Help I need to know if each statement is always, sometimes, or never true

Mathematics

2 answers:

Harman [31]3 years ago

8 0

Always
Sometimes
Always
Always

suter [353]3 years ago

5 0

Never
Always
Sometimes - for example sr(12) / sr(3) = sr(12 / 3) = sr(4) = 2
Always

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Does the function f(x) = 2x^2− 6x + 9 have a minimum or a maximum? Identify its value.

exis [7]

Answer:

minimum value of function is $\frac{45}{8}$ .

Step-by-step explanation:

Given function represents a parabola.

Now, here coefficient of $x^{2}$ is positive , so the parabola will be facing upwards and thus the function will be having a minimum.

Now, as we know that minimum value of a parabolic function occurs at

x = $\frac{-b}{4a}$ .

Where , b represents the coefficient of x and a represents the coefficient of $x^{2}$ .

here, a = 2 , b = -6

Thus $\frac{-b}{4a}$ = $\frac{6}{8}$

= $\frac{3}{4}$

So, at x = $\frac{3}{4}$ minimum value will occur and which equals

y = 2× $\frac{9}{16}$ - $\frac{18}{4}$ + 9 = $\frac{45}{8}$ .

Thus , minimum value of function is $\frac{45}{8}$ .

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2 years ago

3x+2y=0 x-5y=17 Solving system using elimination

horsena [70]

(2,-3) is the answer

6 0

2 years ago

Express the area of the triangle shown below in terms of b and θ only.

Paul [167]

Given a right triangle with base, b and height, h with the angle opposide side h as θ.

The area of a triangle is given by
$A= \frac{1}{2} bh$

But,
$\tan\theta= \frac{h}{b} \\ \\ \Rightarrow h=b\tan\theta$

Therefore, the area of the triangle in terms of b and θ only is given by
$A= \frac{1}{2} b(b\tan\theta)= \frac{1}{2} b^2\tan\theta$