Write AN EQUATION of the line that passes through the given points (-1,4) and (2,-5)

1 answer:

7 0

Answer: y = -3x + 1

step-by-step process
find the slope first using (y-y)/(x-x)
(4-(-5))/(-1-2) = 9/(-3)
m = -3

then use one of the points to find the y-intercept by putting it in y=mx+b, substituting m with -3 (aka the slope) as well
4 = -3(-1) + b
4 = 3 + b
4 - 3 = 3 + b - 3
1 = b

therefore, the equation for the line is: y=-3x+1

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The probability of a train arriving on time and leaving on time is 0.8. The probability of the same train arriving on time is 0.

lys-0071 [83]

To help you with this topic, I would suggest you revise probability trees.

P(train arriving) = 0.8
P(train arriving on time) = 0.84
P(train arriving late) = 0.86

0.8 x 0.86 = 0.688

Answer: 0.688

Hope it helped :)

8 0

3 years ago

Read 2 more answers

The volume of a sphere is decreasing at a constant rate of 116 cubic centimeters per second. At the instant when the volume of t

nirvana33 [79]

Answer:

$\frac{dr}{dt} = -1.325 \ cm/s$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Calculus

Derivatives

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Taking Derivatives with respect to time

Step-by-step explanation:

Step 1: Define

Given:

$V = \frac{4}{3} \pi r^3$

$\frac{dV}{dt} = -116 \ cm^3/s$

$V = 77 \ cm^3$

Step 2: Solve for r

Substitute: $77 = \frac{4}{3} \pi r^3$
Isolate r term: $\frac{77}{\frac{4}{3} \pi} = r^3$
Isolate r: $\sqrt[3]{\frac{77}{\frac{4}{3} \pi}} = r$
Evaluate: $2.63917 = r$
Rewrite: $r = 2.63917 \ cm$

Step 3: Differentiate

Differentiate the Volume Formula with respect to time t.

Define: $V = \frac{4}{3} \pi r^3$
Differentiate [Basic Power Rule]: $\frac{dV}{dt} = \frac{4}{3} \pi \cdot 3 \cdot r^{3-1} \cdot \frac{dr}{dt}$
Simplify: $\frac{dV}{dt} = 4 \pi r^2 \cdot \frac{dr}{dt}$

Step 4: Find radius rate

Substitute in variables: $-116 \ cm^3/sec = 4 \pi (2.63917 \ cm)^2 \cdot \frac{dr}{dt}$
Isolate dr/dt rate: $\frac{-116 \ cm^3/s}{4 \pi (2.63917 \ cm)^2} = \frac{dr}{dt}$
Evaluate: $-1.3253 \ cm/s = \frac{dr}{dt}$
Rewrite: $\frac{dr}{dt} = -1.3253 \ cm/s$
Round: $\frac{dr}{dt} = -1.325 \ cm/s$