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2 years ago

Calculate the distance between the points E=(-2,5) and H=(1, -3) in the coordinate plane.

Mathematics

1 answer:

Furkat [3]2 years ago

5 0

Answer:

The distance between points E and H is 8.49 rounded to the nearest hundreths.

Step-by-step explanation:

You use the distance formula

d=√( (x2-x1)²+(y2-y1)²)

You plug in the points of E and H into the formula where -2 of point E is X1 and 5 of point is is Y1. 1 of point H is X2 and -3 of point H is Y2.

That would look like:

1. d=√( (x2-x1)²+(y2-y1)²)

2. d=√( (1- -2)²+(-3-5)²)

3. d=√( (3)²+(-8)²)

4. d=√ (9+64)

5. √72

Then you'd plug the square root of 72 (√72) into the calculator to get 8.485281374.

If you round it to the nearest hundredth you get 8. 49

Hope you understand. Comment if you don't.

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f(x) is a quadratic function with x-intercepts at (−1, 0) and (−3, 0). If the range of f(x) is [−4, [infinity]) and g(x) = 2x^2

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Answer with Step-by-step explanation:

We are given that function f(x) which is quadratic function.

x -intercept of function f(x) at (-1,0) and (-3,0)

x-Intercept of f means zeroes of f

x=-1 and x=-3

Range of f =[-4, $\infty$ )

g(x)= $2x^2+8x+6=2(x^2+4x+3)$

$g(x)=0$

$2(x^2+4x+3)=0$

$x^2+4x+3=0$

$x^2+3x+x+3=0$

$x(x+3)+1(x+3)=0$

$(x+1)(x+3)=0$

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Therefore, x-intercept of g(x) at (-1,0) and (-3,0).

Substitute x=-2

$g(-2)=2(-2)^2+8(-2)+6=8-16+6=-2$

$g(x)=2(x^2+4x)+6$

$g(x)=2(x^2+2\times x\times 2+4-4)+6=2(x^2+2\times x\times 2+4)-8+6$

$g(x)=2(x+2)^2-2$

By comparing with the equation of parabola

$y=a(x-h)^2+k$

Where vertex=(h,k)

We get vertex of g(x)=(-2,-2)

Range of g(x)=[-2, $\infty$ )

Zeroes of f and g are same .

But range of f and g are different.

Range of f contains -3 and -4 but range of g does not contain -3 and -4.

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Answer:

Step-by-step explanation:

To determine the amount of wrapping paper needed to cover the can, we would determine the total surface area of the cylindrical can. The formula for determining the total surface area of a cylinder is expressed as

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h represents the height of the cylinder.

π is a constant whose value is 3.14

From the information given,

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Radius = diameter/2 = 10/2

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