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3 years ago

What is the midpoint and how do I find it?

Mathematics

1 answer:

Troyanec [42]3 years ago

8 0

Answer:

(0.5,0.5)

Step-by-step explanation:

use the midpoint formula x1+x2/2 and y1+y2/2

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Paraphin [41]

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3 years ago

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ELEN [110]

Answer:

Step-by-step explanation:

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3 years ago

Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29

hram777 [196]

Answer:

$\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }$

Step-by-step explanation:

Hello,

I assume that we are working in $\mathbb{C}$ , otherwise there is only one zero which is 1. Please consider the following.

First of all, we can notice that 1 is a trivial solution as

$p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0$

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

$p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b$

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

$\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }$

Now, we need to find the zeroes of the second factor, meaning finding x so that:

$x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4} \\ \\ x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ (x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\x-2=\pm 5i \ \text{ add 2 } \\ \\ x = 2+5i \ \text{ or } \ x = 2-5i$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

5 0

3 years ago

Question 1 of 10

Kobotan [32]

Answer:

A. x + 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Terms/Coefficients
Factoring

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \frac{x^2 - 25}{x - 5}$

Step 2: Simplify

Factor: $\displaystyle \frac{(x - 5)(x + 5)}{x - 5}$
Divide: $\displaystyle x + 5$

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3 years ago

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Brad has two lengths of copper pipe to fit together. one has a length of 2 5/12 feet and the other has a length of 3 7/12 feet.

elena-s [515]

To find all of the feet of pipe that Brad has, you add both of the lengths of the pipes together. So 2 5/12+3 7/12. Add the numbers together first, 5. Then add the fractions, 5/12+7/12=1. So add 5 and 1 and you get 6 feet of pipe. Hope this helps.

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3 years ago