Which graph shows the solution to the equation f(x)= (x-1)(x+4)

Mathematics

2 answers:

Naya [18.7K]3 years ago

8 0

Answer:

Step-by-step explanation:

We have the function:

$f(x)=(x-1)(x+4)$

This is a quadratic in factored form.

The zeros of our function will be the opposites of our factors.

We have the factors (x-1) and (x+4).

Therefore, the zeros of our function must be at x=1 and x=-4.

Also, notice that the coefficient of our x-variable are both positive.

Therefore, the leading coefficient will also be positive.

So, this means that our graph must curve upwards.

Therefore, our graph must be curving upwards while crossing the points x=1 and x=-4.

So, our answer is D.

mr_godi [17]3 years ago

4 0

Answer:

the firstn one

Step-by-step explanation:

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Twelve round gold medals each with a radius of three inches just fit inside a box with four medals in each of the three rows a r

Anna35 [415]

Answer: The answer is 84 inches.

Step-by-step explanation: It is given that twelve round gold medals fit inside a box where 4 medals are placed in one ray. So, the number of rows in the box is 3.

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Therefore, diameter of each gold medal = 2 × 3 = 6 inches.

The box is obviously in the rectangular form where

$\textup{length} = 6\times 4=24~\textup{inches}\\\textup{and}\\\textup{Breadth}=6\times 3=18~\textup{inches}.$

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6 0

3 years ago

(HMMT Combo 2009) Two jokers are added to a 52 card deck and the entire stack of 54 cards is shuffled randomly. What is the expe

myrzilka [38]

The expected number of cards from the card deck that will be strictly between the two jokers is $\frac{52}{3}$ .

The most popular deck of cards used today is a normal 52-card deck of French-suited playing cards. [a] It is the only standard pack[b] used for playing cards in English-speaking nations; but, in many other nations throughout the world, it is used alongside other traditional, frequently older, standard packs with various suit systems, like those with German-, Italian-, Spanish-, or Swiss suits. The English pattern pack is the only one widely accessible in Britain and America and the most popular pattern of French-suited cards globally. The Belgian-Genoese pattern, which was created in France but is also used widely in Spain, Italy, the Ottoman Empire, the Balkans, and much of North Africa and the Middle East, is the second most popular.

Let all pairs of the positions (m,n) of the jokers are equally likely

$P[0]=P[|m-n|=1]=\frac{53}{\left(\begin{array}{c}54 \\2\end{array}\right)}=\frac{2}{27}$

$P[1]=P[|m-n|=2]=\frac{52}{\left(\begin{array}{c}54 \\2\end{array}\right)}=\frac{104}{1431}$

$P[k]=P|m-n|=k+1=\frac{54-k-1}{\left(\begin{array}{c}54 \\2\end{array}\right)}$

the expected value will be

$\begin{array}{l}\sum_{k=1}^{52} \frac{54-k-1}{\left(\begin{array}{c}54 \\2\end{array}\right)} k \\=\frac{1}{1431}\left(\sum_{k=1}^{52} 53 k-k^{2}\right) \\=\frac{1}{1431}\left(\frac{53}{2}(52)(53)-\frac{1}{6}(52)(53)(105)\right)\\=\frac{52}{3}\end{array}$