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1 year ago

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Mathematics

1 answer:

PIT_PIT [208]1 year ago

5 0

The solution to the equation is p = 1/3 and q = undefined

<h3>How to solve the equation?</h3>

The equation is given as:

p^2 - 2qp + 1/q = (p - 1/3)

The best way to solve the above equation is by the use of a graphing calculator i.e. graphically

However, it can be solved algebraically too (to some extent)

Recall that the equation is given as:

p^2 - 2qp + 1/q = (p - 1/3)

Split the equation

So, we have

p^2 - 2qp + 1/q = 0

p - 1/3 = 0

Solve for p in p - 1/3 = 0

p = 1/3

Substitute p = 1/3 in p^2 - 2qp + 1/q = 0

So, we have

(1/3)^2 - 2q(1/3) + 1/q = 0

This gives

1/9 - 2/3q + 1/q = 0

This gives

2/3q + 1/q = -1/9

Multiply though by q

So, we have

2/3q^2 + 1 = -1/9q

Multiply through by 9

6q^2 + 9 = -q

So, we have

6q^2 + q + 9 = 0

Using the graphing calculator, we have

q = undefined

Hence. the solution to the equation is p = 1/3 and q = undefined

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Convert the following quantities to the indicated units. 57 miles per hour to meters per second

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Answer:

25.481

Step-by-step explanation:

divide by 2.237

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3 years ago

Solve - 4x2 - 4x - 9 = 0, stating your solutions in the form a = bi. Someone please answer!!

PIT_PIT [208]

Answer:

$x=-0.5 \pm -i\sqrt{2}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Standard Form: ax² + bx + c = 0
Quadratic Formula: $x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

Algebra II

Imaginary Roots: √-1 = i
Standard Form: a + bi

Step-by-step explanation:

Step 1: Define

-4x² - 4x - 9 = 0

a = -4

b = -4

c = -9

Step 2: Find roots

Substitute: $x=\frac{4\pm\sqrt{(-4)^2-4(-4)(-9)} }{2(-4)}$
Exponents: $x=\frac{4\pm\sqrt{16-4(-4)(-9)} }{2(-4)}$
Multiply: $x=\frac{4\pm\sqrt{16-144} }{-8}$
Subtract: $x=\frac{4\pm\sqrt{-128} }{-8}$
Factor: $x=\frac{4\pm \sqrt{-1} \cdot \sqrt{128} }{-8}$
Simplify: $x=\frac{4\pm 8i\sqrt{2} }{-8}$
Factor: $x=\frac{4(1\pm 2i\sqrt{2}) }{-8}$
Divide: $x=\frac{1\pm 2i\sqrt{2}}{-2}$
Expand: $x=\frac{-1}{2} \pm \frac{-2i\sqrt{2} }{2}$
Simplify: $x=\frac{-1}{2} \pm -i\sqrt{2}$
Evaluate: $x=-0.5 \pm -i\sqrt{2}$

6 0

3 years ago

The figure shows two similar triangles on a coordinate grid: A coordinate grid is shown from positive 6 to negative 6 on the x-a

SIZIF [17.4K]

From what I know, figure ABC has gotten smaller so you wouldn't use either options that suggests a dilation of 3, because that would mean it got bigger. (But please correct me if I'm wrong.) Also, if you look at the little unit square measurements on the graph, looking at figure ABC, C is 6 units from B, while in figure A'B'C', C' is 2 units from B', which 6÷2=3 meaning that A'B'C' would most likely be a third of its size.

Next the figure is being mirrored over the y-axis which is the vertical line going up and down.

So the answer would be the option that says

"Dilation by a scale factor of 1 over 3 followed by a reflection about the y-axis"

I hope that it's right, because I haven't practiced this in a while, and I hope this made some sense.

5 0

2 years ago

Write in 8 over 74 in simpliest form

choli [55]

4/37 is the answer to your problem

4 0

3 years ago

Read 2 more answers

How many three digit numbers have digits whose sum is greater than 2?

LenaWriter [7]

Answer:

896

Step-by-step explanation:

Let's talk first about how many 3 digit numbers there are. The first 3 digit number is 100 and the last is 999. So there are 999-100+1 numbers that are 3 digits long. That simplifies to 900.

Now let's find how many of those have a sum for the digits being 1, then 2 ? Then take that sum away from the 900 to see how many 3 digit numbers have the sum of their digits being more than 2.

3 digit numbers with sum of 1:

The first and only number is 100 since 1+0+0=1.

We can't include 010 or 001 because these aren't really three digits long.

3 digit numbers with sum of 2:

The first number is 101 since 1+0+1=2.

The second number is 110 since 1+1+0=2.

The third number is 200 since 2+0+0=2.

That's the last of those. We could only use 0,1, and 2 here.... Anything with a 3 in it would give us something larger than or equal to 3.

So there are 900-1-3 numbers who are 3 digits long and whose sum of digits is greater than 2.

This answer simplifies to 896.

3 0

3 years ago

Read 2 more answers

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