You want to prove
[tex]\displaystyle\lim_{x\to1}\frac{4+2x}3=2[/tex]
By the definition of the limit, this means that for any [tex]\varepsilon>0[/tex], we can find [tex]\delta>0[/tex] such that
[tex]|x-1|<\delta\implies\left|\dfrac{4+2x}3-2\right|<\varepsilon[/tex].
In order to get the inequality we want, we need to have
[tex]\left|\dfrac{4+2x}3-2\right|=\left|\dfrac{2x-2}3\right|=\dfrac23|x-1|<\varepsilon\implies|x-1|<\dfrac{3\varepsilon}2[/tex]
so we can pick [tex]\delta=\frac{3\varepsilon}2[/tex].
So here's the proof: Let [tex]\varepsilon>0[/tex] be given, and let [tex]\delta=\frac{3\varepsilon}2[/tex]. Then
[tex]|x-1|<\delta=\dfrac{3\varepsilon}2[/tex]
[tex]\implies\dfrac23|x-1|<\varepsilon[/tex]
[tex]\implies\left|\dfrac{2x-2}3\right|=\left|\dfrac{2x+4}3-1\right|<\varepsilon[/tex]
as required.
What is 7/8 + 5/6 equal to
Answer:
41/24
Step-by-step explanation:
Answer:
41/24
Step-by-step explanation:
transform the expression
21 + 20/24add the numbers
41/24alternate form
1 17/24, 1.70835 to the 4th power times 5 to the 2 power
Answer:
1,250
Step-by-step explanation:
5 to the 4 power is 50,and 5 to the 2 power is 25 and then Multiply them and that should be your answer
Find the next number in the number sequence 3, 6, 10, 15.
Answer:
21
Step-by-step explanation:
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
so...
15 + 6 = 21
brody is working two summer jobs, making $10 per hour babysitting and making $15 per hour cleaning tables. In a given week, he can work a maximum of 13 total hours and must earn at least $150. If x represents the number of hours babysitting and y represents the number of hours cleaning tables, write and solve a system of inequalities graphically and determine on possible solution.
Answer:
10x+15y≥150
Step-by-step explanation:
Graph y≤13−x (shading down)
graph y≥10− 3/2x (shading up)
marissa has $4.40 in quarters and dimes. if she has 5 more quarters than dimes how many of each coin does she have?
Answer:
22
Step-by-step explanation:
Marissa has $4.40 quarter and dimes
she has 5 more quarters than dimes
that means she times
$4.40×5=22
Answer:
Dimes = 9 dimes.
Quarters = 14 quarters.
Step-by-step explanation:
Q = D + 5 (1)
25×Q + 10×D = 440. (2)
From eq(1) substitute the expression for Q into equation (2)
25×(D+5) + 10D = 440
25D + 125 + 10D = 440
35D = 440 - 125
35D = 315
D = 315/35
D = 9
so,
Dimes = 9 dimes.
and,
Quarters = 9+5
= 14 quarters.
Prove:25×Q + 10×D = 440
25×14 + 10×9 = 440
350 + 90 = 440
440 = 440
Proved.
BRAINLIEST
Find an equation of the line that is perpendicular to 2x-3y=3 that passes through the point (1,2)
Answer:
The answer is
[tex]3x + 2y = 7[/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the perpendicular line we must first find the slope of the original line
From the question the original line is
2x - 3y = 3
Write the equation in the general form above
That's
3y = 2x - 3
y = 2/3x - 1
Comparing with the general equation above
Slope = 2/3
Since the lines are perpendicular to each other the slope of the perpendicular line is the negative inverse of the original line
Slope of perpendicular line = - 3/2
So the Equation of the line using point
( 1 , 2) and slope - 3/2 is
[tex]y -2 = - \frac{3}{2} ( x - 1) \\ 2y - 4 = - 3(x - 1) \\ 2y - 4 = - 3x + 3 \\ 3x + 2y - 4 - 3 = 0[/tex]
We have the final answer as
[tex]3x + 2y = 7[/tex]
Hope this helps you
Solve each system of equations by using a table.
y= 3x - 4
y = -2x + 11
Answer:
Step-by-step explanation:
3x - 4 = -2x + 11
5x - 4 = 11
5x = 15
x = 3
3(3) - 4 = 9 - 4 = 5 = y
(3, 5)
Answer:
1.)y=3x-4=5
2.)y=4x-1=7
Please someone answer this right
God bless you all :D
If two lines intersect, then they intersect in exactly one _____ point. line. postulate. plane.
Answer: the answer is A. point
Find the distance between the pair of points: (-6, 4) and (6,4)
Answer:
12.
Explanation:
Use the distance formula to determine the distance between two points.
Find the inverse of f(x)=6x^5-11
Answer:
[tex]f^{-1}(x)=\sqrt[5]{\frac{x+11}{6}}[/tex]
Step-by-step explanation:
So we have the function:
[tex]f(x)=6x^5-11[/tex]
To find the inverse of a function, switch f(x) and x, change f(x) to f⁻¹(x), and solve for f⁻¹(x). So:
[tex]f(x)=6x^5-11\\x=6(f^{-1}(x))^5-11[/tex]
Add 11 to both sides:
[tex]x+11=6(f^{-1}(x))^5[/tex]
Divide both sides by 6:
[tex]\frac{x+11}{6}=f^{-1}(x)^5[/tex]
Take the fifth root of each side:
[tex]f^{-1}(x)=\sqrt[5]{\frac{x+11}{6}}[/tex]
And we're done :)
Answer:
[tex]f^-^1(x)=\sqrt[5]{\frac{x+11}{6} }[/tex]Step-by-step explanation:
[tex]f(x)=6x^5-11\\[/tex]
Let y equal the equation
[tex]y =6x^5-11\\y+11=6x^5\\\\Divide\:both\:sides\:of\:the\:equation\:by \: 6\\\frac{y+11}{6} = \frac{6x^5}{6} \\\\\frac{y+11}{6} = x^5\\ \\Quatric\:root\:both\:sides\\\sqrt[5]{\frac{y+11}{6} } = \sqrt[5]{x^5} \\\\\sqrt[5]{\frac{y+11}{6} } = x\\\\f^-^1(x) = \sqrt[5]{\frac{x+11}{6} }[/tex]
8x - 7x + 6 = 6 help you guys pleases
Steps to solve:
8x - 7x + 6 = 6
~Combine like terms
x + 6 = 6
~Subtract 6 to both sides
x = 0
Best of Luck!
Answer:
0
8x0=0 7x0=0
6+0=6
Step-by-step explanation:
What is 57 divided by 20
Answer:
2.85
Step-by-step explanation:
Answer: 2.85
Step-by-step explanation:
57/20 = 2.85
Please help!!!! This question is on my plato
Answer:
Its D
Step-by-step explanation:
29/1000= 0.029
Answer:
C.
Step-by-step explanation:
29/999 is 0.02929292929292929
The square of X varies inversely as the square root of Y and directly as the variable M. When M = 27 and Y = 16, then X = 9. Find the exact value of Y when M = 7 and X = 2
Answer:
[tex]Y = 441[/tex]
Step-by-step explanation:
Given
M = 27 when Y = 16 and X = 9
Required
Find Y when M = 7 and X = 2
We start by getting the algebraic representation of the given statement
[tex]X^2 \alpha \frac{1}{\sqrt Y} \alpha M[/tex]
Convert the variation to an equation; we have
[tex]X^2 = \frac{KM}{\sqrt Y}[/tex]
Where K is the constant of variation;
When M = 27; Y = 16; X = 9, the expression becomes
[tex]9^2 = \frac{K * 27}{\sqrt{16}}[/tex]
This gives
[tex]81 = \frac{k * 27}{4}[/tex]
Make K the subject of formula
[tex]K = \frac{81* 4}{27}[/tex]
[tex]K = \frac{324}{27}[/tex]
[tex]K = 12[/tex]
Solving for Y when M = 7 and X = 2
Recall that [tex]X^2 = \frac{KM}{\sqrt Y}[/tex]
Substitute values for K, M and X
[tex]2^2 = \frac{12 * 7}{\sqrt{Y}}[/tex]
[tex]4 = \frac{84}{\sqrt{Y}}[/tex]
Take square of both sides
[tex]4^2 = (\frac{84}{\sqrt{Y}})^2[/tex]
[tex]16 = \frac{7056}{Y}[/tex]
Make Y the subject of formula
[tex]Y = \frac{7056}{16}[/tex]
[tex]Y = 441[/tex]
HELP PLEASE I WILL MARK YOU BRAINLIEST Jermias buys 6.5 pounds of ground beef at the grocery store. Ground beef costs $5.50 for one pound. How much does Jeremias spend?*
Answer: $35.75
Step-by-step explanation: 6.5x5.5=35.75
Answer:
the answer is drum rollll
Step-by-step explanation:
7.58
Help i dont understand pls help :(
Answer:
Answer is h(0)=1
Step-by-step explanation:
All you have to do is substitute x with 0 in the original equation.
An opinion poll surveyed 900 people and reported that 36% believe a certain governor broke campaign financing laws in his election campaign.a. Calculate a 95% confidence interval for the population proportion of people who believe the governor broke campaign financing laws. (Round your answers to three decimal places.)
Answer:
The confidence Interval = (0.329, 0.391)
Step-by-step explanation:
Formula for the Confidence Interval for proportion =
p ± z × √p(1 - p)/n
where
p = x/n
From the question
n = 900 people
x = 36% of 900 people
= 36/100 × 900
= 324
z = z score of 95% confidence Interval
z = 1.98
p = x/n
= 324/900
= 0.36
Confidence Interval = p ± z × √p(1 - p)/n
= 0.36 ± 1.96 × √0.36 (1 - 0.36)/900
= 0.36 ± 1.96 ×√0.36 (0.64)/900
= 0.36 ± 1.96 × √0.000256
= 0.36 ± 1.96 × 0.016
= 0.36 ± 0.03136
Confidence Interval = 0.36 ± 0.03136
= 0.36 - 0.03136
= 0.32864
Approximately to 3 decimal places = 0.329
= 0.36 + 0.03136
= 0.39136
Approximately to 3 decimal places = 0.391
Therefore, the 95% confidence interval for the population proportion of people who believe the governor broke campaign financing laws = (0.329, 0.391)
The Black Panther climbed a height of 15 ft and dropped 20 ft. Write each number as an integer and solve.
Answer:
-5
Step-by-step explanation:
15-20
Answer:
-5
Step-by-step explanation:
15-20=-5
integer means whole number
Midpoint (10,4) Endpoint (9,-4), find the coordinates of the other endpoint.
Answer:
(11, 12)
Step-by-step explanation:
Mid point coordinates:
x = (x₁ + x₂)/2y = (y₁ + y₂)/2Since midpoint and one endpoint given (10, 4) and (9, -4), the other endpoint:
x₂ = 2x - x₁ = 2*10 - 9 = 11y₂ = 2y - y₁ = 2*4 - (-4) = 12So the other endpoint is: (11, 12)
Help i dont understand Pls Help :( Given h(x)=-3x-4h(x)=−3x−4, find h(0)h(0).
Answer:
-4
Step-by-step explanation:
So we have the function:
[tex]h(x)=-3x-4[/tex]
To find h(0), substitute 0 for x. Thus:
[tex]h(0)=-3(0)-4[/tex]
Multiply:
[tex]h(0)=0-4[/tex]
Subtract:
[tex]h(0)=-4[/tex]
And we're done!
You have a balance of $213 in a savings account you withdraw $68 one day and $128 the next day without making any deposit what is the new balance
Step-by-step explanation:
Here hope this helps........
Sea level is defined as being at an elevation of O feet. The elevation of land is defined to be its height above or below sea level. The table shows the lowest elevations
in some states. Write the values in order from greatest to least.
Answer:
2,844 ft, 713 ft, 481 ft, 55ft.
Step-by-step explanation:
New Mexico has the highest of the lowest land elevations of the given states, at 2,844 feet. It is followed by Idaho, at 713 feet, which is followed by Nevada, at 481 feet. Arkansas has the lowest land elevation at 55 feet. The elevations in order from highest to lowest are thus 2,844 feet, 713 feet, 481 feet, and 55 feet.
Help me on this please
Answer:
the measure of angle DCF is 75° + 54° = 129°
The surface area S of a single-celled organism may be found by multiplying 4π times the square of the radius r of the cell. Express S as a function of r.
Answer:
[tex]S(r)=4\pi r^2[/tex].
Step-by-step explanation:
It is given that, the surface area S of a single-celled organism may be found by multiplying 4π times the square of the radius r of the cell.
We need to express S as a function of r.
Let r be the radius of the cell and S(r) be the surface area of single-celled organism when radius is r.
According to the question,
[tex]S(r)=4\pi \times r^2[/tex]
[tex]S(r)=4\pi r^2[/tex]
Therefore, the required function is [tex]S(r)=4\pi r^2[/tex].
(x^2+4)^2−11(x^2+4)+24=0
find one solution for this equation
Answer:
Step-by-step explanation:
(x²+4)²-11(x²+4)+24=0
put x²+4=y
y²-11y+24=0
y²-3y-8y+24=0
y(y-3)-8(y-3)=0
(y-3)(y-8)=0
y=3,8
so x²+4=3
x²=-1=i²
x=±i
or x²+4=8
x²=4
x=±2
Give two points with integer coordinates that have a slope of 10/7 between them
Answer:
(0,0) and (7,10)
Step-by-step explanation:
recall that the slope - intercept form of a linear equation can be given as
y = mx + b
where m = slope and b = y intercept
in our case, we are given that slope, m = 10/7, hence our equation becomes
y = (10/7) x + b
since we are not given any information about the y-intercept, we can simply pick a value for b that is most convenient for us.
We pick b = 0, hence the equation simplifies to:
y = (10/7) x ----- eq 1
we can see immediately that if x = 0, y must also = 0
proof if x = 0:
y = (10/7)(0) =0
since 0 is an integer, then (0,0) must be the first point.
we can also observe that for y to be an integer, we must get rid of the denominator 7. We can do this by multiply the right side by 7. Hence we let x = 7:
y = (10/7) x 7
y = 10
hence (7,10) is the second point.
what is the slope of y=-3
Answer:The slope-intercept form is y=mx+b y = m x + b , where m is the slope and b is the y-intercept. Using the slope-intercept form, the slope is 0 .
Step-by-step explanation:
Answer:
The slope of y=-3 is 0.
y=-3 is a horizontal line.
Let me know if this helps :)
If you averaged 400 miles per day, about how many days would a trip of 1990 miles take?
A. about 6 days
B. about 5 days
c. about 3 days
D. about 4 days
E. about 3 dayS
Answer:
B. about 5 days.
Step-by-step explanation:
If you average;
400 miles per day
1990 miles trip would take?
Cross multiplying gives;
[tex]\frac{1990 * 1}{400}[/tex] = 4.975 days
Rounding off the answer to nearest day gives 5 days.
Hence the 1990 miles journey should take about 5 days.
A trip of 1990 miles would take around 5 days if you averaged 400 miles each day. Option B is correct.
What is average?It is described as the single number that embodies the mean value for the specified collection of data or the closed value for each item in the specified set of data.
It is given that, you averaged 400 miles per day,
We have to find the days would a trip of 1990 miles takes.
The number of days is obtained by taking the ratio of the total distance we have to travel to the distance traveled by the person in one day.
Suppose the number of days needed to complete the trip will be x,
x=Total distance/distance in one day
x=1990 / 400
x= 4.975 days
x≈5 days
If you averaged 400 miles each day, a trip of 1990 miles would take around 5 days.
Thus, option B is correct.
Learn more about the average here:
brainly.com/question/24057012
#SPJ2
A blacksmith has been studying vector calculus and wants to calculate the total mass of a curved metal fitting. Given that the metal fitting has a helix shape parameterized by C:[0,π] → IR3 C(t) = (cos (t), sin(t), t) And the density of the metal material is given by the function:f(x,y,z) = 22 How can the black smith calculate the total mass of the fitting and what is this mass?
Answer:
4483.1
Step-by-step explanation:
Helix shape of the metal fitting parameterized :
C(t) = (cos(t), sin(t), t )
This shows that: x = cos(t), y = sin(t), z = t
density of the metal can be represented as
f (x(t), y(t), z(t) = 2z = 2t
To calculate the mass of the fitting an integral is generated below ( attached below is remaining part of the solution )