In interval notation, the domain and range of the function are:
Domain: (-∞, ∞)
Range: [1, ∞)
The domain of a function is the set of all possible values of x that can be plugged into the function. The range of a function is the set of all possible values of f(x) that can be obtained by plugging in values of x into the function.
For the given function f(x) = 9x² + 1, the domain is all real numbers, because any value of x can be plugged into the function. Therefore, the domain is (-∞, ∞).
The range of the function is the set of all possible values of f(x) that can be obtained by plugging in values of x into the function. Since the function is a quadratic with a positive leading coefficient (9), the graph of the function will be a parabola that opens upward. The minimum value of the function will occur at the vertex of the parabola, which is (0, 1). Therefore, the range of the function is [1, ∞).
For more about domain and range:
https://brainly.com/question/28135761
#SPJ11
uiz Instructions Question 4 How many solutions are possible when you solve this system of equations? 2x+y=7 y=-2x+7
There is only one solution when you solve the system of equations 2x+y=7 and y=-2x+7. The one solutions is (2, 3).
To find the solution, you can use the substitution method. This involves solving one equation for one variable and then substituting that expression into the other equation.
First, solve the second equation for y:
y = -2x + 7
Now, substitute this expression for y into the first equation:
2x + (-2x + 7) = 7
Simplify the equation:
2x - 2x + 7 = 7
Combine like terms:
7 = 7
This equation is always true, which means that there is only one solution for this system of equations. The solution is the point where the two lines intersect, which is (2, 3).
Know more about solution here:
https://brainly.com/question/17145398
#SPJ11
Use the given function to evaluate \( f(0) \). Enter your answer with no spaces. \[ f(x)=\left\{\begin{array}{llr} 1+x & \text { for } & x
The given function is a piecewise function and we are asked to evaluate f(0). To do this, we need to find the expression that corresponds to x = 0. We can see that x < 2, so the expression we need to use is 1 + x.
Plugging in x = 0 into this expression gives us:
f(0) = 1 + 0 = 1
Therefore, the answer is 1.
In HTML format, the answer would be:
The given function is a piecewise function and we are asked to evaluate f(0). To do this, we need to find the expression that corresponds to x = 0. We can see that x < 2, so the expression we need to use is 1 + x.
Plugging in x = 0 into this expression gives us:
f(0) = 1 + 0 = 1
Learn more about expression
brainly.com/question/14083225
#SPJ11
f/3+22=17
What is f?
Answer:
To solve for f in the equation:
f/3 + 22 = 17
We need to isolate f on one side of the equation. We can start by subtracting 22 from both sides:
f/3 = 17 - 22
Simplifying the right-hand side:
f/3 = -5
To isolate f, we can multiply both sides by 3:
f = -5 * 3
Simplifying:
f = -15
Therefore, the solution to the equation f/3 + 22 = 17 is f = -15.
A 5-year Treasury bond has a 3.65% yield. A 10-year Treasury
bond yields 6.3%, and a 10-year corporate bond yields 9.75%. The
market expects that inflation will average 3% over the next 10
years (IP10
The real yeild is 0.65%.
The Estimated 10-year Treasury bond yield is 3.65%.
The 10-year Treasury bond yield can be estimated using the 5-year Treasury bond yield and the expected inflation rate of 3%.
This is done by calculating the real yield, which is the difference between the nominal yield and the expected inflation rate.
The 10-year Treasury bond yield can be estimated by adding the real yield of the 5-year Treasury bond to the expected inflation rate of 3%.
Real yield = Nominal yield - Expected inflation rate
Real yield (5-year Treasury bond) = 3.65% - 3% = 0.65%
Estimated 10-year Treasury bond yield = 0.65% + 3% = 3.65%
To know more about Treasury bond click on below link:
https://brainly.com/question/30837260#
#SPJ11
Which has the greater perimeter, a regular pentagon, or a regular hexagon, if they have the same area? Explain why.
If a regular pentagon and a regular hexagon have the same area, then the regular pentagon will have a smaller perimeter than the regular hexagon.
Why would the pentagon have a larger perimeter ?This is because a regular pentagon has less sides than a regular hexagon, which means that the length of each side of the pentagon will be shorter than the length of each side of the hexagon.
The hexagon would therefore have more distance to cover and more sides to be add up before one can get to the perimeter. The pentagon has three less sides than the hexagon and so would have a smaller perimeter.
Find out more on perimeter at https://brainly.com/question/1406118
#SPJ1
Shaq shot 420 baskets in 14 minutes. Find his basket rate in baskets per minute.
Answer:
30 baskets per minute
Step-by-step explanation:
We know
Shaq shot 420 baskets in 14 minutes.
Find his basket rate in baskets per minute.
We take
420 / 14 = 30 baskets per minute
So, the answer is 30 baskets per minute.
Find the following for the given functions.
f(x) = x2, g(x) = 4x − 3
(f + g)(x)
(f − g)(x)
(fg)(x) =
(f/g)(x)
2.) Find the following for the given functions.
f(x) = x2 + 5, g(x) =
7 − x
(f+g)(x)
(f-g)(x)
(fg)(x)
(f/g)(x)
The first step in finding the given operations for the functions is to substitute the expressions for f(x) and g(x) into the operations.
For the first set of functions, f(x) = x2 and g(x) = 4x − 3, we have:
(f + g)(x) = f(x) + g(x) = x2 + (4x - 3) = x2 + 4x - 3
(f - g)(x) = f(x) - g(x) = x2 - (4x - 3) = x2 - 4x + 3
(fg)(x) = f(x)g(x) = x2(4x - 3) = 4x3 - 3x2
(f/g)(x) = f(x)/g(x) = x2/(4x - 3)
For the second set of functions, f(x) = x2 + 5 and g(x) = 7 - x, we have:
(f + g)(x) = f(x) + g(x) = x2 + 5 + (7 - x) = x2 - x + 12
(f - g)(x) = f(x) - g(x) = x2 + 5 - (7 - x) = x2 + x - 2
(fg)(x) = f(x)g(x) = (x2 + 5)(7 - x) = 7x2 - x3 + 35 - 5x
(f/g)(x) = f(x)/g(x) = (x2 + 5)/(7 - x)
The given operations are:
1.) (f + g)(x) = x2 + 4x - 3, (f - g)(x) = x2 - 4x + 3, (fg)(x) = 4x3 - 3x2, (f/g)(x) = x2/(4x - 3)
2.) (f + g)(x) = x2 - x + 12, (f - g)(x) = x2 + x - 2, (fg)(x) = 7x2 - x3 + 35 - 5x, (f/g)(x) = (x2 + 5)/(7 - x)
Learn more about substitute the expressions
brainly.com/question/13660615
#SPJ11
For which two functions does f(x)→+∞ as x→+∞?
Explain your reasoning.
f(x)=14x+3
g(x)=−35x−8
h(x)=2x−1
Amy has 18 coins consisting of nickels, dimes, and quarters. She has the same amount of nickels as quarters. How many of each coin does she have if the value of the coins is $2.20?
a 1 nickel, 16 dimes, 1 quarter
b 3 nickels, 12 dimes, 3 quarters
c 4 nickels, 10 dimes, 4 quarters
d 6 nickels, 4 dimes, 6 quarters
The correct option regarding the amount of coins is given as follows:
c 4 nickels, 10 dimes, 4 quarters
How to obtain the amounts?The amounts are obtained by a system of equations, for which the variables are given as follows:
Variable x: number of nickels.Variable y: number of dimes.Variable z: number of quarters.Amy has 18 coins consisting of nickels, dimes, and quarters, hence:
x + y + z = 18.
She has the same amount of nickels as quarters, hence:
x = z.
Thus:
2x + y = 18
y = 18 - 2x.
She has a total of $2.20 worth of coins, hence:
0.05x + 0.1y + 0.25z = 2.2
0.3x + 0.1y = 2.2
Since y = 18 - 2x, the value of x is obtained as follows:
0.3x + 0.1(18 - 2x) = 2.2
0.1x = 0.4
x = 0.4/0.1
x = 4.
Hence the remaining values are given as follows:
y = 18 - 2x = 18 - 8 = 10.z = x = 4.Meaning that option c is correct.
More can be learned about a system of equations at https://brainly.com/question/30374328
#SPJ1
Kendall just bought a coat at a 25% off sale. She spent $100 for the coat. The next day jolina bought the same coat, but it was not on sale. What is the ratio of what Jolina paid of the coat to what Kendall paid?
Jolina paid 33.33% more than Kendall paid for the coat, as she paid the full price while Kendall received a 25% discount.
To calculate this, first find out how much Kendall paid after the discount. If the original price of the coat was X, then Kendall paid 0.75X, since the discount was 25%. We know that Kendall paid $100 for the coat, so we can set up the equation 0.75X = 100 and solve for X. X turns out to be $133.33.
Since Jolina paid the full price of $133.33 for the coat, the ratio of what Jolina paid to what Kendall paid is:
133.33 / 100 = 4/3 or 1.33:1
Therefore, Jolina paid 33.33% more than Kendall paid for the same coat.
For more questions like Percentages visit the link below:
https://brainly.com/question/17367777
#SPJ11
Are (9g – 11 + 10g) - (12 - 11g+ 13) and -3(-10g + 12) equivalent expressions? Explain.
Yes, these expressions are equivalent expressions.
What are expressions?A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Let's examine the writing style of expressions. A number is 6 times larger than the other number, x, by a factor of 2. The mathematical phrase x/2 + 6 represents this claim. Complex riddles are solved using mathematical expressions.
In the given question,
Expressions are as follows:
(9g-11+10g) - (12-11g+13)
Simplifying it, we get:
30g -36
In the 2nd expression given,
-3(-10g+12) and after simplifying:
30g-36
As the expressions after simplifying are equal to each other, we can say that these are equivalent expressions.
To know more about expressions, visit:
https://brainly.com/question/14083225
#SPJ1
Choose two ratios that describe the collection of baseballs to gloves.
8:4
06:4
02:1
02:4
10
4 of 15 answered
need help?
->>
Two ratios that describe the collection of baseballs to gloves are
8:4 and 2:1 .
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio.
Given,
Number of gloves = 16
Number of baseballs = 8
Ratio of gloves to baseballs
= 16/8
= 8/4 = 8:4
= 2/1 = 2:1
Hence, 8:4 and 2:1 are two ratios that describe the collection of baseballs to gloves.
Learn more about ratio here:
https://brainly.com/question/13419413
#SPJ9
Complete question is:
There are 16 baseballs and 8 gloves,
Choose two ratios that describe the collection of baseballs to gloves.
8:4, 6:4, 2:1, 2:4, 10:4
PLEASE HELP ASAP I WILL GIVE BRAINLIST!
A group of students are interested in creating a life-sized version of a Rubik's Cube, but they want to determine how much paint they will need to cover the entire cube. Their teacher tells them that, compared to an actual Rubik's Cube, their blocks have a scale factor of k=4.5
. In feet, what is the surface area of their Rubik's Cube?
Answer:
Step-by-step explanation:
OK so i'm not really good at this my self but i'll try my best to help you because I don't really do it for the points I do it because I like to help other people. OK so their blocks have a scale factor of k=4.5. OK so I don't know if this is right but what I would do is there are 8 sides to any cube and you have a scale factor of k=4.5 so I would multiply 4.5 and 8 to get a answer of 36ft.
Translate to an inequality and then solve. Five subtracted from a number is greater than twenty-two.
The inequality for this statement is "x - 5 > 22". So, the solution to this inequality is "x > 27".
To translate the given statement into an inequality, we need to identify the variable, the constant, and the inequality sign. The variable is the unknown number, which we can represent with x. The constant is the number 22, and the inequality sign is greater than (>).
So, the inequality can be written as:
x - 5 > 22
To solve for x, we need to isolate the variable on one side of the inequality. We can do this by adding 5 to both sides of the inequality:
x - 5 + 5 > 22 + 5
Simplifying gives:
x > 27
So, the solution to the inequality is x > 27. This means that any number greater than 27 will make the inequality true.
In conclusion, the inequality that represents the statement "Five subtracted from a number is greater than twenty-two" is x > 27.
Know more about inequality here:
https://brainly.com/question/25275758
#SPJ11
The function f(x) will model the roller coaster’s height from the ground in feet over time, measured in seconds since the ride started.
Answer:
1) 12<x<15 is: f(x) = -5(x-12)^2 + 80
2) 15<x<17 is: f(x) = 35
3) 27<x<30 is: f(x) = 2.5x-22.5
Step-by-step explanation:
See the attached image.
1) Plot all the lines as shown
2) Add the inequalities, which will produce the colored regions on DESMOS.
3) Assume that the function having the greatest value in each region is the function that determines the roller coaster's height (My assumption - it is not clear in the problem which function should dominate)
4) for the three regions listed with no corresponding function, identify the line having the greatest value. Thiose are the functions that are noted on the graph and in the answer box above.
5) Take a break
Estrella is the manager of a candy store. She is in charge of buying
candy for the store to sell. She buys candy from a wholesaler for $6 per
pound. The wholesaler also charges a fee of $250 for each bulk
purchase. Estrella then sells the candy for $10 per pound. Calculate the
cost to buy 75 pounds of candy from the wholesaler.
$725
$675
$650
$700
Cost of 75 pound of candy = 75×6 = $450
Additional fee for each bulk = $250
Total = $700
Therefore, $700 is the correct answer.
ABCD is a quadrilateral. a) Calculate the value of x. Optional working x = Answe b) When ABCD is drawn to scale, would the lines AD and BC be parallel or not? A You must justify your answer without using a scale drawing. Justify your answer Yes/No Answe D 3x° 2X° Diagram not drawn to scale to 24.70 C B
The value of x is 45 in the provided assertion, and the cointerior angles do sum up to 180°, indicating that AD and BC are parallel.
Why is parallel important?Parallel in mathematics refers to two lines which never cross one another; picture an equal symbol. Three close pals' parallel lives could be depicted in a tale.
(a)
3x + x + 2x + 90 = 360
6x = 360 - 90
6x = 270
x = 45
(b) The answer will be yes, they would be parallel.
We can justify this using co-interior angles, which state that 2 angles subtended by parallel lines add up to 180°
We can check this with both angles 3x & x, or 2x & 90°.
If AD and BC are parallel, then 3x + x = 180, and since you already found the value of x we can substitute this in:
3(45) + (45) = 180
135 + 45 = 180
180 = 180
So the co-interior angles do add up to 180°, which means that AD and BC are parallel.
To know more about Parallel visit:
https://brainly.com/question/24607467
#SPJ9
Look at this diagram:
a) What fraction is shaded?
b) What percentage is shaded?
Diagram ⬇️
Answer:
fraction 3/9
percentage is 90%
The following TI-
84
Plus display presents some sample statistics.
1-Var-Stats
x
=67
Σ
x=2291
Σx2
=182,361
Sx=8
σx=8.024961059
↓n=29
Part: 0 /
In this case, the mean of the data set is 67, the sum of all the data values is 2291, the sum of all the squared data values is 182,361, the sample standard deviation is 8, the population standard deviation is 8.024961059, and the sample size is 29.
The TI-84 Plus display presents sample statistics for a set of data. The "x" symbol represents the mean, or average, of the data set. The "Σx" symbol represents the sum of all the data values, and the "Σx2" symbol represents the sum of all the squared data values.
These statistics can be used to analyze and interpret the data set. For example, the mean can be used to determine the central tendency of the data, and the standard deviation can be used to measure the spread of the data.
Know more about standard deviation here:
https://brainly.com/question/23907081
#SPJ11
Thomas is putting in a tile floor. He needs to determine the angles that should be cut in the tiles to fit in the corner. The angle in the corner measures 90°. One piece of the tile will have a measure of 24°. Write an equation, and use it to determine the measure of the unknown angle.
The equation can be written as: x + 24° = 90°.
The measure of the unknown angle is 66°.
How to write an equation, and use it to determine the measure of the unknown angle?An algebraic equation is an equation that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.
Let the measure of the unknown angle be x.
Since the angle in the corner measures 90° and one piece of the tile will have a measure of 24°. We can write the equation as:
x + 24° = 90°
The measure of the unknown angle can be determined as follow:
x + 24° = 90°
x = 90° - 24°
x = 66°
Learn more about algebraic equations on:
brainly.com/question/4344214
#SPJ1
Interpret the data in the circle graph. If 560 books were sold at the book fair, find the number of the books that were comic books. Click the icon to view the circle graph. If 560 books were sold at the book fair, of the books were comic books. (Type a whole number.) Help me solve this View an example Get more help. www
The number of comic books is given as follows:
P/100 x 560.
In which P is the percentage equivalent to comic books on the circle graph.
How to obtain the number of comic books?The number comic books sold at the book fair is given by the proportions in the context of the problem.
The circle graph gives the percentage out of each type of book, hence the percentage of comic books is given as follows:
P/100.
Then the amount of comic books is obtained multiplying the percentage by the total amount of 560 as follows:
P/100 x 560.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
What is y=2(x-2)^2+5 in vertex form?
Answer:
y(x)=2*(x+-2)^2+5
Step-by-step explanation:
The difference in the medians is ___ times the IQR
Answer:
1/3
Step-by-step explanation:
You want the difference in medians in terms of the IQR.
IQRThe IQR is the difference of the numbers at the ends of the box.
top distribution: IQR = 12 -6 = 6
bottom distribution: IQR = 14 -8 = 6
MediansThe median of each distribution is the location of the line in the box.
top distribution: median = 11
bottom distribution: median = 9
DifferenceThe difference in medians is 11 -9 = 2. The ratio of that to the IQR is ...
2/6 = 1/3
The difference in medians is 1/3 times the IQR.
<95141404393>
Evaluate 2(d + 9) if d = 8
The radius of a cylindrical water tank is 5.5 ft , and its height is 16 ft. What is the volume of the tank? use 3.14 for pie and round to the nearest whole number will give brainliest
Answer:
8358 cubic ft
Step-by-step explanation:
the volume of a cylindrical tank is given by (πr^3)*hSuppose the chemist divided up the total amount of water so that all 8 beakers
held the same amount.
How much water would each beaker hold?
Show how you know.
The amount of water each beaker would hold is x/8
How much water would each beaker hold?From the question, we have the following parameters that can be used in our computation:
Number of beakers = 8
Represent the size with x
So, we have the following quotient expression
Size of each beaker = x/Number of beakers
Substitute the known values in the above equation, so, we have the following representation
Size of each beaker = x/8
Hence, the amount is x/8
Read more about proportions at
https://brainly.com/question/16828793
#SPJ1
Based on the caterer’s experience, 38% of attendees to events will prefer chicken for the main dish. As the caterer plans for an event attended by 780 individuals, the normal approximation will be used for the binomial with a correction for continuity. In this case, what is the standard deviation of the number that she would expect to prefer chicken, when determining the probability that at less than 300 will prefer chicken? Round your answer to 1 decimal place, e.g. 125.7
Therefore, 13.509 is roughly the standard deviation of the number of attendees who would favour chicken.
what is standard deviation ?The degree of variation or dispersion in a set of data is measured by standard deviation. It calculates how far the data points, on average, deviate from the mean (average) of the data collection. Finding the square root of the data's variation yields the standard deviation. In statistics, the standard deviation is frequently used to characterise the distribution of data and is significant in areas like science, finance, and economics. It can be used to assess the validity of statistical data and to contrast different groups of data.
given
The following formula must be used to determine the standard deviation of attendees who would favour chicken as the main course:
σ = √(np(1-p))
When we change the numbers, we obtain:
σ = √(780 x 0.38 x 0.62) (780 x 0.38 x 0.62)
σ = √(182.616) (182.616)
σ = 13.509
Therefore, 13.509 is roughly the standard deviation of the number of attendees who would favour chicken.
To know more about standard deviation visit:
https://brainly.com/question/23907081
#SPJ1
Solve the system \[ \left\{\begin{array}{rrr} x_{1}+x_{2}+3 x_{3}= & -4 \\ 4 x_{1}+5 x_{2}+5 x_{3}= & 9 \end{array}\right. \] \[ \left[\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \end{array}\right]=[-[]+
x1 = -2, x2 = 1, and x3 = 5.5
This system of equations can be solved by first combining the equations and then isolating one of the variables. To combine the equations, subtract the first equation from the second equation:
4x1 + 5x2 + 5x3 = 9
- (x1 + x2 + 3x3 = -4)
3x1 + 4x2 + 2x3 = 13
Next, isolate one of the variables. In this case, let's isolate x3:
3x1 + 4x2 + 2x3 = 13
- (2x3) - (-2x3) = 0
3x1 + 4x2 = 13
x3 = \frac{13 - (3x1 + 4x2)}{2}
Now that x3 has been isolated, substitute it into one of the original equations and solve for the remaining two variables:
x3 = \frac{13 - (3x1 + 4x2)}{2}
x1 + x2 + 3\left(\frac{13 - (3x1 + 4x2)}{2}\right) = -4
Solve for x2:
x2 = \frac{-4 - x1 - 3\left(\frac{13 - (3x1 + 4x2)}{2}\right)}{4}
Substitute this expression for x2 into one of the original equations and solve for x1:
x1 + \frac{-4 - x1 - 3\left(\frac{13 - (3x1 + 4x2)}{2}\right)}{4} + 3\left(\frac{13 - (3x1 + 4x2)}{2}\right) = -4
Solve for x1 and then plug this value back into the expression for x2 to find x2:
x1 = -2
x2 = 1
x3 = \frac{13 - (-2 + 4x2)}{2}
x3 = \frac{13 - (-2 + 4 \cdot 1)}{2}
x3 = \frac{13 - 2}{2}
x3 = 5.5
Therefore, the solution to the system of equations is x1 = -2, x2 = 1, and x3 = 5.5.
Learn more about system of equations
brainly.com/question/12895249
#SPJ11
If the length of a rectangle is x ^ 2 + 3y and the width is x ^ 2 - 3y , write an expression to represent the area
Answer: x⁴ - 9y²
Step-by-step explanation:
The area of a rectangle is length x width so...
Area = (x² + 3y)(x² - 3y)
Simplify:
Area = x⁴ + 3yx² - 3yx² - 9y²
Area = x⁴ - 9y²
Hope this helps!
What is 2625/21 please iv been stuck on this for 3 hours bro