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4 years ago

HELP PLS What is the slope of the line: -3 -1/3 1/3 3

Mathematics

1 answer:

nadezda [96]4 years ago

6 0

Answer:

Step-by-step explanation:

All you have to do is take that bottom dot and count how many the rise is ----3 and how many the run is -----1.

Therefore, 3/1 is 3

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you are given a fraction in the simplest form. The numerator is not zero. When you write the fraction as a decimal, it is a repe

Tems11 [23]

Answer:

Step-by-step explanation:Let - be a fraction in simplest form, b # 0, written

as a repeating decimal when in decimal form.

Since the only numbers which can be factors of the

denominators lead to a terminating decimal are 1, 2

and 5 (including rising to powers) and combinations

of them, it means that if the denominator has at

least one of the other numbers at the denominator,

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Among the numbers from 1 to 10, the presence of

any of these numbers in the denominator will lead

to a repeating decimal:

3 0

3 years ago

Find an equation of the line having the given slope and containing the given point.

saul85 [17]

Answer:

$y = 4x - 12$

Step-by-step explanation:

The equation of a line has the following format:

$y = mx + b$

In which m is the slope and b is the y-intercept(value of x when y = 0).

In this question:

Slope 4, which means that $m = 4$ .

$y = 4x + b$

Contains point (1,-8).

This means that when $x = 1, y = -8$ . We replace this into the equation to find b. So

$y = 4x + b$

$-8 = 4(1) + b$

$b = -12$

$y = 4x - 12$

4 0

3 years ago

What is the answer to 9-x over 5

Kaylis [27]

Answer:

x = - 6

Step-by-step explanation:

Given

$\frac{9-x}{5}$ = 3

Multiply both sides by 5 to clear the fraction

9 - x = 15 ( subtract 9 from both sides )

- x = 6 ( multiply both sides by - 1 )

x = - 6

7 0

4 years ago

Whenever he visits Dayton, Quincy has to drive 12 miles due north from home. Whenever he

777dan777 [17]

Answer: 20 miles

Step-by-step explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the Pythagorean Theorem:

x^2 = a^2 + b^2

Where x is the hypotenuse of the triangle (in this case the distance between Dayton and Belleville) and a and b are the other sides.

Replacing with the values given:

x^2 = 16^2 + 12^2

x^2 = 256+144

x^2 = 400

x = √400

x = 20 miles

Feel free to ask for more if needed or if you did not understand something.

4 0

3 years ago

Consider the following differential equation. x^2y' + xy = 3 (a) Show that every member of the family of functions y = (3ln(x) +

Veronika [31]

Answer:

Verified

$y(x) = \frac{3Ln(x) + 3}{x}$

$y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{x}$

Step-by-step explanation:

Question:-

- We are given the following non-homogeneous ODE as follows:

$x^2y' +xy = 3$

- A general solution to the above ODE is also given as:

$y = \frac{3Ln(x) + C }{x}$

- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.

Solution:-

- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.

$y' = \frac{\frac{d}{dx}( 3Ln(x) + C ) . x - ( 3Ln(x) + C ) . \frac{d}{dx} (x) }{x^2} \\\\y' = \frac{\frac{3}{x}.x - ( 3Ln(x) + C ).(1)}{x^2} \\\\y' = - \frac{3Ln(x) + C - 3}{x^2}$

- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:

$-\frac{3Ln(x) + C - 3}{x^2}.x^2 + \frac{3Ln(x) + C}{x}.x = 3\\\\-3Ln(x) - C + 3 + 3Ln(x) + C= 3\\\\3 = 3$

- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.

- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

$y( 1 ) = \frac{3Ln(1) + C }{1} = 3\\\\0 + C = 3, C = 3$

- Therefore, the complete solution to the given ODE can be expressed as:

$y ( x ) = \frac{3Ln(x) + 3 }{x}$

- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

$y(3) = \frac{3Ln(3) + C}{3} = 1\\\\y(3) = 3Ln(3) + C = 3\\\\C = 3 - 3Ln(3)$

- Therefore, the complete solution to the given ODE can be expressed as:

$y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{y}$

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6 0

3 years ago