The average rate of change of a (continuous) function f(x) over an interval [a, b] is given by the so-called difference quotient,
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Here we have f(x) = x² + 8x + 12 and the interval is [-10, -2], so the ARoC of f(x) on this interval is
[tex]\dfrac{f(-2) - f(-10)}{-2 - (-10)} = \dfrac{0 - 32}8 = \boxed{-4}[/tex]
what expression is equivalent to 1/3y
1. 1/3(y+12)-12
2. 1/6y+1/3(y+3)
3. 1/6y+1/6(y+12)-2
4. 1/3y+1/3(6-y)
The expression that is equivalent to 1/3y is 1/6y + 1/6(y + 12) - 1/6 * 12
How to determine the equivalent expression?The expression is given as:
1/3y
Express 1/3y as 1/6y + 1/6y
So, we have:
1/6y + 1/6y
Factor out y
1/6y + 1/6(y)
Add 0 to the above equation
1/6y + 1/6(y + 0)
Express 0 as 12 - 12
1/6y + 1/6(y + 12 - 12)
Expand
1/6y + 1/6(y + 12) - 1/6 * 12
Evaluate the product
1/6y + 1/6(y + 12) - 2
Hence, the expression that is equivalent to 1/3y is 1/6y + 1/6(y + 12) - 1/6 * 12
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The expression that is equivalent to 1/3y is 1/6y + 1/6(y + 12) - 1/6 * 12
How to determine the equivalent expression?The expression is given as:
1/3y
Express 1/3y as 1/6y + 1/6y
So, we have:
1/6y + 1/6y
Factor out y
1/6y + 1/6(y)
Add 0 to the above equation
1/6y + 1/6(y + 0)
Express 0 as 12 - 12
1/6y + 1/6(y + 12 - 12)
Expand
1/6y + 1/6(y + 12) - 1/6 * 12
Evaluate the product
1/6y + 1/6(y + 12) - 2
Therefore, the expression that is equivalent to 1/3y is 1/6y + 1/6(y + 12) - 1/6 * 12
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What quadrant is the point (2, -5) in?
Answer:
quadrant 4
Step-by-step explanation:
(2,-5) would be in the 4th quadrant
A surveyor is measuring the distance across a canyon. He sets up two similar right triangles and finds that the length of CD = 12 feet and the length of DE = 16 feet.
If △ABC ~ △EDC, what is the length side AB?
The length side AB is 64 ft , Option D is the correct answer.
What is a Right triangle ?A triangle that has one angle 90 degree is called Right angled Triangle.
From the figure it can be seen that
The triangle CDE is a right Triangle
Applying Pythagoras theorem to find the length of CE
CE² = 12² + 16²
CE = 20 ft
As both the triangles are similar therefore the ratio of the sides will be equal
BC : CD = AC : CE
48 / 12 = AC / 20
AC = 80ft
As Triangle ABC is also a right angled triangle
Applying Pythagoras theorem to find the length of AB
AC² = BC² +AB²
6400 = 48² +AB²
AB² = 4096
AB = 64 ft
Therefore Option D is the correct answer.
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Answer:
64 ft.
Step-by-step explanation:
Keep it simple, just givin' the answer :)
what is the square root of 10,000,000
Answer:
1000√10or 3162.2776601683795
Step-by-step explanation:
what is the square root of 10,000,000?
√10000000
= √2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5
= √26 x 2 x 56 x 5
= 1000√10
or 3162.2776601683795
The additive inverse of an element of x of a set is the number, which when added to x gives the answer 0. In the set {-3, -2, -1, 0, 1, 2, 3}, what is the additive inverse of -2?
Answer:
2
Step-by-step explanation:
the additive inverse of - 2 is 2 , since
- 2 + 2 = 0
What is the approximate length of the radius, r? use 3.14 for . round to the nearest inch. 12 inches 24 inches 38 inches 46 inches
Answer:
2×3.14×r=75
6.28 r=75
r=75/6.28=11.943=12 inch (nearly)
change 5/8 to percentage
Answer: 62.5%
Step-by-step explanation:
First, you must simplify 5/8 into a decimal and then multiply that by 100 to get the percentage of the fraction.
[tex]\frac{5}{8}=0.625[/tex] [tex]0.625*100=62.5[/tex]%
I hope this helps!! Pls give brainliest :)
graph y = − 3/2 x − 3
Answer:
Step-by-step explanation:
THIS WILL BE A STRAIGHT LINE rising to the left as the coefficient of x is negative ( -3/2),
When x = 0 y = -3 so mark the point (0, -3) on your graph paper.
When x = 6, y = -3/2 * 6 - 3 = -9 - 3 = -12
So mark the point (6, -12)
The graph will be the straight line passing through the above 2 points.
The Pine Scrub Rail Trail is 126 miles long. If the Willy-Nilly Bike Club rides 18 miles per day, how many days will it take them to ride from one end of the trail to the other?
A. 6 days
B. 9 days
C. 7 days
D. 8 days
What is the inverse of this function?
8v, for x > 0
Answer:
f(x) = (x/8)^2 for x ≥ 0
Step-by-step explanation:
y = 8 sqrt x switch x and y
x = 8 sqrt y now solve for y
(x/8)^2 = y
need help with work would give more points but poor
Answer:
Step-by-step explanation:
2.5
4 quarts per gallon
8 quarts per 2 gallons
2 quarts is half a gallon since 4 quarts is a full gallon
answer: 2.5
Determine the most precise name for ABCD (parallelogram, rhombus, rectangle, or square). Explain how you determined your answer. You must support your answer using length or slope. A(3, 5), B(7, 6), C(6, 2), D(2, 1)
In the imaged attached, the most precise name for ABCD is known to be rhombus.
What is the shape about?Looking at the shape attached, one can see that the diagonals of a parallelogram are said to be bisecting one other and if it cross at right angles, it is said to be a rhombus.
Using the Diagonal midpoints of AC and BD, the equation will be:
(A+C)/2
(B+D)/2
To find if the midpoints are similar, then:
A +C = (3, 5) +(6, 2) = (9, 7)
B +D = (7, 6) +(2, 1) = (9, 7)
Therefore, from the solution above, the midpoints of the diagonals are the same, making the shape to be a parallelogram.
In terms of Diagonal vectors, the shape will be perpendicular when the figure is a rhombus. So:
AC = C -A = (6, 2) -(3, 5) = (3, -3)
BD = D -B = (2, 1) -(7, 6) = (-5, -5)
So the lengths will be (3√2 vs 5√2).
Note also that the dot-product of these values need to be zero if they are perpendicular and as such:
AC·BD = x1·x2 +y1·y2 = (3)(-5) +(-3)(-5) = -15 +15 = 0
Therefore, one can say that the diagonals are known to different length and are perpendicular bisectors, so the shape above is regarded as rhombus.
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help me solve this give steps as well please
The total cost of 6 wave pool tickets with the discount included would be $73.5.
How to calculate the total value of 6 tickets with the discount?To calculate the total cost we must multiply the value of each ticket by the number of tickets to be purchased, in this case there are 6:
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Help please.. z zzz z Z z z z z z z z z z z z z zz
Solve the following
[tex]5x-2= -9x+8[/tex]
Answer:
5x - 2 = (-9x) + 8
5x + 9x = 8 + 2
14 x = 10
x = 10 / 14
x = 5/7
Answer:
5 / 7
Step-by-step explanation:
Step 1: Move the variables to one side and the numbers to the other. We get 14x = 10.
Step 2: Then we solve for x. x is equal to 10 / 14, which simplifies to 5 / 7.
When planning road development, the road commission estimates the future population using the function represented in the table, where x is the time in years and f(x) is the total population.
What is the significance of 160,000 in the function?
the maximum population of the city
the expected population in 5 years
the initial population at the time of the estimation
the amount of increase in the popu
Considering that 160,000 is the y-intercept of the function, it's significance is given by:
the initial population at the time of the estimation.
What is the y-intercept of a function f(x)?The y-intercept is f(0), that is, the value of y when x = 0, which is interpreted as the initial value of the function.
Researching this problem on the internet, it is found that f(0) = 160,000, hence the significance of 160,000 in the function is given by:
the initial population at the time of the estimation.
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О A. 24
B. 12
О с. 92
D. 46
A
12
46°
46°
C
Answer:
I think A or C.
Step-by-step explanation:
Suppose that the lifetimes of tires of a certain brand are normally distributed with a mean of 74000 miles and a standard deviation of miles. these tires come with a -mile warranty. the manufacturer of the tires can adjust during the production process, but the adjustment of is quite costly. the manufacturer wants to set once and for all so that only of the tires will fail before warranty expires. find the standard deviation to be set. carry your intermediate computations to at least four decimal places. round your answer to at least one decimal place.
The standard deviation will be 6816.9645.
How to compute the standard deviation?From the information given, the mean is 74000 and X is given as 60000.
P[(Z < (-60000 - 74000)/SD] = 0.02
Note that 0.02 will be -2.0537 under the normal distribution table.
-14000/SD = -2.0537
SD = -14000/-2.0537
SD = 6816.9645
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Lily sold 18 items at the street fair. she sold bracelets for $6 each and necklaces for $5 each for a total of $101. which system of equations can be used to find b, the number of bracelets she sold, and n, the number of necklaces she sold? b n = 101 6b 5n = 18 b n = 101 5b 6n = 18 b n = 18 6b 5n = 101 b n = 18 5b 6n = 101
Answer:
[tex]b + n = 18[/tex]
[tex]6b + 5n = 101[/tex]
f(x)=x^2. which of these is g(x) ?
a. g(x)=(1/5x)^2
b. g(x)=5x^2
c.g(x)=(1/4x)^2
d.g(x)=1/5x^2
Answer:
a
Step-by-step explanation:
we know that g(x) means y therefore in this case let's suppose we have the coordinate (5;y) so we must find the corresponding y value
*DO THE TRIAL AND ERROR METHOD*
take any equation above and substitute the value of x of which is 5 and the corresponding value should be 1.
[tex]g(x) = (\frac{1}{5} x) {}^{2} [/tex]
Find the equation of the parabola that has zeros of x = - 6 and x = 6 and a y-intercept of (0, 4)
The equation of the parabola that has zeros of x = - 6 and x = 6 and a y-intercept of (0, 4) would be Y=-1/9(x^2-36).
What is the equation of the parabola that has zeros?Since the zeros are symmetrical to the y axis, the equation can be written as;
y = a(x-b)(x+b),
where a is a scale factor and b is x-intercept.
From the given zeroes
y = A(x-6)(x+6).
Now we can plug in the y-intercept (0,4)
4 = A(0-6)(0+6)
4 = A(-36)
-36A=4
A = -1/9
Therefore the equation would be
Y = -1/9(x-6)(x+6),
or Y=-1/9(x^2-36)
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What is the transformation of C(9, 3) when dilated with a scale factor of 1/3,
using the point (3, 6) as the center of dilation
The transformation of C(9, 3) when dilated with a scale factor of 1/3, using the point (3, 6) as the center of dilation would be an option B: C'(3,1).
What is Dilation transformation?A dilation transformation is a transformation that changes the size of the original figure but the shape remains unchanged.
If any figure is dilated by a scale factor k with the center of dilation as the origin.
Then the change of transformation in each of the vertices of the figure is given:
(x,y) → (kx, ky)
It is given a point C which is located at C(9,3).
Hence, here k=3
We get:
C(9,3) → C'(9×3,3×3)
C(9,3) → C'(27,9) = C'(3,1)
Hence, the transformation of C(9, 3) when dilated with a scale factor of 1/3, using the point (3, 6) as the center of dilation would be an option B: C'(3,1).
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Answer:
(5,5)
Step-by-step explanation:
count from the center
N
32
NEXT QUESTION
C
Patty had four times as many quarters as nickels. She had $12.60 in all. How many nickels and how many quarters did
she have?
G
Which of the following equations could be used to solve the problem?
Answer:
See below
Step-by-step explanation:
q = quarters value = .25 q
n = nickels = 4q value = .05 (4q)
summed = 12.60
.25q + .05(4q) = 12.60 <====== can be used to solve the problem
.45q = 12.60
q = 28 quarters then nickels = 4q = 112
The pipe has a length 29cm, internal diameter 6.5cm and thickness 0.5cm. What is the Volume
Answer:
Length of pipe = 21 cm
Internal diameter = 4 cm
Internal radius = \frac{4}{2} = 2 cm24=2cm
Thickness = 0.5 cm
Outer radius = 2+0.5=2.5 cm
Volume of pipe =\pi R^2 h - \pi r^2 hπR2h−πr2h
Volume of pipe =\frac{22}{7} (2.5)^2 (21)-\frac{22}{7}(2)^2(21)=148.5 cm^3
=\frac{22}{7} (2.5)^2 (21)-\frac{22}{7}(2)^2(21)=148.5 cm^3722(2.5)2(21)−722(2)2(21)=148.5cm3
Hence The volume is 148.5 cubic cm.
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The thickness of a metal pipe is 1.5cm. The inner diameter is 21cm. What is the volume of metal required for a pipe of length 7cm
Solve 2( 32x-5) -4 =11
Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces.
The equation will be given as y = 6x for the given information in the question.
The complete question is as below:-
Mr Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces Which ordered pair is a viable solution if x represents the number of books he orders and y represents the total weight of the books, in ounces?
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Here we are given that the weight of each book is 6 ounces. If there are x number of books, the weight of x books will be 6 times x.
And if y represents the total weight, we can form an equation describing the relation between a number of books and their net weight. The equation can be
y = 6x
Hence all the ordered pairs satisfying the above equation will represent the number of books and the total weight.
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which shows the correct substitution of the values a, b, and c Dr the equation 0=-3x^2-2x+6 into the quadratic formula? Quadratic formula: x= -b±√b^2-4ac/2a
Answer: Option 1
Step-by-step explanation:
Here, a = -3, b = -2, c = 6.
What is m∠M? I don't exactly remember how to do this type on problem...
Answer:
m∠M=98º
Step-by-step explanation
Sum of interior angles;
3x-16+x+6+x = 180
5x = 180-6+16
5x = 190
x = 38º
Angle M;
m<M= 3x - 16 = 3(38)-16= 98º
m∠M=98º
Answer:
<M = 98
Step-by-step explanation:
The sum of the angles of a triangle is 180 degrees
< M + < N + < O = 180
3x-16 + x + x+6 = 180
Combine like terms
5x - 10 = 180
Add 10 to each side
5x-10 + 10 = 180+10
5x = 190
Divide by 5
5x/5 = 190/5
x=38
We want to find <M
<M = 3x-16 = 3*38 -16 = 114-16 =98
It costs $20 a day to rent a car and $30 for a full tank of gas. If Stacy fills up the tank 3 times and has the car rented for 14 days, how much does she owe?
Answer:
$20 × 14 days = $280
&30 × 3 = $90
&280 + $90 = $370
Answer:
For car she owes=
$20 x 14 = $280
For tank she owes=
$30 x 3 = $90
Therfore in total she owes,
$280 + $90 = $370
Which is an example of a statistical question? Questions Question 1 How many pets does Alisha have at home? Question 2 How old were you when you got your first pet? Do you like having a pet? Question 3 Question 4 What is Alisha's pet's name? question 1 O question 2 O question 3 O question 4
Answer:
Do you like having a pet? - statistcal question
Step-by-step explanation:
^^^^
