Answer:
She need to drive more than 2000 miles for the first rental company to be a better deal .
Step-by-step explanation:
Case 1) One car rental company offers a flat rate of $35 per day plus $0.10 per mile
Let m be the no. of miles
She will need the car for 5 days.
So, total cost = [tex]35 \times 5 +0.10m=175+0.10m[/tex]
Case 2) Another car rental company offers the same car for $25 per day plus $0.25 per mile.
Let m be the no. of miles
She will need the car for 5 days.
So, total cost = [tex]25 \times 5 +0.25m=125 +0.25m[/tex]
Now we are supposed to find How many miles would she need to drive for the first rental company to be a better deal?
So, [tex]175+0.10m <125 +0.25m [/tex]
[tex]175+125 <125 +0.25m-0.10m [/tex]
[tex]300 < 0.15m [/tex]
[tex]\frac{300}{0.15} < m [/tex]
[tex]2000 < m [/tex]
So, she need to drive more than 2000 miles for the first rental company to be a better deal
Justine enrolls in a music program. The cost of the program includes a one-time registration fee of $45 and a fee of $9 per lesson. If the average cost per music lesson is $12 and Justine has taken x classes, which equation represents this scenario?
A.12=54/x
B.12=45+9/x
C.12=45+9x/x
D.12=45x+9/x
If Justine has taken x classes of $9 per lesson, then the total fee for these lessons is $9x.
The cost of the program includes a one-time registration fee of $45 and a fee of $9 per lesson. This means that the total cost of the program in terms of x is
$45 + $9x = $(45 + 9x).
If the average cost per music lesson is $12 (includes a registration fee), then the cost of the program is $12x.
Therefore,
12x = 45 + 9x.
Divide this equation by x:
[tex]12=\dfrac{45+9x}{x}.[/tex]
Answer: correct option is C
The correct option is C) [tex]\[12 = \frac{45 + 9x}{x}\][/tex]. The equation that represents this scenario is [tex]\[12 = \frac{45 + 9x}{x}\][/tex].
To understand why option D is correct, let's break down the costs associated with Justine's music program.
1. The registration fee is a one-time cost of $45. This is a fixed amount and does not depend on the number of classes taken.
2. The cost per lesson is $9, and Justine has taken x classes. Therefore, the total cost for the lessons alone is 9x.
3. The average cost per music lesson, including the registration fee, is $12. This average cost is calculated by taking the total cost (registration fee plus the cost of x lessons) and dividing by the number of classes x.
4. The total cost for x classes, including the registration fee, is the sum of the registration fee and the cost of the lessons, which is [tex]\(45 + 9x\)[/tex].
5. To find the average cost per lesson, we divide the total cost by the number of classes x. This gives us the equation [tex]\(\frac{45 + 9x}{x}\)[/tex].
6. We know that the average cost per lesson is $12, so we set the equation equal to 12: [tex]\(12 = \frac{45 + 9x}{x}\).[/tex]
Therefore, the equation that correctly represents the scenario is: c)
[tex]\[12 = \frac{45 + 9x}{x}\][/tex].
two consecutive odd negative integers have a product of 483, find the integers ...?
What is the value of the expression below when r = 2?
9 – 3r
A.12
B.6
C.3
Write the distribution of 7×6=
A cylinder has a volume of 175 cubic units and a height of 7 units. The diameter of the cylinder is
5 units
10 units
12.5 units
The diameter of the cylinder with a volume of 175 cubic units and a height of 7 units is 5 units.
To calculate the diameter of a cylinder, we first need to find the radius using the formula for the volume of a cylinder, V = πr²h. Given that the volume is 175 cubic units and the height is 7 units, the radius comes out to be 5 units. Since the diameter is twice the radius, the diameter of the cylinder is 5 units.
A student gets paid to sell raffle tickets at the school basketball game. He earns $15 a day, plus an extra $0.25 for each raffle ticket he sells and $2 for each hour he works at the game. If d = days, r = raffle tickets, and h = hours, what function can he use to calculate his earnings?
Answer: C. [tex]T=15d+\frac{r}{4}+2h[/tex]
Step-by-step explanation:
Let d = days, r = raffle tickets, and h = hours.
Given: A student earns in a day = $15
Then his earning in d days =$15d
Also, he earns for each riffle = $0.25
Then his earning in for r riffles =$0.25r
And , he earns for each hour he works at the game = $2
Then his earning for h hours = $2h
Then the function he can use to calculate his earnings is given by :_
[tex]T=15d+0.25r+2h\\\\\Rightarrow\ T=15d+\frac{1}{4}r+2h[/tex]
What is 35/10 convert into a decimal?
Heather has $500 in her savings account. she withdraws $20 per week for gas. write an equation heather can use to see how many weeks it will take her to have a balance of $220.
Lauren bought 6 yellow roses, 10 orange roses, and 12 pink roses to make a bouquet. What is the ratio of the number of yellow roses to the total number of roses in Lauren’s bouquet?
4x-6=10x-3
?? i am bad at math lol
A sequence of transformations maps ∆ABC onto ∆A″B″C″. The type of transformation that maps ∆ABC onto ∆A′B′C′ is a_______
.When ∆A′B′C′ is reflected across the line x = -2 to form ∆A″B″C″, _______vertex
of ∆A″B″C″ will have the same coordinates as B′.
Answer:The first one is a Reflection
The second one is B
Step-by-step explanation:
Subtract -34.7 from -7.85
The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located?
Answer:
(1, 3)
Step-by-step explanation:
You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola. The first few steps are as follows. Set the parabola equal to 0 so you can solve for the vertex. Separate the x terms from the constant by moving the constant to the other side of the equals sign. The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out). Let's start there. The first 2 steps result in this polynomial:
[tex]-2x^2+4x=-1[/tex]. Now we factor out the -2:
[tex]-2(x^2-2x)=-1[/tex]. Now we complete the square. This process is to take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. We add 1 into the set of parenthesis. But we actually added into the parenthesis is +1(-2). The -2 out front is a multiplier and we cannot ignore it. Adding in to both sides looks like this:
[tex]-2(x^2-2x+1)=-1-2[/tex]. Simplifying gives us this:
[tex]-2(x^2-2x+1)=-3[/tex]
On the left we have created a perfect square binomial which reflects the h coordinate of the vertex. Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:
[tex]-2(x-1)^2+3=y[/tex]
From this form,
[tex]y=-a(x-h)^2+k[/tex]
you can determine the coordinates of the vertex to be (1, 3)
Answer:
(1,3)
Step-by-step explanation:
Simplify the expression: √18x^4y^3
Answer:
[tex]3x^2y\sqrt{2\cdot y}[/tex]
Step-by-step explanation:
We have been given an radical expression. We are asked to simplify our given expression.
[tex]\sqrt{18x^4y^3}[/tex]
We can rewrite terms of our given function as:
[tex]\sqrt{18\cdot x^4\cdot y^3}[/tex]
[tex]\sqrt{2\cdot 9\cdot x^4}\cdot y^2\cdot y}[/tex]
[tex]\sqrt{2\cdot 3^2\cdot (x^2)^2\cdot y^2\cdot y}[/tex]
Using radical rule [tex]\sqrt[n]{a^n}=a[/tex], we will get:
[tex]3x^2y\sqrt{2\cdot y}[/tex]
Therefore, the simplified form of our given expression would be [tex]3x^2y\sqrt{2\cdot y}[/tex].
Explain how you use the bar model to solve 14-7 equal seven
You drive your car for 3 hours at an average speed at 30 km per hour. how far did you go?
Denver is called the mile-high city because it is at an altitude of 1 mile. how many feet is the
A 13 foot ladder is leaning against a wall. If the point where the ladder meets the wall is 12 feet above the ground, how far from the base of the wall is the the ladder?
A) 1 foot
B) 2 feet
C) 5 feet
D) 22 feet
if (3x^2)+7=0 then (x-1/3)^2
A college writing seminar increased its size by 50% from the first to the second day. If the total number of students in the seminar on the second day was 15 how many students were in the class on the first day
Add.
(5n^2+4n)+(3n^2+6n)
From 2000-2010 a city had a 2.5% annual decrease in population. If the city had 2,950,000 people in 2000, determine the city's population in 2008.
The population of the city in the year 2008 is 2409122.
Important information:
Initial population in 2000 is 2,950,000.Decreasing rate is 2.5%.Exponential formula:According to the exponential decay formula:
[tex]f(t)=a(1-r)^t[/tex]
Where a is the initial value, r is the decay rate and t is the time period.
The difference between 2008 and 2000 is 8.
Substitute [tex]a=2950000, r=0.025, t=8[/tex] in the above formula.
[tex]f(8)=2950000(1-0.025)^8[/tex]
[tex]f(8)=2950000(0.975)^8[/tex]
[tex]f(8)=2409122.8208[/tex]
Round the value to the previous integer.
[tex]f(8)\approx 2409122[/tex]
Therefore, the population of the city in 2008 is 2409122.
Find out more about 'Exponential formula' here:
https://brainly.com/question/23942604
Factor completely: 2x3 + 10x2 + 4x + 20
Prime
(2x + 10)(x2 + 2)
2[(x + 5)(x2 + 2)]
(x + 5)(2x2 + 4) ...?
Answer:
B) 2[(x + 5)(x2 + 2)]
Step-by-step explanation:
Given: 2x^3 + 10x^2 + 4x + 20
Here 2 is a common factor, so we take it out and write the remaining terms in the parenthesis.
2(x^3 + 5x^2 + 2x + 10)
Now let's take (X^3 + 5x^2 +2x + 10), we group and factor them as follows:
(x^3 + 5x^2 + 2x + 10) = x^2(x+5) + 2(x + 5) = (x+5)(x^2 +2)
When we combine them, we get
2x^3 + 10x^2 + 4x + 20 = 2(x+5)(x^2 +2)
Therefore, the answer is B) 2[(x + 5)(x2 + 2)]
Hope this will helpful.
Thank you.
what is the value?
5x+3=4x ?? bit confused
What is the area of ABC below? If necessary, round your answer to two decimal places.
The answer I got from apex was- 106.26
Which statement best describes how to determine whether f(x) = 9 – 4x^2 is an odd function?
Determine whether 9 – 4(–x)^2 is equivalent to 9 – 4x^2.
Determine whether 9 – 4(–x^2) is equivalent to 9 + 4x^2.
Determine whether 9 – 4(–x)^2 is equivalent to –(9 – 4x^2).
Determine whether 9 – 4(–x^2) is equivalent to –(9 + 4x^2).
Answer:
Its CCCCCCCCCCCCCCC aka 3 aka third option
on dredful edge im going nuts
Step-by-step explanation:
The price of a pair of shoes is $63.20. The sales tax rate is 4.5 percent. How much sales tax would you pay if you bought these shoes? A.) $2.84 B.) $3.16 C.) $4.50
52.063 divided into 9.2 rounded to the nearest hundredth
Answer:
The answer is 5.66
Step-by-step explanation:
52.063 divided by 9.2 is 5.65902173913. Then you round of to the nearest hundredth which is two decimal places to the right (so it's 5). Then you round it off one value higher since 9 is above 5. Therefore the final answer is 5.66
Henry has 523 baseball cards. He buys 24 each month. What is a explicit rule for the number of baseball cards Henry has in n months?
Answer:
the answer is a_n= 24n+499 just took the test :)
Step-by-step explanation:
Use the function described below to answer questions 1 - 4.
Yvonne invested $4,000 in a savings account which pays 3.5% interest compounded annually. Use the formula A = P(1 + r)t, where P is the principal, r is the interest rate, and t is the time in years.
1. Approximately, how much money will Yvonne have in 4 years? Round to the nearest cent.
2. Approximately, how much money will Yvonne have in 8 years? Round to the nearest cent.
3. Approximately, how many years will it take for Yvonne to double her money? Write the number of years only.
4 Alex buys a top of the line computer. He did not realize that the computer would lose value so fast. If his computer cost $1800.00 and it depreciates at a rate of 45% each year, in how many years will it be worth less than 1/3 of what he paid for it?