The correct step is to square the binomial (n - 3)² before combining like n terms.
Brayden is working on simplifying the expression 4n – (n - 3)². The correct initial step is not to distribute the negative inside the parentheses, but rather to square the binomial. This involves applying the binomial square formula [tex](a - b)^2 = a^2 - 2ab + b^2[/tex], to the expression inside the parentheses. Therefore, simplification should start with (n - 3)² resulting in [tex]n^2 - 6n + 9[/tex]. After this, Brayden should combine like n terms by adding or subtracting them to simplify the expression further.
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Select the graph for the solution of the open sentence. Click until the correct graph appears. 3|x| > 6
Answer:
Given equation,
3|x| > 6 -----(1)
∵ [tex]\frac{1}{3}>0[/tex]
Thus, multiplying both sides of inequality (1) by [tex]\frac{1}{3}[/tex]
We get,
[tex]|x| > 2[/tex]
⇒ 2 < x or 2 < - x
⇒ 2 < x or -2 > x (when a > b where a > 0, b > 0, If c < 0 ⇒ ac < bc),
⇒ (2, ∞ ) ∪ (-∞, -2)
By plotting the above interval in the number line we can get the graph of the given equation ( shown below )
Complete the comparison: 26 < ? A. 25 B. 54 C. 13 D. 26
What are two items that weigh less than 1 oz
What is the correct data set for the box & whisker plot shown above??
Answer: It’s A.
Step-by-step explanation:
for a p e x
A self-service car wash charges $4 for the initial 5 minutes plus an additional $0.75 for each minute after that. Nick only has $10 to spend on washing his car. Let m represent the number of minutes Nick spends washing his car.
Nick can spend a total of 13 minutes washing his car at the self-service car wash with his $10 budget, accounting for both the initial charge and the additional cost per minute after the first 5 minutes.
Nick is planning to use a self-service car wash that charges $4 for the initial 5 minutes and an additional $0.75 for each minute after that. With a budget of $10, he wants to calculate the number of minutes (m) he can spend washing his car. The cost for m minutes is given by the equation:
Total Cost = Initial Charge + (Additional Charge per minute * Number of extra minutes)
First, subtract the initial charge from the total amount Nick has:
$10 - $4 = $6
This is the amount remaining for the additional minutes. Next, divide this by the additional charge per minute:
$6 / $0.75 per minute = 8 minutes
Therefore, Nick can spend 8 minutes washing his car after the initial 5 minutes, for a total of 13 minutes.
True: If it is a function
False: If it is not a function
{(2, 3), (4, 5), (4, 3), (3, 4)}
Josef says that the range for the car data is greater than the range for the minivan data because the box in the box plot for the car data is wider. Which explains Josef’s error?
Answer:
its a ik it
Step-by-step explanation:
how do you reduce 4/8?
each picnic table seats 6 people how many picnic tables are needed to seat 24 people?
Final answer:
To seat 24 people at picnic tables that each seat 6, you divide 24 by 6, which equals 4 tables needed.
Explanation:
The question is asking how many picnic tables are needed to seat 24 people, if each table seats 6 people. This is a division problem where we need to divide the total number of people by the number of seats at a single table. You divide 24 (the total number of people) by 6 (the number of seats at one table) to find out the number of tables needed.
Here is the calculation: 24 \/ 6 = 4. Therefore, you would need 4 picnic tables to seat 24 people, assuming each person takes one seat and that there are no empty seats.
D^2+d-30/d^2+3d-40 + d^2+14d+48/d^2-2d-48
A. D^2+14d+16/(d+8)(d-8)
B. 2d^2+14d+16/(d+8)(d-8)
C.2d^2+15d+18/2d^2+d-88
D.2d^2+15d+18/(d+8)(d-8)
Eliminate the parameter. x = one divided by two t, y = 3t^3 - 1
Answer:
y = 24x3 - 1
Step-by-step explanation:
None needed YW
A surveyor holds a laser range finder 3 feet above the ground and determines that the range finder is 89 feet from a building and 115 feet from the top of the building. What is the height h of the building? Round your answer to the nearest tenth.
△ABC is reflected to form △A′B′C′ . The vertices of △ABC are A(−7, 1) , B(−5, −3) , and C(−3, 2) . The vertices of △A′B′C′ are A′(−7, −1) , B′(−5, 3) , and C′(−3, −2) . Which reflection results in the transformation of △ABC to △A′B′C′ ?
Find the coefficient of x 4 in the taylor series expansion centered at the origin for the function f(x) = 8 ln(9 + 3x 2 ).
The coefficient of x4 in the Taylor series expansion of the given function is 0.
Explanation:To find the coefficient of x4 in the Taylor series expansion of the function f(x) = 8 ln(9 + 3x2), we need to compute the fourth derivative of f(x) and evaluate it at x = 0.
The Taylor series expansion for a function centered at the origin is given by:
f(x) = f(0) + f'(0)x + f''(0)x2/2! + f'''(0)x3/3! + f''''(0)x4/4! + ...
In this case, we have:
f'''(x) = 48x/(9 + 3x2)
Evaluating f'''(x) at x = 0 gives:
f'''(0) = 0/9 = 0
Therefore, the coefficient of x4 in the Taylor series expansion centered at the origin for the function f(x) = 8 ln(9 + 3x2) is 0.
A segment has endpoints at (3,−4) and (3,−17) How many units long is the segment?
Answer:
what the other person said
Step-by-step explanation:
check all that apply
Answer:
A, D, E
Step-by-step explanation:
Squaring both sides of the inequality, we get
x < 25 . . . . . with the restriction x ≥ 0
The listed numbers that are in the range [0, 25) are 1, 18, 24.
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ava pours 3 gallons of paint equally into 5 cans
You want to have $31,664 in cash to buy a car in 4 years. you expect to earn 11.5% per year on your savings. how much do you need to deposit today if this is the only money you save for this purpose?
You would need to deposit approximately $20,701.27 today if this is the only money you save for the purpose of buying a car in 4 years, considering an expected annual interest rate of 11.5%.
We have,
To determine how much you need to deposit today, we can use the concept of present value (PV).
The present value represents the current value of a future cash flow, accounting for the time value of money and the expected interest rate.
In this case, you want to have $31,664 in cash in 4 years, and you expect to earn an annual interest rate of 11.5%.
Let's calculate the present value using the following formula:
[tex]PV = FV / (1 + r)^n[/tex]
where PV is the present value, FV is the future value, r is the interest rate per period, and n is the number of periods.
Plugging in the values, we have:
[tex]PV = $31,664 / (1 + 0.115)^4[/tex]
Calculating this equation, we find:
[tex]PV = $31,664 / (1.115)^4[/tex]
= $31,664 / 1.530749
PV ≈ $20,701.27
Therefore,
You would need to deposit approximately $20,701.27 today if this is the only money you save for the purpose of buying a car in 4 years, considering an expected annual interest rate of 11.5%.
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Can someone help quickly plz
library library currently has 125 audiobook the library plan purchase the same number of books each month after 4 months the library has 20 more audiobook which equation can be used to determine t and a total number of audio books the library will have after and months
What is the circumference of a circle with a radius of 5.4 inches? Enter your answer as a decimal in the box. Use 3.14 for pi. Round your answer to the nearest tenth. in.
Answer:
33.9
Step-by-step explanation
I got 100% on my test and just wanted everyone to know that it is correct.
I need this equation solved with the work shown please
Martin put 8 pounds of grapes into a bowl. Four friends each took 2/3 pounds from the bowl. What fraction represents the total amount of grapes removed from the bowl ?
Answer:
-8/3
Step-by-step explanation:
i took the test on edg
How many positive integers between 100 and 999 inclusive are divisible by three or four?
The total number of positive integers between 100 and 999 inclusive that are divisible by 3 or 4 is 450.
Explanation:The problem is looking for positive integers between 100 and 999 inclusive, that are divisible by three or four. First, we find out how many numbers between 100 and 999 are divisible by 3 by using the formula: (Last Numbers - First Number) divided by the number you are dividing + 1. Hence, [tex](999 - 102) / 3 + 1 = 300.[/tex] Similarly, for numbers divisible by 4: (996 - 100) / 4 + 1 = 225. However, we must subtract out the numbers that are counted twice because they are divisible by both 3 and 4 (i.e., divisible by 12). To find this, we do [tex](996 - 108) / 12 + 1 = 75.[/tex]
In conclusion, we add the numbers divisible by 3 and those divisible by 4 and subtract the ones that are divisible by both (12). Hence, the total number of positive integers between 100 and 999 inclusive that are divisible by 3 or 4 is [tex]300 + 225 - 75 = 450.[/tex]
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In a normal distribution, most numbers in the data set fall within one standard deviation of the mean. True or False
Answer:
True
Step-by-step explanation:
Which are the solutions of x2 = –5x + 8?
Answer:
The solutions are 1.275 and -6.275
Step-by-step explanation:
Given
x^2 = –5x + 8
First, put all terms in the left side of the equal sign, as follows:
x^2 + 5x - 8 = 0
Then, use the quadratic formula with a = 1 (the coefficient of the quadratic term), b = 5 (the coefficient of the linear term) and c = -8 (the independent term).
[tex]x = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}[/tex]
[tex]x = \frac{-5 \pm \sqrt{5^2 - 4(1)(-8)}}{2(1)}[/tex]
[tex]x = \frac{-5 \pm \sqrt{57}}{2}[/tex]
[tex]x_1 = \frac{-5 + \sqrt{57}}{2}[/tex]
[tex]x_1 = \frac{-5 + 7.55}{2}[/tex]
[tex]x_1 = 1.275[/tex]
[tex]x_2 = \frac{-5 - \sqrt{57}}{2}[/tex]
[tex]x_2 = \frac{-5 - 7.55}{2}[/tex]
[tex]x_2 = -6.275 [/tex]
what is the variable in this algebraic expression 8+6, 4d-2, 7r-15=6, 11+14=25
For this case we have that by definition, a variable is a symbol that can be replaced or that takes a numerical value in an equation or expression, mathematical in general.
Then we have the following options:
A) [tex]8 + 6[/tex]
It is a sum of two real numbers. There are no variables.
B)[tex]4d-2[/tex]
In this case the variable is "d"
C) [tex]7r-15 = 6[/tex]
In this equation, the variable is represented by "r"
D) [tex]11 + 14 = 25[/tex]
It is a sum of two real numbers. There are no variables.
Answer:
A) There are no variables
B) "d"
C) "r"
D) There are no variables
Which expression is equivalent to (2mn)^4/6m^-4n^-2? Assume m=/0 n=/0.
A rectangular window is 1 meter high and 2 meters wide. What is the perimeter of the window in meters? What is it in centimeters?