To find the local and global extrema of the function f(x) = x(25 - x), we first find the derivative and set it equal to zero. Next, we evaluate the function at the critical point and the endpoints of the interval [0, 20]. The local maximum is 156.25 and the global maximum is also 156.25.
Explanation:To find the local and global extrema of the function f(x) = x(25 - x), we can start by finding the critical points. Critical points occur where the derivative of the function is equal to zero or undefined. Let's find the derivative of f(x) first:
f'(x) = 25 - 2x
Setting f'(x) equal to zero, we get:
25 - 2x = 0
Solving for x:
x = 12.5
The critical point is x = 12.5. Now, let's evaluate f(x) at the endpoints of the interval [0, 20] and the critical point:
f(0) = 0
f(20) = 0
f(12.5) = 12.5(25 - 12.5) = 156.25
Therefore, the local maximum is f(12.5) = 156.25 and the global maximum value on the given interval is also f(12.5) = 156.25.
Which statement proves that quadrilateral JKLM is a kite?
∠M is a right angle and MK bisects ∠LMJ.
LM = JM = 3 and JK = LK = .
MK intersects LJ at its midpoint.
The slope of MK is –1 and the slope of LJ is 1.
Answer:
B) LM = JM = 3 and JK = LK = √17
Step-by-step explanation:
just took test, A is wrong, can i get brainliest please?
Answer:
B) LM = JM = 3 and JK = LK = √17
There were m visitors in an exhibition on the first day and 1,200 fewer vistors on the second day. On the third day, the number of vistors was 30% greator than the number of vistors on the second day. What was the average number of vistors over the three days?
Answer:
Step-by-step explanation:
The average number is given by :
[m + (m - 1200) + (m - 1200)(1.30 ] / 3 =
[ 2m + 1.30m - 1200 - 1560] / 3 =
[3.3m - 2760] / 3 =
[1.1 m - 920 ]
Find the value of x, rounded to the nearest tenth.
X multiplied by the side labeled 5 is equal to the line labeled 9 multiplied by the line labeled 5.1
9 x 5.1 = 45.9
x = 45.9 / 5
x = 9.18
x = 9.2
Which of the following is the midpoint between (-8, -1) and (-2, -5)?
(-5, 3)
(5, 3)
(5, -3)
(-5, -3)
Answer:
[-5, -3]
Step-by-step explanation:
Just find the *median* of each coordinate.
Does anyone know this?
Answer:
h(1)= 1
h(4)=5
Step-by-step explanation:
Given
h(x)= x^3 for 1≤x≤3
and
h(x)=5 x>3
Now finding h(1), i.e when x=1
x=1 lies in the range 1≤x≤3 hence putting value x=1 in x^3
h(1)= 1^3
= 1
Now finding h(4), i.e when x=4
x=1 lies in the range x<3 hence putting value x=4 in h(x)=5
h(4)= 5 !
Which is equivalent to 80 1/4 x
In this Multiplication in Algebra question, The expression '80 (1/4) x' is equivalent to '20x'. When the constant 80 multiplies with the fraction 1/4, the product then multiplies with the variable 'x' resulting in a simplified expression '20x'.
The given mathematical expression 80 (1/4) x can be simplified using the rules of multiplication in algebra.
Here the number 80 multiplies with the fraction 1/4 and then by the variable 'x'.
To carry out this operation, first multiply 80 by 1/4 which equals to 20, and then multiply this by 'x', so your final result would be 20x. Hence, the expression 80 (1/4) x is equivalent to 20x.
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The probable question may be:
Which is equivalent to 80 (1/4) x
Write an equation for the vertical translation. y = 2/3x; 4 units down
Answer:
y = [tex]\frac{2}{3}[/tex] x - 4
Step-by-step explanation:
Given y = f(x), then
y = f(x) + c represents a vertical translation
• If c > 0 then shift up by c units
• If c < 0 then shift down by c units
Here the translation is 4 units down ⇒ c = - 4, thus
y = [tex]\frac{2}{3}[/tex] x - 4
The equation of a line y = 2/3x moved 4 units down would be y = 2/3x - 4.
Explanation:In the case of a vertical translation, the equation of a line y = mx + b is altered by adding or subtracting a constant value, which moves the line up or down on the coordinate plane. For example, with the given equation of a line, y = 2/3x, to translate it 4 units down, we subtract 4 from y. Therefore, the equation for the vertical translation would be y = 2/3x - 4.
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PLEASE I NEED THIS TO PASS A TEST AND GRADUATE!!!
Function g is transformed to obtain function h as shown.
(x)=g(x+2)-5
Which statement describes how the graph of h is different from the graph of g?
A. The graph of h is the graph of g shifted 2 units to the right and 5 units up.
B. The graph of h is the graph of g shifted 5 units to the left and 2 units down.
C. The graph of h is the graph of g shifted 5 units to the right and 2 units up.
D. The graph of h is the graph of g shifted 2 units to the left and 5 units down.
Answer:
D. The graph of h is the graph of g shifted 2 units to the left and 5 units down.
Step-by-step explanation:
Graph: h(x) = g ( x + 2 ) - 5
x + 2 means the graph is shifted to left by 2 units.
-5 means to shift the graph down by -2 units
so, the graph of h is the graph of g shifted 2 units to the left and 5 units down.
If vector v has an initial point at P1 and a terminal point at P2, write v as multiples of the basis vectors That is, write v in the form v = ai + bj.
P1 = (−5, −2), P2 = (4, 1) and v = ?
Answer:
v=9i+3j
Step-by-step explanation:
The given vector, v has initial point at P1 = (−5, −2) and terminal point at P2 = (4, 1).
The vector v is found by subtraction the initial point from the terminal point.
v=<4,1>-<-5,-2>
v=<4--5,1--2>
v=<9,3>
We write v as multiples of the basis vectors to obtain:
v=9i+3j
Evaluate.
5 • [(14 + 3 • 30) + 120] + 103 – 10
Answer:
1213
Step-by-step explanation:
simplify
Answer:
1213
Step-by-step explanation:
5 • [(14 + 3 • 30) + 120] + 103 – 10
Evaluate 3*30 first
5 • [(14 + 90) + 120] + 103 – 10
Evaluate 14 + 90 = 104
5 * [104 + 120] + 103 - 10
5 * (224) + 103 - 10
5*(224) + 93
1120 + 93
1213
Helpppp me 10 pointssss
Answer:
C
Step-by-step explanation:
Find the height (h ) above eye level and add 5 to give height from floor level.
Since the triangle is right use the tangent ratio to find h
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{5}[/tex]
Multiply both sides by 5
5 × tan60° = h, hence
h ≈8.66
The height is 8.66 + 5 = 13.66 ≈ 14 ft ( to nearest foot )
Patrica scored 80% on a math test. She missed 4 problems. How many problems were on the test?
Answer:
20
Step-by-step explanation:
Patrica got 80% correct. She missed 4 problems, so that must have been the remaining 20% of the test.
Therefore:
4 = 20% x
Percent means out of 100, so:
4 = (20/100) x
4 = 1/5 x
x = 20
There were 20 problems on the test.
Find the height of a triangle that has an area of 30 square units and a bas measuring 12 units
That answer is 180. The formula is a=bh1/2
What is the range of 19, 12, 13, 3, 0, 0, 0, 0, 0, 0, 2, 13
Answer:
The answer is 19.
Step-by-step explanation:
To find the range you have to subtract the lowest number and highest number in the data set.
19-0=19
Hope this helps.
The range of the given set {19, 12, 13, 3, 0, 0, 0, 0, 0, 0, 2, 13} is 19, which is the difference between the largest (19) and smallest (0) values in the set.
The range of a set of numbers is the difference between the largest and smallest values in the set. To find the range of the given numbers {19, 12, 13, 3, 0, 0, 0, 0, 0, 0, 2, 13}, follow these steps
Step 1: Arrange the numbers in ascending order: {0, 0, 0, 0, 0, 0, 2, 3, 12, 13, 13, 19}.
Step 2: Find the smallest value: 0.
Step 3: Find the largest value: 19.
Step 4: Calculate the range: Largest value - Smallest value = 19 - 0 = 19.
The range of the given numbers is 19.
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Lines LM and QR are graphed on this coordinate plane. Which point is the intersection of lines LM and QR?
na
A. (-3,1)
B. (-3.-3)
c. (1.-3)
D. (1.3)
The first number is the X coordinate and the second number is the Y coordinate.
Looking left to right the lines intersect at X = 1
Looking up and down they intersect at Y = -3
The answer is C. (1,-3)
PLEASE HELP
find the vertex of f(x)=x^2+2x+3 (make sure you show your work)
ANSWER
(-1,2)
EXPLANATION
The given quadratic expression is:
[tex]f(x) = {x}^{2} + 2x + 3[/tex]
The coefficient of the quadratic term is already 1.
So we add and subtract the square of half the coefficient of x.
[tex]f(x) = {x}^{2} + 2x + 1 - 1+ 3[/tex]
We factor the first three terms to obtain
[tex]f(x) =(x + 1)^{2} + 2[/tex]
This is now in the form:
[tex]f(x) = a({x - h)}^{2} +k[/tex]
where (h,k) which is equal to (-1,2) is the vertex.
Ok I got 8 and I know it is wrong someone please help me
I would go with answer D here just because it is the only option over 13, and the hypotenuse is always larger than the other sides. Im not positive on the math behind it though tbh.
on the first day of a local fair, 55 children, 20 adults, and 25 senior citizens were admitted. if children's tickets cost $5.00 each, adults cost $8.00 each and senior citizen tickets cost $6.00 each, what was the mean ticket price for all 100 people who entered?
Answer:
585$
Step-by-step explanation:
multiply 55 by 5, then multiply 20 by 8, last multiply 25 by 6 and add each of the totals to one another.
The mean ticket price is 5.85
What is the volume of a rectangular prism with l = 4 1/2 cm, w = 3 1/2 cm, and h = 6 cm?
Step-by-step explanation:
Volume of a rectangular prism is:
V = lwh
Given that l = 4½, w = 3½, and h = 6:
V = (4½)(3½)(6)
V = 94.5
The volume is 94½ cm³.
The formula for the volume of a rectangular prism is:
V = length x width x height
OR
V = l x w x h
You must plug in the values given in the equation
4[tex]\frac{1}{2}[/tex] x 3[tex]\frac{1}{2}[/tex] x 6
94 1/2 cm^3
Hope this helped!
~Just a girl in love with Shawn Mendes
A rectangular area is to be enclosed with 12m of fencing.
A) what is the maximum area that can be enclosed if the fencing is used on all four sides. What are the dimensions of this optimal shape?
B) Suppose an existing hedge is used to enclose one side. Determine the maximum area that can be enclosed. What are the dimensions in this shape?
C) Suppose two perpendicular hedges enclose the area on two sides. What are the dimensions of the maximum area that can be enclosed?
The correct answer is B
a ticket office sold 553 tickets one day. the receipts totaled $3936. how many $9 adult tickets and how many $6 child tickets were sold
This is the assumption method ;)
Take all tickets to be adult tickets
$9 x 553 = $4977
Then..... $4977 - $3936 = $1041
The difference between the child and adult ticket is $3, so divide $1041 by $3
$1041 divided by $3 = 347
347 is the number of child tickets sold
347 x $6 = $2082
So 553 - 347 = 206 ( no. of adult tickets )
206 x $9 = $1854
Child tickets sold : 347
Adult tickets sold : 206
:0 ITS MAGIC IM SO SMART
Answer:
347 child tickets and 206 adult tickets are sold
Step-by-step explanation:
Let x be the no. of child tickets sold
Let y be the no. of adult tickets sold
A ticket office sold 553 tickets one day.
Equation becomes : [tex]x+y=553[/tex] ---A
Cost of 1 child ticket = $6
Cost of x child tickets = 6x
Cost of 1 adult ticket= $9
Cost of y adult tickets = 9y
Now we are given that the receipts totaled $3936.
So, Equation becomes : [tex]6x+9y=3936[/tex] ---B
Plot A and B
[tex]x+y=553[/tex] ---Green
[tex]6x+9y=3936[/tex] ---Purple
Intersection point = (x,y)=(347,206)
Refer the attached figure
Hence 347 child tickets and 206 adult tickets are sold
i need help please ill give you 20 points
Answer: x < -1
Remember:
A white dot indicates > or <, not ≥ or ≤.In this case, the arrow is pointing to the left, so x must be < -1.Answer: D, or x<-1
Step-by-step explanation:
The arrow on the number line indicates the direction in which the set of numbers represented is going. In this case, the arrow is pointing in the negative direction from -1; so we know that it will be either x < -1 or x ≤ -1
The circle represents whether the set of points is inclusive or exclusive. This is an exclusive case, which means that the point x = -1 is not included in the set of points.
That's how we know the inequality represented by the graph is x < -1
Which is the simplified form of the expression (6 to the power of -2 times 6 to the power of 5) to the -3rd power?
A)6 to the 30th power
B)1 over (6 to the power of 9)
C)6 to the power of 0
D)1 over (6 to the power of 16)
Answer:
B. 1/6^9
Step-by-step explanation:
6^-2 = 1/6^2
1/6^2 * 6^5 = 6^5/6^2 = 6^3
6^(3 * -3) = 6^-9= 1/6^9
Answer:
B) 1 over (6 to the power of 9)Step-by-step explanation:
[tex]\left(6^{-2}\cdot6^5\right)^{-3}\qquad\text{use}\ a^n\cdot a^n=a^{n+m}\\\\=(6^{-2+5})^{-3}=(6^3)^{-3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=6^{(3)(-3)}=6^{-9}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{6^9}[/tex]
Write 4x + y = -17 in slope intercept form.
Answer:
y=-4x-17
Step-by-step explanation:
You want to find the equation for a line that has a slope of -4 and a y-intercept of -17.
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
All you really have to do here is
replace m with -4, which is the slope you gave, and
replace b with -17, the y-intercept you gave,
in the equation y=mx+b.
The equation of the line that has a slope of -4 and a y-intercept of -17 is:
y=-4x-17.
The probability of it snowing in Eastern Canada tomorrow is 0 . 4 0.40, point, 4. The probability of it snowing in Western Canada tomorrow is 2 5 5 2 start fraction, 2, divided by, 5, end fraction. Which of these events is more likely? Choose 1 answer: Choose 1 answer: (Choice A) A It snows in Eastern Canada tomorrow. (Choice B) B It snows in Western Canada tomorrow. (Choice C) C Neither. Both events are equally likely.
Answer:
c
Step-by-step explanation:
Both the events are equally likely so neither can be more likely.
The correct answer is: C Neither. Both events are equally likely.
Given that the probability of it snowing in Eastern Canada tomorrow is 0.4 and that of in Western Canada is 2/5,
We need to determine which of the given events is more likely,
To determine which event is more likely, we compare the probabilities provided for each event:
The probability of it snowing in Eastern Canada tomorrow is 0.4.
The probability of it snowing in Western Canada tomorrow is 2/5, which is equivalent to 0.4.
Since both probabilities are equal (0.4), we can conclude that both events, A (It snows in Eastern Canada tomorrow) and B (It snows in Western Canada tomorrow), are equally likely.
Therefore, the correct answer is: C Neither. Both events are equally likely.
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3^3/3^6
a. 1/27
b 1/9
c 9
d -27
I think the answer is c
Answer:
a. 1/27
Step-by-step explanation:
When dividing exponents and the base is the same, we subtract them
x^a/ x^b = x^(a-b)
3^3/3^6
3^(3-6)
3^(-3)
The negative exponent means it is in the denominator
1/3^3
1/27
Please help..........
Answer:
C
Step-by-step explanation:
This is saying sum 5 and a number and multiply the result by 4
let n be the number then 5 + n is the sum, and
4(5 + n) is 4 times the resultant sum
Jessica borrow $316 for 9 months he paid it off by paying $38.27 monthly what will she pay in finance charges
Answer:
my answer is 34 r 18 I am guessing
Answer:
answer is $28.43
Step-by-step explanation:
You take $38.27x9. Then minus that answer minus $316
Which function is positive for the entire interval [-3, -2]
Answer:
Graph B
Step-by-step explanation:
We are given 4 graphs.
We need to find the function graph which is positive of the entire interval [-3, -2]
It is a closed interval. So it is inclusive of -3 and -2
In these interval the graph of y value must be in positive region.
By looking at the graph, the graph B has positive y-values in the entire interval [-3, -2]
Therefore, the answer is Graph B)
Answer:
Graph 2 represents that the function is positive for the entire interval [-3, -2].
Step-by-step explanation:
We are given four different graphs for different functions. We have to find the graph that is positive for the entire interval [-3,-2].
We make the following observation from the given graphs.
In graph 1, the function has a value of 0 at -3 and and the value decreases from -3 to -2. Thus, the function is negative in the given interval.In graph 2, it can be clearly seen that the function has a positive value, through the entire given interval.In graph 3, the function shows negative value entirely in the given interval.In graph 4, the function exhibits both positive and negative value in the given interval and in not positive in the entire interval.Thus, function in graph 2 is positive for the entire interval [-3, -2].
what is the value of x to the nearest tenth
You will have to use trig to solve this:
The side you have is adjacent to the known angle
The side you are looking for is opposite the known angle
^^^This means you need to use tan:
tan(24) = [tex]\frac{x}{12}[/tex]
.445222 = [tex]\frac{x}{12}[/tex]
^^^input tan(24) into calculator, then multiply 12 to both sides to isolate and solve for x
5.3 ≈ x
Hope this helped!