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Semenov [28]
3 years ago
8

Find the slope of the given points (6, -10) and (-15, 15). Show your work.

Mathematics
1 answer:
charle [14.2K]3 years ago
6 0

Answer:

Step-by-step explanation:

The slope of a line between two points can be calculated by dividing the difference of y values by the difference of x values

in this case

m = \frac{y_2-y_1}{x_2-x_1} = \frac{15-(-10)}{-15-6} = \frac{25}{-21} = \frac{-25}{21}

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For the polynomial function ƒ(x) = −x6 + 3x4 + 4x2, find the zeros. Then determine the multiplicity at each zero and state wheth
murzikaleks [220]

There is a multiple zero at 0 (which means that it touches there), and there are single zeros at -2 and 2 (which means that they cross). There is also 2 imaginary zeros at i and -i.


You can find this by factoring. Start by pulling out the greatest common factor, which in this case is -x^2.


-x^6 + 3x^4 + 4x^2

-x^2(x^4 - 3x^2 - 4)


Now we can factor the inside of the parenthesis. You do this by finding factors of the last number that add up to the middle number.


-x^2(x^4 - 3x^2 - 4)

-x^2(x^2 - 4)(x^2 + 1)


Now we can use the factors of two perfect squares rule to factor the middle parenthesis.


-x^2(x^2 - 4)(x^2 + 1)

-x^2(x - 2)(x + 2)(x^2 + 1)


We would also want to split the term in the front.


-x^2(x - 2)(x + 2)(x^2 + 1)

(x)(-x)(x - 2)(x + 2)(x^2 + 1)


Now we would set each portion equal to 0 and solve.


First root

x = 0 ---> no work needed


Second root

-x = 0 ---> divide by -1

x = 0


Third root

x - 2 = 0

x = 2


Forth root

x + 2 = 0

x = -2


Fifth and Sixth roots

x^2 + 1 = 0

x^2 = -1

x = +/- \sqrt{-1}

x = +/- i

7 0
3 years ago
Which reflection rule, if any, can be used to prove that rectangle A(-8, -3), B(-2,-3), C (-2,-6), D(-8,-6) and rectangle A'(8.-
Zina [86]

Answer:

d

Step-by-step explanation:

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3 years ago
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Vanyuwa [196]

Step-by-step explanation:

Go 2.5 units to the right from the origin (0,0) for your x coordinate

Go 2.5 units down from the origin (0,0) for your y coordinate

Where the lines meet is your point.

7 0
3 years ago
How can you use a compatible number to estimate a quotient when dividing a decimal by a whole number?
8090 [49]

Answer: just follow these simple steps!

Step-by-step explanation:

1. Estimate the quotient.

2. Perform the division. Remember to place a zero in the quotient when the divisor is larger than the dividend. ...

3. Compare your estimate with your quotient to verify that the answer makes sense.

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3 years ago
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V
Vanyuwa [196]

Answer:5

Step-by-step explanation:

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