To find the domain of a function, we need to determine all values of the independent variable (usually denoted as x) for which the function is defined and has a real output.
For example, if we have the function:
f(x) = 1/(x-3)
We need to exclude any values of x that would make the denominator zero, since division by zero is undefined. Therefore, the domain of this function would be all real numbers except x = 3. We could write this as:
Domain: x ∈ ℝ, x ≠ 3
If we have a more complex function, we need to consider any other restrictions on the independent variable that may be imposed by the function.
For instance, if we have the function:
g(x) = sqrt(x-2)/(x+3)
Here, the square root function is defined only for nonnegative values of its argument. Therefore, we need to ensure that x-2 ≥ 0, or equivalently, x ≥ 2. Additionally, the denominator of the fraction cannot be zero, so we need to exclude x = -3. Combining these two conditions, we get:
Domain: x ∈ [2, ∞), x ≠ -3
This means that the function g(x) is defined and has a real output for all values of x greater than or equal to 2, except x = -3.
In general, to find the domain of a function, we need to consider any restrictions on the independent variable imposed by the function itself (such as division by zero, taking the square root of a negative number, etc.), as well as any restrictions that may be imposed by the context in which the function is used (such as physical or mathematical constraints). We then express the domain as a set of values of x that satisfy all the relevant conditions.
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PLEASE HELP FAST.
Marie-Renee wants to hang 4 identical posters on her wall. The wall is 16 feet wide, and there must be at least 5 feet of space total between the posters and between the edges of the wall. How wide can the posters be?
Marie-Renee writes the inequality 4w + 5 ≤ 16 to help her plan. Complete each statement below to describe what w, 4w, 5, and 16 represent in this inequality.
w represents...
4w represents...
5 represents...
16 represents...
Marie-Renee knows to find the acceptable width of each poster, she must first solve the associated equation to find the boundary value for her inequality. Solve 4w + 5 = 16 and show your work.
Does the boundary value you found in part (b) make Marie-Renee’s inequality true or false? Show your work and explain your reasoning.
Write the solution to Marie-Renee’s inequality and interpret it within the context of the problem.
The width of each poster cannot be greater than 11/4 feet or 2.75 feet.
For given expression w represents the width, 4w represents the total width of four posters, 5 represents space between posters and edges of wall, and 16 represents width of the wall.
The boundary value satisfies the inequality.
In the given problem, Marie-Renee wants to hang 4 identical posters on her wall, and she needs to leave at least 5 feet of space total between the posters and between the edges of the wall. Let's assume that the width of each poster is w feet.
The inequality 4w + 5 ≤ 16 represents the maximum space the posters can take on the wall. In this inequality,
w represents the width of each poster,
4w represents the total width of four identical posters,
5 represents the total space between the posters and between the edges of the wall, and
16 represents the total width of the wall.
To find the acceptable width of each poster, we need to solve 4w + 5 = 16.
4w + 5 = 16
4w = 16 - 5
4w = 11
w = 11/4
So, the width of each poster cannot be greater than 11/4 feet or 2.75 feet.
Now, we need to check if the boundary value of w satisfies the original inequality or not.
4w + 5 ≤ 16
4(11/4) + 5 ≤ 16
11 + 5 ≤ 16
16 ≤ 16
Since the boundary value satisfies the inequality, the solution to Marie-Renee's inequality is w ≤ 11/4 or w ≤ 2.75 feet.
Therefore, the width of each poster cannot exceed 2.75 feet, and all four posters can be hung on the 16 feet wide wall with at least 5 feet of space total between them and the edges of the wall.
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Select the correct answer.
If the temperature outside is 86°F, the heat index can be found using the equation y = 0.004x²-0.1243x 84.028. This equation is also the curve of
best fit for the values in the table. In the equation, x represents the relative humidity and y represents the heat index.
Relative Humidity
Heat
If the temperature outside is 86°F and the relative humidity is 55%, the heat index is: C. 89°F.
How to determine the equation of line of best fit?In this scenario, the relative humidity would be plotted on the x-axis (x-coordinate) of the scatter plot while the heat index would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
From the scatter plot which models the relationship between the x-values and y-values, a quadratic equation for the line of best fit when the temperature outside is 86°F, is given by:
y = 0.004x²- 0.1243x + 84.028
when x = 55%, the heat index can be calculated as follows;
y = 0.004(55)²- 0.1243(55) + 84.028
y = 89.2915 ≈ 89°F
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10. A pizza with a diameter of 5 inches is divided into 8 sectors
of equal area.
What is the approximate area of each pizza slice? Round
your answer to the nearest hundredth.
O
O
The approximate area of each pizza slice is 2.45 sq inches
What is the approximate area of each pizza slice?From the question, we have the following parameters that can be used in our computation:
Diameter = 5 inches
This means that
Radius, r = 5/2 inches
Evaluate
Radius, r = 2.5 inches
The approximate area of each pizza slice is calculated as
Area = Circle area/number of sectors
So, we have
Area = 3.14 * 2.5^2/8
Evaluate
Area = 2.45 sq inches
Hence, the approximate area of each pizza slice is 2.45 sq inches
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What’s the equation and solution?
The equation for the rectangle is adding the interior angles:
x + x - 5 + 71 + y + 21 = 360°
Solving that for y, we will get:
2x + y + 87 = 360
How to find the equation?Remember that the sum of the interior angles of any figure with 4 sides must be 360°.
Then we can write an equation:
x + x - 5 + 71 + y + 21 = 360°
2x + y + 87 = 360
Solving it for y:
y = 273 - 2x
Now there is a clear problem in the diagram because the angle in the bottom left is clearly larger than 90°, but it says that the angle measures 71°, so there we have a problem.
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13x−6y=22
x=y+6
Please help first come first surve
Answer:
The answer is
x= -2
y= -8
Step-by-step explanation:
x=y+6
substitute into equation 1
13(y+6)-6y=22
13y+78-6y=22
13y-6y=22-78
7y=-56
divide both sides by 7
7y/7= -56/7
y= -8
x=y+6
x= -8+6
x= -2
Find the sum of x+9 and 7x^- 2x+1.
The sum of given two expressions x+9 and 7x²-2x+1 results in the expression 7x² - x + 10.
To find the sum of two expressions, we simply add their like terms.
The given expressions are x+9 and 7x²-2x+1.
The first expression has two terms - x and 9.
The second expression has three terms - 7x², -2x, and 1.
We cannot add the terms of the two expressions directly since they are not like terms. However, we can simplify the expressions and then add the like terms.
First, we can simplify the second expression by combining the like terms -2x and 1.
7x² - 2x + 1 = 7x² - (2x - 1)
Now, we can add the like terms from both expressions.
(x + 9) + (7x² - 2x + 1) = x + 7x² - (2x - 1) + 9
= 7x² - x + 10
Note that we could also have added the two expressions without simplifying the second expression first. We would get the same result.
(x + 9) + (7x² - 2x + 1) = x + 7x² - 2x + 9 + 1
= 7x² - x + 10
In either case, the final answer is 7x² - x + 10.
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question in the picture
1.) The average monthly income for Brianna would be = $1,850
2.) The average monthly expenses for Brianna would be =$3,145
3.) The total monthly cash flow = =$ −1,295
How to calculate the monthly income for Brianna?The monthly pay check after tax = $1600
The annual scholarship stipend = $3000
That is 3000/12 = $250
Therefore, the average monthly income = 1600+250 = $1,850.
The average monthly expenses = 700+120+75+140+25+110+100+300+250+(12000+1000+1500+800+600/12)
= 1820 + 15900/12
= 1820 + 1325
= $3,145
The monthly cash flow = 1850-3145 =$ −1,295
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You invest a lump sum of $1,500 into a bank account that offers 7.75%
simple interest.
1) How much interest is earned each year? $
2) How much money will be in the account after 20 years? $
1. intrest earned per year $116.25
2. total after 20 years $3,825
116x20= $2325
$1500+ 2325=3825
The makers of a new app recorded the number of times the app was downloaded each day for the first year the app was available.
Select the correct methods they could use to describe the data.
To describe how the number of daily downloads varies, they could use the median value. To describe how the number of daily downloads varies, they could use the mean absolute deviation.
To describe how the number of daily downloads varies, they could use the maximum value. To summarize the number of daily downloads with a single number, they could use the mean value.
To summarize the number of daily downloads with a single number, they could use the interquartile range. To summarize the number of daily downloads with a single number, they could use the minimum value.
The best method to describe data is use median value for how number of daily downloads varies, and mean value or interquartile range for number of daily downloads. So, correct options are A, D and E.
The median value is a measure of central tendency that represents the middle value of a set of data. It is useful to describe how the number of daily downloads varies, as it gives an idea of the typical value of the dataset.
However, mean absolute deviation is a measure of dispersion that describes how far the data values are from the mean. It is not an appropriate method to describe how the number of daily downloads varies, as it does not give information about the distribution of the data.
The maximum value is a measure of the largest value in a dataset, which can provide information on the upper limit of the number of daily downloads. However, it is not an appropriate method to describe how the number of daily downloads varies, as it does not give information on the spread or distribution of the data.
The mean value is a measure of central tendency that summarizes the data with a single number, but it may not be the best choice if the data is skewed or has outliers.
The interquartile range is a measure of dispersion that summarizes the spread of the middle 50% of the data. It can be used to summarize the number of daily downloads with a single number, but it does not give information on the typical or extreme values of the dataset.
The minimum value is a measure of the smallest value in a dataset, which can provide information on the lower limit of the number of daily downloads. However, it is not an appropriate method to summarize the number of daily downloads with a single number, as it does not give information on the spread or distribution of the data.
So, correct options are A, D and E.
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A spherically shaped hot air balloon has a
diameter of about 27 meters when fully inflated.
What is the volume of the hot air balloon when it
is fully inflated?
Answer: 7725.5775
Step-by-step explanation:
d=27
r=d/2=27/2=13.5
the volume of the spherical balloon= 3.14*r^3
= 3.14*(13.5)^3
= 7725.5775
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What are the steps for constructing an inscribed circle in
using only a compass and a straightedge?
Answer:
Find the angle bisectors and draw them.
The point where they meet is the center of the circle.
Make a circle which goes through the point where the angle bisector and sides meet.
Step-by-step explanation:
HELP DUE IN 30 MINUTES! I have an ice cream cone that has a radius of 1in and a height of 3in. How can you find how much ice cream could fit in the cone?
Answer:
Step-by-step explanation:
just do how tall times the diamiter divided by the
Determine whether the statement below is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
logb (x3 + y3) = 3 logb x + 3 logby
Using rules for logarithms we can see that the statement is false.
Is the statement true or false?Here we have the equation:
logₐ(x^3 + y^3) = 3logₐ(x) + 3logₐ(y)
And we want to see if it is true.
First, remember two rules:
logₐ(x^n) = n*logₐ(x)
and:
logₐ(x) + logₐ(y) = logₐ(x*y)
Then, the right side of the statement can be rewritten as:
3logₐ(x) + 3logₐ(y)
3(logₐ(x) + logₐ(y)) = 3*logₐ(x*y) = logₐ((x*y)^3)
And that is different to what we got in the statement, so the statement is false.
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group of students conduct an investigation to learn more about pea plants. Their data are summarized below. Plant Water per day (mL) Height after 2 weeks (cm) 1 20 11 2 50 18 3 100 24 4 20 16 Which is the independent variable in the investigation?
If Group of students conducted an investigation to learn about "pea-plants", then the "independent-variable" is "Water-per-day (mL)".
The "Independent-Variable" is defined as a variable which is controlled by the researcher.
In the investigation of the "pea-plants", the amount of water per day (mL) given to the plants is the independent variable because it is the variable that is intentionally varied by the students.
The students are manipulating the amount of water given to each plant to observe the effect it has on the height of the plant after two weeks.
By controlling the amount of water given to each plant, the students can determine whether there is a relationship between water intake and plant growth.
Therefore, water given to plants per-day will be the "independent-variable".
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The given question is incomplete, the complete question is
Group of students conduct an investigation to learn more about pea plants. Their data are summarized below.
Plant Water per day (mL) Height after 2 weeks (cm)
1 20 11
2 50 18
3 100 24
4 20 16
Which is the independent variable in the investigation?
a. Find x. The figure is not drawn to scale. b. Is the triangle equilateral, isosceles, or scalene? Explain.
*
0 points
Captionless Image
Answer: Based on the given figure above, we can conclude that the triangle is an isosceles triangle. By definition, an isosceles triangle is a triangle that has at least two equal sides. Since this is an isosceles triangle, 8x-10 =6x. Now we can solve for x. So,
8x-10 =6x
8x-6x = 10
2x =10
x= 5.
Therefore, the value of x in the figure is 5. Hope this is the answer that you are looking for.
which of the following representations show y as a function of x
The option that is a representation that shows y as a function of x is the graph in option 2. The answer is B.
What is a Function?A function is any relation or table of values which may be represented in a graph that has only one possible y value that is assigned to each x-value.
The first option is not a function because x-value 0 has two corresponding y-values, 4 and 9.
In the third option, we also have two y-values, 5 and -5, that is assigned to one x-value, 0. So, it is not a function.
The graph in option 2 represents y as a function of x, because no two y-values is assigned to the same x-value.
The answer is: B.
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A man earns $65000. He pays 18% of that in tax. (a) Calculate how much he has left, after paying the tax. (b) He invests $4500 and earns 6% interest per annum. Calculate the interest after 2 years. (c) He takes out a loan to buy a car. The price of the car is $24750. He pays $25740 altogether. What is the percentage interest?
a) The amount left after paying the tax is $53300.
(b) The interest after 2 years is $540.
(c) The percentage interest is 4%.
We have,
a)
The amount of tax the man pays.
= $65000 x 0.18
= $11700
Therefore, he has left.
= $65000 - $11700
= $53300
(b)
The interest earned after 2 years.
= $4500 x 0.06 x 2
= $540
(c)
The total amount of interest paid on the loan.
= $25740 - $24750
= $990
The percentage interest.
= ($990 / $24750) x 100%
= 4%
Thus,
(a) The amount left after paying the tax is $53300.
(b) The interest after 2 years is $540.
(c) The percentage interest is 4%.
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Hello, I hope you are having a great day so far, I was wondering if someone ca (seriously) help me and not play around. I really need an Answer asap as soon as possible
PLEASE HELP (I NEED AN ANSWER QUICK!)
Answer:
the corresponding sides are proportional
Use a net to find the surface area of the prism.
A. 426m2
B. 213m2
C. 306m2
D. 336m2
The surface area of the rectangular prism in this problem is given as follows:
A. 426 m².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas. -> net method.
The dimensions for this problem are given as follows:
5 m, 12 m and 9 m.
Hence the surface area of the prism is given as follows:
S = 2(5 x 12 + 5 x 9 + 12 x 9)
S = 426 m².
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Is the factions are proportional 1/2 and 2/4?
Yes, the fractions 1/2 and 2/4 are proportional
What is a fraction?A fraction can simply be defined as an expression that is used in the representation of the part of a whole.
This could be a whole number, a whole element, a whole material or a whole elemeent.
In mathematics, there are different types of fractions.
These fractions are enumerates thus;
Mixed fractionsSimple fractionsProper fractionsImproper fractionsComplex fractionsFrom the information given, we have that;
If 1/2 and 2/4 are proportional, that is, if equal
2/4 = 1/2
Cross multiply the values
4 = 4
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I need help please geometry not my strong suit
The image point of (-7, -8) after the sequence of transformations is given as follows:
(-4.5, -4).
How to obtain the coordinates of the image point?The original coordinates are given as follows:
(-7, -8)
The first transformation is a dilation with a scale factor of 1/2, meaning that each coordinate is multiplied by 1/2, hence:
(-3.5, -4).
The second transformation is a translation of one unit left, meaning that one is subtracted from the y-coordinate, thus the image point after the sequence of transformations is given as follows:
(-4.5, -4).
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The data table shows the numbers of eggs laid by
individual chickens in a year
What is the median number of eggs laid in a year?
A. 231
B. 229
C. 230
D. 234,6
The value of the median number of eggs laid in a year is,
⇒ 231
We have to given that;
The data table shows the numbers of eggs laid by individual chickens in a year.
Now, We can arrange it into ascending order as;
⇒ 222, 229, 229, 231, 234, 235, 262
Since, There are 7 terms
Hence, Median is,
= (7 + 1)/2
= 4th term
= 231
Thus, The value of the median number of eggs laid in a year is,
⇒ 231
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Answer:
A. 229 is correct
answer D.231 is wrong
GIVNING BRINLIE$T
Order the numbers from greatest to least based on their absolute value.
|−25
|, |0.5|, |−34
|, |0.35|
Answer:
|-34|, |-25|, |0.5|, |0.35| is the correct order.
hi can someone help with this question
Based on the information, we can infer that the investment was made 11.53 years ago.
How to calculate how many years ago was the investment made?To calculate how many years ago was the investment mafe we have to can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial amount invested)
r = the interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Let's start by finding the initial principal (P) by working backwards from the final amount (A):
A = P(1 + r/n)^(nt)
31372.0 = P(1 + 0.022/1)^(14)(1 + 0.022+0.007/1)^(1(t-4))
Simplifying, we get:
31372.0 = P(1.093248)(1.029)^(t-4)
P = 27500 euros (initial investment)
Now we can solve for t:
31372.0 = 27500(1.093248)(1.029)^(t-4)
1.1412 = (1.029)^(t-4)
log(1.1412) = log(1.029)^(t-4)
t - 4 = log(1.1412)/log(1.029)
t = log(1.1412)/log(1.029) + 4
t = 11.53
Therefore, the investment was made about 11.53 years ago.
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Jasmine sold 5 cherry pies and 12 Lemmon mer
Answer:
6
Step-by-step explanation:
this is if you meant: Jasmine sold 5 cherry pies and 12 lemonade how much more did Jasmine sell of lemonade than cherry pies
Solve for BC: 3√2 A B C
Sides AB = 3√2 and BC = 6.
The given triangle ABC is a right-angled triangle, as ∠BAC = 90°.
In the given right triangle ABC,
Hypotenuse of the triangle = BC
Base and height = AC and AB.
Also, we see from the diagram that ∠ACB and ∠ABC are equal.
∴ Triangle ABC is isosceles, with sides AC = AB = 3√2.
Now, by Pythagoras' theorem,
Hypotenuse² = Base² + Height²
Or, BC² = AC² + AB²
Or, BC² = (3√2)² + (3√2)²
⇒ BC² = 36
Or, BC = 6
Hence, sides AB = 3√2 and BC = 6.
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The product of p is and -8 is less than 24
The statement The product of p is and -8 is less than 24 as an expression is -8p < 24
Writing the statement as an expression
From the question, we have the following parameters that can be used in our computation:
The statement represented as
The product of p is and -8 is less than 24
Less than is represented using the symbol <
So, we have
The product of p is and -8 is less than 24: The product of p is and -8 is < 24
Represent products as *
So, we have
The product of p is and -8 is less than 24: -8p < 24
Hence, the expression is -8p < 24
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Name the characteristics a shape has to have to be defined as the following
quadriatera
Triangle
square
Answer:
A quadrilateral is a shape that has four straight sides and four angles.
A triangle is a shape that has three straight sides and three angles.
A square is a special type of quadrilateral that has four straight sides of equal length and four right angles.
ELECTRICAL POTENTIAL The electrical potential between two electrons is given by a formula has the form 1/r + 1/ 1-r
In a case whreby the electrical potential between two electrons is given by a formula has the form 1/r + 1/ 1-r the simpification of the expression is 1/r(1-r).
How can the expression be simplified?Looking at the expression we can see that it is adion of two expression which implies that we will need to perform an addition operation then later simplified the result, this is been done below
We can find the LCM as r(1-r)
(1-r +r)/ r(1-r)
=1/r(1-r)
Therfore, after performing the addition operation as well as the simplification, then the the simpification of the expression is 1/r(1-r).
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complete question;
The electrical potential between two electrons is given by a formula has the form 1/r + 1/ 1-r simplify the expression.
Jodi’s car used 12 gallons of gas to travel 456 miles. How many miles did her car travel per gallon of gas? Show work
Answer:
To find the number of miles Jodi's car traveled per gallon of gas, we need to divide the distance traveled by the amount of gas used:
miles per gallon = distance traveled / amount of gas used
distance traveled = 456 miles
amount of gas used = 12 gallons
miles per gallon = 456 miles / 12 gallons
miles per gallon = 38 miles/gallon
Therefore, Jodi's car traveled 38 miles per gallon of gas.
Answer:
38 miles
Step-by-step explanation:
Set up your division: 456 / 12
456 divided by 12 is 38
So, Jodi's car travels at 38 miles per gallon of gas.
