Answer and Step-by-step explanation:
Given:
Charges includes 10 hour per month = $50
Charges for additional hour = $9
Piecewise definition of cost F(x) for a month in which a member use a car for hours.
Find limits?
Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist.
Lim x → 10- F(x) = 50$
Lim x → 10 [ 9x – 70] = 9( 10) – 70
= 90 – 70
= 20 > 10
Limit does not exist.
Lim x → 10+ F(x) = 50$
Lim x → 10+ F(x) = Lim x → 10+ [90x – 70]
= 90 – 70
= 20 > 10
Limit does not exist.
Lim x → 10 F(x) = 50$
An integer or an decimal.
The limit does not exist.
The piece wise definition of the cost [tex]f(x)[/tex] for a month in which a member uses a car for [tex]x[/tex] hours is given by the equation,[tex]f(x)= 50+9(x-10)[/tex].
Given,
Membership plan is [tex]\$50[/tex] per month.
We have to write a piece wise definition of the cost [tex]f(x)[/tex] for a month in which a member uses a car for [tex]x[/tex] hours.
Here, [tex]\$[/tex][tex]$50[/tex] per month fees includes 10 hours of driving each month, so the cost for a month is given as,
[tex]f(x)= 50+9(x-10)[/tex]
Here [tex]x[/tex] is the no. of additional hours for the month.
Further,
[tex]f(x)= 9x-40[/tex].
Now at,
[tex]lim _{x \to 10^+}f(x) = 9\times 10-40\\[/tex]
Or,
[tex]f(x)= 90-40\\f(x)=50[/tex]
Similarly, at left limit,
[tex]lim _{x \to 10^-}f(x) = 9\times (-10)-40[/tex]
Or,
[tex]f(x)=-90-40[/tex]
[tex]f(x)=-130[/tex]
Finally at [tex]x=10[/tex], [tex]f(x)=9\times10-40[/tex]
[tex]f(x)=90-40\\f(x)=50[/tex]
Since [tex]lim{x \to}10^+[/tex] [tex]\neq limx\to 10^-\neq f(x) (at x= 10)[/tex]
So the required function [tex]f(x)[/tex] is discontinuous at [tex]x=10[/tex]
Hence the piece wise definition of the cost [tex]f(x)[/tex] for a month in which a member uses a car for [tex]x[/tex] hours is given by the equation,[tex]f(x)= 50+9(x-10)[/tex].
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What is the answer to this
A ball is thrown from the top row of seats in a stadium. The function h(t) = −16t2 + 64t + 80 gives the height, h, in feet, of the ball t seconds after it is thrown. How long will it be before the ball hits the ground?
Answer:
Step-by-step explanation:
Given the height of the ball expressed as:
h(t) = −16t^2 + 64t + 80
The ball hits the ground the when h(t) = 0
Substitute h(t) = 0 and find t as shown:
h(t) = −16t^2 + 64t + 80
0 = −16t^2 + 64t + 80
−16t^2 + 64t + 80 = 0
Divide throigh by -16
t^2-4t-5 = 0
t^2-5t+t-5 = 0
t(t-5)+1(t-5) = 0
(t+1)(t-5)= 0
t+1 = 0 and t - 5 = 0
t = -1 and t = 5
time can not be negative:
t = 5seconds
Hence it will take 5 secs before the ball his the ground
Solving a quadratic equation, it is found that the ball hits the ground after 5 seconds.
The height of a ball after t seconds is given by:
[tex]h(t) = -16t^2 + 64t + 80[/tex]
It hits the ground at the values of t for which:
[tex]h(t) = 0[/tex]
Then
[tex]-16t^2 + 64t + 80 = 0[/tex]
Simplifying by -16:
[tex]t^2 - 4t - 5 = 0[/tex]
Which is a quadratic equation with coefficients [tex]a = 1, b = -4, c = -5[/tex].
Then:
[tex]\Delta = (-4)^2 - 4(1)(-5) = 36[/tex]
[tex]x_{1} = \frac{-(-4) + \sqrt{36}}{2} = 5[/tex]
[tex]x_{2} = \frac{-(-4) - \sqrt{36}}{2} = -1[/tex]
We want the positive value, thus, the ball hits the ground after 5 seconds.
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PLEASE HELP!!!
There are 800 students who attend Park Middle School. There are 1.5 times as many boys as there are girls. Assign variables to the unknowns.
you just purchased a new hooded sweatshirt for $24. the total cleaning cost is $2 total because it will be washed with other sweatshirts. you will wear the sweatshirt 18 times this winter. calculate the cost per wearing.
Answer:
Step-by-step explanation:
espera y termino y te ayudo vale que me falta poco vale
Question 9 What are the disadvantages of using a histogram instead of a dot plot?
Answer:
A histogram shows the frequencies of data in different intervals. So, you cannot read individual values off a histogram alone. With a detailed enough dot plot, you could get very close to the actual team payrolls for each league. A histogram does not give this precision.
Step-by-step explanation:
Plato sample answer
The price of a stock in a company drops $27 every hour. What integer represents
the change in the Stock price after 5 hours?
Answer:
2.25 and 11.25
Step-by-step explanation:
27/12=2.25 twelve is the number of hours and 27 is the total drop in price
2.25*5=11.25 because 2.25 is the drop per hour you want to multiple that by five hours.
if 6 pounds of apples cost $9, how much would 21 apples cost?
Fiecare dintre cei 180 de elevi ai unei școli vorbește cel puțin una dintre limbile germană și engleză . Dintre aceștia, 92 vorbesc limba germană și 130 vorbesc limba engleză. *
Numărul elevilor care vorbesc ambele limbi sunt in numar de
Elevii care vorbesc numai germana sunt în număr de
Elevii care vorbesc numai engleza sunt în număr de
PLEASE HELP BEFORE 4 PM!!!
1. 641 divided by 43
2. 4684 divided by 27
3. 6455 divided by 64
Answer:
1. Its about 14.90697674418605. I’m not sure if u want it rounded up if u want it rounded up to the nearest whole it would be 15 if I wanted it rounded up to the nearest tenth then it would be 14.9
2. It’s about 173.4814814814815. I wasn’t sure if I wanted this one rounded up too. Rounded up to the nearest whole it would be 173 and rounded up to the nearest tenth it would be 173.5
3. It’s about 100.859375. I wasn’t sure on this one too. Rounded up to the nearest whole would be 101 and rounded up to the nearest tenth it would be 100.9
Step-by-step explanation:
i need help with this!
Answer:
to convey the parametric expression to be use the explosions
A one dimensional object with no endpoint is a?
A.ray
B.line segment
C.line
D.point
Answer:
its line fjfjfjjejjdjdj
As per the given condition, the required one dimensional object with no end point is a line.
What is a ray?"In geometry, a ray can be defined as a part of a line that has a fixed starting point but no end point. It can extend infinitely in one direction.
On its way to infinity, a ray may pass through more than one point. When naming a ray, it is denoted by drawing a small ray on top of the name of the ray. "
What is a line segment?"A line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints."
What is a line?"A line is a one-dimensional object, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. "
What is a point?"A point is a primitive notion that models an exact location in the space, and has no length, width, or thickness. In modern mathematics, a point refers more generally to an element of some set called a space."
Given, a one dimensional object with no endpoint.
Therefore, the require object is a line.
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Which expression represents a quadratic expression in complete factored form?
A. (x+4)(x-3)
B. (x-1)(3x-9)
C. (2x+4)(x+3)
D. (x-2) + (x+3)
ANSWER PLSSSSSSSSSSSSS, thanks.
Answer:
A. (x+4)(x-3)
Step-by-step explanation:
x+4=0 or x-3=0
x=-4 or x=3
Answer:
Have a great rest of your day :)
Step-by-step explanation:
If the absolute value of x is 4, what is the value of x?
A) -16 or 16
B) -4
C) -4 or 4
D) 4
the correct answer is option C) - 4 or 4.
If the absolute value of x is 4,
| x | = 4
it means that x can be either positive or negative, but its distance from zero is 4 units.
This indicates that x can be 4 units to the right of zero or 4 units to the left of zero.
x = ± 4
Therefore, the possible values of x are - 4 and 4.
Thus, the correct answer is option C) - 4 or 4.
Both - 4 and 4 have an absolute value of 4, fulfilling the condition specified in the problem statement.
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can you guy help me quick wit this please
Alex has to fill his 10 gallon fish tank with water. He only has a 1 pint bucket. How many times will he have to fill his bucket to fill the tank?
Answer:
80
Step-by-step explanation:
8 pints in a gallon so then you multiply 8 x 10 and get 80
Point M (-3, 6) and point 'N (1,-1) are located on a coordinate
grid.
HURRY!!! PLEASE I WILL GIVE BRAINLIEST!!
2 QUESTIONS: 1. Based on the diagram and congruent marks, what would be a correct congruence statement and the most likely reason the triangles might be congruent? (picture included) 2. Based on the diagram and congruent marks, what would be a correct congruence statement and the most likely reason the triangles might be congruent?
Answer:
Step-by-step explanation:
number one is SAS
1. B. ΔJKE ≅ ΔLYE because SAS.
2. E. No enough information to prove the triangles are congruent.
What is the SAS Theorem?The SAS theorem is a triangle congruence theorem which states that two triangles which have two pairs of corresponding sides that are congruent and a pair of corresponding included angles that are congruent are congruent triangles.
1. Based on the SAS theorem we can conclude that: B. ΔJKE ≅ ΔLYE because SAS.
2. In the triangles given, we are only given that they have two pairs of corresponding congruent sides. No known congruent sides were given. Therefore, we don't have enough information. The answer is: E. No enough information to prove the triangles are congruent.
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Simplify each of the following powers of i.
i^99
Answer:
i= sqrt (-1)
If the power is
- even then the value could be -1 or 1
-odd then the value could be -i or i
99 is odd so now is
-i if (99+1)/2 is even or is
i is (99+1)/2 is odd
Now check (99+1)/2= 100/2= 50,
50 is even so
i^99 = -i
Step-by-step explanation:
Bob is hiking down a 12-mile country trail. He could hike at 3 mph for the first two hours and then go the rest of the way at 5 mph or he could just go the whole way at 4 mph. How long would each of these options take? Which option is the faster?
Answer:
The first option would take:
The second option would take:
The faster option is the:
Answer: The first option would take: 3.2 hr
The second option would take: 3 hr
The faster option is the: second
Step-by-step explanation:
Answer:
Below in bold.
Step-by-step explanation:
Speed = distance / time.
First option:
Walking at 3mph for 2 hours will give 2*3 = 6 miles.
So for 6 miles travelling at 5 mph he will take 6/5 = 1.2 hours.
Total time = 3.2 hours.
Second option:
Walking for 12 miles at 4 mph will take him 12/4 = 3 hours.
The fastest option is the second one.
What is equal to d? I’m sorry but I need help.
At one gas station gas cost $2.75 per gallon write an equation that relates the total cost C to the number of gallons of gas purchased G write as algebraic expression with variables for an answer
which set of order pairs represents a function?
Answer:
3rd line
Step-by-step explanation:
Arrange the steps to solve the equation V3+3-V23-1= -2.
-Simplify to obtain the final radical term on one side of the equation.
-Raise both sides of the equation to the power of 2.
-Apply the Zero Product Rule.
-Use the quadratic formula to find the values of x.
-Simplify to get a quadratic equation
-Raise both sides of the equation to the power of 2 again.
Answer:
1. Raise both sides of the equation to the power of 2.
2. Simplify to obtain the final radical term on one side of the equation.
3. Raise both sides of the equation to the power of 2 again.
4 . Simplify to get a quadratic equation.
5. Use the quadratic formula to find the values of x.
please help ! i would mark brainliest to the first answer.
x^2 = 4 py
where p<0
Step-by-step explanation:
I think this is it but I am not sure
Eliza walked 1 1/2 miles in 2/3 of a hour. what is her walking rate in miles per hour?
How much money will it cost to buy the paint? Show all work
Answer:
Step-by-step explanation:
Circle:
diameter = 30 ft
r = 30/2 = 15 ft
Area = πr²
= 3.14 * 15*15
= 706.50 square feet
Triangle:
base (b) = 30 ft
height (h) = 20 ft
Area = [tex]\frac{1}{2}bh[/tex]
[tex]=\frac{1}{2}*30*20\\\\=30*10[/tex]
= 300 square feet
Area of four triangles = 4 * 300
= 1200 square feet
Area to be painted blue = area of circle + area of 4 triangles
= 706.50 + 1200
= 1906.50 square feet
Area painted by one bucket blue paint = 350 sq. feet
Number of paint buckets needed = 1906.50 ÷ 350
= 5.44
= 6
6 buckets of blue paint is needed.
Cost of 6 buckets of blue paint = 85.50 * 6
= $ 513
Each part of the design needs two coats.
So Cost for two coats = 2 * 513
= $ 1026
Square:
Side = 40 ft
Area of square = side *side
= 40*40
= 1600 sq. ft
Area of square to be painted yellow = area of square - area of circle
= 1600 - 706.50
= 893.50 sq.ft
Area painted with one bucket of yellow paint = 250 sq. ft
Number of yellow paint buckets needed = 893.50 ÷ 250
= 3.574
= 4
4 buckets of yellow bucket is needed
Cost of 4 buckets of yellow bucket = 64.50 * 4
= $ 258
Each part of the design needs two coats.
So Cost for two coats = 2 * 258
= $ 516
Last week, Tanya had $43 in her checking
account. She deposited $50 and wrote a check
for $92. How much money is left in her account?
Answer:
She would have $1 left in her account.
Step-by-step explanation:
43 + 50 = 93
93 - 92 = 1
Hope this helps..?
Answer:
$1
Step-by-step explanation:
We start off with $43.
Tanya deposits $50 to her account.
50+43=93.
She has $93 now.
She writes a check for $92.
93-92=1.
Man, Tanya is broke no cap.
1. What is the value of 125 - 34 + 7 x 3?
a.) 294
c. 112
b. 252
d. 70
Answer:
c
Step-by-step explanation
7x3=21
125-34=91
91+21=112
what is 1x7791789x79188037891883+8904781982994
Answer:
6.17016491E20
Step-by-step explanation:
what is the value of the expression if m=2 and n-6?
Answer:
where is the expression
Step-by-step explanation:
（＾_＾）（＾_＾）（＾_＾）