The domain of a function is not always all real numbers.
We know that the domain of function is the set of all possible input values for which the function is well defined.
And the range of function is the set of all possible output values for given input.
As we know the domain of a function, f(x), is all real numbers when there are no restrictions on what we can take input for x, as all real numbers would make function f(x) true.
But the domain of a function is not always all real numbers.
consider the function f(x) = 1/x
This function is not defined for x = 0
So, the domain of above function f(x) is R - {0}
Also, we know that the domain of a logarithmic function is all non-zero positive real numbers.
Thus, the domain is not always set of all real numbers.
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The shaded triangle has an area of 16 ft².
Find the area of the entire rectangle.
Be sure to include the correct unit in your answer.
ft ft²
X
ft
The area of given figure is 32 ft².
The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
Given,
the shaded are of shape is 16 ft²
As, twice the area of triangle equals the area of rectangle
⇒ (16 + 16) ft²
⇒ 32 ft²
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Complete Question -
The ale price of a pring break vacation package i $209. 99 the travel agent aid by booking early, you aved $35. Find the percent decreae in price
The percent decrease in price for booking early for a spring break vacation package is 16.5%.
This was calculated by taking the amount of money saved ($35) and dividing it by the original price of the package ($209.99). Then, the resulting decimal was multiplied by 100 to convert it into a percentage.
Mathematically, the calculation looks like this:
(35/209.99) ×100 = 16.5%.
The 16.5% decrease in price is a substantial savings and could be used to purchase additional items or activities during the vacation. Booking early is often a great way to save money on vacation packages, since travel agents and companies often lower the prices to incentivize travelers to book in advance.
It is important to remember, however, that the savings may not always be 16.5%. Depending on the travel agent or company, the percentage of savings may vary. Additionally, some packages may not offer any savings at all. Therefore, it is important to do research and compare different packages before booking.
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How do you find the x-intercept and point of a quadratic equation?.
Answer:
Step-by-step explanation:
plug in a 0 for y and simplify the equation
because 0*(constant of y)=0, so
x*(constant of x)=something, so
something/(constant of x)=x
ans is (x, 0)
Simplify the expression
using only positive exponents.
The expression is simplified to y⁹/12x². Option A
What are index forms?The index form of a number can be described as that number written as an exponential expression.
It is also seen as a single number that is raised to another number.
Other names for index forms are standard forms and scientific notation.
From the information given, we have that;
3x^⁻⁴y⁵/(2x³y⁻⁷)⁻²
expand the exponential bracket of the denominator by mutiplying the values
3x^⁻⁴y⁵/2x⁶y⁻¹⁴
Now, divide the expression into parts, we have;
3/-4 (x^⁻⁴y⁵/2x⁶y⁻¹⁴)
Since we are finding the quotient, subtract the exponents of the denominator from the numerators, we get;
3× -4(x⁻⁴⁺⁶y⁵⁻¹⁴)
Now, add or subtract the exponential values, we get;
-12(x⁻²y⁻⁹)
y⁹/12x²
Hence, the correct option is y⁹/12x²
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What is the circumference of a circle with a diameter of 62 centimeters?
Answer:194.78 cm
Step-by-step explanation:
if a figure is dilated by a factor of 6, the area of the figure will change by a factor of _____.
how would i solve this
Note that the expression when simplified translates to x = -6 (Option 1)
What is a math expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms.
√(x + 14) - √2x + 5) = 1
To solve this, we must square all elements on both sides of the equation. That is:
√(x + 14)² - √(2x + 5)² = 1²
⇒ x + 14 + 2x + 5 = 1
Collect like terms to arrive at:
3x = -18
x = -18/3
x = -6
Thus the answer to the above expression is x= -6
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LInda, Laura, Loraine, and Lila run on a relay team. Each run 0. 5 kilometer. How far doe the team run altogether?
Answer: Linda, Laura, Loraine, and Lila run 2 kilometers altogether.
Step-by-step explanation:
0.5 + 0.5 + 0.5 + 0.5 = 2 km
I hope this helps!
60% of tudent like wimming, 40% like dancing, 20% of tudent that like wimming like dancing , how many tudent don't like wimming
So, 40% of students don't like swimming.
We know that 60% of students like swimming, and 40% of students like dancing. We also know that 20% of students that like swimming also like dancing.
First, we can find the number of students that like swimming and dancing by multiplying the percentage of students that like swimming by the percentage of students that like dancing and also like swimming:
20% * 60% = 12%
This means that 12% of students like both swimming and dancing.
To find the percentage of students who don't like swimming, we can subtract the percentage of students who like swimming from 100%.
100-60 = 40%
So, 40% of students don't like swimming.
It's important to note that if the problem had provided a total number of students this information would have been useful to calculate the exact number of students who don't like swimming.
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What was the intensity of the earthquake on the Richter scale?.
The intensity of the earthquake on the Richter scale of magnitude 5.3 can be calculated for moderate earthquakes, and a strong earthquake can be estimated at magnitude 6.3.
The idea of a logarithmic earthquake magnitude scale was first developed by Charles Richter in the 1930s to measure the magnitude of earthquakes occurring in Southern California using relatively high frequency data from a nearby seismometer station. Developed. The magnitude of an earthquake is expressed on a scale called the Richter scale. The Richter scale is a base 10 logarithmic scale, meaning that each magnitude is ten times stronger than the last. So 2 is 10 times stronger than 1 and 3 is 100 times stronger. On the Richter scale, the increment is the amplitude of the wave. In the Richter scale, magnitude is represented by whole numbers and decimals. More destructive earthquakes are usually between magnitude 5.5 and 8.9. A truly destructive earthquake is an earthquake that exceeds magnitude 7 on the Richter scale.
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What is a polynomial sum?.
Two polynomials simply mean to sum the coefficients of the same powers, if these situations occur. the result of adding two polynomials will always be another polynomial.
A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).
In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.
Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.
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How do you calculate equivalent form?.
To calculate equivalent form of an algebraic expression we can use the following :
1) distributing property
2) factoring.
Two mathematical expressions are said to be equivalent if they yield the same result upon solving them. To represent equivalent form an equality (=) sign is used. 3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. To calculate equivalent form by using Distributive Property :
Start with an algebraic expression. Let's take an example 2x(3y + 2).Distribute the multiple 2x throughout the rest of the equation. That is multiplying 2x by 3y and by 2, we get 6xy + 4x.This is our equivalent expression. It can be represent as equality : 2x(3y + 2) = 6xy + 4x.To calculate equivalent form Using Factoring :
Identify the common factors in the expression. If possible divide the equation to find an equivalent expression.Let the expression 5xy + 4x, in this case, both numbers 4 and 5 are co-prime. As we see that there is common factor, x. Take the other common factors: x(5y + 4).This gives you an equivalent form . Again, the equality form, 5xy + 4x = x(5y + 4). Thus, the required equivalent form is determined.
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Follow this link to view Juan’s work. Critique Juan’s work by justifying correct solutions and by explaining any errors he made. For any errors made, provide and explain a correct response. Be sure to explain each key aspect of the graph.
Juan's observations are correct, but his incorrect observation is asymptote: x = 0
What is an exponential function?An exponential function is a mathematical function of the following form: f(x) = aˣ. where x is a variable, and a is a constant called the base of the function.
Given is a graph of an exponential function.
Juan's observations are :-
Initial value: –3
Base: 3
Asymptote: x = 0
Domain: {x | x > 0}
Range: {y | all real numbers}
Studying the graph, we can say his observations are correct but his comment on Asymptote: x = 0 is wrong because, the equation of the horizontal asymptote of the graph of is y = 0, which is the x-axis.
Other than, Asymptote: x = 0, all his comments are true.
Hence, the incorrect observation is asymptote: x = 0
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Please help this question is on my test and if u help me and it’s right I will memorize the answer u gave me. Btw 20 points
The expression for the width is x (b) The perimeter of the rectangle in terms of x is x +8
What is perimeter?You should understand that the perimeter of a rectangle is the distance round the rectangle
The given parameters that will help us to understand and solve the question are
Length = 4 inwidth = xArea = 2x+24Area = length * width
This implies that 2x +24 =4x
Collecting like terms =4 = 4x-2x
2x = 24
Therefore x = 24/2 = 12
b) The perimeter is = L+W+L+W
Perimeter = 2L+w
Where W =x
Perimeter = 2(2x+24) +2(x)
The perimeter = 4x+48 +2x
Therefore the perimeter = 6x+48 or x+8
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I drove 10 mile north 14 mile eat 16 mile north 2 mile eat 4 mile north how far am I
The total distance traveled is 46 miles.
Distance Traveled:
Distance traveled is the path covered by a body to get from a starting point to an endpoint in a certain period of time, at a certain velocity. Time and velocity play a major role in measuring the distance traveled. The distance travel formula is: d = v x t
To determine the total distance you have traveled, you will need to add up all the distances you have driven in each direction.
You drove 10 miles north, 14 miles east, 16 miles north, and 2 miles east, 4 miles north.
10 miles north + 14 miles east + 16 miles north + 2 miles east + 4 miles north = 46 miles
So, you have traveled 46 miles.
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The monthly cot of driving a car depend on the number of mile driven. Lynn found that in May it cot her $428 to drive 460 mi and in June it cot her $494 to drive 680 mi. (a) Expre the monthly cot C a a function of the ditance driven, d, auming that a linear relationhip give a uitable model
Rate does Lynn's cost increase for every additional mile she drives will be $0.25
The following is the linear relationship between the two variables:
Eq. 1: C f(d) = m*d + k
where m and k are evaluation-needed constants
Find m: We'll determine the angle of the line connecting the points (480, $380) and (800, $460).
Line slope (m) equals $0.25 per mile
Consider one of the two positions and enter (480,$380) in Eq 1 to find k.
k = 380 - 0.25(480) = $260
The line's equation is C f(d) = 0.25*d + 260.
This equation may be used to plot the graph for section a.
The rate of cost per mile is determined by the graph's slope when the units are scrutinized; as a result, $0.25
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Sol divided the following polynomial and made a mistake (x³ + 8x - 16) + (x-2)
There are an equal number of roots as long as there are x powers. As a result of the four xs, the polynomial in this situation has four roots.
How can the roots of a polynomial be found given its factored form?Finding the roots of the polynomial will allow you to solve it. P(x) = 0 is obtained by setting each factor to 0 and then calculating x. The polynomial equation can be solved by factoring. For every factor, a value of 0 should be used. 2x4 = 0; (x - 6) = 0; (x + 1) = 0 the answer to x, please.
It's important to note this even if there are only two genuine roots. The final two roots of this equation, which contain the integer I, are not real because I appears in both of them.
There are an equal number of roots as long as there are x powers. As a result of the four xs, the polynomial in this situation has four roots.
The complete question is,
Calculate the overall number of roots for each polynomial function using the factored form. f (x) = (x + 2)(x - 1) (x - 1) (x - 1) [x - (4 + 3i)] [x - (4 - 3i)].
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list the sides of triangle MNP from least to greatest if m =64 degrees and n = 48 degrees
pls help
Answer:
Click or copy the link and that is the answer
https://www.leonschools.net/cms/lib/FL01903265/Centricity/Domain/3141/ch%205%20review%20answers.pdf
Step-by-step explanation:
hope it helps :)
mark me as brainliest!
if not try this (copy or paste)
mehttps://www.leonschools.net/cms/lib/FL01903265/Centricity/Domain/3141/ch%205%20review%20answers.pdf
Answer:MP, NP, MN
Step-by-step explanation:
ANSWER THE QUESTIONS WITH STEPS FOR BRAINLESS
the last answer choice on number 7 is (c) I don’t know
You can find the inverse of any function y=f(x) by reflecting it across the line y=x.
Hence, Option A is correct.
The inverse function is denoted by f-1 or F-1 if the function is denoted by f or F.In mathematics, an inverse function is a function that reverses the action of a function. The inverse of f is denoted if it exists and only if f is a bijective function.The function that "undoes" what f did can be defined as the inverse of f since it "acts on" numbers and transforms them. Alternatively put,A function that can change into another function is referred to as being inverse or anti.To know more about inverse of function here
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What is the solution of the system of equations y 4x 4 y 3x 3?.
After solving, the solution of the pair of equation is (-1, 0).
In the given question, we have to find the solution of the system of equations y = 4x + 4 and y = -3x - 3.
The given equations are:
y = 4x + 4.....................(1)
y = -3x - 3.....................(2)
Now putting the value of y from equation 1 to the equation 2
4x + 4 = -3x - 3
Subtract 4 on both side, we get
4x = -3x - 7
Add 3x on both side, we get
7x = -7
Divide by 7 on both side, we get
x = -1
Now putting the value of x in equation 1
y = 4(-1) + 4
y = -4 + 4
y = 0
Hence, the solution of the pair of equation is (-1, 0).
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The complete question is:
What is the solution of the system of equations y = 4x + 4 and y = -3x - 3?
hep me with the question please!
Answer:
i can not see the question
Step-by-step explanation:
please upload a New photo
HELP THIS WAS DUE YESTERDAY!!!!!!!!!!!!
The possible outcomes for rolling one six-sided die are shown below.
Molly rolled a six-sided die 20 times. The numbers she rolled are shown below.
What is the probability that Molly will roll a four on her next roll?
A.1/6
B.1/5
C.1/3
D. 1/4
What is the distance between the points 2 0 and (- 2 0?.
The required distance between given pair of points ( 2, 0 ) and ( -2,0 ) is equal to 4 units.
As given in the question,
Given pair of points in the coordinate plane is represented by the coordinates
( x₁ , y₁ ) = ( 2, 0 )
( x₂ , y₂ ) = ( -2,0 )
Apply the standard formula to calculate the distance between two pair of points in the coordinate plane is :
= √(x₂ - x₁ )² + ( y₂ - y₁ )²
Substitute the values in the formula and calculate the distance between two pair of points :
= √ ( -2 - 2 )² + ( 0 - 0 )²
= √(-4)² + 0²
= √16
= 4
Therefore, the required distance between the given pair of points ( 2, 0 ) and ( -2,0 ) is equal to 4 units.
The above question is incomplete , the complete question is:
What is the distance between the pair of points (2, 0) and (-2, 0) ?
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Answer: The answer is 2
Step-by-step explanation:
find the value of x
Answer:
x = 73⁰
Step-by-step explanation:
all values show are measures of exterior angles
the sum of all exterior angles for any polgon is 360 degrees
to find 'x':
50 + 48 + 59 + x + x + 58 + 39 = 360
combine like terms:
2x + 214 = 360
2x = 146
x = 73
How do you find the sides of a 30 60 90 triangle?.
A 30-60-90 triangle is a special type of right triangle that has angles of 30 degrees, 60 degrees, and 90 degrees. It has the following properties:
The side opposite the 30-degree angle is half the length of the hypotenuse (the side opposite the 90-degree angle).
The side opposite the 60-degree angle is √3 times the length of the side opposite the 30-degree angle.
To find the sides of a 30-60-90 triangle, you can use these properties.
If you know the length of the hypotenuse (the side opposite the 90-degree angle), you can find the length of the other two sides using the following formulas:
The side opposite the 30-degree angle: hypotenuse / 2
The side opposite the 60-degree angle: (√3) * (hypotenuse / 2)
If you know the length of one of the other two sides, you can use the above formulas to find the length of the hypotenuse and the other side.
For example, if you know the length of the side opposite the 30-degree angle, you can find the length of the hypotenuse by multiplying it by 2 and the length of the side opposite the 60-degree angle by multiplying it by √3
In summary:
The hypotenuse is always twice the length of the shorter leg.
The longer leg is √3 times the length of the shorter leg.
The hypotenuse is always the longest side in a 30-60-90 triangle.
Write an equation of the line that passes through (−1,3)
and is parallel to the line y=2x+2
.
The linear equation parallel to the line y=2x+2 is:
y = 2x + 5
How to write the equation of the line?A general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept.
Two lines are parallel if the lines have the same slope, then for example for:
y = 2x + 2
A parallel line will be:
y = 2x + b
And the line must pas through (-1, 3), then:
3 = 2*-1 + b
3 = -2 + b
3 + 2= b
5 = b
Then the linear equation is:
y = 2x + 5
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Jacob walks 2/5 kilometres in 1/4 hour. what is jacobs speed in kilometres per hour?
Jacob's speed in kilometers per hour is equal to 8/5 kilometers per hour.
What is speed?In Science, speed can be defined as the distance covered by a physical object or body per unit of time. This ultimately implies that, speed is a scalar quantity because it has magnitude but no direction.
Mathematically, the speed of a physical object or body can be calculated by using this formula;
Speed = distance/time
Substituting the given points into the speed formula, we have the following;
Speed = 2/5/(1/4)
Speed = 2/5 × 4/1
Speed = 8/5 kilometers per hour.
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An investor invested a total of $3,200 in two mutual funds. One fund earned a 6% profit while the other earned a 4% profit. If the investor's total profit was $152, how much was invested in each mutual fund?
$1200 was invested at a mutual fund of 6% profit while $2000 was invested at a mutual fund of 4% profit
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Let x represented the money at 6% profit and y represent the money at 4% interest. A total of $3200 was invested, hence:
x + y = 3200 (1)
If the investor's total profit was $152, therefore:
0.06x + 0.04y = 152 (2)
From both equations:
x = 1200, y = 2000
$1200 was invested at 6% while $2000 was invested at 4%
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What is the solution of the equation 2x y 5 and 3x 2y 4?.
Solving the 2 equations will give us the value of x to be -14 and that of y to be 33.
Here we have two equations
2x + y = 5 and 3x - 2y = 4
Now we will use the substitution method to solve the equations
The first equation is
2x + y = 5
or, y = 5 - 2x [1]
Let 3x - 2y = 4 be equation 2
Substituting the value obtained in equation [1] in [2] we get
3x - 2(5 - 2x) = 4
or, 3x - 10 + 4x = 4
or, x = -14 [3]
Substituting the value of x obtained in equation [3] to equation [1] we get
y = 5 - 2(-14)
or, y = 5 + 28
or, y = 33
Hence, x = -14 and y = 33
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Complete Question
What is the solution of the equations 2x + y = 5 and 3x - 2y = 4?
Muic player A: y= 191x-32
Muic player B: y=-x^2200x20
A. On what day did the company ell the ame number of each player?
B. How many player were old on that day?
a. On the 13th day the company sold the same number of each player.
b. 2,451 players were sold on that day.
a. The day on which the company sold the same number of players can be calculated by equating the values of y that we have ;
y = 191x-32 and y = -x² + 200x + 20
Equating both, we have;
191x-32 = -x² + 200x + 20
⇒x² -200x + 191x-20-32 = 0
⇒x²-9x-52 = 0
⇒x²-13x + 4x -52 = 0
⇒x(x-13)+4(x-13) = 0
⇒(x-13)(x+4) = 0
⇒x = 13 or -4
as days cannot be negative, so we choose only x = 13
This means that the company sold equal numbers of players on the 13th day.
b. To get the number of players sold on that day, we select any of the y equations and substitute x = 13
Thus, y = 191x -32; 191(13) - 32 = 2,451 players
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The complete question is:
The equation below models the numbers of two portable music players (y) and days after both players were introduced (x).
Music player A: y=191x-32 and music player B: y=-x^2+200x+20
1. on what day(s) did the company sell the same number of each player?
2. how many players were sold on THAT day (use your answer from #1
