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3 years ago

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At the Bristol County Fair, there is a baking contest that awards a first prize and a second prize to the best pies baked. There

are 56 entrants to the contest this year.
In order to determine how many ways there are to award prizes, you should use a __[blank 1]__. There are __[blank 2]__ ways to award the prizes.

Enter either the word permutation or the word combination for blank 1, and then enter the number that correctly fills in blank 2.

1 answer:

4vir4ik [10]3 years ago

3 0

Answer:

1: Permutation

2: 3080

Step-by-step explanation:

As order matters, (first place as opposed to second place) this must be a permutation.

For first place, there are 56 different contestants that could win it, while once first place is selected, there are only 55 to get second. This means that

56*55=3080

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If a polynomial has one root in the form a-V6, it has a second root in the<br> form of a _Vb.

e-lub [12.9K]

Answer:

radical form, they occur as two conjugates.

That is,

The conjugate of (a + √b) is (a - √b) and vice versa.

To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.

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2 years ago

It took Everly 55 minutes to run a 10-kilometer race last weekend. If you know that 1 kilometer equals 0.621 mile, how many minu

m_a_m_a [10]

55/6.21 = x/1....55 mins to 6.21 miles = x min to 1 mile
cross multiply
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3 0

3 years ago

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5-2(2x - 3) = 12<br><br> Cual es el resultado de x?

postnew [5]

Answer:

<h2> $x = - \frac{1}{4}$ </h2>

Step-by-step explanation:

5-2(2x - 3) = 12

<u>Expanda los términos en el corchete</u>

Eso es

5 - 4x + 6 = 12

<u>Agrupar términos similares</u>

Envíe las constantes al lado derecho de la ecuación y aquellas con variables al lado izquierdo

Tenemos

- 4x = 12 - 5 - 6

- 4x = 1

Divide ambos lados entre - 4

<h3> $- \frac{4x}{ - 4} = - \frac{1 }{4}$ </h3>

Tenemos la respuesta final como

<h3> $x = - \frac{1}{4}$ </h3>

Espero que esto te ayude

8 0

3 years ago

Suppose a, b denotes of the quadratic polynomial x² + 20x - 2022 & c, d are roots of x² - 20x + 2022 then the value of ac(a

Alja [10]

<h3><u>Correct Question :- </u></h3>

$\sf\:a,b \: are \: the \: roots \: of \: {x}^{2} + 20x - 2020 = 0 \: and \: \\ \sf \: c,d \: are \: the \: roots \: of \: {x}^{2} - 20x + 2020 = 0 \: then \:$

$\sf \: ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d) =$

(a) 0

(b) 8000

(c) 8080

(d) 16000

$\large\underline{\sf{Solution-}}$

Given that

$\red{\rm :\longmapsto\:a,b \: are \: the \: roots \: of \: {x}^{2} + 20x - 2020 = 0}$

We know

$\boxed{\red{\sf Product\ of\ the\ zeroes=\frac{Constant}{coefficient\ of\ x^{2}}}}$

$\rm \implies\:ab = \dfrac{ - 2020}{1} = - 2020$

And

$\boxed{\red{\sf Sum\ of\ the\ zeroes=\frac{-coefficient\ of\ x}{coefficient\ of\ x^{2}}}}$

$\rm \implies\:a + b = - \dfrac{20}{1} = - 20$

Also, given that

$\red{\rm :\longmapsto\:c,d \: are \: the \: roots \: of \: {x}^{2} - 20x + 2020 = 0}$

$\rm \implies\:c + d = - \dfrac{( - 20)}{1} = 20$

and

$\rm \implies\:cd = \dfrac{2020}{1} = 2020$

Now, Consider

$\sf \: ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d)$

$\sf \: = {ca}^{2} - {ac}^{2} + {da}^{2} - {ad}^{2} + {cb}^{2} - {bc}^{2} + {db}^{2} - {bd}^{2}$

$\sf \: = {a}^{2}(c + d) + {b}^{2}(c + d) - {c}^{2}(a + b) - {d}^{2}(a + b)$

$\sf \: = (c + d)( {a}^{2} + {b}^{2}) - (a + b)( {c}^{2} + {d}^{2})$

$\sf \: = 20( {a}^{2} + {b}^{2}) + 20( {c}^{2} + {d}^{2})$

$\sf \: = 20\bigg[ {a}^{2} + {b}^{2} + {c}^{2} + {d}^{2}\bigg]$

We know,

$\boxed{\tt{ { \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta) }^{2} - 2 \alpha \beta \: }}$

So, using this, we get

$\sf \: = 20\bigg[ {(a + b)}^{2} - 2ab + {(c + d)}^{2} - 2cd\bigg]$

$\sf \: = 20\bigg[ {( - 20)}^{2} + 2(2020) + {(20)}^{2} - 2(2020)\bigg]$

$\sf \: = 20\bigg[ 400 + 400\bigg]$

$\sf \: = 20\bigg[ 800\bigg]$

$\sf \: = 16000$

Hence,

$\boxed{\tt{ \sf \: ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d) = 16000}}$

<em>So, option (d) is correct.</em>

4 0

2 years ago

Someone please answer this!!

OleMash [197]

Here's the solution,

The given triangle is a <em><u>Right</u></em><em><u> </u></em><em><u>angled</u></em><em><u> </u></em><em><u>triangle</u></em><em><u>,</u></em>

So, by applying <em><u>Pythagoras</u></em><em><u> </u></em><em><u>theorem</u></em><em><u>:</u></em>

=》

${c}^{2} = {4}^{2} + 3 {}^{2}$

=》

${c}^{2} = 16 + 9$

=》

${c}^{2} = 25$

=》

$c = \sqrt{25}$

=》

$c = 5$

value of c = 5 miles

6 0

3 years ago

Read 2 more answers