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11Alexandr11 [23.1K]
3 years ago
10

What is the equation for a line that passes through the points (5,-4) and (-10,17

Mathematics
1 answer:
maria [59]3 years ago
7 0

Answer:

The equation of the line is 7 x +5 y = 15.

Step-by-step explanation:

Here the given points are ( 5, -4) & ( -10, 17) -

Equation of a line whose points are given such that

( x_{1},y_{1} ) & ( x_{2}, y_{2}  )-

 y - y_{1}   = \frac{y_{2} - y_{1}  }{x_{2} - x_{1}}  ( x - x_{1}  )

i.e.  <em>y - (-4)= \frac{17 - (-4)}{-10 - 5}  ( x- 5)</em>

<em>      y + 4 = \frac{17 + 4}{ -15} ( x - 5)</em>

<em>      y + 4 = \frac{21}{-15}  ( x - 5 )</em>

<em>      ( y + 4)  =  \frac{7}{- 5} ( x - 5)</em>

<em>      5 (y + 4 ) = - 7 (x - 5 )</em>

<em>      5 y + 20 = -7 x + 35</em>

<em>      7 x + 5 y = 15</em>

Hence the equation of the required line whose passes trough the points ( 5, -4) & ( -10, 17)  is 7 x + 5 y = 15.

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A van travels 260 miles on 13 gallons of gas. Find how many gallons the van needs to travel 500 miles?
FinnZ [79.3K]

Answer:

  25 gallons

Step-by-step explanation:

Assuming miles-per-gallon is a constant, the amount of gas is proportional to the miles driven:

  gallons/(500 mi) = (13 gal)/(260 mi)

  gallons = (500 mi)/(260 mi)(13 gal) . . . . multiply by 500 mi

  gallons = 25 gal . . . . do the arithmetic

The van will need 25 gallons of gas to go 500 miles.

6 0
4 years ago
The population of Brazil was 162,300,000 in 1995. It was growing at a rate of about 2% per decade. Predict the population, to th
stiv31 [10]

Answer:

The population is 168,900,000 to the nearest hundred thousand

Step-by-step explanation:

In this question, we are tasked with calculating the population of Brazil given its population in 1995 and her growth rate per decade.

Mathematically, we use an exponential function to calculate this population.

This can be written as P = I(1 + r)^n

where P is the population in 2015 which we are looking for,

I is the initial population which is 162,300,000

r is the rate of increase per decade given as 2% = 2/100 = 0.02,

n is the number of times between the years we are expecting this growth. The difference between the years 2015 and 1995 is 20 years which signifies 2 decades(1 decade is 10 years). Thus our n is 2

We plug these values into the equation above;

P = 162,300,000(1+0.02)^2

P = 162,300,000(1.02)^2

P = 168,856,920 which is 168,900,000 to the nearest hundred thousand

7 0
3 years ago
If f(x) = 8 – 10x and g(x) = 5x + 4, what is the value of (fg)(-2)?
Shkiper50 [21]

Answer:

68

Step-by-step explanation:

I'm going to assume you meant "what is the value of f(g(-2))?"

g(-2) = 5(-2) + 4 = -6

f(-6) = 8 - 10(-6) = 68

6 0
3 years ago
Can anyone help me with 15a b c
Pie

a. The independent variable is r. The dependent variable is m.

b. The domain is the set of numbers used in the independent variable. You can rent 0 videos, or 1 video, or 2 videos, etc., up to the amount of money you have. If you rent 0 videos, you are left with m = 30 - 3r = 30 - 3(0) = 30 - 0 = 30 dollars. If you rent 10 videos, you will have m = 30 - 3(10) = 30 - 30 = 0 dollars left. The domain is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. The range is {0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30}. Both the domain and range are discrete.

c. I can't do it online.

7 0
3 years ago
A pound of popcorn is popped for a class party. The popped corn is put into small popcorn boxes that each hold 120 popped kernel
V125BC [204]
Let x be the no of boxes.

120x = 14501
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Upon division the quotient +1 = The no of boxes required and 
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6 0
3 years ago
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