The average rate of change of the given function is 12.
The average rate of change of function f on interval [a,b] is:
f(b) -f(a)/b-a
we have interval [x₁,x₂]
[x₁,x₂] = [3,5]
f(3) = x²₊4x
f(3) = 3²+4(3)
f(3) = 21
f(5) = x²₊4x
f(5) = 5²+4(5)
f(5) = 45
f(x₂) -f(x₁)/x₂-x₁
⇒ 45-21/5-3
= 24/2
= 12
The average rate of change of function f(x) = x²+4x on interval [3,5]
is 12.
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y=-x+4
x + 2y = -8
How many solutions does this linear system have?
a. one solution: (8,0)
b. one solution: (0,8)
c. no solution
d. infinite number of solutions
The linear system of equation has one solution as x = 16 and y = -12.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
The given system of equation are :
y=-x+4..........(1)
x + 2y = -8......(2)
Now, solving the above using substitution of y in equation (2) :
x + 2y = -8
x+2(-x+4) = -8
x-2x+8 = -8
-x = -16
x = 16
Now, substituting back x value in equation (1) we get :
y = -x+4
y = -16 +4
y = -12
Therefore, The linear system of equation has one solution as x = 16 and y = -12.
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A plumber has a 20Foot
Answer:
14
Step-by-step explanation:
I think the question is whether: "a plumber has a 20-foot piece of PVC pipe. how many 7/5 foot pieces can be cut from the 20-foot piece?"
Tom bought a pencil case for $60 and sold it to gain a profit of 20% on his cost price.
(a) How much money did he gain? (b) How much money did he sell the pencil case for?
help please rn please help
Answer: the answer is MO=5
Step-by-step explanation:
EASY QUESTION 20 POINTS
Answer:(7/9)^12
Step-by-step explanation:
Answer:
C. (7/9)^12
Step-by-step explanation:
(49/81)^6 = (7^2/9^2)^6 = (7/9)^(2x6) = (7/9)^12
Kenneth measured a hotel and made a scale drawing. The scale he used was 1 inch = 4 feet. The actual length of a room in the hotel is 20 feet. How long is the room in the drawing
Answer:
The room is 5 inches in the drawing.
Step-by-step explanation:
If the room is 20 feet and each inch in his drawing measures 4 feet what you need to do is see how many times 4 goes into 20.
4 times 5 = 20
So the answer would be 5
Hope it helps! =D
Find the slope of the line graphed below.
PLEASE PLEASE PLEASE HELPP ME GUYS
Answer: m=2
Step-by-step explanation:
Highlighted points: (0, 4) and (-4, -4)
m=(y2-y1)/(x2-x1)
m=(-4-4))/(-4-0)
m=(-8)/(-4)
m=2
For the function
f(x) = x + 10/6x + 4, consider the following.
(a)Find the vertical and horizontal asymptotes for the graph of f.
Vertical:
Horizontal:
b)Find f^ −1.
f^ −1(x) =
c)Find the vertical and horizontal asymptotes for the graph of
f^ −1
Vertical:
Horizontal:
Show all steps.
Using the concepts of asymptotes and inverse function, we have that:
a) For f, the vertical asymptote is x = -2/3 and the horizontal asymptote is y = 1/6.
b) The inverse function is: [tex]y = f^{-1}(x) = \frac{4x - 10}{1 - 6x}[/tex]
c) For the inverse function, the vertical asymptote is x = 1/6 and the horizontal asymptote is y = -2/3.
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.For this problem, the function is given by:
[tex]f(x) = \frac{x + 10}{6x + 4}[/tex]
The zero of the denominator is:
6x + 4 = 0
6x = -4
x = -4/6 = -2/3.
Hence the vertical asymptote is x = -2/3.
The horizontal asymptote is given as follows:
[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{x + 10}{6x + 4} = \lim_{x \rightarrow \infty} \frac{x}{6x} = \lim_{x \rightarrow \infty} \frac{1}{6} = \frac{1}{6}[/tex]
How to find the inverse function?To find the inverse function of a function y = f(x), we exchange x and y then isolate y.
Exchanging x and y, we have that:
[tex]x = \frac{y + 10}{6y + 4}[/tex]
Applying cross multiplication:
x(6y + 4) = y + 10
6xy - y = 10 - 4x
y - 6xy = 4x - 10
y(1 - 6x) = 4x - 10
[tex]y = f^{-1}(x) = \frac{4x - 10}{1 - 6x}[/tex]
Applying the same procedure, for the inverse function, the vertical asymptote is x = 1/6 and the horizontal asymptote is y = -2/3.
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You can fill a 15-gallon tank of gas for $53.08 or buy gas for $3.60/gallon.
Answer: the better option would be to fill your tank up 15 gallons for $53.08
If you were to multiply 3.60 by 15, you would get 54.
53.08 < 54, therefore 53.08 is the better option.
Hope this helps!
finding the common difference
5,11,____ , 23,29,____…
Answer:
5,11 , 17, 23, 29, 35
Step-by-step explanation:
Answer:
5, 11, 17, 23, 29, 36
Step-by-step explanation:
To get from 5 to 11, we add 6. Similarly, to get from 11 to _, we add 6, and get 17. This also works with 29 to _. We get 36.
5 1/2 x 1 1/4
put in simplest form
Answer:
6 7/8
Step-by-step explanation:
First we would need to turn the 5 1/2 into a improper fraction. Then, do the same for the 1 1/4 as well. To do this, multiply the denominator by the whole number and then add the numerator. Once you get those values, you simply multiply across, meaning the numerators get multiplied together and the denominators get multiplied together. The value you get is the improper fraction form of the simplest form. Then you can convert it back to a mixed fraction if that is the form you need. To do this divide the numerator by the denominator. Now we have a value of 11/2 x 5/4 = 55/8. So divide 55 by 8 and leave the remainder in fraction form. Therefore the answer should be 6 7/8, after it is reduced.
I hope this helps, have a blessed day! :)
Logan's bakeshop makes cupcakes that cost $.95 each. Logan knows that 20% of the cupcakes will spoil. Assume Logan wants a 35% markup on cost and produces 60 cupcakes. What should Logan charge for each cupcake?
The amount Logan should charge for each cupcake is $1.60 based on the markup of 35%
What is equivalent inputs for 60 cupcakes?
The equivalent inputs for 60 cupcakes, means the number of cupcakes that the materials used would have yielded in cupcakes if there was no wastage, hence, the cost per unit needs to be expressed to include 20% wastage
equivalent cost per unit=$0.95/(1-20%)=$1.1875
The 35% markup needs to be added to the equivalent cost per unit since markup is the profit as a percentage of cost
selling price=$1.1875*(1+35%)
selling price=$1.60
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Graph the line with a slope of 1/3 passing through point (-1, -1)
Considering the expression of a line, the line is y= 1/3x -2/3 and the graph of this line is shown in the attached image.
Definition of lineA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing the value of slope m, substituting this value and the value of the point in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
Line in this caseIn this case, you know:
The line has a slope of 1/3The line passes through point (x,y)=(-1, -1)Substituting the value of the slope m:
y= 1/3x +b
Substituting the point to calculate the value of b:
-1= 1/3×(-1) + b
-1= -1/3 + b
-1 + 1/3= b
-2/3= b
Finally, the line is y= 1/3x -2/3 and the graph of this line is shown in the attached image.
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The sum of three consecutive odd numbers is 177. Find the number. Step by step please
Answer:
57, 59 and 61
Step-by-step explanation:
Let the first odd number be n The next consecutive odd number is n + 2 and the next one after that is n + 4
(consecutive odd numbers have difference of 2 between them. For example if 7 is the first odd number next one is 9(7+2) and the next one is 11(7+4)
We are given that the sum of the numbers is 177. So we have the following equation:
n + (n + 2) + (n +4) = 177
Simplifying gives
n + n + 2 + n + 4 = 177
Collect like terms:
n + n + n + 2 + 4 = 177
3n + 6 = 177
Subtract 6 from both sides
==> 3n = 177 - 6
==> 3n = 171
Divide by 3 both sides
3n/3 = 171/3
n = 57 and this is the first of the odd numbers
The next odd number is 57+ 2 = 59
and the next one after that is 59 + 2 = 61 (same as 57 + 4)
The vertices of a figure are given. What are the coordinates of the image after the given dilation? Identify the type of dilation?
Q (-3,0), R (-3,6), T (4,6), U (4,0)
k=1/3
The new images has vertices Q´(-1, 0), R´(-1, 2), T´(4/3, 2), U´(4/3, 0) and the type of dilation is contraction.
When we dilate the points of a given figure, we simply multiply each x-coordinate and y-coordinate by the scale factor.
Here the points are Q (-3,0), R (-3,6), T (4,6), U (4,0) and the scale factor is
k = 1/3
Therefore,
⇒ Q (-3,0) → Q´ (-3 × 1/3,0 × 1/3) = (-1, 0)
⇒ R (-3,6) → R´ (-3 × 1/3, 6 × 1/3) = (-1, 2)
⇒ T (4,6) → T´ (4 × 1/3, 6 × 1/3) = (4/3, 2)
⇒ U (4,0) → U´ (4 × 1/3, 0 × 1/3) = (4/3, 0)
Thus, the new images has vertices Q´(-1, 0), R´(-1, 2), T´(4/3, 2), U´(4/3, 0) and the type of dilation is contraction
What is dilation?
Dilation is the process of modifying the dimensions of an object or shape by varying some scale variables. For instance, a circle with a radius of 10 units gets shrunk to a circle with a radius of 5 units. This technique is applied in photography, fine art, logo design, and other fields.
Four fundamental categories of transformations exist in geometry.
These are:
RotationTranslationReflectionResizing or DilationLearn more about Dilation
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Solve the system by back substitution.
-2x - 4y - z - 3w = -5
y + 6z + 2w = 8
4z + 4w = 8
-4w = -12
Solution should be set like {( _ , _ , _ , _ )}
Answer:
w = 3, x = -35/2, y = 8, z = -1
Step-by-step explanation:
Solve the following system:
{-3 w - 2 x - 4 y - z = -5
{2 w + y + 6 z = 8
{4 z + 4 w = 8
{-4 w = -12
In the fourth equation, look to solve for w:
{-3 w - 2 x - 4 y - z = -5
{2 w + y + 6 z = 8
{4 z + 4 w = 8
{-4 w = -12
Divide both sides by -4:
{-3 w - 2 x - 4 y - z = -5
{2 w + y + 6 z = 8
{4 z + 4 w = 8
{w = 3
Substitute w = 3 into the first, second, and third equations:
{-9 - 2 x - 4 y - z = -5
{6 z + y + 6 = 8
{4 z + 12 = 8
{w = 3
In the third equation, look to solve for z:
{-9 - 2 x - 4 y - z = -5
{6 z + y + 6 = 8
{4 z + 12 = 8
{w = 3
Subtract 12 from both sides:
{-9 - 2 x - 4 y - z = -5
{6 z + y + 6 = 8
{4 z = -4
{w = 3
Divide both sides by 4:
{-9 - 2 x - 4 y - z = -5
{6 z + y + 6 = 8
{z = -1
{w = 3
Substitute z = -1 into the first and second equations:
{-4 y - 2 x - 8 = -5
{y = 8
{z = -1
{w = 3
Substitute y = 8 into the first equation:
{-2 x - 40 = -5
{y = 8
{z = -1
{w = 3
In the first equation, look to solve for x:
{-2 x - 40 = -5
{y = 8
{z = -1
{w = 3
Add 40 to both sides:
{-2 x = 35
{y = 8
{z = -1
{w = 3
Divide both sides by -2:
{x = -35/2
{y = 8
{z = -1
{w = 3
Collect results in alphabetical order:
Answer: {w = 3, x = -35/2, y = 8, z = -1
Calculate (multiply (1-2i)(6+5i)
Answer:
-7 i + 16
Step-by-step explanation:
Simplify the following:
(-2 i + 1) (5 i + 6)
(1 - 2 i) (6 + 5 i) = (1) (6) + (1) (5 i) + (-2 i) (6) + (-2 i) (5 i):
6 + 5 i - 2 i×6 - 2 i×5 i
-2×6 = -12:
6 + 5 i + -12 i - 2 i×5 i
-2 i×5 i = -2 i^2 5:
6 + 5 i - 12 i + -2 i^2×5
i^2 = -1:
6 + 5 i - 12 i - 2-1×5
-2 (-5) = 10:
6 + 5 i - 12 i + 10
6 + 5 i - 12 i + 10 = (6 + 10) + (5 i - 12 i) = 16 - 7 i:
Answer: -7 i + 16
Answer: your answer to this question would be 16-7i
Step-by-step explanation:
A dietitian at a hospital wants a patient to have a meal that has 53 grams of protein, 41 grams of carbohydrates, and
87.5 milligrams of vitamin A. The hospital food service tells the dietitian that the dinner for today is salmon steak,
baked eggs, and acorn squash. Each serving of salmon steak has 20 grams of protein, 30 grams of carbohydrates,
and 1 milligram of vitamin A. Each serving of baked eggs contains 20 grams of protein, 3 grams of carbohydrates, am
25 milligrams of vitamin A. Each serving of acorn squash contains 3 grams of protein, 20 grams of carbohydrates, an
37 milligrams of vitamin A. How many servings of each food should the dietitian provide for the patient?
How many servings of each food should the dietitian provide? Select the correct choice below and fill in any answe
boxes within your choice.
salmon steak (x),
baked eggs (y), and acorn squash (z).
OA. The dietitian should provide
(Simplify your answers.)
OB. There are an infinite number of combinations of servings of salmon steak (x), baked eggs (y), and acorn
squash (z) that the dietitian can provide. Using ordered triplets, the solution can be written as {(x,y,z) | x=
y=
z is any real number}
(Simplify your answers. Type expressions using z as the variable as needed.)
OC. There are no combinations of servings of each food that the dietitian can provide.
nwm życzę powodzenia kolego drogi
For the piecewise function, find the values g(-6), g(1), and g(8).
The output values of g(-6), g(1), and g(8) in the given piecewise function are -1, 6 and -6 respectively.
What are the output values of g(-6), g(1), and g(8) in the given piecewise function?Given the piecewise function in the question;
x + 5, for x ≤ 1
g(x) = {2 - x, for x > 1
g(-6) = ?g(1) = ?g(8) = ?Determine the output value of g(-6), -6 falls in the domain of x ≤ 1,
Hence;
g(x) = x + 5
g(-6) = -6 + 5
g(-6) = -1
Determine the output value of g(1), 1 falls in the domain of x ≤ 1,
Hence;
g(x) = x + 5
g(1) = 1 + 5
g(1) = 6
Determine the output value of g(8), 8 falls in the domain of x > 1,
Hence;
g(x) = 2 - x
g(8) = 2 - 8
g(8) = -6
Therefore the output values of g(-6), g(1), and g(8) in the given piecewise function are -1, 6 and -6 respectively.
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The radius of a circle is 12 inches. What is
the diameter?
Answer:
diameter is 24 inches
Step-by-step explanation:
diameter is basically two times the radius
Solve.
3z +2y-z = 8
2z+22=-4
z+3y=4
Answer:
(1, 1,-3)
Step-by-step explanation:
Rewrite using an exponent.
Answer:
2[tex] {}^{5} [/tex]
Step-by-step explanation:
2×2×2×2×2 = 2[tex] {}^{5} [/tex]
An airplane takes 5 hours to travel a distance of 3900 miles with the wind. The return trip takes 6 hours against the wind. Find the speed of the plane in still air and the speed of the wind.
The speed of the plane in still air is ____ MPH and the speed of the wind is ____ MPH.
The speed of plane in still air is 715 MPH and the speed of the wind is 65 MPH
Distance travelled by airplane = 3900 miles
Time taken by the plane to travel the distance with the wind = 5 hours
Time taken by the plane to travel the distance against the wind = 6 hours
Let the speed of the plane in still air be x
Let the speed of the wind be y
Finding the speed of the air and airplane when distance is covered with the wind using the formula:
Speed of airplane + Speed of wind = Distance/Time
x + y= 3900/5
x + y = 780------(1)
Finding the speed of the air and airplane when distance is covered against the wind using the formula:
Speed of airplane - Speed of wind = Distance/Time
x - y = 3900/6
x - y = 650------(2)
Equating (1) and (2) we get:
2x = 1430
x = 715
Putting x = 715 in (1) we get:
y = 65
So, Speed of airplane in still air is 715 MPH and Speed of wind is 65 MPH
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At Keller's Bike Rentals, it costs $15 to rent a bike for 4 hours.
How many dollars does it cost per hour of bike use?
Answer:
3.75
Step-by-step explanation:
15/4=3.75
Answer:
12 1/3
Step-by-step explanation:
because when you find the total cost plus divide it gives u the answer
The store is selling lemons at $0.65 each. Each lemon yields about 2 tablespoons of juice. How much
will it cost to buy enough lemons to make two 9-inch lemon pies, each requiring half a cup of lemon
juice?
The cost of buying lemons to make two 9-inch lemon pies is $5.20.
What is the total cost?The first step is to convert cup to tablespoons
1 cup = 16 tablespoons
one 9-inch lemon pie would require 8 tablespoons (16 /2)
two 9-inch lemon pie would require 16 tablespoons (8 x 2)
The second step is to determine how much lemons would be needed.
Lemons needed = table spoons needed / table spoon one lemon would yield
16 / 2 = 8 lemons
The total cost of lemons needs to make the pies = cost of one lemon x number of lemons needed
8 x 0.65 = $5.20
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hans bought three books at a bookstore. Here are the prices(in dollars). 6,19.1,6.97 what is the total amount Hans paid at the bookstore
Answer:
$32.07
Step-by-step explanation:
Just add them together.
two complementary angles are X + 4 degree and 2 x - 7 degree find the value of x
Answer:
x+4+2x-7=180
3x-3=180
3x=183
x=61
[tex] \rm \int_{0}^1 \int_{0}^1x \bigg \{ \frac{1}{1 - xy} \bigg \}dydx \\ [/tex]
The fractional part vanishes when the argument is an integer; in this case, for
[tex]\left\{\dfrac1{1-xy}\right\} = 0 \iff \dfrac1{1-xy} = n \iff xy = \dfrac{n-1}n[/tex]
which are hyperbolas in the [tex](x,y)[/tex]-plane.
Observe that between neighboring hyperbolas, we have
[tex]\dfrac{n-1}n < xy < \dfrac n{n+1} \\\\ ~~~~ \implies \dfrac1{n+1} < 1-xy < \dfrac1n \\\\ ~~~~ \implies n < \dfrac1{1-xy} < n+1 \\\\ ~~~~ \implies \left\{\dfrac1{1-xy}\right\} = \dfrac1{1-xy} - \left\lfloor\dfrac1{1-xy}\right\rfloor = \dfrac1{1-xy} - n[/tex]
Split up the integral over [tex][0,1)^2[/tex] along the curves [tex]xy=\frac{n-1}n[/tex]. The subregions somewhat resemble the layers or scales of an onion (see attached plot with the first 5 "scales").
Let [tex]S_n[/tex] denote the [tex]n[/tex]-th ([tex]n\in\Bbb N[/tex]) "scale", starting from the blue region closest to the origin and counting diagonally upward in the direction of (1, 1).
In Cartesian coordinates, the integral over [tex]n[/tex]-th "scale" is
[tex]\displaystyle \iint_{S_n} x \left(\frac1{1-xy} - n\right) \, dy \, dx \\\\\\ ~~~~~~~~= \int_{(n-1)/n}^{n/(n+1)} \int_{(n-1)/(nx)}^1 x \left(\frac1{1-xy} - n\right) \, dy dx \\\\\\ ~~~~~~~~~~~~~ + \int_{n/(n+1)}^1 \int_{(n-1)/(nx)}^{n/((n+1)x)} x \left(\frac1{1-xy} - n\right) \, dx[/tex]
(see attached plot of the 2nd "scale" for reference)
The integral is trivial, so I'll leave it to you to confirm that it drastically reduces to
[tex]\displaystyle \iint_{S_n} x \left(\frac1{1-xy} - n\right) \, dy \, dx = \frac1{2n (n+1)^2} = \frac12 \left(\frac1n - \frac1{n+1} - \frac1{(n+1)^2}\right)[/tex]
Now we recover the original integral by summing over [tex]\Bbb N[/tex].
[tex]\displaystyle \int_0^1 \int_0^1 x \left\{\frac1{1-xy}\right\} \, dy \, dx = \frac12 \sum_{n=1}^\infty \left(\frac1n - \frac1{n+1} - \frac1{(n+1)^2}\right) \\\\ ~~~~~~~~ = \frac12 \left(\left(1-\frac12\right)+\left(\frac12-\frac13\right)+\left(\frac13-\frac14\right)+\cdots\right) - \frac12 \sum_{n=2}^\infty \frac1{n^2} \\\\ ~~~~~~~~ = \frac12 - \frac12 \left(\sum_{n=1}^\infty \frac1{n^2} - 1\right) \\\\ ~~~~~~~~ = \frac12 - \frac12 \left(\frac{\pi^2}6 - 1\right) = \boxed{1 - \frac{\pi^2}{12}}[/tex]
Kristen goes on a cave tour with her family. They climb down to 8 meters below ground level.
Then they climb the opposite of -8 meters to return to ground level.
How many meters did they climb in all? Enter your answer in the box
Answer:
16 meters is the answer of this question
Полоску бумаги разрезали на 7 частей. После этого самую большую
из полученных частей снова разрезали на 7 частей. Затем снова самую большую
из полученных частей разрезали на 7 частей. Так поступили много раз: на
каждом шаге самую большую часть разрезали на 7 частей. Могло ли в итоге
получиться 500 частей?
Answer:
2556285=68358556
Step-by-step explanation:
+58385-5838688(68589)8999=9858288