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2 years ago

Select the correct answer.

Mathematics

1 answer:

Hitman42 [59]2 years ago

8 0

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the function is not given. So, I will make an assumption.

A quadratic function is represented as:

$f(x) = ax^2 + bx + c$

If $a > 0$ , then the function has a minimum x value

E.g. $f(x) = 4x^2 - 5x + 8$ ------ $4 > 0$

Else, then the function has a maximum x value

E.g. $f(x)= -4x^2 -5x + 8$ ---- $-4 < 0$

The maximum or minimum x value is calculated using:

$x = -\frac{b}{2a}$

For instance, the maximum of $f(x)= -4x^2 -5x + 8$ is:

$x = -\frac{-5}{2*-4}$

$x = -\frac{5}{8}$

So, the maximum of the function is:

$f(x)= -4x^2 -5x + 8$

$f(-\frac{5}{8}) = -4 * (-\frac{5}{8})^2 - 5 *(-\frac{5}{8}) +8$

$f(-\frac{5}{8}) = 9.5625$

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frosja888 [35]

Answer:

Step-by-step explanation:

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3 years ago

A patrolman spends 25% every day completing paperwork. The patrolman’s shift each day is 8 hours. How much of his time does he s

fredd [130]

Assuming the man works 8 hours straight without breaks:

25% is the same as 1/4 of something.

So, we just have to figure out what 1/4 (one quarter) of 8 equals.

You can think of it as a pizza cut into 8 slices. One slice is equivalent to one hour for the patrolman.

If we take away 1/2 (half) of the pizza, we have 4 slices, right? Since we start with 8 slices, half of that equals 4 slices. In other words, 50% (half) of the pizza = 4 slices.

Now, 25% (one quarter) of the pizza will equal half of what is left:

If we know that 50%=4 slices (or 4 hours), then 25% must be 2 slices (or 2 hours).

That's it! 25% of 8 hours = 2 hours.

***So, the patrolman spends 2 hours each day completing paperwork.***

Lets check our work:
We know 8 hours (or 8 slices)= 100%
(We know this because
8 slices = 1 whole pizza, or 100% of a pizza. Similarly,
8 hours = 1 whole shift or 100% of the man's shift ).

So

25% + 25% + 25% + 25% = 100%

If 100% of the mans shift = 8 hours:

2+2+2+2 = 8

It checks out!

Hope this helps!

4 0

3 years ago

Mallorie has $5 in her wallet.if this is 10% of her monthly allowance what is her monthly allowance

marta [7]

5=.1*x
divide both side by .1
5/.1=x
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3 years ago

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Which of the following is the linear parent function?A.F(x) = 2xB.F(x) = |x|C.F(x) = x2D.F(x) = x

Daniel [21]

The linear parent function is f(x)=x

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3 years ago

Find all possible values of α+

const2013 [10]

Answer:

$\rm\displaystyle 0,\pm\pi$

Step-by-step explanation:

please note that to find but α+β+γ in other words the sum of α,β and γ not α,β and γ individually so it's not an equation

===========================

we want to find all possible values of α+β+γ when tanα+tanβ+tanγ = tanαtanβtanγ to do so we can use algebra and trigonometric skills first

cancel tanγ from both sides which yields:

$\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \alpha ) \tan( \beta ) \tan( \gamma ) - \tan( \gamma )$

factor out tanγ:

$\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \gamma ) (\tan( \alpha ) \tan( \beta ) - 1)$

divide both sides by tanαtanβ-1 and that yields:

$\rm\displaystyle \tan( \gamma ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{ \tan( \alpha ) \tan( \beta ) - 1}$

multiply both numerator and denominator by-1 which yields:

$\rm\displaystyle \tan( \gamma ) = - \bigg(\frac{ \tan( \alpha ) + \tan( \beta ) }{ 1 - \tan( \alpha ) \tan( \beta ) } \bigg)$

recall angle sum indentity of tan:

$\rm\displaystyle \tan( \gamma ) = - \tan( \alpha + \beta )$

let α+β be t and transform:

$\rm\displaystyle \tan( \gamma ) = - \tan( t)$

remember that tan(t)=tan(t±kπ) so

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm k\pi )$

therefore when k is 1 we obtain:

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm \pi )$

remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus

$\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm \pi )$

recall that if we have common trigonometric function in both sides then the angle must equal which yields:

$\rm\displaystyle \gamma = - \alpha - \beta \pm \pi$

isolate -α-β to left hand side and change its sign:

$\rm\displaystyle \alpha + \beta + \gamma = \boxed{ \pm \pi }$

when is 0:

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta \pm 0 )$

likewise by Opposite Angle Identity we obtain:

$\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm 0 )$

recall that if we have common trigonometric function in both sides then the angle must equal therefore:

$\rm\displaystyle \gamma = - \alpha - \beta \pm 0$

isolate -α-β to left hand side and change its sign:

$\rm\displaystyle \alpha + \beta + \gamma = \boxed{ 0 }$

and we're done!

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3 years ago

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