The given inequality holds for the open interval (2.97,3.03)
It is given that
f(x)=6x+7
cL=25
c=3
ε=0.18
We have,
|f(x)−L| = |6x+7−25|
= |6x−18|
= |6(x−3)|
= 6|x−3|
Now,
6|x−3| <0.18 then |x−3|<0.03 ----->−0.03<x-3<0.03---->2.97<x<3.03
the given inequality holds for the open interval (2.97,3.03)
For more information on inequality click on the link below:
https://brainly.com/question/11613554
#SPJ4
Although part of your question is missing, you might be referring to this full question: For the given function f(x) and values of L,c, and ϵ0, find the largest open interval about c on which the inequality |f(x)−L|<ϵ holds. Then determine the largest value for δ>0 such that 0<|x−c|<δ→|f(x)−|<ϵ.
f(x)=6x+7,L=25,c=3,ϵ=0.18
.
a. How much do 4 dozen buttons cost?
It costs 6$ for 48 buttons
b. How many dozens of buttons can the organizers buy for $27?
the cost of 4 dozens of buttons will be $ 6 and the organizers can buy 216 buttons for $ 27.
We are given that:
Cost of 48 buttons = $ 6
48 buttons = $ 6
Divide both sides by 48:
1 button = $ 6 / 48 = $ 1 / 8
Now, the cost of 4 dozen buttons will be:
4 dozen buttons = 12 × 4 = 48
So, the cost will be 4 6 only.
For $ 27, the organizers can buy:
Number of buttons = 27 ÷ 1 / 8
Number of buttons = 27 × 8
Number of buttons = 216 buttons.
Therefore, the cost of 4 dozens of buttons will be $ 6 and the organizers can buy 216 buttons for $ 27.
Learn more about cost here:
https://brainly.com/question/2021001
#SPJ9
A
line passes through the point (-4, 3) and has a slope of 4
Write an equation in slope-intercept form for this line.
Step-by-step explanation:
the slope-intercept form :
y = ax + b
"a" being the slope, "b" being the y-intercept (the y value when x = 0).
but we have the slope and a point.
so, we can start with the point-slope form and then transform it :
y - y1 = a(x - x1)
"a" is again the slope, (x1, y1) is the given point.
so, we have
y - 3 = 4(x - -4) = 4(x + 4) = 4x + 16
y = 4x + 19
and that's it.
17 cm/min=________m/h
Answer: .17 m/h
Step-by-step explanation: One centimeter is .01 meters/one hundredth of a meter, so you just need to move the decimal two digits to the right to convert.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Find the average rate of change of each function over the interval [0, 3]. Match each representation with its respective average rate of change.
The identify each representation's associated average rate of change. The average rate of change for the functions r, q, p is 5, 5, 7/3 over the range [0.3].
Given that,
We have to find over the range [0, 3], calculate each function's average rate of change. The identify each representation's associated average rate of change.
The equation for f(x) average's rate of change across [a,b] is
m=[tex]\frac{f(b)-f(a)}{b-a}[/tex]
The function provided is
r(x)=x²+2x-5
r(0)=(0)²+2(0)-5=-5
r(3)=(3)²+2(3)-5=9+6-5=15-5=10
Now,
m₁=[tex]\frac{r(3)-r(0)}{3-0}[/tex]
m₁=[tex]\frac{10+5}{3}[/tex]
m₁=15/3
m₁=5
It is clear from the graph that q(0)=2 and q(1)=3.
Now,
m₂=[tex]\frac{q(1)-q(0)}{1-0}[/tex]
m₂=[tex]\frac{3+2}{1}[/tex]
m₂=5/1
m₂=5
It is evident from the above table that s(0)=-2 and s(3)=5.
Now,
m₃=[tex]\frac{s(3)-s(0)}{3-0}[/tex]
m₃=[tex]\frac{5+2}{3}[/tex]
m₃=7/3
Therefore, The average rate of change for the functions r, q, p is 5, 5, 7/3.
To learn more about average visit: https://brainly.com/question/24057012
#SPJ1
A tour guide organizes vacation packages at a beachside town. There are 7 hotels, 5 cabins, 4 meal plans, 3 escape rooms, and 2 amusement parks. The tour guide chooses either a hotel or a cabin and then selects one of each of the remaining options. FInd the total number of possible vacation packages.
Answer:
84
Step-by-step explanation:
7x5x4x3= 84
a subset $b$ of the set of integers from 1 to 100, inclusive, has the property that no two elements of $b$ sum to 125. what is the maximum possible number of elements in $b$? (a) 50 (b) 51 (c) 62 (d) 65 (e) 68
We get the number of elements in the set B will be 62.
The universal set is A consists of the primary one hundred positive integers.
Set B is a subset of A.
One possibility is that B consists of the primary 62 positive integers.
Then only, the greatest quantity that may be shaped through the sum of any factors of set B is 123.
The number of elements in set B is equal to 62.
We also can selectively interchange one or more elements of B and and add them in complement of B
In most of these instances the number of elements in set B might be 62.
Therefore, we get the number of elements in the set B will be 62.
Learn more about set here:
https://brainly.com/question/2166579
#SPJ4
Solve for "x"
4 (2x (2x - 1) - 1 (2x - 1)) = 0
Answer:
x = 1/2 or 0.5
Step-by-step explanation:
4 • ((2x • (2x - 1)) - (2x - 1)) = 0
The rule says: To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (2x-1) and the exponents are :
1, as (2x-1), is the same number as (2x-1)1
and 1, as (2x-1) is the same number as (2x-1)1
The product is therefore, (2x-1)(1+1) = (2x-1)2
4 • (2x - 1)2 = 0
4.2 Solve : (2x-1)2 = 0
(2x-1) 2 represents, in effect, a product of 2 terms which is equal to zero
For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means: 2x-1 = 0
Add 1 to both sides of the equation :
2x = 1
Divide both sides of the equation by 2:
x = 1/2 = 0.500
Answer:
x = 1/2.
Step-by-step explanation:
4 (2x (2x - 1) - 1 (2x - 1)) = 0
(2x (2x - 1) - 1 (2x - 1)) = 0
(2x - 1) is common to both parts.
(2x - 1)(2x - 1) = 0
2x - 1 = 0
x = 1/2.
( x - 10) (4x - 10) find the measure of each angle
Answer:
Step-by-step explanation:
disribute it
The graph of y=f(x) is shown below. Find all values of xx where f(x)=3
help me understand this.
Answer:
the standing line is the "Y line"
the line laying down is the "X line"
wherever the line touches on the y and x line is where it intercepts
for the x it intercepts at 25 since it touches the x line between 20 and 30
for the y line it intercepts at - 55 since it touches the y line in between - 50 and - 60
twice the sum of 9 and y is less than or equal to 5y
Answer:
y [tex]\leq[/tex] -6.5
Step-by-step explanation:
2(9+y) [tex]\leq[/tex] 5
(distribute)
18 + 2y [tex]\leq[/tex] 5
(isolate variable)
2y [tex]\leq[/tex] 5 - 18
(simplify)
2y [tex]\leq[/tex] -13
(isolate variable)
y [tex]\leq[/tex] -6.5
i need help with this question please
Answer:
5x-30
Step-by-step explanation:
x+15+4x-45
5x+14-45
5x-30
A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 28 feet more
than the length of the shortest side. Find the dimensions if the perimeter is 144 feet.
According to the solving the dimensions of the triangles are as follow:
a . 29
b. 58
c. 57
What is meant by dimensions?A mathematical space's dimension is defined informally as the smallest number of coordinates required to specify any point within it. Thus, a line has a dimension of one since only one coordinate is required to identify a point on it - for example, the point at 5 on a number line.
How many dimensions are contained within a triangle?2-D shapes really had no thickness and they can only be measured on two sides. Two-dimensional objects include the square, circle, rectangle, and triangle.
According to the given data:x=length of the shortest side
2x=length of another side
x+28=length of the third side
144=x+2x+x+28
144=4x+28
144-28=4x
116=4x
x=116/4
x=29 feet (one side)
Putting the value of x to find second side
2x=58 feet (second side)
x+28= 57 feet (third side)
the perimeter of the triangle = sum of all the sides
= 29+58+57
=144
To know more about dimension visit:
https://brainly.com/question/12811633
#SPJ9
5-3y+6= 5(y − 1)
How do I solve it with work
Please help me with this problem im confused.
Answer: A. D.
Step-by-step explanation:
A.
x-b-3<0
x-b-3+3<0+3
x-b<3 (yes)
B.
0>b-x+3
0+x>b-x+3+x
x>b+3
x-b>b+3-b
x-b>3 (no)
C.
x<3-b
x+b<3-b+b
x+b<3 (no)
D.
-3<b-x
-3+3<b-x+3
0<b-x+3
0+x<b-x+3+x
x<b+3
x-b<b+3-b
x-b<3 (yes)
Answer:
A and D
Step-by-step explanation:
Option A
[tex]\begin{aligned}& \textsf{Given inequality}: & x-b-3 & < 0\\& \textsf{Add 3 to both side}: \quad & x-b-3+3 & < 0+3\\& \textsf{Simplify}: & x-b & < 3\end{aligned}[/tex]
Option B
[tex]\begin{aligned}& \textsf{Given inequality}: & 0 & > b-x+3\\& \textsf{Add $x$ to both sides}: & 0+x & > b-x+3+x\\& \textsf{Simplify}: & x & > b+3\\& \textsf{Subtract $b$ from both sides}: \quad& x-b & > b+3-b\\& \textsf{Simplify}: & x-b & > 3\end{aligned}[/tex]
Option C
[tex]\begin{aligned}& \textsf{Given inequality}: & x & < 3-b\\& \textsf{Add b to both sides}: \quad & x+b & < 3-b+b\\& \textsf{Simplify}: & x+b & < 3\end{aligned}[/tex]
Option D
[tex]\begin{aligned}& \textsf{Given inequality}: & -3 & < b - x\\& \textsf{Divide both sides by -1}: \quad & \dfrac{-3}{-1} & > \dfrac{b}{-1}-\dfrac{x}{-1}\\& \textsf{Simplify}: & 3 & > -b+x\\& \textsf{Simplify}: & x-b & < 3\end{aligned}[/tex]
Note: When multiplying or dividing by a negative number in an inequality, remember to flip the inequality sign.
What is the equation of the line that passes through the point (-1, 5) and is parallel to the line y = -3x + 5?
y=-x3+143
y=3x+8
y=-3x+2
y=x3+163
Step-by-step explanation:
Lines which are parallel have equal gradients.The gradient of the given straight line is -3 meaning that the gradient of the new equation will be -3now we have y=-3x +c following the general equation of a straightline.Substituting the given point we have [tex]5 = -3( - 1) + c \\ c = 5 - 3 \\ c = 2 \\ the \: new \: equation \: will \: then \: be \: y = - 3x + 2[/tex]Answer:
I have completed it also
Step-by-step explanation:
what the person ontop of me said it correct
2-78.
Decide if each pair of triangles below is similar. If the triangles are similar,
justify your conclusion by stating the similarity condition you used. Also,
describe a possible sequence of transformations that would carry one onto
the other. If the triangles are not similar, explain how you know they are
not similar.
The pair of triangles is similar with the ASA similarity condition
How to decide if each pair of triangles is similar?The figure that completes the question is added as an attachment
From the figure, we have the following properties:
Two angles are congruent; This is indicated by the marks on one angle, and the corresponding right angleAlso, the hypotenuse of both triangles are similarThis means that the pair of triangles is similar with the ASA similarity condition.
Since the triangles share the same point
So, the transformation to carry the triangles onto one another is dilation
Hence, the pair of triangles is similar with the ASA similarity condition
Read more about similar triangles at:
https://brainly.com/question/14285697
#SPJ1
obtain expressions in component form for the position vectors having the following polar coordinates.
Expressions in component form for the position vectors having the polar coordinates are:
a) -12 cos(40)i + 12sin(40) j = -9.19i + 7.71j
b) 3cos(40) i + 3 sin(40) j = 2.29i + 1.92j
c) -24cos(48)i - 24sin(48) j = -16.059i - 17.83j
Polar coordinates can be found in :Use one or more of the following equations: cos=xr, sin=yr, tan=yx, and r=x2+y2 to convert rectangular coordinates to polar coordinates.
What exactly are polar coordinates?The polar coordinate system is indeed a two-dimensional coordinate system in which the distance from a reference point and the angle from a reference direction are used to determine each point's location on a plane. The polar axis is the ray emanating from the pole inside the reference direction. The pole is the point of reference.
According to the Given information:Let the +x and +y represent, respectively, the unit vectors represented by I and j.
(a) 12.6 m, 130° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= m.
-12 cos(40)i + 12sin(40) j
= -9.19i + 7.71j
(b) 3.60 cm, 70.0° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= cm.
3cos(40) i + 3 sin(40) j
= 2.29i + 1.92j
(c) 24.0 in., 206° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= in.
-24cos(48)i - 24sin(48) j
= -16.059i - 17.83j
To know more about polar coordinates visit:
https://brainly.com/question/11657509
#SPJ4
I understand that the question you are looking for is:
Obtain expressions in component form for the position vectors having the following polar coordinates.
(a) 12.6 m, 130° counterclockwise from the +x axis
[tex]\overrightarrow{\mathrm{R}}[/tex]= m
(b) 3.60 cm, 70.0° counterclockwise from the +x axis
[tex]\overrightarrow{\mathrm{R}}[/tex]= cm
(c) 24.0 in., 206° counterclockwise from the +x axis
[tex]\overrightarrow{\mathrm{R}}[/tex]= in.
what is 2.56 - 8.9 =
Answer:
-6.34
Step-by-step explanation:
If you used a number line, it'll help! Start at 2.56, and go back (to the left) 8.9, and you will arrive at -6.34
I meed you to explain this
Answer:
Bread
Step-by-step explanation:
question 7(multiple choice worth 1 points) (03.01 lc) what is the length of the unknown side of the right triangle? a right triangle with hypotenuse x and legs 5 and 12 13 17 25 60
The length of the unknown side of the right triangle is 13
What is a right angle triangle?A right triangle (American English), sometimes known as a right-angled triangle (British), is a triangle with one angle that is a right angle (i.e., a 90-degree angle), or two sides that are perpendicular. The link between is the basis of trigonometry.
between the right triangle's angles and sides.
The side across from the right angle is the hypotenuse (side c in the figure). Legs are the sides closest to the ideal angle (or catheti, singular: cathetus). The side a that is next to angle B and across from angle A is referred to as side b, and the side a that is next to angle A and across from angle B is referred to as side a.
Right triangles are referred to as Pythagorean triangles and their side lengths as Pythagorean if all three of their sides are integer lengths.
[tex]\sqrt{(12)^2+(5)^2}=13[/tex]
To know more about right angle triangle, visit:
https://brainly.com/question/3770177
#SPJ4
Help please (work provided )
Answer:
150 degrees
Step-by-step explanation:
Vertical angles
What is the sum of [4 -6 8] and [10 2 0]
Answer:
[14 -4 8]
Step-by-step explanation:
[4+10 -6+2 8+0]
[14 -4 8]
you work as an assistant coach on the university swim team and earn $13 per hour. one day, you decide to skip the hour-long practice and go to the county fair instead, which has an admission fee of $10
23$ is the total cost .
What is cost and example?
The definition of cost is to be valued at something or to lose. A loaf of bread costing $3 is an example of a cost. Giving up your freedom in order to grant freedom to another person is an illustration of cost.Fixed and variable costs are the two main categories of expenses incurred by enterprises. Variable costs change with output, whereas fixed costs do not. Overhead costs are another name for fixed expenses. They must be paid whether a company produces 100 or 1,000 widgets.the total cost = 13$ + 10$= 23$ because he losses a hour in work .
13$ and additionally spending 10$ in carnival .
Learn more about cost
brainly.com/question/15135554
#SPJ4
an object moves along a parabolic path defined by the equation in such a way that the y-value is decreasing at a constant rate of 2 units per second. at what rate is the x-coordinate changing when x
So the change of rate of x is -1/3 .
The Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Given that object is decreasing at constant rate of 2 units per second so we have [tex]y = 2x^2 + 1[/tex]
[tex]\frac{dy}{dt} = 4x \frac{dx}{dt}[/tex]
given dy/dt = -2
when x = 3/2
-2 = 4(3/2) dx/dt
-2 = 6 dx/dt
dx/dt = -2/6
= -1/3
Hence the change of rate of x is -1/3 .
To learn more about differentiation visit brainly.com/question/14036956
SPJ4
18 Shifting the origin to another point (h,k) without Changing the directions of the axes. If P(x,y) with reference to original axes changes to P(X,Y) with reference new axes then i) x=X-h, y=Y-k ii) x=X-h,y=Y+k iii) x= x+h, y=Y+k iv)x=x-y=Y-k
If we shift the origin without changing the direction and point P(x, y) is changed to P(X, Y) then the new coordinates will be x = X + h and y = Y + k.
Shifting of origin is the phenomenon of changing the coordinates of the origin which is generally (0, 0) to another point which has coordinated (h, k). This phenomenon is usually carried out graphically. This is done when there is difficulty to solve the problems in coordinate geometry when we take the origin at (0, 0).
If we shift the origin which is at P(x, y) to another point (h, k) then the coordinates of new point P(X, Y) will be
x = X + h and y = Y + k
If h is positive, then coordinates will be x = X + h and if h is negative then coordinates will be x = X - h. If k is positive, then coordinates will be y = Y + k and if k is negative then coordinates will be y = Y - k.
Learn more about Shifting of Origin at:
brainly.com/question/27648576
SPJ9
Helppp!!!! Quick as anyone can!!! will give brainliest!!!!!
Answer: A is the same and equivalent
B is different not equivalent
C is the same and equivalent
Step-by-step explanation:
I'm on Edmund
100⁰ - 2x 2x + 20° 5x -40°
solve for x
This could be wrong, but I think your answer is [tex]x=-2x^3+\frac{900^{\circ \:}x-360^{\circ \:}}{9}[/tex]
---------------------------------------
Hope this helps!
Have a great day and God bless! :)
1. Kia said she could put
together 14 out of 25 gift bags
for a contest. She has already
made 5 gift bags. What
percent of the 25 gift bags
does Kia still have to make?
The percentage of bags that Kia still has to make for the contest is 36 %.
We are given that:
Kia has to make 14 bags out of 25 bags.
Now, she has already made 5 gift bags.
The number of bags she still has to make = 14 - 5 = 9
Now ,we need to find the percentage of 9 from the total of 25 so to get the percentage of bags that Kia still has to make.
So, we get that:
Percentage = 9 / 25 × 100 %
Percentage = 9 × 4 %
Percentage = 36 %
Therefore, we get that, the percentage of bags that Kia still has to make for the contest is 36 %.
Learn more about percentage here:
https://brainly.com/question/843074
#SPJ9
two soccer players are warming up by kicking soccer balls at a goalie. the two players are located 10 yards apart, and the angle from each player to the goalie is 64° and 75°, respectively. what is the distance from the farthest soccer player to the goalie?
Using the law of sines, it is found that the distance from the farthest soccer player to the goalie is 14.723 yards.
Given,
The distance between the two players = 10yards
The angle from each player to the goalie is 64° and 75°, respectively
We have to find,
the distance from the farthest soccer player to the goalie.
In this problem, considering that the sum of the internal angles of a triangle is of 180º, the angle that the goalie makes with the players is given by:
∠A = 180-(∠B+∠C)
∠A = 41°
Using Sine rule
AC/Sin B = BC / Sin A
AC = 10yrd*Sin75°/Sin41°
AC = 14.723 yards
The farthest distance is of 14.723 yards.
To know more about "law of sines"
Refer this link:
https://brainly.com/question/12271113
#SPJ4