I will post a graph and using it you have to figure out 4 things.
(i.) (lim x->60-) f(x)
(ii.) (lim x->60+) f(x)
(iii.) What can you conclude about (lim x->60) f(x)? How is this shown by the graph?
(iv.) What aspect of costs of renting a car causes the graph to jump vertically by the same amount at its discontinuities?
Answers
(ii.) (lim x->60+) f(x) = 68
(iii.) It can be concluded that the function is not continuous at x = 60 which is shown on the graph by the gap in the two lines at x = 60.
(iv.) the fixed cost causes the graph to jump vertically at the points of its dicontinuities.
Related Questions
How much of the circle is shaded? Write your answer with as a simplified fraction, with an explanation. Thank you.
Answers
Five Twenty-Eighths
or,
5/28
Hope this Helps!
help with secx/sinx-sinx/cosx
Answers
1/cos(x)sin(x) - sin(x)/cos(x)
(1 - sin²(x))/[sin(x)cos(x)]
cos²(x) / sin(x)cos(x)
cos(x)/sin(x)
cot(x)
A bedroom set lists for $12,000 and carries a trade discount of 30 percent. Freight (FOB shipping point) of $150 is not part of list price. Calculate the delivered price of the bedroom set including the freight. Assume a cash discount of 2 percent:
Answers
$12,000 - $3,600 = $8,400
With a cash discount:
$8,400 * 0.98 = $8,232
Including the freight:
$8,232 + $150= $8,382
Answer:
The delivered price is $8,382.
You purchase a home for $125,000. The value of the property increases by 1.9% every year. After ten years, you decide to sell the home. In the meantime, you have made renovations and improvements to the house which increase its sale value by $48,300. How much will you sell the house for, to the nearest hundred dollars?
Answers
We can use the formula:
F = P · ( 1 + i )^n
where: P = $125,000, i = 0.019 ( 1.9 %), n = 10
F = $125,000 · ( 1 + 0.019 )^10
F = $125,000 · 1.019^10
F = $125,000 · 1.207096
F = $150,887
And we have to add $48,3000 ( for renovations and improvements )
$150,887 + $48,300 = $199,187 ≈ $199,200
Answer: You will be sell the house for $199,200.
Answer:
$199,200
Step-by-step explanation:
Use implicit differentiation to find dy/dx.
ln xy + 5x = 30. Please write out the steps.
Answers
Final answer:
To find dy/dx using implicit differentiation, differentiate both sides of the equation with respect to x. Then apply the chain rule and simplify.
Explanation:
To find dy/dx using implicit differentiation, we first differentiate both sides of the equation with respect to x. Let's go through the steps:
ln(xy) + 5x = 30Differentiate both sides with respect to x:d/dx[ln(xy) + 5x] = d/dx[30]Apply the chain rule to differentiate ln(xy):(1/xy) * (x(dy/dx) + y) + 5 = 0Simplify the equation:x(dy/dx) + y + 5xy(dy/dx) = 0Collect terms with dy/dx:dy/dx = -(y + 5xy)/(x + 5xy)
Given the two equations below, determine which statement best describes the graph of the equations.
y=1/2x-3
y=-2x+16
Select answer A The two lines given by the above equations are perpendicular. Select answer
B The two lines given by the above equations coincide. Select answer
C The two lines given by the above equations are parallel.
D The two lines given by the above equations intersect (but are not perpendicular). ...?
Answers
The two lines given by the above equations intersect (but are not perpendicular) is the best description of the two graphs.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Answer: Option A.
Step-by-step explanation:
The lines that we have is:
y = (1/2)x - 3
y = -2x + 16
Now, two lines of the shape y1 = a1*x + b1 and y2 = a2*x + b2 are parallel if both lines have the same slope, this means that a1 = a2.
Those lines are perpendicular if a1 = -1/a2
now, the slope in the first equation is (1/2) and in the second equation is -2.
so a1 = 1/2
-1/a1 = -(2) = a2
so the two lines are perpendicular, the correct option is A
A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 45 dumpster loads of waste removed. In week 10, there were 30 dumpster loads removed. Assume that the reduction in the amount of waste each week is linear. Write an equation in function form to show the amount of trash removed each week.
f(x) = - 3x + 45
f(x) = 3x + 45
f(x) = - 3x + 60
f(x) = 3x + 60
Answers
The correct answer is:
[tex]\[\boxed{f(x) = -3x + 60}\][/tex]
To find the linear equation representing the amount of trash removed each week, we need to determine the slope and the y-intercept.
Given:
- In week 5, there were 45 dumpster loads.
- In week 10, there were 30 dumpster loads.
Step 1: Calculate the Slope
The slope m of a line is calculated by:
[tex]\[m = \frac{y_2 - y_1}{x_2 - x_1}\][/tex]
Here,[tex]\((x_1, y_1) = (5, 45)\) and \((x_2, y_2) = (10, 30)\).[/tex]
[tex]\[m = \frac{30 - 45}{10 - 5} = \frac{-15}{5} = -3\][/tex]
Step 2: Write the Equation in Point-Slope Form
Using the point-slope form of the equation [tex]\( y - y_1 = m(x - x_1) \):[/tex]
[tex]\[y - 45 = -3(x - 5)\][/tex]
Step 3: Convert to Slope-Intercept Form [tex]( \( y = mx + b \) )[/tex]
Simplify the equation:
[tex]\[y - 45 = -3(x - 5)\][/tex]
[tex]\[y - 45 = -3x + 15\]\[y = -3x + 15 + 45\]\[y = -3x + 60\][/tex]
Thus, the equation in function form that shows the amount of trash removed each week is:
[tex]\[f(x) = -3x + 60\][/tex]
Therefore, the correct answer is:
[tex]\[\boxed{f(x) = -3x + 60}\][/tex]
Mr. Thom makes $25,900/year salary as a document processor. He has made the following chart in order to divide his weekly paycheck into his accounts: Expense type Account Weekly deposits Essential (Fixed) 1st Checking account $219 Essential (Variable) 1st Checking account $115 Non-essential 2nd Checking account $40 Other (Unexpected) Emergency savings account $20 Other (Predictable) Education investment fund $10 Other (Predictable) Retirement investment fund $40 Other (Predictable) Emergency savings account $15 Total paycheck $498 Unfortunately, he has made a mistake in adding the numbers and has not allocated all of the paycheck. If he deposits the difference into the two emergency savings accounts, how much total per week can he then put towards emergency savings?
Answers
Answer:
C. 74
Step-by-step explanation:
NOTICE: Edge loves moving things around SO IT MIGHT NOT BE C FOR YOU But its fore sure 74
Final answer:
Mr. Thom can put $59 per week towards emergency savings.
Explanation:
To find the total amount that Mr. Thom can put towards emergency savings per week, we need to calculate the difference between his total paycheck and the sum of his weekly deposits into the other accounts. From the given information, his total paycheck is $498, and the sum of his weekly deposits into the other accounts is $219 + $115 + $40 + $10 + $40 + $15 = $439. We can subtract the sum of the weekly deposits from the total paycheck to find the difference, which is $498 - $439 = $59. This is the amount that Mr. Thom can put towards emergency savings per week.
**PLEASE HELP??? ****STUCK ON THIS!!!!
Suppose that f(w) varies inversely with w and f(w) = 0.75 when w= 8.
What is f(w) when w= 2?
A.) 12
B.) 6
C.) 3
D.) 1.5
My answer choice is C.) 3. I'm not very confident in my answer so..... :/
Answers
Answer:
C.3
Step-by-step explanation:
We are given that
f(w) varies inversely with w.
f(w)=0.75 when w=8
We have to find the value of f(w) when w=2
According to question
[tex]f(w)\propto\frac{1}{w}[/tex]
[tex]f(w)=\frac{k}{w}[/tex]
Where k=proportionality constant
Substitute the given values then, we get
[tex]0.75=\frac{k}{8}[/tex]
[tex]k=0.75\times 8[/tex]
[tex]k=6[/tex]
Substitute the value of k then, we get
[tex]f(w)=\frac{6}{w}[/tex]
Substitute the value of w=2
Then, we get
[tex]f(w)=\frac{6}{2}=3[/tex]
[tex]f(w)=3[/tex]
Hence, option C is true.
Which of the following has a graph that is a straight line?
Equation 1: y = 2x + 7
Equation 2: y2 = x − 1
Equation 3: y = 2x2 + 4
Equation 4: y = 3x3
Answers
Find the value of 3x + 2 when 7+ x = 5
Answers
x= 5-7
x= -2
3.(-2)+2
-6+2
-4
HELP ASAP!!!
The markup on candy at the discount store is 45%. A bag of candy has a wholesale cost of $1.15. What will be the retail price for the candy?
A. $1.45
B. $1.60
C. $1.67
D. $1.78
Answers
Answer:
Option C. $1.67
Step-by-step explanation:
The price of a bag of candy at wholesale = $1.15
The markup on candy at the discount store = 45%
The retail price for the candy = 1.15 +(45% × 1.15)
= 1.15 + ([tex]\frac{45}{100}[/tex]×1.15)
= 1.15 + (0.45 × 1.15)
= 1.15 + 0.5175
= 1.6675 ≈ $1.67
The retail price for the candy would be $1.67.
Which of these can be a result of inflation?
Businesses grow cautious about spending
The government has to cut spending
The price of household items increases
Workers benefit from a lower cost of living
Answers
Among the choices the one that can be a result of inflation is The price of household items increases
The price of household items increases is a result of inflation, option C is correct.
Inflation typically leads to a general rise in prices across the economy.
As the value of money decreases, it takes more money to purchase the same goods and services.
Therefore, the prices of household items, along with other consumer goods, tend to increase during periods of inflation.
However, it's important to note that inflation does not affect all goods and services uniformly.
Some prices may rise more rapidly than others, leading to changes in relative prices.
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Identify the factors of x2 + 25y2. ...?
Answers
Answer:
(x-5y)^2 or (x-5y)(x-5y).
Step-by-step explanation:
hope this helps have a nice day! :D
Final answer:
To find the factors of x² + 25y², use the properties of complex numbers like i² = -1. The factors are (x + 5yi)(x - 5yi), representing complex conjugates.
Explanation:
The factors of x² + 25y² are (x + 5yi)(x - 5yi).
To factorize the expression, we use the fact that i² = -1, so we can rewrite 25y² as (5y)²
By factoring this expression, we can see that it represents a sum of two squares in the form of complex conjugates.
How do you use the half angle formula for
sin (5π/12)?
Answers
To determine sin(5π/12) using the half-angle formula, we establish a known cos value for the double of the angle, i.e., cos(5π/6)=-√3/2. Substituting it into the half-angle sin formula: Sin(5π/12)=±√{(1+√3/2)/2}. Simplifying gives Sin(5π/12)=√{3+√3/4}.
Explanation:The half angle formula for sine is given by:
Sin(x/2) = ±√{(1 - cos x) / 2}
To solve for sin(5π/12) using the half angle formula, we would look for an angle whose double is easily recognized in terms of standard angles (multiples of 30° or 45°). Luckily, the double of 5π/12 is 5π/6, a recognizable angle, and we know that cos(5π/6) = -√3/2.
Step 1: Substitute cos x value (-√3/2) into the formula:
Sin(5π/12) = √{(1 - (-√3/2 )) / 2}
Step 2: Simplify the expression inside the square root:
Sin(5π/12) = √{(1 + √3 / 2) / 2}
Step 3: Calculate the square root:
Sin(5π/12) = ± √{3 + √3 / 4}
Usually, we choose the positive root for a result in the first or second quadrant and the negative root for a result in the third or fourth quadrant. Since the angle 5π/12 is in the first quadrant, we choose the positive root:
Sin(5π/12) = √{3 + √3 / 4}
So, sin(5π/12) using the half angle formula is √{3 + √3 / 4}.
Learn more about Half Angle Formula here:https://brainly.com/question/30400810
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What is the vertex of the parabola defined by the equation(x − 2)^2 = -12(y − 2)?
Answers
(x^2-4x-20)/-12=y
quadratic => vertex is (-b/2a,f (-b/2a))
Note it is a minimum since coefficient a is positive
Where is the answer to the expression 3 − 6 located on a horizontal number line?
Answers
solve for x. 27^(2x)=9^(x-3) ...?
Answers
[tex] 27^{2x} = 9^{(x-3)} \\ (3^{3} )^{2x} = (3^{2}) ^{(x-3)} \\ \\ (x^{a} )^{b}= x^{a*b} \\ 3^{3*2x} =3^{2*(x-3)} \\ 3^{6x} =3^{(2x-6)} [/tex]
Now, logarithm both sides of the equation:
[tex]log(3^{6x} )=log(3^{(2x-6)}) \\ \\ log (x^{a}) =a*log(x) \\ 6x*log(3)=(2x-6)*log(3)[/tex]
Divide both sides of the equation by log(3):
[tex]6x=2x-6 \\ 6x-2x = -6 \\ 4x = -3 \\ x = - \frac{4}{3} [/tex]
Which is the most accurate name for the polygon shown?
concave pentagon
convex pentagon
concave hexagon
convex hexagon
Answers
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the first equation is substituted into the second equation.
8x – y = –9
4x – 3y = –22
4x – 3(–8x – 9) = –22
4x – 3(8x + 9) = –22
4(8x + 9) – 3y = –22
4(–8x – 9) – 3y = –22
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the first equation is substituted into the second equation.
8x – y = –9
4x – 3y = –22
4x – 3(–8x – 9) = –22
4x – 3(8x + 9) = –22
4(8x + 9) – 3y = –22
4(–8x – 9) – 3y = –22
Answers
If we are to use substitution method in order to solve the following system, the new equation would be 4x – 3(8x + 9) = –22, the answer is the second option.
Here is how I got the answer.
Let's take 8x - y = -22
So y = 8x + 22
Now, substitute the value of y to 4x – 3y = –22
and we get 4x - 3(8x +9) = -22.
Hope this answer helps.
Answer:
The answer is "4x - 3(8x +9) = -22."
Step-by-step explanation:
I just finished the test and got it right.
which of the following comparisons is false 4 liters< 1 gallon, 1 foot< 1 meter, 25 grams< 1 ounce, 10 kilometer< 9 miles
Answers
1 Liter = 1.005 Quarts
4 Quarts = 1 Gallon
4 Liters = 1.05 Gallons
41 2/3 divided by 4 1/4
Answers
Suppose R is a symmetric and transitive relation on a set A, and there is an element a in A for which aRx for every x in A. Prove that R is reflexive. ...?
Answers
let b∈A
then, aRb
and by symmetry, bRa
and by transitivity,bRa,aRb⇒bRb
Hope this is the answer that you are looking for.
Thank you for posting your question here in brainly.
Rewrite the fractions with their LCD.
(1)/(3x-9y),(6)/(5x-15y)
A.
2/8x-21y and 2/8x-21y
B.
5(x-3y)/15(x-3y) and 18(x-3y)/15(x-3y)^2
C.
5/15(x-3y) and 18/15(x-3y)
D.
5/15x-135y and 18/15x-135y
Answers
Which of the expressions are not polynomials? Check all that apply.
A. 8x^10 + 2x^5
B. 5x^-1 + 4x^-2
C. x^5 + 2
D. 5x^5
E. x2 +(square root of x) + 4
F. x^2-(square root of x ) -3 ...?
Answers
B. 5x^-1 + 4x^-2
E. x2 +(square root of x) + 4
F. x^2-(square root of x ) -3
(Method: check polynomials lesson)
To get to work, matt walks 0.75 miles from his house to the bus stop and rides the bus 3.8 miles to his office. if he walks at a pace of 3.6 miles per hour and the bus drives at an average speed of 15 miles per hour, how long is his commute?
Answers
9/5 times c plus 32 how do solve this
Answers
if it is equal to 0 then
c=-32 ×5/9
c = -160/9
Answer:
9/5×c+32 I.e.
if it is equal to 0 then
c=-32 ×5/9
c = -160/9
Step-by-step explanation:
What is is the answer for g-9=-19?
Answers
2. Alice Hall, who loves to cook, makes an apple cake (serves 6) for her family. The recipe calls for 2 1/2 pounds of apples, 2 1/4 cups of flour, 1/5 cup of margarine, 1 1/4 cups of sugar and 4 eggs. Since guests are coming, she would like to make this cake so it will serve 24. How many pounds of apples should she use?
...?
Answers
24--->x
x=24*2 1/2/6=4*2 1/2=4*5/2=10 pounds of apples
Answer:
10 pounds
Step-by-step explanation:
We are given that Alice hall makes an apple cake (serves 6) for her family
Apples=[tex]2\frac{1}{2}=\frac{5}{2}[/tex]pounds
Flour=[tex]2\frac{1}{4}=\frac{9}{4}[/tex] cups
Margarine=[tex]\frac{1}{4}[/tex] cups
Sugar=[tex]1\frac{1}{4}=\frac{5}{4}[/tex] cups
Eggs=4
For 6 persons , apples required =[tex]\frac{5}{2}[/tex] pounds
For 24 persons=[tex]\frac{\frac{5}{2}}{6}\times 24[/tex]
For 24 persons=[tex]\frac{5}{12}\times 24=10[/tex] pounds
Hence, she should use 10 pounds of apples.
Integrate (2 ln x)/x ...?
Answers
u = ln x
d u = d x / x
----------------
[tex] \int { \frac{2 lnx}{x} } \, dx = \\ \int {2u} \, du = \\ =2* u^{2}/2 = u^{2}= [/tex]
= ln² x + C