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3 years ago

Write an equation of the line that passes through (3, 1) and (0, 10). y

Mathematics

1 answer:

const2013 [10]3 years ago

7 0

Answer:

Step-by-step explanation:

(10 - 1)/(0 - 3) = -9/3 = -3

y - 1 = -3(x -3)

y - 1 = -3x + 9

y = -3x + 10

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For the equation y=5x+4, determine the value of y when x=−1.

Furkat [3]

Step-by-step explanation:

y = 5x + 4, x = -1

y = 5(-1) + 4

y = -5 + 4

y = -1

5 0

3 years ago

Use the appropriate substitutions to write down the first four nonzero terms of the Maclaurin series for the binomial (1+3x)^(-1

PolarNik [594]

Answer:

First term=1

Second term=-x

Third term= $2x^2$

Fourth term = $-\frac{28}{3!}x^3$

Step-by-step explanation:

We are given that function

$f(x)=(1+3x)^{-1/3}$

We have to find the first four non zero terms of the Maclaurin series for the binomial.

Maclaurin series of function f(x) is given by

$f(x)=f(0)+f'(0)x+\frac{1}{2!}f''(0)x^2+\frac{1}{3!}f'''(0)x^3+....$

$f(0)=(1+3x)^{\frac{-1}{3}}=1$

$f'(x)=-\frac{1}{3}(1+3x)^{-\frac{4}{3}}(3)=-(1+3x)^{-\frac{4}{3}}$

$f'(0)=-1$

$f''(x)=\frac{4}{3}\times 3 (1+3x)^{-\frac{7}{3}}$

$f''(0)=4$

$f'''(x)=-4\times \frac{7}{3}\times 3(1+3x)^{-\frac{10}{3}}$

$f'''(0)=-28$

Substitute the values we get

$(1+3x)^{-\frac{1}{3}}=1-x+\frac{4}{2!}x^2+\frac{-28}{3!}x^3+...$

$(1+3x)^{-\frac{1}{3}}=1-x+2x^2+\frac{-28}{3!}x^3+...$

First term=1

Second term=-x

Third term= $2x^2$

Fourth term = $-\frac{28}{3!}x^3$

5 0

3 years ago

Solve the system of equations using the linear combination method. {4x−3y=12;7x−3y=3

Lemur [1.5K]

<span>4x−3y=12
7x−3y=3 Important: you have two -3y terms. Mult one eqn by -1 to
obtain +3y, and then add the 2 equations together:

4x - 3y = 12
-7x+3y = -3
----------------
-3x = 9, so x = -3. Subst. -3 for x in the first original equation to find y:

4(-3) - 3y = 12, or -3y = 24. Then y = -8.

Solution is (-3, -8).

It's important that you check this answer by subst. (-3, -8) back into either one of the original equations.

</span>

5 0

3 years ago

Solve each one step equation, use your answers to navigate through the maze. Show your work on a separate page

mixas84 [53]

Answer:

Step-by-step explanation:

I think thats how its done, sorry for messy handwriting

5 0

3 years ago

A jar contains 8 red marbles numbered 1 to 8 and 12 blue marbles numbered 1 to 12. It alse has 5 white marbles numbered 100, 200

Inga [223]

Answer:

Probability of red marbles = 8/25

Step-by-step explanation:

Complete question

A jar contains 8 red marbles numbered 1 to 8 and 12 blue marbles numbered 1 to 12. It alse has 5 white marbles numbered 100, 200, 300, 400, and 500. A marble is drawn at random from the jar. Find the probability of the given event.

a) The marble is red

Total number of marbles = 8+12+5 = 25

Probability of red marbles = total number of red marbles/Total marbles

Probability of red marbles = 8/25

5 0

3 years ago