The slope of the linear equation C(x) = 8x + 50 is 8, indicating an $8 charge per mile, and the y-intercept is 50, the flat towing fee. Similar service-based costs from other examples also follow this linear model, with their unique slopes and y-intercepts corresponding to the per-hour or per-mile charges and flat fees.
Explanation:The function C(x) = 8x + 50 represents the cost of towing a vehicle, where C is the cost in dollars, and x is the number of miles the vehicle is towed. The slope of this line is 8, which indicates that the cost increases by $8 for every mile the vehicle is towed. The y-intercept is 50, representing the flat fee charged regardless of the distance towed, which is the cost when x (the number of miles) is 0.
Relating to the other examples provided, we can see a pattern in how these equations are structured for service-based costs. For instance, in Aaron's Word Processing Service, the total cost equation is y = 32x + 31.50, where the slope is 32 representing the hourly charge, and the y-intercept is 31.50, the fixed cost. Similarly, for Ethan's household appliance repairs, the equation is y = 20x + 25, with a slope of 20 and a y-intercept of 25. All these models illustrate how fixed fees and variable rates per service hour or mile can be represented in a linear equation format.
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7.67,7,7.72,7.38 least to greatest
Keri walks her dog every morning the length of the walk is 0.55 km on each weekday on each weekend day the walk is 1.4 times as long as a walk on a weekday how many kilometers does keri walk in one week
Keri walks approximately 4.29 kilometers in one week.
Explanation:Keri walks her dog every morning. On weekdays, the length of the walk is 0.55 km. On weekends, the walk is 1.4 times as long as a walk on a weekday. To find out how many kilometers Keri walks in one week, we need to calculate the total distance she walks on weekdays and weekends.
Distance walked on weekdays = 0.55 km per day
Distance walked on weekends = 1.4 * 0.55 km per day = 0.77 km per day
Total distance walked in one week = (distance on weekdays * number of weekdays) + (distance on weekends * number of weekends)
Since there are 5 weekdays and 2 weekend days in a week, we can calculate the total distance:
Total distance walked in one week = (0.55 km * 5) + (0.77 km * 2) = 2.75 km + 1.54 km = 4.29 km
Keri walks approximately 4.29 kilometers in one week.
solve
(b-2ya^2)(3b-3ya^2)
Here we are given the expression:
[tex](b-2ya^{2})(3b-3ya^{2})[/tex]
We will use foil method to solve this expression.
The word FOIL is an acronym for the four terms of the product:
First ("first" terms of each binomial are multiplied together)
Outer ("outside" terms are multiplied—that is, the first term of the first binomial and the second term of the second)
Inner ("inside" terms are multiplied—second term of the first binomial and first term of the second)
Last ("last" terms of each binomial are multiplied)
Using this method let us simplify our expression.
[tex](b-2ya^{2})(3b-3ya^{2})[/tex]
=[tex]3b^{2}-3bya^{2}-6bya^{2}+6y^{2}a^{4}[/tex]
Now combining like terms we have:
=[tex]3b^{2}-9bya^{2}+6y^{2}a^{4}[/tex]
Answer: [tex](b-2ya^{2})(3b-3ya^{2})[/tex] simplifies to [tex]3b^{2}-9bya^{2}+6y^{2}a^{4}[/tex]
Answer:
The answer is 3b² - 9bya² - 6y²a².
Explanation:
(b - 2ya²)(3b-3ya²)
3b² - 3bya²-6bya²-6ya²
3b² - 9bya² - 6y²a².
Answer would be 3b² - 9bya² - 6y²a².
For a store contest,4 out of every 65 people who visited the store will receive a free dvd. If 455 people visit the store, how many dvds were given?
Answer:
28 dvds were given if 455 people visit the store.
Step-by-step explanation:
4 out of every 65 people who visited the store will receive a free dvd.
Suppose, [tex]x[/tex] dvds were given if 455 people visit the store.
Now, according to the ratio of "people who got dvd" to "total number of people" , the equation will be.........
[tex]\frac{4}{65}=\frac{x}{455}\\ \\ 65x= 455*4=1820\\ \\ x=\frac{1820}{65}=28[/tex]
So, the number of dvds given is 28.
Answer:
28
Step-by-step explanation:
Given that there is a store contest. Out of 65 people who visit the store only 4 will be receiving a free dividend.
Remaining 61 will not receive.
There were 455 people who visited the stores.
Of these 455/65 times 4 persons would be given dividends.
i.e. Since 4 out of 65 would be given
no of visitors who received dividend= 455(4)/65 = 7(4) = 28
Hence answer is 28 persons would receive dividend.
#1.-7/9 x 3/5 a.-27/45 b.-7/15c.7/15 d.27/45
Answer: B
Step-by-step explanation:
[tex]\frac{-7}{9} * \frac{3}{5} = \frac{-7(3)}{9(5)} = \frac{-7(3)}{3 * 3(5)} = \frac{-7}{3(5)} = \frac{-7}{15}[/tex]
Jennifer grandmother buys carrots at the farm stand she and her three grandchildren equally shares the carrots the total weight of the carrots is 28kg how many kilograms of carrots will jennifer get
Solution: We are given that the Jennifer's grandmother bought 28 kg of carrot.
Also we are given that 28 kg of carrot are to be divided into 4 persons.
Therefore, the number of kilograms of carrots that Jennifer will get is:
[tex]\frac{28}{4}[/tex]
[tex]7[/tex] kg
[tex]\therefore[/tex] Jennifer gets 7 kilograms of carrot.
Matter is anything that
A. has mass and takes up space.
B. has only one physical state.
C. is important to human society.
D. contains two elements combined chemically.
The answer is A. Matter is anything that has mass and takes up space
Jerry walked a dog from 6:40 am to 7:30am . If he was paid $6 per hour how much did he earn
Answer:
Amount Jerry earned is $5
Step-by-step explanation:
Jerry is paid $6 per hour.
First we need to find the number of hours he walked the dog.
From 6.40 am to 7.30 am we have 50 minutes. Jerry walked the dog for 50 minutes.
An hour has 60 minutes.
We need to find how much Jerry gets paid for a minute.
Amount paid for a minute = [tex]\frac{$6}{60}[/tex]
=$[tex]0.1[/tex]
Therefore,
Amount paid for 50 minutes = $[tex]0.1[/tex] * [tex]50[/tex] minutes
=$[tex]5[/tex]
Which linear inequality is represented by the graph? y ≤ 1/2x + 2
y ≥ 1/2x + 2
y ≤ 1/3x + 2
y ≥ 1/3x + 2
Answer:
I can confirm that the answer is in fact A
Step-by-step explanation:
I took the test and got it right ( edge 2021 )
The linear inequality represented by the graph is y ≤ 1/2x + 2. The correct option is A.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to, > ‘greater than, or < ‘less than.
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The given inequality y ≤ 1/2x + 2 is represented on the graph attached with the answer below.
In the graph, the linear line cut x-axis at ( -4, 0 ) and y-axis at ( 0, 2 ). And inequality covers the whole space below the line y = 1/2x + 2.
The linear inequality represented by the graph is y ≤ 1/2x + 2. The correct option is A.
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A yogurt costs 45p hair many can be bought with £5
11
5 pound = 500 pence
500 pence/ 45 pence= 11.1111111
An albatross can fly 400 kilometers in 8 hours at a constant speed using d as distance and t as number of hours. An equation that represents this situation is d=50t what are two contants of proportionality for the relationship between distance in kilometers and number of hours? What is the relaionship between the two values?
Answer:
Constant of Proportionality is 50.
Step-by-step explanation:
Albatross can fly 400 kilometers in 8 hours.
'd' represents the distance and 't' represents the number of hours.
The equation [tex]d=50t[/tex] represents the relationship between the distance and time.
Now, in the equation shown above 50 is the constant of proportionality, and 50 represents the rate of change of distance with time.
The constant of proportionality tells us the rate of change between two variables.
So for every 1 hour of time the distance covered is 50 kilometers.
Please Help!! I have a 99 in this class. If I get a 45 on a project that’s worth 50% of my grade, what would my grade be?
So I always go to this site for grade calculations
https:// rogerhub. com /final-grade-calculator/
So go down to "I already took my final" or something like that
So with you having a 99, then got a 45% on a project that's worth 50% of your grade, your grade unfortunately drops 72%.
Find the distance between -3 and 4. A) -12 eliminate b) -7 c) -1 d) 7
The formula of a distance between A and B = |B - A|.
We have -3 and 4. Substitute:
|4 - (-3)| = |4 + 3| = |7| = 7
Answer: d) 7Simplify the algebraic expression 3(2x+3y)-(4x+2y
A 20-foot length of wire is to be cut into 2 pieces, so that the longer piece is two feet longer than two times the shorter piece. Find the length of each piece.
2x+2=20-x
3x=18
x=6
2nd=14
is 106.06 bigger than 106.60? I really hate math and i got normal schoolwork to do as well
106.60 is bigger round up on it and you get 107
math help what is x? please keep
Apples = X
Pears = Y
3x+2y = 0.60
pears cost 2X-0.05 replace Y with this:
3X +2(2x-0.05) = 0.60
Simplify:
3X + 4X-0.10 = 0.60
Simplify:
7X -0.10 = 0.60
Add 0.70 to each side:
7X = 0.70
Divide both sides by 7:
X = 0.70 / 7
X = 0.10
Apples cost 0.10 each.
Pears cost 2x-0.05 = 2(0.10) - 0.05 = 0.20 - 0.05 = 0.15 each
The 1906 earthquake in San Francisco had a magnitude of 8.3 on the richter scale. At the same time in Japan an earthquake with magnitude of 4.9 caused minor damage. How many times more was the San Francisco earthquake that the Japan earthquake?
In 1906 in San Francisco the magnitude of earthquake on richter scale was 8.3.
In the same year the magnitude of earthquake on richter scale in Japan was 4.9.
Now we have to find how many times more was the San Francisco earthquake that the Japan earthquake.
The amount of energy released in an earthquake is very large, so a logarithmic scale avoids the use of large numbers.
The formula used for these calculations is:
[tex]M=log_{10}(\frac{I}{I_{0}})[/tex]
Where M is the magnitude on the richter scale, I is the intensity of the earthquake being measured and I₀ is the intensity of a reference earthquake.
So because the magnitude is a base 10 log, the Richter number is actually the exponent that 10 is raised to in order to calculate the intensity of the earthquake.
So the difference in magnitudes of the earthquakes can be calculated as follows:
[tex]M=log_{10}(\frac{10^{8.3}}{10^{4.9})}[/tex]
M=3.4
Answer: The San Francisco earthquake was 3.4 times more than Japan earthquake.
Final answer:
The San Francisco earthquake released approximately 2510 times more energy than the earthquake in Japan, calculated using the Richter scale.
Explanation:
To determine how many times stronger the San Francisco earthquake was compared to the earthquake in Japan, we refer to the Richter scale, which is a logarithmic scale. A one-unit increase on this scale represents a ten-fold increase in amplitude of the seismic waves and roughly a thirty-fold increase in energy released. Therefore, to calculate the difference between a magnitude 8.3 earthquake and a magnitude 4.9 earthquake, we subtract the smaller magnitude from the larger one (8.3 - 4.9 = 3.4) and then calculate 10 raised to the power of this difference.
[tex]10^(3.4)[/tex] = 10 x 10 x 10 x 2.51 (approximately), which simplifies to about 2510 times more energy released by the San Francisco earthquake compared to the earthquake in Japan.
A school year has 4 quarters. What percent of a school year is 7 quaters
Final answer:
7 quarters represent 175 percent of a school year since 7 divided by 4, then multiplied by 100 equals 175%. This means 7 quarters is more than the duration of one standard school year.
Explanation:
To calculate what percent of a school year 7 quarters represent, we need to compare 7 quarters to the total number of quarters in a standard school year. Since we know that a school year consists of 4 quarters, we can set up a proportion to determine the percentage.
Step 1: Identify the total number of quarters in a school year, which is 4.
Step 2: Identify the number of quarters we're focusing on, which is 7.
Step 3: Set up a fraction to represent the portion, which is 7 divided by 4 (7/4).
Step 4: Convert this fraction to a percentage by multiplying by 100. So, (7/4) × 100 = 175%.
Therefore, 7 quarters represent 175 percent of a school year, which implies more than one full school year.
HELP ASAP PLEASE!!!
How many seconds are there in 782 minutes?
Use the factor: 1 min= 60 sec
A. 782 sec
B. 13 sec
C. 46,920 sec
D. 0.077 sec
C. 46,920 seconds is your answer
Answer:
Step-by-step explanation:
C. 46,920 sec
If x > 0 and y < 0, where is the point (x, y) located?
If x > 0 and y < 0 then the point (x, y) is located in Quadrant IV.
Look at the picture.
Answer:
II
Step-by-step explanation:
If 6 times a number is added to -4, the result is 10 times the number. Find the number.
the number is - 1
let the number be n then 6 times the number is 6n and added to -4 is
- 4 + 6n = 10n ( equal to 10 times the number )
subtract 6n from both sides
- 4 = 4n ( divide both sides by 4 )
[tex]\frac{-4}{4}[/tex] = n , hence n = - 1
Writing Polynomial Function Given a y-Intercept
We already got
f(x)= a(x-2)(x-3)(x-5)
We got [tex]a=\frac{1}{6}[/tex]
first we multiply the parenthesis in f(x)
f(x)= a(x-2)(x-3)(x-5)
[tex]f(x)= a(x^2-5x+6)(x-5)[/tex]
[tex]f(x) = a(x^3 - 10 x^2 + 31 x - 30)[/tex]
Replace the value of 'a'
[tex]f(x) = \frac{1}{6}(x^3 - 10 x^2 + 31 x - 30)[/tex]
Multiply 1/16 inside the parenthesis
[tex]f(x) = \frac{1}{6}x^3 - \frac{5}{3} x^2 + \frac{31}{6} x - 5[/tex]
What is the factored form of the expression over the complex numbers?
121x^2+36y^2
(11x−6iy)(11x−6iy)
(11x+6y)(11x−6y)
(11x+6iy)(11x−6iy)
(11x+6iy)(11x+6iy)
It's the third answer. This is because since there is no middle term where both variables are combined, that would lead to the signs of the 2 factors to be different. However, that still leaves 2 answers, 3 and 2. If we were to square i, you would get -1. This is because √-1 is equal to i. i^2 would be -1. Since the sign in the unfactored expression is positive and not negative, that would mean that the i in the factoring turned it around. that leads us to believe that answer 3 is the correct answer.
For every ten sheets of stickers you buy at a craft store, the total cost increases 20.50.
Answer:
cost of one sheet of sticker = 2.05
Step-by-step explanation:
given that for every 10 sheets of stickers total c0st increases 20.50
i.e. cost of 10 sheets of stickers = 20.50
When we purchase 1 sheet the price would be reduced.
In other words, direct variation is there for sheets of papers and costs
Hence for 1 sheet of stickers cost would be less than 10 sheets.
So divide by 10
Cost of 1 sheet of sticker = 20.50/10 = 2.05
Last year a business had profits of 8,000 this year it profit are five time as great what are this year profits
What can be concluded about the sequence? The common ratio of the sequence is 2. The common difference of the sequence is 2. The next term of the sequence is represented by the point (5, 64). The next term of the sequence is represented by the point (5, –64).
The given information suggests that the sequence is a geometric sequence. The common ratio is 2, and the common difference is 2. The next term of the sequence can be found using the coordinates (5, 64) and (5, -64).
Explanation:The given information about the sequence suggests that it is a geometric sequence.
If the common ratio is 2, it means that each term is obtained by multiplying the previous term by 2.
If the next term is represented by the point (5, 64), it means that the 5th term of the sequence is 64. Using the formula for a geometric sequence, we can find the first term: a * (2^(5-1)) = 64, where a is the first term of the sequence.
Similarly, if the next term is represented by the point (5, -64), it means that the 5th term of the sequence is -64. Using the formula for a geometric sequence, the first term is -8.
Select all that apply.
To solve an equation with a variable, which of the follow are done?
Inverse operations are used
Addition is always used
The variable needs to be isolated
The value of the variable should be guessed first
answer is inverse operations are used
Answer:
The variable needs to be isolated and inverse operations are used.
Write a quadratic equation with the given roots. Write the equation in the form of ax^2+bx+c=0 where a b and c are integers
You haven't provided the required roots, but I can tell you how to do this kind of exercises in general.
If the [tex] x^2 [/tex] coefficient is 1, i.e. the equation is written like [tex] x^2+bx+c=0 [/tex], then you can say the following about the coefficients b and c:
[tex] b [/tex] is the opposite of the sum of the roots[tex] c [/tex] is the multiplication of the roots.So, for example, if we want an equation whose roots are 4 and -2, we have:
[tex] 4+(-2) = 4-2 = 2 \implies b = -2 [/tex][tex] 4 \cdot (-2) = -8 \implies c = -8 [/tex]So, the equation is [tex] x^2-2x-8=0 [/tex]
If your roots are rational, you can work like this: suppose you want an equation with roots 3/4 and 1/2. You have:
[tex] \dfrac{3}{4}+\dfrac{1}{2} = \dfrac{3}{4}+\dfrac{2}{4} = \dfrac{5}{4} \implies b = -\dfrac{5}{4} [/tex][tex] \dfrac{3}{4} \cdot \dfrac{1}{2} = \dfrac{3}{8} \implies c = \dfrac{3}{8} [/tex]And so the equation is
[tex] x^2 - \dfrac{5}{4} + \dfrac{3}{8} = 0 [/tex]
In order to have integer coefficients, you can multiply both sides of the equation by 8:
[tex] 8x^2 - 10 + 3 = 0 [/tex]
Determine the graph behavior at the zero(s) of the polynomial function f(x)=x^2 - 6x+9
[tex]f(x)=x^2-6x+9=(x-3)^2[/tex]
This a perfect square so the x-axis is a tangent at x=3
The correct answer is C
See graph
Given function is f(x) = x² -6x +9.
It is a quadratic function whose graph is an upward open parabola.
The zero(s) of the given function would be at x-intercepts of the graph i.e. y = 0.
It means 0 = x² -6x +9
We can solve this quadratic equation using factorization as follows:-
0 = x² -6x +9
0 = x² -3x -3x +9
0 = x(x-3) -3(x-3)
0 = (x-3)(x-3)
Therefore, x = 3 with multiplicity two.
Hence, option C is correct, i.e. The graph of the function touches the x-axis at x = 3.