1. f(216) is equal to 3.
2. The solution x = 3 is valid.
3. p(x) = x⁴ - 2x³ - 14x² - 2x - 15, the maximum number of real roots is 4.
1. To find f(216) when f(x) = log(x), we substitute 216 for x in the function:
f(216) = log₆(216)
= log₆(6³)
= 3 log₆(6)
= 3 x 1
= 3
Therefore, f(216) is equal to 3.
2. To solve the equation √(6x - 3) = √(4x + 3), we can square both sides of the equation to eliminate the square roots:
(√(6x - 3))² = (√(4x + 3))²
6x - 3 = 4x + 3
6x - 4x = 3 + 3
2x = 6
x = 3
Since both sides of the equation are equal, the solution x = 3 is valid.
3. For the function p(x) = x⁴ - 2x³ - 14x² - 2x - 15,
we can determine the maximum number of real roots by examining the degree of the polynomial.
The highest power of x in the polynomial is 4, which means the polynomial is of degree 4.
Therefore, in the given polynomial p(x) = x⁴ - 2x³ - 14x² - 2x - 15, the maximum number of real roots is 4.
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A small auditorium has 20 seats in the first row and each successive row contains 2
additional seats. If there are 12 rows in the auditorium, how many seats are in this
auditorium?
O 384
O 372
O 330
O 264
Answer:
330.
Step-by-step explanation:
Count all the way up. The first row is 20, then goes, 22,24,26,28,30,32,34,36,38,40. These are the number of seats for all 12 rows, since we added 2 each row. Add them all together including 20 to get 330 seats. The whole auditorium has 330 seats.
Hope this helps!
As per arithmetic Progression, there are 372 seats in the given auditorium.
What is an arithmetic progression?"Arithmetic Progression is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value."
Given, the auditorium has 20 seats in the first row.
Then, each successive row contains 2.
We can assume it as an arithmetic progression.
Here, the first term(a) is 20.
The common difference(d) is 2.
Total number of terms(n) is 12.
Therefore, the sum of all the terms is
\(= \frac{n}{2}[2a + (n-1)d]\\= \frac{12}{2}[2(20) + (12-1)2]\\= 6[40+(11)2)]\\= 6(40+22)\\= 6(62)\\= 372\)
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PLEASE HELP I NEED THIS IS DUE IN AN HOUR!!! 40 POINTS!!!Sherelle and Venita’s grandmother said that one of the bags has a coin from 1916. What reasons might Sherelle give for saying that the 1916 coin is most likely in her bag? What reasons might Venita give for saying that the 1916 coin is most likely in her bag? Whose bag do you think is more likely to contain the 1916 coin? Explain your reasoning. Answer:
Answer:
I dont know about Sherelle, but Venita's grandmother can give a reason that as she is from older age, most probably, the coin can be in her bag...... And the coin, according to me will be in grandmother's bag....
Hope it helps!!!
Which of the following expressions will have a product greater than 4? pls answer with the questions in the pic
Answer:
Answer D
Step-by-step explanation:
Multiply them all out. D is 4.04
Answer: D is correct I took the test without having to see the answer just wanted to help u out:)
Step-by-step explanation:
car buyer bought a used car for $20,250. The car depreciates by 11% per year. The following equation describes the value of the car, where y represents the number of years since the car was purchased. v ( y ) = 20 , 250 ( 1 − 0.11 ) y Which equation is equivalent and can be used to determine the value of the car 6 months after it was purchased? v ( y ) = 20 , 250 ( 0.89 ) 6 v ( y ) = 20 , 250 ( 0.89 ) 6 v ( y ) = 20 , 250 ( 0.89 1 12 ) 6 v ( y ) = 20 , 250 ( 0.89 1 12 ) 6 v ( y ) = 20 , 250 ( 0.89 ) 1 12 ( 0.89 ) 6 v ( y ) = 20 , 250 ( 0.89 ) 1 12 ( 0.89 ) 6 v ( y ) = 20 , 250 ( 0.89 ) 6 ( 0.89 ) 6
The equation that can be used to determine the value of the car after 6 months is v(y) = 20,250(0.89)^6/12
What is deprecation?
Depreciation is the rate of decrease in value of an asset. When an asset depreciates, it declines in value with the passage of time.
What equation represents the value of the car after 6 months?The formula that can be used to represent depreciation is:
FV = P (1 + r)^n
FV = Future value P = Present value R = interest rate N = number of yearsv(y) = 20,250(1 - 0.11)^t
v(y) = 20,250(0.89)^6/12
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convert the rectangular equation to a polar equation that expresses r in terms of theta. y=1
The polar equation that expresses r in terms of theta for the rectangular equation y=1 is: r = 1/sin(theta)
To convert the rectangular equation y=1 to a polar equation, we need to use the relationship between polar and rectangular coordinates, which is:
x = r cos(theta)
y = r sin(theta)
Since y=1, we can substitute this into the equation above to get:
r sin(theta) = 1
To express r in terms of theta, we can isolate r by dividing both sides by sin(theta):
r = 1/sin(theta)
Therefore, the polar equation that expresses r in terms of theta for the rectangular equation y=1 is:
r = 1/sin(theta)
This polar equation represents a circle centered at the origin with radius 1/sin(theta) at each angle theta.
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Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several markets in the southern U.S. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow. Click on the datafile logo to reference the data.
The given situation is that Dixie Showtime Movie Theatres, Inc. owns and runs a network of movie theatres in a number of southern American markets. The business owners are interested in estimating weekly gross revenue as a function of advertising expenditures. The information below, which relates to regression analysis, is for data for a sample of eight markets for a recent week.
Regression Analysis: In regression analysis, we look at how one or more independent variables and a dependent variable are related. Weekly revenue and advertising expenditures are the independent and dependent variables in the presented problem, respectively.
The relationship between the dependent variable and the independent factors needs to be estimated. To calculate the relationship between the dependent and independent variables, we use a regression equation.
We can estimate the regression equation by the least squares method.
The least squares method is the method of estimating the coefficients of the regression equation that minimizes the sum of the squared deviations between the observed and predicted values of the dependent variable.
We use statistical software to estimate the regression equation and interpret the output of the regression analysis.
The output of regression analysis includes an estimated regression equation, coefficient of determination, t-tests for testing the significance of individual coefficients, an F-test for testing the overall significance of the regression equation. The output also includes other statistics like standard error, t-value, p-value, etc. that help us to understand the statistical significance of the estimated coefficients of the regression equation.
However, It appears that there are gaps in the data for a recent week for a sample of eight markets. To estimate weekly gross revenue as a function of advertising expenditures and provide a final answer, the data is required.
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A wheel of radius 14 inches is rotating 15degrees/s round answers to 2 decimal places
the nth term of a sequence is n²+20
work out the first 3 terms of the sequence
The first 3 terms of the sequence are 21, 24 and 29
Working out the first 3 terms of the sequenceFrom the question, we have the following parameters that can be used in our computation:
n² + 20
This means that
f(n) = n² + 20
The first 3 terms of the sequence is when n = 1, 2 and 3
So, we have
f(1) = 1² + 20 = 21
f(2) = 2² + 20 = 24
f(3) = 3² + 20 = 29
Hence, the first 3 terms of the sequence are 21, 24 and 29
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Translate
Solve the equation.
3m= 5(m + 3)-3
HELP
Answer:
m = -6
Step-by-step explanation:
3m= 5(m + 3)-3
Distribute
3m = 5m +15 -3
Combine like terms
3m = 5m +12
Subtract 5m
3m-5m = 5m+12-5m
-2m = 12
Divide by -2
-2m/-2 = 12/-2
m = -6
2x² + 3 = 39 extracring square roots
Answer:
x=9
Step-by-step explanation:
first, subtract 3 from both sides so 2x^2=36, then, divide both sides by 2 so x^2=18 and divide 18 by 2 and 9^2=18
Answer:
x = ± 3\(\sqrt{2}\)
Step-by-step explanation:
2x² + 3 = 39 ( subtract 3 from both sides )
2x² = 36 ( divide both sides by 2 )
x² = 18 ( take square root of both sides )
x = ± \(\sqrt{18}\) = ± \(\sqrt{9(2)}\) = ± ( \(\sqrt{9}\) × \(\sqrt{2}\) ) = ± 3\(\sqrt{2}\)
k(x) = 6 + 100
k(-5) =
Answer:
731
Step-by-step explanation:
#1Use the Laws of Logarithms to expand the expression.
ln (r/ 5s)
#2 Use the Laws of Logarithms to combine the expression.
log2(x2 − 49) − log2(x − 7)
1. Expanding the expression ln(r/5s) using the laws of logarithms:
ln(r/5s) = ln(r) - ln(5s)
2. Combining the expression log2(\(x^2\) - 49) - log2(x - 7) using the laws of logarithms:
\(log2(x^2 - 49) - log2(x - 7) = log2((x^2 - 49)/(x - 7))\)
what is expression?
In mathematics, an expression refers to a combination of numbers, variables, and mathematical operations, without an equal sign, that represents a value or a mathematical relationship. Expressions can be as simple as a single number or variable, or they can involve complex combinations of terms and operations.
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Which sport is the most popular in
the word?
Answer:
Football/Soccer
The simple sport of soccer only needing a ball and two goals, is a fun easy game to do. And nationally, soccer has the most positive impact on people
Answer:
association football also known as soccer
What scale factor was applied to the first diamond to get the resulting image?
(21 points)
The scale factor was applied to the first diamond is 2.5
How to determine the scale factorFrom the question, we have the following parameters that can be used in our computation:
The diamonds
The scale factor is calclated as
scale factor = Diamond 2/Diamond 1
Substitute the known values in the above equation, so, we have the following representation
scale factor = 1.5/0.6
Evaluate
scale factor = 2.5
Hnce, the scale factor is 2.5
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Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement
Answer:
The answer is "\(\frac{3}{7}\)"
Step-by-step explanation:
Please find the complete question:
The dilation scale factor will be the same:
\(=\frac{\text{Picture to Center Gap}}{\text{Related pre-image distance to the middle}}\)
Throughout the picture, the distance is \(CP'=6\), while the equivalent distance is \(CP=14\). The factor of scale is then\(=\frac{CP'}{CP} =\frac{6}{14} =\frac{3}{7}\)
The decrease because if a factor of scale is below 1 and a factor of scale is higher than 1. Dilation is a reduction since \(\frac{3}{7}<1\), therefore the scale factor is \(\frac{3}{7}\).
The scale factor of the given dilation is; 6/14 and the dilation is a reduction
Transformations
The image of the object undergoing transformation is missing and so i have attached it.
From the attached object, we se that CP = 14.
Also CP' = 6
Thus; Scale factor is 6/14
Now, reduction is reducing the dimensions while enlargement is increasing the dimensions by a scale factor.
Since the denominator of the scale factor is greater than the numerator, then there is a reduction.
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22 elephants is 65% of what
number of elephants?
Answer:
The Answer Is: 33.846153846154
round to the digit needed
Step-by-step explanation:
I got 60p and 70p but that doesn't work, so i need help pls. again, pretty simple question but mt brain isn't working
Step-by-step explanation:
let's reffer to:
gumbo (x)
raspberry (y) so,
8x + 9y =14. 3 (1)
6x + 3y = 8.1 (2)
devide (2) by 3
2x + y = 2.7
y = 2.7 - 2x (3)
substitute 3 in 1
8x + 9(2.7 - 2x) = 14.3
8x + 24.3 - 18x = 14.3
10 x = 10
x = 1 (ANS)
and y = 0.7 (ANS)
Answer:
Hello There the correct answer to this is The first one is 1029.6 Because you need to multiply 8 x 9 then it will be 72 and then multiply 72 x 14.30 it will be 1029.6 it will the same the Second one is 145.8 Because you you need to multiply the first one multiply 6 x 3 which that 18 the multiply 18 x 8.10 which that will be 145.8 SO both of these answer are the same.
Hope It Helps!
ItsNobody
The sum of three consecutive integers is 27. Find the value of the greatest of the three.
Answer: The greatest of the three is 10.
Step-by-step explanation:
27/3=9 so the numbers will be around nine.
8+9+10=27
Answer:
Let x represent the value of the smallest of the three consecutive integers.
Then, the value of the middle integer is x+1, and the value of the greatest integer is x+2.
Since the sum of the three integers is 27, we have:
x + (x+1) + (x+2) = 27
Combining like terms, we have:
3x + 3 = 27
Subtracting 3 from both sides, we have:
3x = 24
Dividing both sides by 3, we have:
x = 8
Therefore, the value of the smallest integer is 8, the value of the middle integer is 8+1 = 9, and the value of the greatest integer is 8+2 = 10.
Thus, the value of the greatest integer is 10.
Step-by-step explanation:
Five jobs P1, . . . , P5 arrive at a processor at time 0, 1, 2, 3, 4 and the lengths of their CPU bursts are 8, 2, 5, 2, 3, respectively. draw the Gantt Chart and calculate the average waiting time and the average response time using FCFS: First-Come-First-Served
The Gantt Chart for the given jobs using FCFS (First-Come-First-Served) scheduling algorithm is as follows:
Job Start Time End Time
P1 0 8
P2 8 10
P3 10 15
P4 15 17
P5 17 20
The average waiting time and average response time can be calculated as follows:
To calculate the average waiting time, we need to find the difference between the start time of each job and its arrival time, and then take the average.
Average Waiting Time = (0 + 8 + 10 + 15 + 17) / 5 = 10 ms
To calculate the average response time, we consider the time from when a job arrives to when it first starts executing (which is the same as waiting time in FCFS).
Average Response Time = Average Waiting Time = 10 ms
In FCFS scheduling, jobs are executed in the order of their arrival, without any preemption. Therefore, the waiting time for a job is the sum of the lengths of all previous CPU bursts. In this case, since the jobs arrive in sequential order, the waiting time for each job is simply the sum of the CPU burst lengths of the preceding jobs.
The average waiting time represents the average amount of time each job has to wait before starting its execution. The average response time, in the case of FCFS, is the same as the average waiting time since the response time is defined as the time from arrival to the start of execution.
In this example, both the average waiting time and average response time for FCFS are 10 ms.
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2x-5y=20
What is y and what is x
Answer:
x=10 and y=4
Im not sure if this is correct but I looked it up and it said it was right
Answer:
x = 5/2y + 10y = 2/5x - 4(if you're looking for intercepts then: x = 10, y = -4)
Step-by-step explanation:
\(\sf{2x - 5y = 20\)
\(\sf{Finding~x:\)
\(2x - 5y = 20\)
\(+ 5y = + 5y\)
↪ 2x = 5y + 20
\(\frac{2x}{2} = \frac{5y}{2} + \frac{20}{2}\)
x = 5/2y + 10\(\sf{Finding~y:}\)
\(2x - 5y = 20\)
\(-2x~ = ~~~~-2x\)
↪ -5y = -2x + 20
\(\frac{-5y}{-5} = \frac{-2x}{-5} + \frac{20}{-5}\)
y = 2/5x - 4--------------------
Hope this helps!
The area of a right triangle is dirctly proportional to the
base of the triangle. The area of a triangle is 42 square
units for a base length of 12 units. Find the area of a triangle
having a base of 10 units.
If the base length of the triangle is 10 units. Then the area of the triangle will be 35 square units.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
The region of a right triangle is straightforwardly relative to the foundation of the triangle. The region of a triangle is 42 square units for a base length of 12 units.
The proportionality is given below.
A ∝ b
A = kb
Where A is the area, b is the base length, and k is the constant.
The ratio of Area to base length remains constant.
If the base length of the triangle is 10 units. Then the equation is given as,
A / 10 = 42 / 12
Simplify the equation, then we have
A / 10 = 42 / 12
A = 35 square units
If the base length of the triangle is 10 units. Then the area of the triangle will be 35 square units.
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Televisions per household
Which number represents the mode of the data?
2
3
4
1
Answer:
2
Step-by-step explanation:
The mode is the number in a data set that occurs most frequently, and we can see that number 2 is seen more times than any other number (6 times), so the answer is 2.
92% of what number is 345
Answer:
375
Step-by-step explanation:
Formula+ Number x 100/percent= 345x100/92=375
Which is equivalent to 2^5?
Answer:
Are there certain options?
Step-by-step explanation:
2^5 is in other words 2x2x2x2x2
the answer to this is 32
Hope I helped?
Answer:
32
Step-by-step explanation:
Coach Walker wants to buy equal numbers of footballs and basketballs for her PE class. The footballs cost $9 each, and the basketballs cost $7 each. Coach Walker has $208 for the purchase. How many of each type of ball can she buy?
Answer:
13 footballs and 13 basketballs
Step-by-step explanation:
Let f = footballs
b = basketballs
f=b since we are buying an equal number
9f+7b = 208
Substitute f=b
9f+7f = 208
16f = 208
Divide by 16
16f/16 = 208/16
f=13
We are buying 13 footballs
Since f=b
We are buying 13 basketballs
Engineers and architects often use transformed shapes to design objects or structures. Analyze a building or structure around you, and describe the transformations that you see using geometric vocabulary. How does the transformed shape contribute to the design of the object?
The way that transformed shapes contribute to the design of objects is by making them more efficient to get the most out of their characteristics.
What is the application of transformation in architecture and engineering?Architecture is a term that defines the technique of projecting, designing and building, modifying the human habitat based on the proper use and function of spaces.
Engineering is a term that defines the use of scientific principles to design and create machines, structures, and other objects.
The two disciplines named above primarily utilize modified shapes to design and then build objects and structures. This tells us that they make modifications out of geometric shapes to get the most out of an element as required.
For example, it is common knowledge that engineers and architects who design and build a house must modify the geometric figures of the square, rectangle and triangle to create their spaces with:
Appropriate amplitude
The most efficient lighting
Their roof is properly inclined with a good slope so that on rainy days, the rainwater on the roof properly discharges to the side of the house.
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I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!!
O’Barr charges $25 for customized shirts and $15 for customized mugs. It cost $80 to make x shirts and y mugs. Which equation represents this situation?
25x + 15y = 80
40yx = 80
15x + 25y = 80
15x + 80y = 25
Answer:
25x + 15y =18
Step-by-step explanation:
that is the answer cause x goes with shirts and y with mug and lastly 80 is the total
Yui is buying beverages for her friends. She buys a total of 6 bottles of water and sports drinks. Bottles of water cost $1.50 each, and sports drinks cost $2.50 each. She spends a total of $10. Write a system of equations to represent the information, and use substitution to determine how many of each type of drink Yui buys.
Answer:
Let x be the number of bottles of water that Yui buys, and y be the number of sports drinks. The first equation represents the total number of bottles:
x + y = 6
The second equation represents the total cost:
1.5x + 2.5y = 10
To solve for x and y, we can use substitution. Solving the first equation for y in terms of x:
y = 6 - x
Substituting this expression for y into the second equation:
1.5x + 2.5(6 - x) = 10
Expanding and simplifying the right side:
1.5x + 15 - 2.5x = 10
-x + 15 = 10
Subtracting 15 from both sides:
-x = -5
Dividing both sides by -1:
x = 5
Substituting this value for x back into y = 6 - x:
y = 6 - 5
y = 1
So Yui buys 5 bottles of water and 1 bottle of sports drink.
Step-by-step explanation:
Could someone uh, help me? I’m a bit confused.
PLEASE I WILL MARK BRAINLIEST
JUST TELL ME HOW TO SLOVE IT
Answer:
x=5
Step-by-step explanation:
So first we want to find x by itself, so we can subtract 4 from both sides:
x=5
That is your simple answer!
Step-by-step explanation:
\( \huge{ \sf{x + 4 = 9}}\)
~ Move 4 to right hand side and change it's sign :
⟼ \( \huge{ \sf{x = 9 - 4}}\)
~ Subtract 4 from 9
⟼ \( \huge{ \sf{x = 5}}\)
\( \red{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \bold{ \text{5}}}}}}}\)
Hope I helped ! ♡
Have a wonderful day / night ツ
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