Answer:
(0,0)
Step-by-step explanation:
For this, you need to use the midpoint formula.
(-3) + 3 2 + (-2)
-------------- , ----------------
2 2
This leads to:
-3 + 3 = 0 -> 0/2
x = 0
3 + (-3) = 0 -> 0/2
The answer is:
(0, 0)
A farmer purchased 480 meters of fencing, and will build a rectangular pen with it. To enclose the largest possible area, what should the
pen's length and width be? Model the pen's area with a function, and then find its maximum value.
To enclose the largest possible area, the pen's length should be__and width should be__.
The largest possible area will be 14400 meters², the pen's length should be 120 meters, and the width should be 120 meters.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
Let's assume that the length of the pen would be x.
We have been given the perimeter as 480 meters.
Let w be the width of the rectangle and l be the length of the rectangle
The perimeter of a rectangle = 2(l+w)
So, 480= 2(x + w)
240 = x + w
w = 240 - x
Length = x and width = (240 – x)
Area = x(240 - x) = 240x - x²
To get the maximum area, we equate the first derivative of the area to zero.
A = 240x - x²dA/dx = 240 - 2x = 0
2x = 240
x = 120
So, width = 240 – x = 240 – 120 = 120.
Maximum area = length × width
Maximum area = 120 × 120 = 14400 meters²
Thus, the pen should be 120 meters long and 120 meters wide, with a maximum possible area of 14400 meters².
To learn more about the maximum area click here:
https://brainly.com/question/9282694
#SPJ1
Given the function R(x) = x-7/x+2 find the values of a that make the function less than or equal to zero. Write the solution in interval notation
The solution for the function R(x) = x - 7 / x + 2 ≤ 0 is −2<x≤7 or x (-2, 7].
What is function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
Given:
The function R(x) = x - 7 / x + 2
The given condition x - 7 / x + 2 ≤ 0
Solve the inequality as shown below
Here, the critical points are x = 7 and x = -2
Check the denominator for the critical point, x = -2 will not be suitable for the function as it becomes undefined,
Thus
−2<x≤7 or x (-2, 7]
Therefore, the solution for the function R(x) = x - 7 / x + 2 ≤ 0 is −2<x≤7 or x (-2, 7].
To know more about function:
https://brainly.com/question/5975436
#SPJ1
helppppp plsssssss
what is the average rate of change of the function on the interval from x = 3 to x = 5? f(x)=10(2)x Enter your answer in the box.
The average rate of change of the function on the interval from x = 3 to x = 5 is 40.
What is meant by average rate of change?In mathematics, the average rate of change is a measure of how much a dependent variable (such as y) changes in proportion to a change in the independent variable (such as x). It is calculated by dividing the change in the dependent variable by the change in the independent variable during a certain time period. If the value of y rises by 5 units when the value of x rises by 2 units, the average rate of change is 5/2 Equals 2.5 per unit change in x. Calculus students frequently use this idea to compute the slope of a line on a graph or to calculate the rate at which a function changes. It is a crucial idea in several domains.
How to solve?
f(x) = 10(2)x,the interval is from x = 3 to x = 5
At x = 3, 10(2)3 = 80
at x = 5, 10(2)5 = 160
total change over the interval from x = 3 to x = 5 is 160 - 80 = 80.
the length of the interval is 5 - 3 = 2,
average rate of change is 80 / 2 = 40.
To learn more about average rate of change, visit:
https://brainly.com/question/28744270
#SPJ1
please help please I need i real bad
Answer:
C
Step-by-step explanation:
Answer:
I think the Answer choice = C
Step-by-step explanation:
Suppose you go to work for a company that pays one penny on the first day, 2 cents on the second day, 4 cents on the third day and so on.
Hint: use an= a1 (r)^n-1 and Sn= a1 (1-r^n) / 1 - r
A. If the daily wage keeps doubling, what would your income be on day 31? Give your answer in dollars NOT pennies.
Income on day 31 = $ __________
B. If the daily wage keeps doubling, what will your total income be for working 31 days? Give your answer in dollars NOT pennies.
Total Income for working 31 days = $ _________
Using the given function, the income for day 31 is
$10,737,418.24the total Income for working 31 days is
$21 474 836.47 How to find the income on day 31Using the given function an = a1 (r)^n-1
where
a1 = first day = 1
r = common ratio = 2
The income on day 31, n = 31
= 1 * 2^(31 - 1)
= 2^30
= 1,073,741,824 cents
= $10,737,418.24
Total Income for working 31 days n = 31
Using Sn= a1 (1-r^n) / 1 - r
Sn = (1 * (1 - 2^31)) / (1 - 2)
Sn = (1 - 2^31)) / - 1
Sn = (1 - 2147483648) /-1
Sn = 2147483647
Sn = 2,147,483,647 cents
Sn = $21 474 836.47
Learn more about geometric progression at:
https://brainly.com/question/12006112
#SPJ1
find the inverse of
f(x) = 4x + 2 over 3
Answer: f^-1(x)=(3x-2)/4
Step-by-step explanation:
1. Change the x and y
y=(4x+2)/3 → x=(4y+2)/3
2. Swap sides (optional)
x=(4y+2)/3 → (4y+2)/3=x
3. Multiply the equation by 3 on both sides
(4y+2)/3=x → (3)*(4y+2)/3=x*(3)
4. Subtract 2 from both sides
(3)*(4y+2)/3=x*(3) → 4y=3x-2
5. Divide 4 from both sides
4y=3x-2 → y=(3x-2)/4
6 Substitute f^-1(x) for y
y=(3x-2)/4 → f^-1(3x-2)/4
If a person weighs 290 lbs, how much of a dosage should they get every 4 hours if they need to be
administered 11.9 mg/kg? Round to 1 decimal.
290 lbs is the same as 131.542 kg.
So, they should be administeted (131.542)(11.9) mg, which is about 15.65 mg.
|6y-7|=-1 solve please
Answer:
no solution
Step-by-step explanation:
You want the solution to the absolute value equation |6y -7| = -1.
AnalysisThe expression on the left side of the equal sign is the output of the absolute value function. That output can never be negative: all negative input values are transformed to positive output values by the absolute value function.
The expression on the right side is negative. There is no value of the variable that will make the absolute value function give a negative output. There can be no solution.
Which set of rational numbers is arranged from least to greatest? (4 points) a −3.5, negative 1 over 4 , 2, 1 over 3 b −3.5, negative 1 over 4 , 1 over 3 , 2 c 2, 1 over 3 , negative 1 over 4 , −3.5 d negative 1 over 4 , 1 over 3 , 2, −3.5
The set of rational numbers arranged from least to greatest is -3.5, -1/4, 1/3, 2, which is option (b).
What is a rational number?Any number that can be represented as the ratio of two integers and where the denominator is not zero is referred to as rational.
The given sets of rational numbers are:
(a) -3.5, -1/4, 2, 1/3
(b) -3.5, -1/4, 1/3, 2
(c) 2, 1/3, -1/4, -3.5
(d) -1/4, 1/3, 2, -3.5
Note that 1/4 = 0.25 and 1/3= 0.33
Therefore, the set of rational numbers arranged from least to greatest is -3.5, -1/4, 1/3, 2, which is option(b).
Learn more about rational numbers:
https://brainly.com/question/24398433
#SPJ1
Clara and toby are telemarketers. yesterday, Clara reached 6 people in 12 calls, while Toby reached 7 people in 13 phone calls. If they continue at those rates, who will reach more peoples in 40 phone calls? How many more?
Step-by-step explanation:
Firstly we determine how many people clara will reach in 40 phone calls.
6 people=12 calls
X people=40 calls.
make X the subject of the formula.
X=(6×40)÷12=20
So clara will reach 20 people in 40 phone calls.
Now lets determine how many people Toby will reach in 40 phone calls.
7 people=13 calls
Y people=40 calls.
Therefore making Y the subject of the formula we have,
Y=(7×40)÷13=21 people.
So toby will reach more people in 40 calls
NO LINKS!! You have 4 contestants in the second heat of the big race:
The equations for the contestants are:
1. Mr. Pace: y= 3/4x + 4
2. Mr. Glintz: y= 2/3x + 7
3. Ms. Liskey: y= 3x
4. Mr. Brininger: y= 1/2x + 10
Answer:
Part (c):
1st Place: Ms. Liskey2nd Place: Mr. Glintz3rd Place: Mr. Pace4th Place: Mr. BriningerPart (d):
1st Pass: Mr Pace Time: 1.78 s (2 d.p.)2nd Pass: Mr Glintz Time: 3 s3rd Pass: Mr Brininger Time: 4 sPart (e):
y = 3x + 2Step-by-step explanation:
Given equations:
[tex]\textsf{1.\;\;Mr.\;Pace}: \quad y = \dfrac{3}{4}x + 4[/tex]
[tex]\textsf{2.\;\;Mr.\;Glintz}: \quad y = \dfrac{2}{3}x + 7[/tex]
[tex]\textsf{3.\;\;Ms.\;Liskey}: \quad y = 3x[/tex]
[tex]\textsf{4.\;\;Mr.\;Brininger}: \quad y = \dfrac{1}{2} + 10[/tex]
Plot the lines on the given coordinate plane.
(See attachment).
Draw a line at y = 25 to represent the distance at the finish line.
Find the points of intersection of the linear equation of each contestant and the finish line equation y =25. The point with the smallest x-value is the contestant who is first place.
Mr Pace
[tex]\begin{aligned}\implies 25&= \dfrac{3}{4}x + 4\\\dfrac{3}{4}x&=21\\x&=28\; \sf seconds\end{aligned}[/tex]
Mr Glintz
[tex]\begin{aligned}\implies 25&= \dfrac{2}{3}x + 7\\\dfrac{2}{3}x&=18\\x&=27\; \sf seconds\end{aligned}[/tex]
Mr Liskey
[tex]\begin{aligned}\implies 25&= 3x\\x&=8.33\; \sf seconds\;(2\;d.p.)\end{aligned}[/tex]
Mr Brininger
[tex]\begin{aligned}\implies 25&= \dfrac{1}{2}x + 10\\\dfrac{1}{2}x&=15\\x&=30\; \sf seconds\end{aligned}[/tex]
Therefore, the order in which the contestants reached the finish line is:
1st Place: Ms. Liskey2nd Place: Mr. Glintz3rd Place: Mr. Pace4th Place: Mr. BriningerFrom inspection of the attached graph, Ms Liskey (red line) passes all three contestants. To find the time at which she passes the other contestants, substitute her equation into the contestant's equation and solve for x.
Mr Pace
[tex]\begin{aligned}\implies 3x&= \dfrac{3}{4}x + 4\\\dfrac{9}{4}x&=4\\x&=1.78\; \sf seconds\;(2\;d.p.)\end{aligned}[/tex]
Mr Glintz
[tex]\begin{aligned}\implies 3x&= \dfrac{2}{3}x + 7\\\dfrac{7}{3}x&=7\\x&=3\; \sf seconds\end{aligned}[/tex]
Mr Brininger
[tex]\begin{aligned}\implies 3x&= \dfrac{1}{2}x + 10\\\dfrac{5}{2}x&=10\\x&=4\; \sf seconds\end{aligned}[/tex]
Therefore:
1st Pass: Mr Pace Time: 1.78 s (2 d.p.)2nd Pass: Mr Glintz Time: 3 s3rd Pass: Mr Brininger Time: 4 sIf you want to win the race, either:
increase the slope of Ms Liskey's equation: y = 4xor add a value to Ms Liskey's equation: y = 3x + 240! points Which expression is equivalent to 2x + 7y + 4x - 3y * 1 point
6x + 10y
6x - 10y
6x + 4y
6x - 4y
A number is between 41 and 46. It has prime factors of 2 and 11. What is the number?
The answer you are looking for would be 44.
Step-by-step explanation:Here,
The number lies between 41 and 46 are 42, 43, 44, and 45
From the straightforward observation and according to the condition that must be divisible by 2 and 11 there is only one number that is divisible by both 2 and 11 is 44.
You can learn more about this question here at:
https://brainly.com/question/19794181
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
How do I solve this?
11) (Level 2):
I believe if you just multiply the shaded area (10x6), then maybe subtract the non-shaded area (20cm and 10 cm). After doing this process, I believe you will get: 200-60 = 140! (But then again I could be wrong, I’ll admit it I’m not a pro but at least I gave effort!)
Fraction: 14/10
Decimal: 1.4
Percent: 140%
12) (Level 3):
I have absolutely no idea about this question and I don’t want to guess! Sorry!
Solve the following quadratic
function by factoring:
f(x)=x²-10x+9
Enter the number that belongs in the green box.
x = 9; x = [?]
Answer:
1
Step-by-step explanation:
x²-10x+9 = 0
(x-9)(x-1) = 0
x-9 = 0 => x=9
x-1 = 0 => x=1
The functions f(x) and g(x) are shown in the graph. What is g(x)?
Given f(x)=ln x, evaluate
a) f (e⁴)
b) f (e ㏑ 5)
c) f (e³ ㏑ 5)
The natural logarithms of the given questions are f(e⁴) = 4, f(e ㏑ 5) = 5, and f(e³ ㏑ 5) = -0.5108.
What is the natural logarithm?
A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Given,
f(x) = ln x,
a) f(e⁴)
f(e⁴) = In(e⁴)
= 4In(e)
= 4 * 1
f(e⁴) = 4
b) f(e ㏑ 5)
= f(e⁻⁵)
= [tex]f(e^{\frac{1}{5} })[/tex]
= In(1) - In(e⁵)
= 0 - 5In(e)
= 5*1
f(e ㏑ 5) = 5
c) f(e³ ㏑ 5)
[tex]= f(e^{\frac{3}{5} })[/tex]
= In(3) - In(e⁵)
= ln(3) - ln(5)
f(e³ ㏑ 5) = -0.5108
Hence, The natural logarithms of the given questions are f(e⁴) = 4, f(e ㏑ 5) = 5, and f(e³ ㏑ 5) = -0.5108.
To learn more about the natural logarithm visit,
https://brainly.com/question/305900
#SPJ4
SOLVE FOR P
-2p = -3p + 8
P=
Answer:
P= 8
Step-by-step explanation:
-1 (-2p = -3p + 8)
2p = 3p - 8
-p = -8
p = 8
to check this...
-2(8) = -3(8) + 8
-16 = -24 + 8
-16 = -16
10 = 2(x - 2)
How would I solve for X?
Answer:
x = 7Step-by-step explanation:
10 = 2(x - 2)
How would I solve for X?
10 = 2(x - 2)
10 = 2x - 4
14 = 2x
x = 7
--------------------
check
10 = 2(7 - 2)
10 = 2 x 5
10 = 10
the answer is good
Answer:
x=7
Step-by-step explanation:
Given:
A linear equation is given as:
[tex]10=2(x-2)[/tex]
To Find:
The objective is to solve the equation and find the value of x.
Explanation:
[tex]10=2(x-2)\\[/tex]
⇒ [tex]\frac{10}{2}=x-2[/tex]
⇒[tex]5=x-2[/tex]
⇒ [tex]x=7[/tex]
Final Answer :
The value of x is 7.
A positive integer is 6 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is frac(5,9), then find the two integers.
The two integers are equal to 1 and 7 respectively.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Let x represent the smaller number. Then the given relationships say ...
1/x + 2/(x+6) = 9/7
Multiplying by 7x(x+6), we have ...
7(x+6) +14x = 9x(x+6)
9x² +54x = 21x +42 . . . . .eliminate parentheses, swap sides
9x² +33x = 42 . . . . . . . . ...subtract 21x
3x² +11 -14 = 0 . . . . . . . . . .subtract 42 and divide by 3
(3x +14)(x -1) = 0 . . . . . . . . factor
Values of x that make this true are x = 1 and x = -14/3. Then for the positive integer x=1, the other integer is x+6=7.
Therefore, the two integers are equal to 1 and 7 respectively.
To know more about an expression follow
https://brainly.com/question/4686531
#SPJ1
Hector saved $726 in 6 months. he saved the same amount each month. How much did hector save each month? I don’t have the answer and I don’t get it !
Answer:
He saved $121
Step-by-step explanation:
All you have to do is divide $726/6 which gives you $121.
Solve the system of equations using any method
y = x^2 + 4
y = 2x + 4
The solution of the system of equation is as follows;
x = 2y = 8How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method.
Let's solve the system of equation using substitution method as follows:
y = x² + 4
y = 2x + 4
Therefore,
2x + 4 = x² + 4
x² - 2x = 0
x² = 2x
x = 2
Let's find y
y = 2x + 4
y = 2(2) + 4
y = 4 + 4
y = 8
learn more on system of equation here: https://brainly.com/question/2290547
#SPJ1
Connor borrows $8,000 at a rate of 19% interest per year. What is the amount due at the end of 7 years if the interest is compounded continuously?
$14,576.95
$30,248.35
$43,791.58
$29,215.37
Answer:
Step-by-step explanation:
30,248.35
PLEASE HELP WILL GIVE BRAINLIST -3(0.5+3p)=-6(p-5.9) show ur full work in liner questions form i will get my alt and answer to get u brainliST
50 POINTS!!
Answer:
p = - 123/10 = -123/10 = -12.3
Step-by-step explanation:
-3(0.5 + 3p) = -6(p - 5.9)
Use the distributive property to multiply -3 by 0.5 + 3p
-1.5 - 9p = -6 (p - 5.9)
Use the distributive property to multiply -6 by p - 5.9
-1.5 - 9p = -6p + 35.4
Add 6p to both sides
-1.5 - 3p = 35.4
Add 1.5 to both sides
-3p = 35.4 + 1.5
Add 35.4 and 1.5 to get 36.9
-3p = 36.9
Divide both sides by -3
p = 36.9/-3
Expand 36.9/-3 by multiplying both numerator and the denominator by 10.
p = 369/-30
Reduce the fraction 369/-30 to lowest terms by extracting and canceling out 3.
p = -123/10
Write 50.001 in word form
Find the Maclaurin series of the following functions.
(b) g(x) = sin(3x^2)
The Maclaurin series of sin(3x²) up to n = 3 is
[tex]=3x^2-\dfrac{9}{2}x^6+\frac{81}{40}x^{10}+\ldots[/tex]
The function is given in the question as
g(x) = sin(3x²)
Taylor (Maclaurin) series of sin(3x²) up to n = 3
A Maclaurin series is given by f(x),
[tex]f\left(x\right)=f\left(a\right)+\frac{f^'\left(a\right)}{1!}\left(x-a\right)+\frac{f^{''}\left(a\right)}{2!}\left(x-a\right)^2+\frac{f^{'''}\left(a\right)}{3!}\left(x-a\right)^3+\ldots[/tex]
[tex]f\left(x\right)=f\left(0\right)+\frac{f^'\left(0\right)}{1!}\left(x\right)+\frac{f^{''}\left(0\right)}{2!}\left(x\right)^2+\frac{f^{'''}\left(0\right)}{3!}\left(x\right)^3+\ldots[/tex]
We need to do to get the desired polynomial is to calculate the derivatives, evaluate them at the given point, and plug the results into the given formula.
f⁽⁰⁾(x) = f(x) =sin(3x²)
Evaluate the function at the point: f(0)=0
1st derivative: f(1)(x)=(sin(3x²))′ = 6xcos(3x²)
1st derivative at the given point: (f(0))′=1
2nd derivative: f(2)(x)=(f(1)(x))′=(6xcos(3x²))′=−36x2sin(3x2)+6cos(3x²)
Evaluate the 2nd derivative at the given point: (f(0))′′=6
3rd derivative: f(3)(x)=(f(2)(x))′=(6xcos(3x²))′=−36x2sin(3x²)+6cos(3x²)
Evaluate the 3rd derivative at the given point: (f(0))′′′=0
Now, use the calculated values to get a polynomial:
[tex]g(x)=0+\frac{0}{1!}x+\frac{6}{2!}x^2+\frac{0}{3!}x^3+\frac{0}{4!}x^4+\frac{0}{5!}x^5[/tex]
Thus, the Maclaurin series of sin(3x²) up to n = 3 is
[tex]=3x^2-\dfrac{9}{2}x^6+\frac{81}{40}x^{10}+\ldots[/tex]
To learn more about the Maclaurin series click here:
https://brainly.com/question/24188694
#SPJ1
Dance lessons are offered at two studios. The cost of dance lessons at each studio is shown. • Studio Q charges a $30 registration fee plus $80 per month. . Studio R charges a $105 registration fee plus $65 per month. after how many months will the total cost of the dance lessons be equal at the two studios? What will the cost be?
Answer:
5 months and the cost is $430
Step-by-step explanation:
Let's start by figuring out the equations for both dance studios.
Q : 30 registration fee plus 80 per month.
R : 105 registration fee plus 65 per month.
We can use the variable m for months.
Registration is a flat fee, so that will be it's own term. Plus the costs per month. We will multiply the costs per month times months, m.
Q : 30 + 80m
R : 105 + 65m
Now, if we want to find out how many lessons until the costs are equal, we need to make the two equations equal to each other.
80m + 30 = 65m + 105
Now, we work backwards to find out what m is.
Subtract 30 on both sides.
80m = 65m + 75
Subtract 65m on both sides
15m = 75
Divide by 15 on both sides to isolate m.
m = 5
After 5 months, the total cost of the dance lessons will be equal at the two studios. To find out the cost, we must multiply the months back in. We can substitute 5 in for any of the equations as they are equal. I will use 80m + 30.
80(5) + 30 = ?
400 + 30 = ?
430 = ?
The cost for both studios will be equal at 5 months, with a cost of $430.
4.40x2.50
i really need this please
Answer:
11
Step-by-step explanation:
If it is correct, could you please give me brainliest? I would really appreciate it! Thank you!
What are the distances from the point (x, y) to the focus of the parabola and the directrix?
Select two answers.
distance to the focus: √(x+3)²+(y-3)²
distance to the directrix: |y+4|
distance to the focus: √(x+3)²+(y-2)²
distance to the focus: √(x-2)²+(y+3)²
distance to the directrix: |y-4|
distance to the directrix: |x-4|
The distances from the point (x,y) are given as follows:
Distance to the focus: √(x+3)²+(y-2)².Distance to the directrix: |y - 4|.How to obtain the distance between two points?Suppose that we have two points with coordinates given by [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
The shortest distance between them is given by the equation presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The coordinates of the focus of the parabola are given as follows:
(-3,2).
Hence the distance of the point (x,y) to the focus of the parabola is given as follows:
√(x+3)²+(y-2)².
The equation that defines the directrix is given as follows:
y = 4.
The y-coordinate of the point is of:
y.
Hence the distance is of:
|y - 4|.
More can be learned about the distance between two points at https://brainly.com/question/7243416
#SPJ1
Which statement is true about the algebraic expression 450 −15t?
A student has 450 marbles. Each of their t friends gives them 15 marbles. The expression represents the total marbles the student has.
A student has 450 marbles. They give t marbles to each of their 15 friends. The expression represents the total marbles the student is left with.
A student has 450 marbles. They give t marbles to one of their friend and 15 marbles to another. The expression represents the total marbles the student is left with.
A student has 450 marbles. One of their friends gives them t marbles and another friend gives them 15 marbles. The expression represents the total marbles the student has.
PLEASE HELP I'M SOOO CONFUSED
The statement that is true about the algebraic expression 450 −15t is B. A student has 450 marbles. They give t marbles to each of their 15 friends. The expression represents the total marbles the student is left with.
What is the definition of an algebraic expression?In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.
In this case, when a student has 450 marbles. They give t marbles to each of their 15 friends.
The expression represents the total marbles the student is left with will be:
= 450 - (15 × t)
= 450 - 15t
Learn more about expressions on:
https://brainly.com/question/2164351
#SPJ1