1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
love history [14]
3 years ago
6

HELPP MEEE PLEASEEEEE!

Mathematics
1 answer:
snow_lady [41]3 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.

You might be interested in
Four bakers used the following amounts of flour and sugar in their favorite cake recipe. Which bakers use the same flour to suga
eduard

bakers a and d


[6:4 is the same as 3:2]


(hope this helps, if so, please give brainliest x)

7 0
3 years ago
can someone help me with this i have autism and my parents aren't home I need some help with this pls will give brainly
svetoff [14.1K]
I can barely see the majority of the questions
i cant do all but to multiply fractions, you just multiply the numerator and the denominator together
so 3 2/3 x 6
change 3 2/3 to an improper fraction
9/3 x 6/1 = 27/3 which is 9/1 reduced
10 x 1 2/3 is 10/1 x 5/3 = 50/3
3 0
3 years ago
Read 2 more answers
A flower bed has the shape of a rectangle 7 yards long and 3 yards wide. what is its area in square feet? be sure to include the
Nadusha1986 [10]
21 square yards. Length times width (7 times 3) equals 21
6 0
3 years ago
Write an algebraic expression for the phrase.<br><br> the sum of f and 6
Wittaler [7]

Answer:

f+6

f+6 =(f+6)

6 0
3 years ago
A safety regulation states that the minimum height of a handrail is 30 inches. The maximum height is 38 inches. Write an absolut
atroni [7]

Answer:

Step-by-step explanation:

Minimum height=30

Maximum height=38

Write an absolute value equation:

Center: 34

Distance: 4

Equation: |x-34|=4

3 0
3 years ago
Other questions:
  • I need help with 3-6
    10·1 answer
  • what is the slope- intercept form of the equation of the line that passes through the points (-3,2) and(1,5)
    14·1 answer
  • Question 30(Multiple Choice Worth 1 points) (01.01) Given the equation 2x − 5 = 8, which order of operations completely solves f
    5·1 answer
  • Deandre and Eduardo when to the farmers market. Deandre purchased 15 tomatoes and 12 ears of corn, and Eduardo purshased 3 tomat
    7·1 answer
  • Emily had 10 carrot sticks to snack on during her hike. She ate 6 of the sticks. Her friend gave her 3 more sticks after the hik
    14·1 answer
  • Lia earned $4.50 in 5 hours. How much does she make per hour?
    14·2 answers
  • What is the volume of this prism? )<br> cm<br> thing
    7·1 answer
  • Solve For X <br> A 3 <br> B 30<br> C 60<br> D 90
    8·1 answer
  • Five percent of canned goods get bumps or dents in the cans during manufacturing. Let X = the number of cans that are inspected
    5·1 answer
  • Mr. Jones bought a piece of land for 60 000. The land increased in value by 20% in a year. The new value of the land is​
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!