Thomas is building rectangular boxes. The table shows the area in square feet, f(x), of the bottom of a box when one side of the box is x feet long. Choose the function that represents the data. f(x) = x2 + 2x f(x) = 2x2 f(x) = 2x
Answers
Answer:
c
Step-by-step explanation:
A function assigns the values. The correct option is C, f(x)=2x².
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that the table shows the area in square feet, f(x), of the bottom of a box when one side of the box is x feet long. Now, the function that can represent this table can be found by substituting the values in the function and checking if the two sides are equal or not.
A.) f(x)= x²+2x
f(1) should be equal to 2.
f(x)= x²+2x
f(1)= 1²+2(1) = 3
Thus, this is not the correct function.
B.) f(x)= x²/2
f(1) should be equal to 2.
f(x)= x²/2
f(1)= 1²/2 = 0.5
Thus, this is not the correct function.
C.) f(x)=2x²
f(1) should be equal to 2.
f(x)=2x²
f(1)= 2(1)² = 2
Also, f(2) should be equal to 8.
f(x)=2x²
f(1)= 2(2)² = 8
Thus, this is the correct function.
D.) f(x)=2x
f(1) should be equal to 2.
f(x)=2x
f(1)= 2(1) = 2
Also, f(2) should be equal to 8.
f(x)=2x
f(1)= 2(2) = 4
Thus, this is the correct function.
Hence, the correct function that represents the area of the box is f(x)=2x².
The complete question is,
Thomas is building rectangular boxes. The table shows the area in square feet, f(x), of the bottom of a box when one side of the box is x feet long.
x 1 2 3 4 5
f(x) 2 8 18 32 50
A.) f(x)= x²+2x
B.) f(x)= x²/2
C.) f(x)=2x²
D.) f(x)=2x
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Related Questions
Explain the cosine rule and sine rule while also saying how to use it and provide examples (keep it in simple terms)
Answers
Answer:
Sure, I'll explain the cosine rule and sine rule in simple terms:
The cosine rule (also known as the law of cosines) is used to find the length of a side or the measure of an angle in a triangle given the lengths of the other sides and the angle between those sides. It states that c^2 = a^2 + b^2 - 2ab cos(C), where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.
Here's an example of how to use the cosine
Suppose we have a triangle with sides a=6, b=8, and an angle between them c=45 degrees. We want to find the length of the remaining side of the triangle, side a.
Using the cosine rule:
a^2 = b^2 + c^2 - 2bc * cosA
where A is the angle opposite side a, we can plug in our values and solve for a:
a^2 = 8^2 + 6^2 - 2(8)(6) * cos(45)
a^2 = 64 + 36 - 96 * 0.707
a^2 = 10.56
a = sqrt(10.56)
a = 3.25 (rounded to two decimal places)
Therefore, the length of side a is approximately 3.25 units.
Answer:
Step-by-step explanation:
I NEED HELP WITH THIS!!
Question: solve the one-step equation.
r-6=7
Answers
Answer:
r = 13
Step-by-step explanation:
r-6=7
Add 6 to each side
r-6+6=7+6
r = 13
Expand the expression -12(4c - 3d) using the Distributive Property
Answers
Answer:
-48c - 37d
Step-by-step explanation:
Multiply both numbers by -12.
The expanded form of the expression is -48c+36d
What is Distributive Property?According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Given that, we have to expand the expression -12(4c - 3d) using the Distributive Property,
We know that the rule for distributive property is :
a(b+c) = ab+ac
Therefore,
-12(4c - 3d)
= -12(4c)+12(3c)
= -48c+36d
Hence, the expanded form of the expression is -48c+36d
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Objective: Use ratios, rates, and proportions to solve application problems
1. There is a special at the store: $34 for 7 roses. Harry is trying to figure out if it's a good deal. Help Harry figure out the unit price (round to 2 decimal places)
2. Paul's car will go 49 kilometers on 7 tanks. Paul wants to know how fuel-efficient the car is. Please help by computing the ratio. (round to 2 decimal places)
3. Jade can travel 42 miles in 4 hours. Please calculate Jade's rate of speed. (round to 2 decimal places)
4. Fiona found 47 pens for $3. Please help Fiona by figuring out the ratio. (round to 2 decimal places)
5. Tanya's car will go 45 meters on 7 gallons. Tanya wants to know how fuel-efficient the car is. Please help by computing the ratio. (round to 2 decimal places)
6. Sara can travel 23 feet in 11 hours. Please calculate Sara's rate of speed. (round to 2 decimal places)
7. Deb found 56 tulips for $8. Please help Deb by figuring out the ratio. (round to 2 decimal places)
8. There is a special at the store: $57 for 9 limes. Ruth is trying to figure out if it's a good deal. Help Ruth figure out the unit price (round to 2 decimal places)
9. Ruth found 50 chairs for $10. Please help Ruth by figuring out the ratio. (round to 2 decimal places)
10. Erin can travel 62 meters in 3 seconds. Please calculate Erin's rate of speed. (round to 2 decimal places)
Answers
wAaAa im very confused, help
16. Convert the following mixed fraction to decimals.
3 1/5 =
a)3.2
b) 4.2
c) 5.2
Answers
Answer:
The answer would be 3.2, since .2 is equivalent to 1/5 ^^
If Joe wants to purchase a ball that costs $15 and has a 15% off discount, how much does Joe have to pay
Please explain with proof
Answers
(The easiest way of calculating discount is, in this case, to multiply the normal price $15 by 15 then divide it by one hundred. So, the discount is equal to $2.25. To calculate the sales price, simply deduct the discount of $2.25 from the original price $15 then get $12.75 as the sales price.)
Answer:
You will pay $12.75
Step-by-step explanation:
(x^-2)^3 Simplify & express answers using positive exponents
Answers
Answer: 1/(x^6)
Step-by-step explanation:
(x^-2)^3=
(x^(-2*3))=
(x^(-6))=1/(x^6)
Answer:
1/\(x^{6}\)
Step-by-step explanation:
(x^-2)^3
If you have parentheses around an exponent, you multiply them together.
x^-6
Change it to reciprocal so it is 1/\(x^{6}\)
Proof:
\(x^{-2}\) × \(x^{-2}\) × \(x^{-2}\) = \(x^{-2 - 2 - 2}\) = \(x^{-6}\)
The single most powerful authority in medieval Europe was:
a
William the Conqueror
b
The King of France
c
Charlemagne
d
The Pope
Answers
Answer: its D pope
Step-by-step explanation:
The teacher gave a true and false quiz where P(true) = 0.5 for each question. Interpret the likelihood that the first question will be true.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event.
Answers
Answer:
This value is not possible to represent probability of a chance event.
Step-by-step explanation:
There is not enough information to determine the answer
HELP!!
is 50.24 and 50.23 rational or irrational numbers pls explain pls pls
its easy i know but my brain hurts
Answers
Answer:
50.23 and 50.24 are both rational numbers.
Step-by-step explanation:
Rational numbers can be written like a ratio.
●Whole numbers (2, 15, 77) are rational bc just put a 1 underneath it (2/1, 15/1, 77/1) now its a ratio.
●Fractions are rational bc the fraction is exactly the ratio (1/2, 5/8, 65/111)
●Decimals that "terminate" that is end or stop are rational like your problem (50.23, 50.24) and ALSO decimals that repeat (2.33333..., 7.666666...) We can do some math on these and find the ratio that is equal to the decimal.
50.23
= 50 + 23/100
= 50•(100/100) + 23/100
= 5000/100 + 23/100
= 5023/100
50.23 is equal to 5023/100.
50.24 = 5024/100 = 2512/50 = 1256/25
Briefly, decimals that do not end either with no pattern or even with a pattern, but not repeating...they are Irrational. (pi, e, and any weird 4.531874569131187732678...no pattern, and 3.1121231234pattern but not a repeat)
Square roots of not-a-perfect square are Irrational (sqrt3, sqrt7, sqrt24) probably tmi, but hope this helps!
At a neighborhood block party, Marcus brought 5/6 of a gallon of hot chocolate to share. When he got home, he still had 1/12 of a gallon left in the container. How much not chocholate did his neighbors drink?.
Thank you!
Answers
Answer:
0.747 or 747/1000
Step-by-step explanation:
5/6 - 1/12 = ?
turn into decimals
5/6 = 0.83
1/12 = 0.083
then subtract .83 - .083 which = .747
0.747 into a fraction 747/1000
Answer:
Step-by-step explanation:
PLS I NEED HELP If you have a bank account, you need to know how to add and subtract decimals. Complete the problems below to balance the account. For each problem, you will use your answer from the problem before it as your starting balance. For example, the amount at the end of question 1 will be the starting balance in question 2.
You start with $50.00 in your account. Your parent gives you $12.50. How much is in your account now?
A. $72.50
B. $62.50
C. $37.50
Answers
Answer:
$62.50
Step-by-step explanation:
B.62.50 I hope this helps
Proof that the formula Fn = Fn-1 + Fn-2 works
Fibonacci python
Answers
IV. The sum of the first n Fibonacci numbers with even indices is
f2 + f4 + ... + f2n = f2n+1 - 1.
Proof:
From II,
f1 + f2 + f3 + ... + f2n = f2n+2 - 1.
When we subtract the result from III, we get the desired result.
Example:
f2 + f4 + f6 + f8 + f10 + f12 = 1 +3 + 8 + 21 +55 +144
= 232
= f13 - 1 .
V. The sum of all (fn+1)/ (fn )
converges to the Golden Ratio.
3/1 + 5/3 + 8/5 + 13/8 .... converges to ) / 2.
Proof that Rn converges to the Golden Ratio:
Let R = lim Rn as n approaches infinity
= lim f n+1 / f n as n approaches infinity
= lim fn + fn-1 /fn as n approaches infinity
= lim (1 + fn-1/ fn) as n approaches infinity
= 1 + lim (fn-1 /fn ) as n approaches infinity
= 1 + 1/ lim (fn-1 /fn ) as n approaches infinity
= 1 + 1/R
So, R = 1 + 1/R,
or R^2 = R + 1,
R^2 - R - 1 = 0,
R = ( ) / 2
= ( ) / 2
Since Rn is positive, Rn = ( ) / 2 .
Thus, Rn converges to the Golden Ratio.
Using a proportion, how can we find 12% of 125? Please show your proportion set up and all work. HELP ME ASAPPPPPPPPP THE CORRECT ANWSER GETS A BRAINLIST I HAVE 3MINS SOMEONE PLEASE!!!!!
Answers
Answer: 15
Step-by-step explanation:
Write 12% as a fraction: 12/100
Since, finding the fraction of a number is same as multiplying the fraction with the number, we have: 12/100 of 125.
12/100 × 125
If you are using a calculator, enter 12÷100×125 which will give you 15 as the answer.
What is the measurement of the longest line segment in a right rectangular prism that is 11.2 centimeters long, 6.6 centimeters wide, and 6 centimeters tall?
Answers
Answer:
Step-by-step explanation:
3.1313109
Answer: the answer should equal 3.131
Step-by-step explanation: as this is the measurement of the longest line in right rectangular prism.
Please got brainliest
Due soon, pls help, will give brainly and points, useless get reported.
Answers
Answer:
A. 100.48
Step-by-step explanation:
2(pi) 16
c= 2pi(radius)
2 x 3.14 which is 16 (PI= 3.14)
C= 2PI(radius)
That should give the answer
Jan had $219 in her savings account she withdraws $6 a week to buy lunch. Assuming she does not deposit any more money. Write a linear function to represent how much money (y) jan will have after x weeks
Answers
Answer:
y = 219 -6x
Step-by-step explanation:
The money she will have remaining (y), will be the amount of money she started with subtracted by the amount of money spent each week multiplied by the number of weeks (x)
-6.5x+3<19-2.5x whats x
Answers
Answer:
I don't know I'm sorry:/
PLEASEEEEEE HELPPPP!!!!!!
Answers
The spinner has a total of 6 possible outcomes, and each outcome has a different probability of occurring. To find the probability of an outcome, we divide the number of ways that outcome can occur by the total number of possible outcomes.
The possible outcomes and their frequencies are:
2 appears once
6 appears twice
8 appears three times
Therefore, the probabilities of the different outcomes are:
P(2) = 1/6 = 0.1667 or approximately 16.67%
P(5) = 0/6 = 0 or 0%
P(6) = 2/6 = 0.3333 or approximately 33.33%
P(8) = 3/6 = 0.5 or 50%
Note that the sum of all the probabilities must equal 1, since one of the outcomes must occur. In this case, 0.1667 + 0 + 0.3333 + 0.5 = 1, so we can be confident that we have calculated the probabilities correctly.
What is Probability?Probability is a branch of mathematics that deals with the study of random events and their outcomes. It is concerned with predicting the likelihood of a particular event occurring based on the available information.
In probability, an event is a set of outcomes, and the probability of an event is a number between 0 and 1 that indicates the likelihood of the event occurring. A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain.
In order to calculate probabilities, we need to identify the possible outcomes of an event and determine how likely each outcome is. The sum of the probabilities of all possible outcomes must always equal 1.
In the example given, the spinner has six possible outcomes, and each outcome has a different probability of occurring. By dividing the number of ways each outcome can occur by the total number of possible outcomes, we can calculate the probability of each outcome.
Probability is used in many fields, including statistics, finance, and science. It is an important tool for decision-making and risk analysis, and it can help us to make predictions about future events based on past data.
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Marcos is doing a charity.
the first week he earns $56.25
the second week he earns $65.45
In the third week, he earns $29.04
In the 4th week, he earns $33.33.
How much money did he earn in 4 weeks combined?
Answers
Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.
Which of the following represents a line that is perpendicular to the line with the equation y=-2x-5
a.y-2=-½ (x-3)
b.x-2y=12
c.-2x+4y=10
d. y-2=2(x+5)
Answers
Corrects answers only
Which of the following statements show a characteristic of a statistical question?
The question is focused.
There is a population that is being studied.
The distribution can be broken in categories.
The question allows for surveys to be conducted.
Answers
Answer:
There is a population that is being studied.
Answer:
The answer is B. Hope this helps!
Which scenario can be modeled by the linear function
y = -15x + 500?
A. The temperature on Jupiter is
15℉ and increases by 500℉ every day.
B. There is a population of 500 giraffes in Western Africa that decreases by 15 giraffes each year.
C. A carpet cleaning service charges $500 plus an additional $15 for every hour.
D. A membership fee for a movie streaming service is free, but each rental costs $15.
Answers
If the perimeter of a triangle is 31 ft and two of the side lengths are 15 ft and 10 ft, what is the length of the third side?
A. 56 ft
B.25 ft
C.16 ft
D.6 ft
Answers
Answer:
D would be the answer
Step-by-step explanation:
31 - 15 = 16
16 - 10 = 6
Enter the next 3 terms from the geometric sequence below.
3
,
−
6
,
12
,
.
.
.
Answers
Answer:
-24, 48, -96
Step-by-step explanation:
The number before multiplies by -2.
3*-2=-6
and so on.
Hope this helps. Have a nice day.
Anil wants to multiply 5, 6, and 3. Which expression could Anil write in the box to
show a way to multiply these numbers?
5 x 6 x 3=0
5 x 18
30 + 3
11 + 3
11 x 3
(NO FILES OR LINKS!)
Answers
Answer:
5x18
Step-by-step explanation:
5x6x3 and 5x18 equal 90
And 5 x18 because 18=6*3
Tasty Treats Baking Company asked a random sample of
100
100100 students in the senior class at Ridgemont High School the question, “Do you prefer chocolate or butterscotch Tasty Treats?” Everyone surveyed had to pick one of the two answers, and
42
%
42%42, percent said they preferred chocolate.
Based on this data, which of the following conclusions are valid?
Choose 1 answer:
Choose 1 answer:
(Choice A) About
42
%
42%42, percent of all students at Ridgemont High prefer chocolate.
A
About
42
%
42%42, percent of all students at Ridgemont High prefer chocolate.
(Choice B) About
42
%
42%42, percent of all students in the senior class at Ridgemont High prefer chocolate.
B
About
42
%
42%42, percent of all students in the senior class at Ridgemont High prefer chocolate.
(Choice C)
42
%
42%42, percent of this sample preferred chocolate, but we cannot conclude anything about the population.
C
42
%
42%42, percent of this sample preferred chocolate, but we cannot conclude anything about the population.
Answers
(Choice B) About 42% of all students in the senior class at Ridgemont High prefer chocolate.
We can only draw conclusions about the sample that was surveyed, which in this case is the senior class at Ridgemont High School. The survey found that 42% of the sample preferred chocolate, so we can conclude that about 42% of the senior class at Ridgemont High School prefer chocolate. We cannot make any conclusions about the entire population of students at the school, or any other population outside of the surveyed sample.
Pls help! Will give brainliest!!
Answers
Considering area (A) of garden as 30 square feet:
30 = x(2x+7)
Now we need to expand it:
x(2x+7) = 2x^2 + 7x
2x^2 + 7x = 30
Adding this into an Algebra calculator gives us 5/2 or 2.5
So x = 2.5
To prove this:
2(2.5) + 7 = 12
14 * 2.5 = 30
(2x+7) x = 30
you can distribute to make this easier
2x^2 + 7x = 30
you can plug this into quadratic formula by setting the equation =0, so:
2x^2 +7x -30 = 0
where 2x^2 = a
7x = b
and -30 = c
you can plug this into your calculator and get an answer of
X = 2.5
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What does integers have to do with Square Roots?
x-34=xy=78
\(\sqrt{x}\) = 91,xy=t
Please Help no dumb answers please. :)
Answers
From the examples given it is unclear.
If you know that the square root of some number, x, is 91, you can square 91 to find the value of x.
91² = 8281. Both numbers are integers. 91 can be factored-- 91=7 × 13. Both are prime factors and integers, but not square roots of 91
-34 is an integer, factors could be -2 and 17 or -17 and 2 prime factors and integers. But the square root of -34 is an imaginary number.
78 is not a multiple of -34 so if you are trying to get factors xy of 78 and -34, at least one factor will not be an integer, and the square root is probably irrational-- not an integer.
Maybe confusing, but I'm attempting a sensible discussion of the question.
Yasin has tried to work the size of the angle marked g in the regular decagon below, using the fact that exterior angles sum to 360°. His workings are shown below.
a) Write a sentence to explain what Yasin has done wrong.
b) What is the size of angle g? Show all your workings.
Answers
well, Yasin is correct, the exterior angles are all 36° each, however "g" is including more than just that, Check the picture below.
Answer: 36 is wrong
Step-by-step explanation: 360 - 36 = 324 degrees