.000054 + (2.3 x 10-5)

Find the greatest common factor of 22

dedylja [7]

We cannot find the greatest common factor because the GCF is between two numbers not one

8 0

3 years ago

HELPP MEEE PLEASEEEEE!

snow_lady [41]

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.

5 0

3 years ago

Four Questions, 60 points & Brainliest! (Please show all steps)

pogonyaev

Answer:

a) -2, 1 and 2

b) 4

Step-by-step explanation:

The given equation is:

g(x) = (x + 2)(x - 1)(x - 2)

Part a1 and a2) Finding zeros of the function

By zeroes of the function we mean the points the graph where the value of the function is zero. In order to find the zeroes of the function we equate the function equation to zero and find the corresponding values of x. This is shown below:

0 = (x + 2)(x - 1)(x - 2)

According to the zero product property, we can write:

x + 2 = 0 ⇒ x = -2

x - 1 = 0 ⇒ x = 1

x - 2 = 0 ⇒ x = 2

Therefore, the zeroes of the given function are -2, 1 and 2. In ordered pairs we can write these as (-2, 0), (1, 0) and (2, 0)

Part b1 and b2) y-intercept of the function

y-intercept is the point on the graph where the function crosses the y-axis. Since on y-axis, the value of x coordinate is zero, in order to find the y-intercept we simply substitute zero for all occurrences of x. This is shown below:

g(0) = (0 + 2)(0 - 1)(0 - 2)

g(0) = 2(-1)(-2)

g(0) = 4

Thus, the y-intercept of the function is 4, which in ordered pair can be written as (0, 4)

Part c) End behavior of the graph

End behavior of the graph depends on:

Sign of the leading coefficient
Degree of the function

Degree of the function is 3 i.e. odd and sign of leading coefficient is positive. This means the end behavior of the graph will be:

Rising towards Right end
Falling towards Left end

Part d) Graph of polynomial

Based on all the above discussion, a graph of the function can be plotted. The graph is attached below.

4 0

3 years ago

2/3< x/8 <7/8 what number could replace x to make a true statement 3 4 5 6

ICE Princess25 [194]

Answer:

6

Step-by-step explanation:

Multiply all three sides by 8 to get x by itself

16/3 < x < 7

5 1/3 < x < 7

so it’s between 5 and 1/3 and 7. the only answer between those two would be 6. 3 and 4 is too less. 5 is also too less.

5 0

3 years ago

Read 2 more answers

Two consecutive even integers have a sum of 46

eduard

Two consecutive even integers have a sum of 46 are 22 and 24

hope it helps

5 0

3 years ago

Read 2 more answers