Answer:
(-2, 21) and (2, -11) let me know if anything didn't make sense
Step-by-step explanation:
Try and put the symbols in, so for x to the third power write x^3 just makes it all much easier.
The turning point is when a graph changes from increasing to decreasing, or the other way around. What this means is that its slope is changing from positive to negative, or the other way around.
The derivative allows you to find the slope at any point of a graph. If you are unfamiliar witht his concept let me know and I can go more into it.
Since the derrivative tells you the slope, if you find a spot where it equals 0 then you know before that point it was positive or negative, and then after that point it was the opposite. In other words it changes, so it's exactly what we are looking for. Also if a derrivative is ever non existant, like in the square root function the numbers under the square root cannot be negative, so any x value that makes them negative doesn't exist, this means you would want to check these point too because they can be turning points as well.
There are certain special cases where a derivative does not coss 0, and if that happens then the original function does not have a turning point. So keep that in mind.
The derivative is 3x^2 - 12. So we want to find when this equals 0. We also know it always exists so only need to worry about the 0s. Hopefully you are familiar with quadratics having two zeroes, if not let me know.
3x^2 - 12 = 0
3x^2 = 12
x^2 = 4
x = 2 and-2
So these are the turning points. You should double check though and choose an x value below -2, then between -2 and 2, then larger than 2 and make sure the signs swap.
These are the x values of the turning points. Solve f(x) at these points to find the y values. so f(-2) = (-2)^3 - 12(-2) + 5 = 21 and f(2) = -11 so now we know the turning points are (-2, 21) and (2, -11)
The coordinates of the turning points of f(x) are (-2, 21) and (2, -11).
What is differential equation?An equation containing derivatives of a variable with respect to some other variable quantity is called differential equations. The derivatives might be of any order, some terms might contain product of derivatives and the variable itself, or with derivatives themselves.
The turning point is when a graph changes from increasing to decreasing, or the other way around that means, its slope is changing from positive to negative.
Given that the derivative of f(x) = x³ – 12x + 5 is 3x² - 12.
Since the derrivative tells the slope, if you find a spot where it equals 0 then before that point it was positive or negative, and then after that point it was the opposite.
The derivative is 3x² - 12.
3x² - 12 = 0
3x² = 12
x² = 4
Thus, x = 2 and-2
So, these are the turning points.
Now Solve f(x) at these points to find the y values.
so f(x) = x³ – 12x + 5
f(-2) = (-2)³ - 12(-2) + 5 = 21
f(2) = -11
Hence, the coordinates of the turning points of f(x) are (-2, 21) and (2, -11).
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ2
Will Mark Brainlest helpppp plssss
Answer:
C = [tex]\left[\begin{array}{ccc}-2&-4\\-1&1\\\end{array}\right][/tex]
Step-by-step explanation:
A = B+ C then
C = A - B
C = [tex]\left[\begin{array}{ccc}2&-5\\-1&4\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}4&-1\\0&3\\\end{array}\right][/tex] (subtract corresponding elements )
= [tex]\left[\begin{array}{ccc}2-4&-5-(-1)\\-1-0&4-3\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}-2&-4\\-1&1\\\end{array}\right][/tex]
Help what is x
When x^5 is 225
Answer:
Solution given:
x^5=225
we have
x=[tex] \sqrt[5]{225} [/tex]
x=2.9541
Hello!
[tex] \bf {x}^{5} = 225[/tex]
Extract the radical on both sides of the equation.[tex] \bf x = \sqrt[5]{225} [/tex]
[tex] \bf x ≈2.95418[/tex]
Answer: x ≈ 2,95418
Good luck! :)
[tex]x + 0.25 = -0.25[/tex]
Answer:
x = -0.5
Step-by-step explanation:
x + 0.25 = -0.25
x = -0.25 - 0.25
x = -0.5
As an estimation we are told 5 miles is 8 km.
Convert 34.5 km to miles.
Answer:
The answer is 21.43731
a^4+b^4 phân tích thành nhân tử
a^4+b^4=(a^2)^2+(b^2)^2
=(a^2+b^2)^2–2a^2b^2
=(a^2+b^2)^2—(√ 2ab)^2
=(a^2+√ 2ab+b^2)(a^2-√ 2ab+b^2)
Must click thanks and mark brainliest
Let $x$ be the smallest number in the following list, and let $y$ be the second smallest number (that is, the smallest number other than $x$). \[ 5, \qquad -22, \qquad \frac{-4}{7}, \qquad \frac{-3}{-5}, \qquad 3, \qquad \frac{-8}{13} \]Find $\frac{x-y}{y}$. Express your answer as a fraction in simplest form.
Answer:
139/4
Step-by-step explanation:
and find that\[
\frac{4}{7}\cdot \frac{13}{13} = \frac{4\cdot 13}{91}=\frac{52}{91}, \text{and}
\]\[
\frac{8}{13}\cdot \frac{7}{7} = \frac{8\cdot 7}{91} = \frac{56}{91}.
\]Thus $\frac{8}{13}$ is larger than $\frac{4}{7}$, which tells us that $-\frac{8}{13}$ is smaller than $-\frac{4}{7}$. Thus, $x=-22$, $y=-\frac{8}{13}$, and\begin{align*}
\frac{x-y}{y}&=\frac{-22-\left(-\frac{8}{13}\right)}{-\frac{8}{13}}\\
&=\left(-22\cdot \frac{13}{13}+\left(\frac{8}{13}\right)\right)\cdot \left(-\frac{13}{8}\right)\\
&=\left(\frac{-286+8}{13}\right)\cdot \left(-\frac{13}{8}\right)\\
&=\left(-\frac{278}{13}\right)\cdot \left(-\frac{13}{8}\right)\\
&=\boxed{\frac{139}{4}}.
\end{align*}
Describe the pattern in the following sequence and list the next three terms:
4, 8, 16, 32, ...
I’ll mark brainliest! Please help me
Please help me with this problem.
Answer:
1/4a -1/6b + 1/10c
Step-by-step explanation:
1/2 a -1/3 b + 1/5c + -1/4a + 1/6 b - 1/10c
Combine like terms
1/2a - 1/4a -1/3b + 1/6b +1/5c - 1/10 c
2/4a -1/4a -2/6b + 1/6b +2/10c -1/10c
1/4a -1/6b + 1/10c
2. Standard 6.NS.B
Hot dogs come in packages of 10. Hot dog buns come in packages of 8. Elliott would
like to buy the smallest number of hot dog buns and hot dogs so that he will have
exactly one hot dog per bun.
Part A
How many packages of buns and hot dogs must he buy? Show your work and explain
your thinking.
Answer:
4 packages of hot dogs and 5 packages of hot dog buns.
Step-by-step explanation:
Find the least common multiple of 10 and 8, which is 40.
a 9-ft roll of wrapping paper costs $6.48, what is the price per inch?
Answer: $0.06 per inch
Concept:
When encountering questions that ask for unit price, follow the statements to get the answer. For example, this question asks the price per inch. Therefore, in the actual answer, use the total price given divided by the number of inches.
Solve:
Price = $6.48
Inch = 9 × 12 = 108 in
1 ft = 12 inchPrice / Inch = 6.48 / 108 = $0.06 per inch
Hope this helps!! :)
Please let me know if you have any questions
Ms. Sutton recorded the word counts and scores of the top ten essays in a timed writing contest. The table shows her data.
A 3-row table with 10 columns. The first row is labeled essay rank with entries 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The second row is labeled essay score with entries 9.7, 9.5, 9.5, 9.0, 8.9, 8.9, 8.5, 8.4, 8.2, 7.0. The third row is labeled word count with entries 324, 352, 337, 318, 299, 304, 290, 291, 278, 250.
How does the word count of an essay relate to its score in the contest?
Word count tends to decrease as the score decreases.
Word count tends to increase as the score decreases.
Word count tends to remain constant as the score decreases.
Word count has no apparent relationship to the score of the essay.
Unmark this question
Answer:
The word count tend to decrease as the score decreases
Step-by-step explanation:
The 3-row table is presented as follows;
[tex]\begin{array}{ccc}Essay \ Rank&Essay \ Score&Word \ Count\\1&9.7&324\\2&9.5&352\\3&9.5&337\\4&9.0&318\\5&8.9&299\\6&8.9&304\\7&8.5&290\\8&8.4&291\\9&8.2&278\\10&7.0&250\end{array}[/tex]
The relationship between the values on the Word Count column and the values on the Essay Score column is that as the Essay Score decreases from the top down to the last row, the values on the Word Count generally decreases in the same manner (top down decrease)
Therefore, the Word Count decreases as the Essay Score decreases.
What is the equation of the graph
Answer:
[tex]y = 2x^2 + 1[/tex]
Step-by-step explanation:
The graph you see there is called a parabola. The general equation for the graph is as below
[tex]y = a*x^2 + b[/tex]
To find the equation we need to find the constants a and b. The constant b is just how much we're lifting the parabola by. Notice it's lifted by 1 on the y axis.
To find a it's a little more tricky. Let's use the graph to find a value for a by plugging in values we know. We know that b is 1 from the previous step, and we know that when x=1, y=3. Let's use that!
[tex]3 = a * (1)^2 + 1\\2 = a[/tex]
Awesome, we've found both values. And we can write the result.
[tex]y = 2x^2 + 1[/tex]
I'll include a plotted graph with our equation just so you can verify it is indeed the same.
0.25(4f-3)=0.005(10f-9)
Simplify the following
Answer:
apoco la propiedad asociativa en los siguiente ejercicio 25x11x18=
The graph of the function f(x) = (x + 2)(x - 4) is shown. Which describes all of the values for which the graph is negative and increasing?
all real values of x where x < -2
all real values of x where -2 < x < 4
all real values of x where 1 < x < 4
all real values of x where x < 0
Answer:
C. All real values of x where 1 < x < 4
Step-by-step explanation:
The function is negative below the zeros which would be from -2 to 4.
It would be increasing from the vertex which is 0 to 4.
Therefore, C makes the most sense out of all the choices.
Answer:
C was correct
Step-by-step explanation:
The midpoint of a segment is (6,−4) and one endpoint is (13,−2). Find the coordinates of the other endpoint.
A. (20, -6)
B. (-1, 0)
C. (-1, -6)
D. (20, 0)
Answer:
(-1,-6)
Step-by-step explanation:
(13 + x)/2 = 6
13+x= 12
x = -1
~~~~~~~~~~~~~~~
(-2 + y ) / 2 = -4
-2 + y = -8
y = -6
The coordinates of the other endpoint will be (-1,-6). The correct option is C.
What is the midpoint of the line?Divide the measurement of the distance between the two end locations by 2. The middle of that line is located at this separation from either end.
A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
Given that the midpoint of a segment is (6,−4) and one endpoint is (13,−2).
The x- coordinate will be calculated as:-
(13 + x)/2 = 6
13+x= 12
x = -1
The y-coordinate will be calculated as:-
(-2 + y ) / 2 = -4
-2 + y = -8
y = -6
Therefore, the coordinates of the other endpoint will be (-1,-6). The correct option is C.
To know more about midpoints of the line follow
https://brainly.com/question/24431553
#SPJ2
"A parabola has the equation y=3x^2+ 6x- 12 . What are the coordinates of the vertex? (You must solve by factoring)!!!!!" I NEED THE ANSWER TO THIS FAST WITH STEPS I'm a grade 10 academic student by the way
y = 3x ^ 2 + 6x- 12
(a=3; b=6; c= -12)
• Ta có Δ=b^2 -4ac
= 6^2 -4*3*( -12)
=180
• X= (-b+√Δ)/2a
≈ 3.2
• X= (-b-√Δ)/2a
≈ -3.2
Khi đó: y= 948/25
Và: y= -12/25
Vậy : A(3.2: 948/25)
B(-3.2; -12/25)
Step-by-step explanat bion :
428363939+42724289292952926263938
Answer:
4.2724289e
+22
Step-by-step explanation:
mzmznznxnxnznxn no n n j j h h h h h h hh h h &
In the number 9663 which places contain digits where one dogit is 10 times as great as the other?
Answer: Hundreds and tens place values (the two copies of '6')
Explanation:
We're looking for where the digits are the same, which would be those two copies of '6'
The first 6 on the left is in the hundreds place. It represents 600
The other 6 is in the tens place, and it represents 60
The jump from 60 to 600 is "times 10".
find the missing length indicated
Answer:
240
Step-by-step explanation:
We are given a right triangle. Based on the leg rule, the following equation shows how the length of a leg in a right triangle relates with the segments connected to the hypotenuse:
Hypotenuse/leg = leg/part
Where,
Hypo = 400
Leg = x
Part = 144
Substitute
400/x = x/144
Cross multiply
400*144 = x*x
57,600 = x²
√57,600 = x
240 = x
x = 240
What is the slope of a line that is perpendicular to the line whose equation is
y= 4x – 3?
Answer:
-1/ 4
Step-by-step explanation:
y = 4x-3 has a slope of 4 because the equation is in slope intercept form
y = mx+b where the slope is m
Perpendicular lines have slopes that are negative reciprocals
-1/ 4 is the slope of a line that is perpendicular to y = 4x-3
please answer asap no wrong answers pls
Hi there!
[tex]\large\boxed{\frac{1}{5}, \frac{21}{5}}[/tex]
In order to set each equation equal to each other, we must have them both equal the same variable.
Rearrange the top equation to make it equal to y:
x - y = -4
Add 4 to both sides and add y to both sides:
x + 4 = y
Now, we can set both equations equal to each other:
x + 4 = 5(x + 1)² - 3
Begin solving by expanding the square binomial:
x + 4 = 5(x² + 2x + 1) - 3
Simplify:
x + 4 = 5x² + 10x + 5 - 3
x + 4 = 5x² + 10x + 2
Bring all terms to one side:
0 = 5x² + 9x - 2
Factor:
0 = (5x - 1)(x + 2)
Set the other factor equal to 0:
5x - 1 = 0
5x = 1
x = 1/5
Plug in this value of x into an original equation:
1/5 - y = -4
1/5 + 4 = y
1/5 + 20/5 = y
y = 21/5
1 pump can fill a pool in 8 hours the other pump can fill the pool in 10 hours if both of the pumps were turned on at the same time to fill the pool how long will it take
Answer:
4 4/9 hoursStep-by-step explanation:
In one hour pump1 can fill 1/8 of the tank and pump2 can fill 1/10 of the tank.
Two pumps can fill:
1/8 + 1/10 = 5/40 + 4/40 = 9/40 of the tank in one hourTime required to fill the tank:
1/(9/40) = 40/9 = 4 4/9 hoursJames wants to tile his floor using tiles in the shape of a trapezoid. To make the pattern a little more interesting he has decided to cut the tiles in half along the median. The top base of each tile is 12 inches in length and the bottom base is 16 inches. How long of a cut will John need to make so that he cuts the tiles along the median? O A. 2 inches B. 4 inches O C. 14 inches O D. 28 inches
Answer:
Choice C. 14 inches
Step-by-step explanation:
Middle between 12 and 16 inches.
Figure ABCD is a parallelogram.
What is the perimeter of ABCD?
A
4y - 2
B
14 units
VX
0 38 units
3x - 1
44 units
2x + 2
49 units
D
2y + 6
С
Answer:
3rd option, 44 units
Step-by-step explanation:
3x-1 = 2x+2
or, x = 3
so each side, 3×3-1 = 8
4y-2 = 2y+6
or, y = 4
so each side, 4×4-2 = 14
so perimeter
= 2(8+14)
= 44 units
Answered by GAUTHMATH
Please help me.
List the sides of MNP in ascending order:
m< M = 15, m < N= 75
Answer:
Take a look at this: https://brainly.com/question/14269575?referrer=searchResults
Step-by-step explanation:
Which ordered pair can be plotted together with these four points, so the resulting graph still represents a function?
•(2, -1)
•(2, -2)
•(-2, 2)
•(-1, 2)
Answer:
-1,2 can be plotted together with these four points ...
Point Q is located at (-4, 6). Point R is located at (8, 6).
What is the distance from point Q to point R?
Step-by-step explanation:
Hi there!
Given;
Point Q is located at (-4, 6). Point R is located at (8, 6).
Note: Use distance formula.
Now;
[tex](d) = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]
Keep all values;
[tex](d) = \sqrt{ {(8 + 4)}^{2} + ( {6 - 6)}^{2} } [/tex]
Simplify;
[tex](d) = \sqrt{( {12)}^{2} } [/tex]
Therefore, the distance is 12 units.
Hope it helps!
please help asap, see attached photo. This is due in 1 hour!!! please answer both questions. Both 5 and 6
Answer:
A and C
Step-by-step explanation:
5) logx+log(x+9)=2
log(x(x+9))=2, log(x^2+9x)=2
6) log(x^2+9x)=2
(x^2+9x)=36 or 6^2
What is the length of the dotted line in the diagram below? Round to the nearest tenth. *Will mark brainliest*
Answer:
The dotted line is 4.9
Step-by-step explanation:
The lower triangle is a right triangle so we can use the Pythagorean theorem
a^2+b^2 = c^2
where a and b are the legs and c is the hypotenuse
2^2 + 4^2 = c^2
4+16 = c^2
20 =c^2
Taking the square root of each side
sqrt(20) = c
The upper rectangle has a length of sqrt(20) and a height of 2
We can use the Pythagorean theorem
a^2+b^2 = c^2
where a and b are the legs and c is the hypotenuse to find the diagonal
2^2 + (sqrt(20))^2 = c^2
4+20 = c^2
24 = c^2
Taking the square root of each side
sqrt(24) = c
4.898979486=c
Rounding to the nearest tenth
4.9 =c
What is 200% of 20? Thanks!
Answer:
40
Step-by-step explanation:
200% x 20
200/100 x 20
(200 ÷ 100) x 20
200 x 20 ÷ 100
4,000 ÷ 100 = 40
