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3 years ago

Calculate the distance between the points (-1, 3) and (4, -1).

Mathematics

2 answers:

BigorU [14]3 years ago

5 0

The distance between those two points is 41 and in decimal form to the nearest tenth, that's 6.4

Explanation:

Use the distance formula: √(x2 - x1)² + (y2 - y1)²

Then we plug in our x's and y's:

√(4 - (-1))² + ((-1) - 3)²

Then you simplify:

√(5)² + (-4)² = √25 + 16

√41 (And if you need to, you can put this into decimal form.)

Tamiku [17]3 years ago

3 0

Answer:

6.4

Step-by-step explanation:

Use the distance formula and then fill in points for the variables.

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Find all x-coordinates of points (x,y) on the curve y = [(x - 5 )^6]/(x - 6 )^8

Genrish500 [490]

Answer:

Step-by-step explanation:

To obtain all coordinates of points (x,y) on the curve y = [(x - 5 )^6]/(x - 6 )^8, we deduce the value of X for which y is undefined as thus,

(x - 6 )^8 = 0

: (x - 6 ) = 0 : X=6

Therefore, all x-coordinates of points (x,y) on the curve are values of X < 6

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3 years ago

The polynomial function y = x3 -3x2 + 16x - 48 has only one non-repeated x-intercept. What do you know about the complex zeros o

earnstyle [38]

• First way to solve:
We'll manipulate the expression of the equation:

$y=x^3-3x^2+16x-48\\\\ y=x^2(x-3)+16(x-3)\\\\ y=(x-3)(x^2+16)$

If we have y=0:

$x-3=0~~~or~~~x^2+16=0\\\\ x=3~~~or~~~x^2=-16\\\\ x=3~~~or~~~x=\pm\sqrt{-16}\\\\ x=3~~~or~~~x=\pm4i$

Then, the function has one real zero (x=3) and two imaginary zeros (4i and -4i).

Answer: B

• Second way to solve:

The degree of the function is 3. So, the function has 3 complex zeros.

Since the coefficients of the function are reals, the imaginary roots are in a even number (a imaginary number and its conjugated)

The function "has only one non-repeated x-intercept", then there is only one real zero.

The number of zeros is 3 and there is 1 real zero. So, there are 2 imaginary zeros.

Answer: B.

3 0

3 years ago

-2(3x+5y)=10 in slope intercept form

lesantik [10]

Answer:

The equation in the slope-intercept form is:

y = -3/5x - 1

Step-by-step explanation:

Given the equation

$-2(3x+5y)=10$

We know that the slope-intercept form of a line equation is

$y = mx+b$

where

m is the slope

b is the y-intercept

Writing the equation in slope-intercept form

-2(3x+5y)=10

-6x -10y = 10

Add 6x to both sides

-6x -10y + 6x = 10 + 6x

-10y = 10 + 6x

Divide both sides by -10

-10y / -10 = (10 + 6x) / -10

y = -3/5x - 1

Thus, the equation in the slope-intercept form is:

y = -3/5x - 1

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2 years ago

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Mamont248 [21]

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Answer:

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3 years ago