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love history [14]
2 years ago
6

HELPP MEEE PLEASEEEEE!

Mathematics
1 answer:
snow_lady [41]2 years ago
5 0

Let $a=x+\tfrac{5}{2}$. Then the expression $(x+1)(x+2)(x+3)(x+4)$ becomes $\left(a-\tfrac{3}{2}\right)\left(a-\tfrac{1}{2}\right)\left(a+\tfrac{1}{2}\right)\left(a+\tfrac{3}{2}\right)$.

We can now use the difference of two squares to get $\left(a^2-\tfrac{9}{4}\right)\left(a^2-\tfrac{1}{4}\right)$, and expand this to get $a^4-\tfrac{5}{2}a^2+\tfrac{9}{16}$.

Refactor this by completing the square to get $\left(a^2-\tfrac{5}{4}\right)^2-1$, which has a minimum value of $-1$.

Similar to Solution 1, grouping the first and last terms and the middle terms, we get $(x^2+5x+4)(x^2+5x+6)+2019$.

Letting $y=x^2+5x$, we get the expression $(y+4)(y+6)+2019$. Now, we can find the critical points of $(y+4)(y+6)$ to minimize the function:

$\frac{d}{dx}(y^2+10y+24)=0$

$2y+10=0$

$2y(y+5)=0$

$y=-5,0$

To minimize the result, we use $y=-5$. Hence, the minimum is $(-5+4)(-5+6)=-1$, so $-1+2019 = \boxed{\textbf{(B) }2018}$.

Note: We could also have used the result that minimum/maximum point of a parabola $y = ax^2 + bx + c$ occurs at $x=-\frac{b}{2a}$.

Solution 4

The expression is negative when an odd number of the factors are negative. This happens when $-2 < x < -1$ or $-4 < x < -3$. Plugging in $x = -\frac32$ or $x = -\frac72$ yields $-\frac{15}{16}$, which is very close to $-1$. Thus the answer is $-1 + 2019 = \boxed{\textbf{(B) }2018}$.

Solution 5 (using the answer choices)

Answer choices $C$, $D$, and $E$ are impossible, since $(x+1)(x+2)(x+3)(x+4)$ can be negative (as seen when e.g. $x = -\frac{3}{2}$). Plug in $x = -\frac{3}{2}$ to see that it becomes $2019 - \frac{15}{16}$, so round this to $\boxed{\textbf{(B) }2018}$.

We can also see that the limit of the function is at least -1 since at the minimum, two of the numbers are less than 1, but two are between 1 and 2.

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On Saturday, 45% of the music Brianna listened to was country songs. She listened
storchak [24]

Brianna listen 60 songs on Saturday !

<u>Step-by-step explanation:</u>

Here we have , On Saturday, 45% of the music Brianna listened to was country songs. She listened  to 27 country songs on Saturday. How many songs did Brianna listen to on  Saturday .Let's find out:

Let Brianna listens x songs ! So , 45% of x songs is 27 songs , i.e.  On Saturday, 45% of the music Brianna listened to was country songs. She listened  to 27 country songs on Saturday as :

⇒ \frac{45(x)}{100} =27

⇒ \frac{45(x)}{100}(\frac{100}{45}) =27(\frac{100}{45})

⇒ x =27(\frac{100}{45})

⇒ x =\frac{2700}{45}

⇒ x =60

Therefore , Brianna listen 60 songs on Saturday !

8 0
3 years ago
Anyone wanna help with this iready question?
Illusion [34]

Answer:

3 ticket = 21 $

5 ticket = 35$

so 1 ticket = 7$

9 ticket = 63$

2$ discount

total amount = 61$

Mark my answer as brainlist answer.

7 0
3 years ago
A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the
Vinvika [58]

Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

0 = 4*L*L^2 - 4*(2744 cm^3)

4*(2744 cm^3) = 4*L^3

2744 cm^3 = L^3

∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

8 0
2 years ago
PLEASE HELP
Mumz [18]
Well to do this, we need to know the least common multiple (LCM) of 6 and 8. Lets list the factors out.

6, 12, 18, 24, 30, 36
8, 16, 24, 32, 40, 48

As we can see, the least common multiple of 6 and 8 is 24.

Now we know that there are 8 plates per package and 8 goes into 24 3 times, so  naturally Shaniya needs 3 packages of plates

Hope this helped!!! :)
7 0
3 years ago
You need to ride an average of at least 25 miles per day for five consecutive
Elena-2011 [213]

Answer:

14 miles

Step-by-step explanation:

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