r=1.9937\\\\\Rightarrow\ r=\dfrac{1.9937}{15}0.132913333333\approx0.1329=13.29\%$

Hence, the annual interest rate = 13.29%

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3 years ago

Write the equation of the line that passes through (6, 1), m = -3

JulijaS [17]

Answer:

y = - 3x + 19

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 3, thus

y = - 3x + c ← is the partial equation

To find c substitute (6, 1) into the partial equation

1 = - 18 + c ⇒ c = 1 + 18 = 19

y = - 3x + 19 ← equation of line

8 0

2 years ago

15% of customers that come to your

Helen [10]

Answer:

Number of customers (double taco)= 45

Step-by-step explanation:

Giving the following information:

Double taco order rate= 15% = 0.15

Total number of customers= 300

<u>To calculate the number of customers that order two tacos, we need to use the following formula:</u>

Number of customers (double taco)= Double taco order rate*total number of taco

Number of customers (double taco)= 0.15*300

Number of customers (double taco)= 45

7 0

2 years ago

What is the surface area of this triangular pyramid?

noname [10]

I believe it would be 44.75 sq yards

5 0

1 year ago

Help i dont understand this

Igoryamba

I’m not extremely good at math but I think you need to make -x-y=1 into y=mx+b form and then solve your new equation!

4 0

3 years ago