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4 years ago

Hence explain how you know that x^2-8x+20 is always positive

Mathematics

2 answers:

Tasya [4]4 years ago

6 0

If you complete the square you get

${(x - 4) }^{2} + 4$

and as any number squared is positive and 4 is positive, the result must be positive

Leya [2.2K]4 years ago

6 0

Answer:

x^2-8x+20=x^2-2*x*4+4^2+4=(x-4)^2+4

so (x-4)^2 is positive or zero (but +4 is always positive)

Step-by-step explanation:

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Valentin [98]

9514 1404 393

Answer:

A. -1 ≤ x ≤ 3

Step-by-step explanation:

The range is the horizontal extent of the graph--the set of x-values for which the function is defined. Here, the graph extends from x = -1 to x = 3, with both end points included. The range is ...

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3 years ago

Solve the formula for the indicated variable. C=2 (3.14r), for r

JulijaS [17]

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3 years ago

Let g(x)= 2x and h(x)= x^2+4 evaluate (h•g)(-5)

Nataliya [291]

Answer:

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4 years ago

A bacterial culture starts with 3000 bacteria and increases to 48,000 after 3 hours, find the doubling time:

STatiana [176]

4

3000 times 2 = 6000
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5 0

3 years ago

Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed b

klemol [59]

Imagine right triangle PHF, where P - park, H - home and F - football field, then PH, PF are legs and HF is hypotenuse . Denote point L to be library. You know that point L lies on the segment FH and FL=8, LH=2. Also you know that PL is an altitude to the hypotenuse.

Use the property of altitude drawn from the vertex of right angle to the hypotenuse (the length of the altitude is geometrical mean between legs' projections onto hypotenuse):

$PL=\sqrt{HL\cdot LF},\\ PL=\sqrt{2\cdot 8}=\sqrt{16} =4$ mi.

This means that the distance between park and libriry is 4 miles.

Consider right triangle PLF ( angle L is right angle and PF - hypotenuse). By the Pythagorean theorem,

$PF^2=PL^2+LF^2,\\ PF^2=4^2+8^2,\\ PF^2=16+64=80,\\ PF=\sqrt{80} =4\sqrt{5}$ mi. The distance between park and football field is $4\sqrt{5}$ miles.

Answer: the distance between park and libriry is 4 miles and the distance between park and football field is $4\sqrt{5}$ miles.

6 0

3 years ago