The interval over which f(x) = x² - x - 1 has an average rate of change of zero is (1/2, 1/2) as it is the only point at which the average rate of change is zero.
An average rate of change of zero means that the function is not increasing or decreasing over the interval in question. To find the interval over which f(x) has an average rate of change of zero, we need to find the critical points of the function. A critical point is a point at which the function's derivative is equal to zero or is undefined.
The derivative of f(x) = x² - x - 1 is:
f'(x) = 2x - 1
Setting f'(x) = 0, we get:
2x - 1 = 0
Solving for x, we get:
x = 1/2
Since this is the only critical point of the function, it is the point where the function has an average rate of change of zero. To determine the interval, we need to check the sign of the function's derivative on either side of the critical point.
f''(x) = 2 > 0
So x = 1/2 is the minima of the function
f'(x) = 2(1/2) - 1 = 0, at x = 1/2
so f'(x) > 0 for x < 1/2 and f'(x) < 0 for x > 1/2
Therefore the interval over which f(x) has an average rate of change of zero is (1/2, 1/2) or {1/2}.
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Please I need the answer ASAP
Answer:
option C is correct answer of this question
Answer:
the answer is c 2 teaspoons
Step-by-step explanation:
if you divide 84 by 21 you would get 4. then you multiply 1/2 by 4 and get 2 teaspoons.
Name the triangle
Please help fast
Answer:
B. Equilateral
It is an equilateral triangle
As we can see all sides are equal.
Equilateral Triangle
Step-by-step explanation:
Brian is tiling a patio and ran out of tiles. The width of the remaining area of ⅔ yard. The length of the remaining area is 4 yards. What is the area Brian has left to tile?
Answer:
Area of the remaining patio = 2.67 square yards
Step-by-step explanation:
Width of the remaining area of the patio = [tex]\frac{2}{3}[/tex] yards
Length of the remaining area of the patio = 4 yards
Since, area of the remaining area of the rectangular patio
= Length × Width
= [tex]\frac{2}{3}\times 4[/tex]
= [tex]\frac{8}{3}[/tex]
= 2.67 square yards
Therefore, area of the remaining area of the patio = 2.67 square yards
10 POINTS FOR WHOEVER ANWSERS!
Answer:
Infinitely many solutions
Step-by-step explanation:
In the adjoining equilateral triangle PQR , X , Y and Z are the middle points of the sides PQ , QR and RP respectively. Prove that XYZ is also an equilateral triangle.
~Thanks in advance !
Answer:
See Below
Step-by-step explanation:
Statements: Reasons:
[tex]1)\text{ } \Delta PQR\text{ is equilateral}[/tex] Given
[tex]2)\text{ }PQ=QR=RP[/tex] Definition of Equilateral
[tex]3)\text{ } X, Y, Z\text{ are the midpoints of } PQ, QR, RP[/tex] Given
[tex]4)\text{ } PX=XQ[/tex] Definition of Midpoint
[tex]5)PQ=PX+XQ[/tex] Segment Addition
[tex]6)\text{ } PQ=2XQ[/tex] Substitution
[tex]7)\text{ } QY=YR[/tex] Definition of Midpoint
[tex]8)\text{ }QR=QY+YR[/tex] Segment Addition
[tex]9)\text{ } QR=2QY[/tex] Substitution
[tex]10)\text{ } 2XQ=2QY[/tex] Substitution
[tex]11)\text{ } XQ=QY[/tex] Division Property of Equality
[tex]12)\text{ } XQ=PX=QY=YR[/tex] Transitive Property
[tex]13)\text{ } RZ=ZP[/tex] Definition of Midpoint
[tex]14)\text{ } RP=RZ+ZP[/tex] Segment Addition
[tex]15)\text{ } RP=2RZ[/tex] Substitution
[tex]16)\text{ } 2XQ=2RZ[/tex] Substitution
[tex]17)\text{ } XQ=RZ[/tex] Substitution
[tex]18)\text{ } XQ=PX=QY=YR=RZ=ZP[/tex] Transitive Property
[tex]19)\text{ } \angle Q\cong \angle R\cong \angle P[/tex] Definition of Equilateral
[tex]20)\text{ } \Delta XQY\cong \Delta YRQ \cong \Delta ZPX[/tex] SAS Congruence
[tex]21)\text{ } XY\cong YZ\cong ZX[/tex] CPCTC
[tex]22)\text{ } \Delta XYZ\text{ is equilateral}[/tex] Equilateral Triangle Theorem
Answer:
this is your answer. thanks, for great point
One coffee and two slices of cake cost 8 dollars in total. Two coffees and 3 slices of cake cost 14 dollars in total. What are the individual prices of one coffee and of one slice of cake?
Answer:
Step-by-step explanation:
coffee=c
cakes=d
c+2d=8
2c+3d=14
c=8-2d
2(8-2d)+3d=14
16-4d+3d=14
-d=-2
d=2
c+4=8
c=4
coffee=4 dollars each
cakes=2 dollars each
The price of coffee is $4 and price of slice of cake is $2.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
One coffee and two slices of cake cost 8 dollars in total.
Two coffees and 3 slices of cake cost 14 dollars in total.
let the price of coffees sold be x
let the price of slices of cake sold be y
Then, the system of equations are
x+ 2y = 8
2x+ 3y = 14
On solving
2(8- 2y)+ 3y= 14
16 - 4y + 3y= 14
-y= -2
y= 2
and, x = 8- 2(2)= 8- 4= 4
Hence, price of coffee is $4 and price of slice of cake is $2.
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Find the slope of a line that passes through the points (-1, -3) and (2, -2).
Answer:
Step-by-step explanation:
(-2 + 3)/(2 + 1) = 1/3 is the slope
can anyone help me create 3 Algebra Word Problems
verify that the segments are parallel
Answer:
We know that lines AB and CD are parallel because if you expand them, we know they will never touch.
Step-by-step explanation:
Please help!!
Given f(x) = 3x-4 and g(x) = 2x+6 , find (fog)(x)
Answer:
[tex](f\circ g)(x)=6x+14[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]f(x)=3x-4\text{ and } g(x)=2x+6[/tex]
And we want to find:
[tex](f\circ g)(x)[/tex]
This is equivalent to:
[tex]=f(g(x))[/tex]
Then by substitution:
[tex]=f(2x+6)=3(2x+6)-4[/tex]
Evaluate:
[tex]=f(g(x))=6x+18-4=6x+14[/tex]
Therefore:
[tex](f\circ g)(x)=6x+14[/tex]
The dimensions of a square are altered so that one dimension is increased by 7 feet, while the other is decreased by 2 feet. The are of the resulting rectangle is 90ft^2. Find the original area of the square.
Answer:
64 ft^2
Step-by-step explanation:
(x+7)(x-2)=90
x^2-2x+7x-14=90
x^2+5x-104=0
factor
(x+13)(x-8)=0
x=-13
x=8 ft original square side
area=8x8=64
Answer:
64 ft^2
Step-by-step explanation:
The ministry of health was interested in the relationship between the office habits of workers and health issues. Each year, they distributed a survey to all workers in the public sector that contained various questions on work habits as well as a standard health questionnaire. After 5 years they gathered and analyzed the entire data.
A) Sample study
B)Experiment
C) Observational Study
The researchers found that those workers who reported taking regular 10-minute breaks during the workday were 41% percent more likely to develop cancer over the next five years than workers who didn't leave their offices during the workday
A)The result suggests that there’s a positive correlation between taking 10-minute breaks during the day and developing cancer in public workers.
B) The result suggests that starting to take 10-minute breaks during the workday will increase the risk of developing cancer for a teacher.
C)The result suggests that if a public worker takes 10-minute breaks during the workday, he has a 41% chance of developing cancer.
D)The result suggests that starting to take 10-minute breaks during the workday will increase the risk of developing cancer for a public worker.
Answer:
Step-by-step explanation:
The answer for the second part of the question would be.
C)The result suggests that there's a positive correlation between taking 10-minutes breaks during the say and developing cancer in public workers.
The correct option is A, The result suggests that there’s a positive correlation between taking 10-minute breaks during the day and developing cancer in public workers.
What is correlation?The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when another data value is increased or decreased respectively.
The health ministry only distributes forms to workers every five years to collect information on office jobs and worker health concerns. They are just monitoring the workers, and the survey allows them to assess and establish a link between office employment and worker health concerns. Therefore, it is an observational study.
The conclusion that can be concluded from this study is that there’s a positive correlation between taking 10-minute breaks during the day and developing cancer in public workers.
Hence, the correct option is A, The result suggests that there’s a positive correlation between taking 10-minute breaks during the day and developing cancer in public workers.
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Last year there were 80 members in chess club this year membership decreased by 20% how many members are there? Sorry
Answer:64 people
Step-by-step explanation: total no. of members=80
%decrease=20
20/100 x 80=16(people that left)
people rem.=80-16
Line G has a slope of -2/3. Line age is perpendicular to G. What is the slope of line h?
Perpendicular lines has negative reciprocal slopes.
"Negative reciprocal" is just a fancy way of
saying flip the fraction and change the sign.
So flipping the fraction gives us -3/2 and change the sign to get +3/2.
Extra 13 points on this
Answer and Step-by-step explanation:
This graph is linear. The graph would look like this:
#teamtrees #WAP (Water And Plant) #PAW (Plant And Water)
#PAWG (Plant And Water Gang)
What is the value of x in the equation 4(2x + 12) = 0? a −8 b −6 c 6 d 8
Answer:
the answer is b:-6
Step-by-step explanation:
hoped I helped:)
help help please!!!! thank youuu
Answer:
*Most of these, you just have to get the variable by itself. To check, put the answer in for the letter.*
1. b+8=14
Subtract 8 from both sides
b=6
Check: 6+8=14 ——— 14=14
2. 25-t=15
Subtract 25 from both sides
-t = -10 ––Divide both sides by -1
t=10
Check: 25-10=15 ——— 15=15
3. 9p=81
Divide both sides by 9 to get p alone
p=9
Check: 9(9)=81 ——— 81=81
4. y/7= 2
Multiply both sides by 7 to cancel out the fraction
y=14
Check: 14/7=2 ——— 2=2
5. y+6=10
Subtract 6 from both sides
y=4
Check: 4+6=10 ——— 10=10
6. f-4=9
Add 4 to both sides
f=13
Check: 13-4=9 ——— 9=9
7. 8d=48
Divide both sides by 8 to get d alone
d=6
Check: 8(6)=48 ——— 48=48
8. 10 = r/5
Multiply both sides by 5 to cancel out the fraction
50 = r
Check: 10=50/5 ——— 10=10
9. 15=x/3
Multiply by 3 to cancel out the fraction
45=x
Check: 15=45/3 ——— 15=15
1. 2x + 7 = 2x - 7
2. 3x + 8 = -2x + 8
3. 4(x + 1) = 4x + 4
Answer:
Consider left and right sides of the equations as linear functions.
Then:
1. The equation 1 has lines with the same slope (2) but different y-intercepts (7 and -7), therefore the lines are parallel and no solution.2. The lines have different slopes (3 and 2), therefore they intersect and there is one solution.3. After opening the parenthesis we get both sides same, meaning the lines are same and overlap. The equation has infinitely many solutions.Select all names that apply to the number 3/7
Answer:
WYM
Step-by-step explanation:
10 Points<>I need help ASAP!!!
Answer:
Step-by-step explanation:
A and D
how to calculate perimeter
Answer:
To calculate perimeter add all the sides of the particular shape.
I hope this helps!
Square perimeter formula: P = 4a
Rectangle perimeter formula: P = 2(a + b)
Triangle perimeter formulas:
P = a + b + c or
P = a + b + √(a² + b² - 2ab * cos(γ)) or
P = a + (a / sin(β + γ)) * (sin(β) + sin(γ))
Circle perimeter formula: P = 2πr
Circle sector perimeter formula: P = r(α + 2) (α is in radians)
Ellipse perimeter formula: P = π(3(a + b) - √((3a + b) * (a + 3b)))
Quadrilateral / Trapezoid perimeter formula: P = a + b + c + d
Parallelogram perimeter formulas:
P = 2(a + b) or
P = 2a² + √(2e² + 2f² - 4a²) or
P = 2(b + h/sin(α))
Rhombus perimeter formulas:
P = 4a or
P = 2√(e² + f²)
Kite perimeter formula: P = 2(a + b)
Annulus perimeter formula: P = 2π(R + r)
Regular polygon area formula: P = n * a
Find the area. Simplify your answer.
Answer:
x = 26
Step-by-step explanation:
it is a right angle so
(x+4)3=90
3x+12=90
-12 -12
3x = 90-12
3x = 78
/3 /3
x = 26
Find the missing part .
Please help me by solving this!
Answer:
Ani age is 21
Biju age is 18
Step-by-step explanation:
let Ani age be X
let Biju age be Y
the difference of their age is 3
i.e X - Y = 3......,....(equ. 1)
let Dharam age be A
let Cathy age be B
i.e A = 2x
B = y/2
the difference of their age is 30
Y/2 - 2x = 30..... (equ. 2)
from equ.1 X = ( 3+y).........( equ.3)
y/2 - 2(3+y) = 30
y/2 - 6 + 2y = 30
multiply both side by 2
y - 6 + 2y = 60
y + 2y = 60 - 6
3y = 54
Y = 18
from equ.3
X = 3+Y where y is 18
X = 3+18 = 21
PLS CAN SOMEONE HELP ME PLS
Answer:
20 m
Step-by-step explanation:
Let the length of the perpendicular dropped from vertex C to segment AB be x
By geometric mean property:
[tex]x = \sqrt{16 \times 9} \\ \\ x = \sqrt{144} \\ \\ x = 12 \: m \\ \\ By \: Pythagoras \: Theorem: \\ \\ Distance \: across \: the \: pond \\ \\ = \sqrt{ {16}^{2} + {12}^{2} } \\ \\ = \sqrt{256 + 144} \\ \\ = \sqrt{400} \\ \\ = 20 \: m[/tex]
Carlin pays $ 25 for her monthly phone service and $.02 for each minute m of talk time. Which expression represents her monthly bill?
A. 2m + 25 B. 25m + 0.02 C. .02m + 25 D. 25m + 2
Answer:
I think the answer B
If not then, sorry
Levi resolveu a expressão, 8×(-3)+7×5+(– 10)² ÷ 50, mas apagou o resultado. Resolva você também essa expressão e encontre o resultado. *
Answer:
61
Step-by-step explanation:
8×(-3)+7×5+(-10)²÷50
apply the PEMDAS rule or (parenthesis, exponent, multiplication,division,addtion,subraction)
24+7×5+(-10)²÷50
24+7×5+100÷50
24+35+100÷50
24+35+2
61
use greatest common factor and distributive property to write equivalent expressions 5x+20y
Answer:
I think it is 5 if I did it right
S
Greg’s family went to the movie theater and bought tickets and popcorn. They spent $35 altogether with $9.50 spent on popcorn. Write an equation that can be used to find out how much money x they spent on tickets.
Answer:
x + 9.50 = 35
Step-by-step explanation:
The missing variable in this case is the number of dollars they spent on tickets. In total, combined the tickets and popcorn is equal to 35$,
We already know the amount they spent on popcorn.
X, the amount they spent on tickets + 9.50=35
The town of Passaic had 58,753 people in 1990 and 71,509 people in 2014.
PART A: Find the percent change in population. Explain/Show your
work.
PART B: Was it a percent increase or decrease? Explain how you know.
please help mee
Answer:
21.71% increase
Step-by-step explanation:
increase = Increase ÷ Original Number × 100
12756/58753*100
0.217112318*100
21.71% increase.
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