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3 years ago

Write an equation in standard form of the line passing through the points (12, 3) and (-3, 8).

Mathematics

1 answer:

aliya0001 [1]3 years ago

6 0

Answer:

x + 3y = 21

Step-by-step explanation:

$(x_{1},y_{1})=(12,3) \\\\(x_{2},y_{2})=(-3,8)\\\\Slope= \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\= \dfrac{8-3}{-3-12}= \dfrac{5}{-15}\\\\= \dfrac{-1}{3}$

Equation of the line: y =mx+ b

$y = \dfrac{-1}{3}x+b\\\\\\Plugin \ x = 12 \ and \ y=3 \ in \ the \ above \ equation\\\\3= \dfrac{-1}{3}*12+b\\\\3= -4+b\\\\3+4 = b\\\\b = 7\\\\\\\y= \dfrac{-1}{3}x+7\\\\$

Multiply the equation by 3

3y = -x + 21

x + 3y = 21

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prisoha [69]

Answer:

x= -1/2 = -0.500

x=4

Step-by-step explanation:

2x^2-7x-4=0

2x^2-8x+1x-4=0

2x(x-4)+1(x-4)=0

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checking the solution

2(-1/2)^2-7(-1/2)=4..... 4=4

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3 years ago

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mina [271]

Answer:

The most helpful representation would be option C.

Step-by-step explanation:

The horizontal distance traveled corresponds to one of the roots of the quadratic equation.

h(x) = -0.01(x-150)(x+4)

In this case, option c presents the roots of the polynomial, which answers are

x = -4

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Since we are talking about positive distances, the first option gets discarded.

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4 years ago

The population of a town is 14,000 and is decreasing at a rate of 1.5% each year. Write an exponential decay equation to find th

sergejj [24]

Answer: the population after 10 years is 12036

Step-by-step explanation:

We would apply the formula for exponential growth which is expressed as

A = P(1 - r)^ t

Where

A represents the population after t years.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

P = 14000

r = 1.5% = 1.5/100 = 0.015

t = 10 years

Therefore, the exponential decay equation to find the population of the town after 10 years is

A = 14000(1 - 0.015)^10

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3 years ago

What is 56 1/4 as a fraction in simplest form?

Luba_88 [7]

We have to simplify $56 \frac{1}{4}$ %

This is a mixed fraction, with 56 as the whole number part and $\frac{1}{4}$ as the fractional part

Such a fraction can be simplified as:

Denominator of simplified fraction = Denominator of mixed fraction

and Numerator of simplified fraction = (Denominator of mixed fraction × Whole number) + (Numerator of simplified fraction)

⇒ Denominator of simplified fraction = 4

and Numerator of simplified fraction = (4 × 56) + (1)

⇒ Numerator of simplified fraction = 225

Hence, the mixed fraction in its simplest form is $\frac{225}{4}$

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