Find the domain and range of function
Answers
Domain: (-∞, ∞) - all real numbers Range: (-∞, 2] - all real numbers less than or equal to 2.
To find the domain and range of the function 2 - |x - 5|, we need to consider the possible values for the input variable (x) and the corresponding output values.
Domain:
The domain of a function represents the set of all possible input values for which the function is defined. In this case, the function 2 - |x - 5| is defined for all real numbers. There are no restrictions or limitations on the values that x can take. Therefore, the domain is (-∞, ∞), which means that the function is defined for all real numbers.
Range:
The range of a function represents the set of all possible output values that the function can produce. To determine the range, we consider the possible values of the function for different input values.
The expression |x - 5| represents the absolute value of the quantity (x - 5). The absolute value function always produces non-negative values. So, |x - 5| will always be non-negative or zero.
When we subtract |x - 5| from 2, we have 2 - |x - 5|. The resulting values will range from 2 to negative infinity (2, -∞).
Therefore, the range of the function 2 - |x - 5| is (-∞, 2].
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Note the complete questions is
Find the domain and range of function 2 - |x - 5| ?
Related Questions
The measure of one small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles
Answers
Answer:
x + x - 45 = 90
2x - 45 = 90
2x = 135
x = 67.5, so x - 45 = 22.5
The other two angles measure 22.5° and 67.5°.
The probability of getting heads on a single coin flip is ;
2
The probability of getting nothing but heads
on a series of coin flips decreases by
2
for each additional coin flip. Enter an exponential function for the
probability p(n) of getting all heads in a series of n coin flips. Give your answer in the form a (b)'. In the
event that a = 1, give your answer in the form (b)'.
Answers
A department store manager noted that the sales of furniture contributed 20% of the store's profits in the year 2015 and 29% in the year 2016.
Of the following choices, which two statements about furniture sales are true?
a.) There was a 45% increase in furniture sales.
b.) Furniture sales rose by 45 percentage points.
c.) There was a 31% increase in furniture sales.
d.) There was a 9% increase in furniture sales.
e.) Furniture sales rose by 31 percentage points.
f.) Furniture sales rose by 9 percentage points.
Answers
Answer:
There was a 45% increase in furniture sales.
Furniture sales rose by 9 percentage points.
Step-by-step explanation:
absolute difference = new - old
29-20= 9 percentage points
absolute difference / initial value = 9/20 = .45 * 100 = 45%
Two statements which are true about furniture sales are \((a)\) There was a \(45\%\) increase in furniture sales and \((f)\) Furniture sales rose by \(9\) percentage points.
What is percentage ?Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Percentage \(=\frac{Obtained\ number}{Total\ number}\ * 100\)
We have,
Sales of furniture in \(2015=20\%\)
Sales of furniture in \(2016=29\%\),
So,
Change in Percentage \(=29-20=9\%\)
i.e.
Sales rise by \(9\%\) points,
And,
Increase in Percentage \(=\frac{9}{20}\ *100=45\%\)
Hence, we can say that Two statements which are true about furniture sales are \((a)\) There was a \(45\%\) increase in furniture sales and \((f)\) Furniture sales rose by \(9\) percentage points.
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The test scores for a group of students are shown.
60, 69, 79, 80, 86, 86, 86, 89, 90, 100
Calculate the five number summary of the data set? Minimum = First Quartile (Q1) = Median = Third Quartile (Q3) = Maximum = What is the interquartile range (IQR) Which test score is an outlier?
60
69
90
100
Answers
Answer:
Minimum=60
First Quartile(Q1)=79
Median=86
Third Quartile (Q3)=89
Interquartile range (IQR)=10
Un coche tarda 12 minutos en dar la vuelta a un circuito si va a una velocidad de 80 km/h. Cuánto tiempo tardara en recorrer el mismo circuito si va a una velocidad de 100 km/h?
Answers
A sample of matter experiences a decrease in average kinetic energy as it continues to cool. One would anticipate that the particles will eventually come to a complete stop. The temperature at which particles should theoretically stop moving is absolute zero. Thus, option B is correct.
What theory directly contradicts concept of absolute zero?
All molecules are predicted to have zero kinetic energy and, as a result, no molecular motion at absolute zero (273.15°C). Zero is a hypothetical value (it has never been reached).
Absolute zero signifies that there is no kinetic energy involved in random motion. A substance's atoms don't move relative to one another.
Therefore, Kinetic energy because it can create heat which goes against the absolute zero. A gas molecule's kinetic energy tends to zero when the temperature reaches absolute zero.
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Rewrite the equation in vertex form by completing the square: y=4x^2+24x-7
Answers
Given:
\(y=4x^2+24x-7\)Required:
We need to rewrite the given equation in vertex form.
Explanation:
Consider the equation.
\(y=4x^2+24x-7\)\(y=2^2x^2+(2\times6\times2\times x)-7\)\(y=(2x)^2+(2\times6\times2x)-7\)Add and subtract 36 on the left side of the equation.
\(y=(2x)^2+(2\times12\times x)-7+36-36\)\(y=(2x)^2+(2\times12\times x)+36-36-7\)\(y=(2x)^2+(2\times12\times x)+6^2-43\)\(\text{ Use }a^2+2ab+b^2=(a+b)^2.\text{ Here a =2x and b=6.}\)\(y=(2x+6)^2-43\)Final answer:
\(y=(2x+6)^2-43\)g(t)=−(t−1)
2
+5g, left parenthesis, t, right parenthesis, equals, minus, left parenthesis, t, minus, 1, right parenthesis, squared, plus, 5
What is the average rate of change of
�
gg over the interval
−
4
≤
�
≤
5
−4≤t≤5minus, 4, is less than or equal to, t, is less than or equal to, 5?
Answers
The average rate of change over is 1.
Given that;
the function is,
⇒ g (t) = - (t - 1)² + 5
Hence, We need to determine the average rate of change over the interval - 4 ≤ t ≤ 5.
The value of G(-4):
The value of G(-4) can be determined by substituting t = -4 in the function
⇒ g (t) = - (t - 1)² + 5
Thus, we have,
⇒ g (t) = - (-4 - 1)² + 5
⇒ g (t) = - 20
Thus, the value of G(-4) = -20
The value of G(5):
The value of G(5) can be determined by substituting t = 5 in the function , we get,
⇒ g (t) = - (t - 1)² + 5
⇒ g (t) = - (5 - 1)² + 5
⇒ g (t) = - 11
Thus, the value of G(5) is, -11
Now, Average rate of change:
The average rate of change can be determined using the formula,
⇒ G(b) - G (a) / (b - a)
where, a = - 4 and b = 5
Substituting the values, we get,
⇒ G(5) - G (-4) / (5 - (-4))
⇒ ( - 11 - (- 20)) / 9
⇒ 9/9
⇒ 1
Thus, the average rate of change over the interval is. 1.
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Answer question for a b or c
Answers
Answer: A
Step-by-step explanation:
Let the number of books be b. Then, we want:
\(0.75b < 15\\\\b < 20\)
Answer:
c
Step-by-step explanation:
.75 x 20=15 and c has the less than or equal to sign
determine the value of X?
Determine the Magnitude of FTD?
Answers
The value of x is 50 and FTD = 130°
How to find the value of x?Both of the angles in the diagram must have the same measure because are vertical, then:
3x - 20 = 2x + 30
3x - 2x = 30 + 20
x = 50
That is the value of x.
And we can see that FTD = 2x + 30 = 2*50 + 30 = 130
That is the measure.
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15. A botanist collected data on the different elevations at which a certainplant grows. The data collected by the botanist are shown.275, 300, 370, 425, 425, 450, 500,500, 550, 600, 600, 650, 725, 725, 800Which box plot correctly represents the data collected by the botanist?200300400500600700800200300400500600700800HHHHH200 300 400 500600+++800700200300+400500600700800
Answers
In order to find the correct box plot, first let's calculate the median of the data set.
The set is already in crescent order, and it has 15 elements, so the median will be the 8th element, which is 500.
This value is represented by the middle line in the box plot. Since there are two options with the median = 500, let's calculate the first interquartile.
If we consider just the first 7 elements, the middle term will be the 4th element, so the first interquartile is 425.
Looking at the options, the one with first interquartile equal 425 is the first one (option A).
1. A target is divided into 100 squares colored in dark blue, white, and light blue. Amber throws a beanbag that lands on the target.
co
9 25
dark blue
What is the probability that it will land on a dark blue square?
26
white
light blue
Answers
The probability of landing on the dark blue target is 2/5.
Finding probabilityProbability is the ratio of required to the total possible outcomes of an event.
The required outcome = dark blue= 25Total possible outcomes= entire sample Space = 100P(dark blue ) = 40/100
divide through by 20
P(dark blue ) = 2/5
Therefore, the probability of landing on target is 2/5
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Find the volume of a pyramid whose height is 15.7 inches and whose base is a rectangle with
dimensions of 7.6 inches and 12.4 inches.
Answers
Answer: V = 493.19
Step-by-step explanation:
V=1/3bh
7.6*12.4=94
94*15.7=1479.568
1479.568*1/3=493.19
A= Round your answer to the nearest hundredth. 5 B 7 ? A
Answers
Answer:
35.54Step-by-step explanation:
Use tan-1 (5÷7)
Use tan()to get your answer
Question
From a point P on a level ground and directly west of a pole, the angle of elevation of the top of the pole is 45° and from point Q east of the pole, the angle of elevation of the top of the pole is 58°. If |PQ|= 10m, calculate, correct to 2 significant figures, the:
a) distance from P to the pole;
b) height of the pole.
Answers
a) The distance from point P to the pole is: 6.2 m
b) The height of the Pole is: 6.2 m
How to find the distance and height from angle of elevation?The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.
Now, we are given that:
The angle of elevation of the top of the pole = 45°
Angle of elevation of the top of the pole = 58°.
|PQ|= 10m
a) PR is distance from point P to the pole and using trigonometric ratios, gives us:
PR/sin 58 = 10/sin(180 - 58 - 45)
PR/sin 58 = 10/sin 77
PR = (10 * sin 58)/sin 77
PR = 8.7 m
b) P O can be calculated with trigonometric ratios as:
P O = PR * cos 45
P O = 8.7 * 0.7071
P O = 6.2 m
Now, the two sides of the isosceles triangle formed are equal and as such:
R O = P O
Thus, height of pole R O = 6.2 m
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100 Point! Need help please, thanks a lot!
How many solutions does the system of equations have?
2x = -10y + 6 and x + 5y = 3
How many solutions does the system of equations have?
y = 6x + 2 and 3y - 18x = 12
How many solutions does the system of equations have?
x - 3y = 15 and 3x - 9y = 45
How many solutions does the system of equations have?
y - 7x = -14 and 7y -49x = -2
Answers
Answer:
1- only one 13/9y = 8/9
2- zero
3-zero
4-zero
Step-by-step explanation:
hope this helps :)
1- only one 13/9y = 8/9
2- zero
3-zero
4-zero
Help me ASAP pleasee!!!!!
Answers
Answer:
umm i think itz 16
Step-by-step explanation:
fycfyuyvt6vb
Answer:
X would be 16 since
x= 8
------
cos(8)
Jermaine kicked a soccer ball at a speed of 24 feet per second. If the ball never leaves the ground, then it can be represented by the function H(t) = −16t2 + 24t. Determine the time the ball traveled. (1 point) t = 24 seconds t = 8 seconds t = 1.5 seconds t = 0.67 seconds
Answers
The time that the ball traveled is given as follows:
1.5 seconds.
How to obtain the time traveled by the ball?The quadratic function determining the ball's height after t seconds is given as follows:
H(t) = -16t² + 24t.
The roots of the quadratic function in this problem are given as follows:
-16t² + 24t = 0.
16t² - 24t = 0
8t(2t - 3) = 0.
Hence we apply the factor theorem as follows:
8t = 0 -> t = 0.2t - 3 = 0 -> 2t = 3 -> t = 1.5.Hence the time is given as follows:
1.5 - 0 = 1.5 seconds.
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Please help I was sick and missed out on class.Thank you
Answers
Answer:
-1/2
Step-by-step explanation:
(-1-(-5)/(1-9)
(-1 + 5)/-8
4/-8
- 1/2
To calculate the distance between two points, we have to:
We have that the points are: (x₁ = 9, y₁ = -5) and (x₂ = 1,y₂ = -1). To calculate the slope, we apply the following formula:
\(\boldsymbol{\sf{m=\dfrac{\Delta y}{\Delta x} \iff m=\dfrac{y_2-y_1}{x_2-x_1} }}\)
Substitute data into the formula and solve:
\(\boldsymbol{\sf{m=\dfrac{-1-(-5) }{1-9 }=\dfrac{4}{-8}=-0.5000 }}\)
Slope of the line that passes through the points (9,-5) and (1,-1) is 4/-8.To learn at:https://brainly.com/question/29402342To learn at:https://brainly.com/question/28865634To learn at:https://brainly.com/question/28121859To learn at:https://brainly.com/question/17004654To learn at:https://brainly.com/question/28922474To learn at:https://brainly.com/question/25243069Make a list of all possible rational zeros of f(x)=5x^3+7x^2−81x+45, and then use this list to find all of the functions’ rational zeros, if any exist.
Rational Zero Candidates: ±
Rational Zeros:
Answers
The zeroes of the polynomial are x=3, x=-5 and x=3/5
What are Zeroes of the polynomial?The locations where a polynomial becomes zero overall are known as the zeros of the polynomial. The term "zero polynomial" refers to a polynomial with a value of zero . The highest power of the variable x is referred to as a polynomial's degree. A linear polynomial is a polynomial with degree 1.
Given:
f(x)=5x³+7x²−81x+45.
let us take x= 3
5(27)+7(9)-81(3)+45
=135+63-243+45
= 243-243
=0
So, 3 is a root of polynomial and x-3 is factor of Polynomial.
Now, divide 5x³+7x²−81x+45 by x-3 we get 5x²+22x-15
Now, factorise 5x²+22x-15.
= 5x²+25x-3x-15
= 5x( x+ 5) - 3(x+ 5)
= (5x - 3)( x+ 5)
Then, x= 3/5 and 5
Hence, the zeroes of the polynomial are x=3, x=-5 and x=3/5
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I WILL GIVE BRAINLIEST TO WHOMEVER ANWRS
Answers
Answer:
8000
Step-by-step explanation:
Answer:
994
Step-by-step explanation:
We have the expression:
\((8+t)^3-6\)
And we want to evaluate it when t=2.
Hence, we will substitute 2 for t and evaluate. Therefore:
\(=(8+2)^3-6 \\\\ =(10)^3-6\\ \\ =1000-6\\\\=994\)
Therefore, our final answer is 994.
Question 8(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
A new gaming chair costs $455.95. You have already saved $155.95 and earn $37.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
37.5 + 155.95w = 455.95; w = 8
37.5w + 155.95 = 455.95; w = 8
37.5w − 155.95 = 455.95; w = 16
37.5w − 455.95 = 155.95; w = 16
Answers
37.5w + 155.95 = 455.95; where w = 8; signifies the number of weeks required to babysit the business in order to purchase the gaming chair.
How do equations work?A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. For instance, in English, an equation is any properly stated formula that consists of two expressions linked by the equals sign, whereas in French, an equation is described as containing one or more variables. To solve a variable equation, identify the values of the variables that cause the equality to hold true. The answer is known as the values of the variables that must satisfy the equality.
Equations can be categorized as identities or conditional equations.
w = (455.95-155.95)/(37.50)
=300/37.50
=8
So, number of weeks = 8
As a result, w = 8 and 37.5w + 155.95 = 455.95 is the solution.
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A conglomerate of Christmas tree growers in Oregon wants to know if there is a difference in preference for live Christmas trees between urban and rural regions of the state. They randomly surveyed 160 rural households that put up a Christmas tree the previous season and found that 64 had used a live tree. In a separate random survey, 89 of 261 urban household had put up a live tree the previous season. The 95% confidence interval for the difference of the true proportion of all households (rural - urban) in Oregon that preferred a live tree is between -0.036 and 0.154. Based on the confidence interval, is there convincing evidence that the two population proportions are different
Answers
Answer:
0 is part of the confidence interval, which means that there is not convincing evidence that the two population proportions are different.
Step-by-step explanation:
Based on a confidence interval for the difference of proportions, there will be significant evidence that the proportions are different if 0 is not part of the confidence interval for the difference of proportions.
In this question:
Confidence interval between -0.036 and 0.154
0 is part of the confidence interval, which means that there is not convincing evidence that the two population proportions are different.
Use the ratio table to solve the persent problem. What is 40% of 75?
Answers
Answer:
30
Step-by-step explanation:
40 percent *75
= (40/100)*75
= (40*75)/100
= 3000/100 = 30
Liberty Middle School has 600 students. In Anna’s class, 3 out of 8 students walk to school. How many students at the school can be expected to walk to school?
Answers
Answer:
um
Step-by-step explanation:
3/8×600
=225 student walk home
225 number of students at the school can be expected to walk to school.
What is proportion ?
A proportion is an equation based on the equality of two ratios.
It is given that :
3 out of 8 students walk to school, therefore, out of 600 students the students walk to school let say x is calculated using ratio that is equating 3/8 with x/600 to get value of x :
3/8 = x/600
x = 3 . 600/ 8
x = 225
Therefore, 225 number of students at the school can be expected to walk to school.
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Question 3
{(-1, 1), (1, 1), (-2, 4), (2,4)}
Is the relation a function and why?
Ayes each input has exactly one output
Byes each output has been repeated
C no the inputs are not repeated
D no the inputs cannot have the same output
Answers
The given relation {(-1, 1), (1, 1), (-2, 4), (2, 4)} is a function because: A. yes each input has exactly one output.
What is a function?In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two (2) or more variables such as an ordered pair.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range).
In this context, we can reasonably infer and logically deduce that given relation is a function because each input variable (domain) has exactly an output variable (range) as illustrated below;
x F(x)
-1 1
1 1
-2 2
2 4
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No
0.7
What’s the percentage
Answers
Answer: 70%
Step-by-step explanation:
0.7
----- x 100% = 70%
1
Answer:
70%
Step-by-step explanation:
When turning a decimal into a percent always bring the decimal point two places to the right.
0.7.0.
070%
70%
a) You have a piece of string that is 36m long. find the areas of all the shapes you can make which have a perimeter of 36m. b) A piece of land has an area of 100m². How many meters of wire fencing is needed to enclose it?
Answers
a. The areas of the square is 81m² and for rectangle is 72m²
b. The perimeter of the square is 40m
What are the areas of all the shapes you can make which have a perimeter of 36m?a. To determine the area of the shapes in which we have that have a perimeter of 36m, we can consider rectangle and square.
For a square;
Perimeter of square = 4L
36 = 4L
L = 9m
The area of the square will be L² = 9² = 81m²
For a rectangle;
The perimeter of rectangle is;
P = 2(L + W)
We can assume that two numbers which will represent the length and width are;
L = 12m, W = 6m or L = 6m, W = 12m
A = 12 * 6 = 72m²
b.
The area of the wire is 100m², the perimeter for this can be calculated when we consider square and rectangle;
Perimeter of square = 4L
Area of square = L² = 100m²
L = 10m
The perimeter of the wire is 4(10) = 40m
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Please help me answer this question please...
Answers
answer is here about stem and leaf
Evaluate the following expression.
(-3)0
Answer here
Answers
The expression (-3)0 has a value of 0 when evaluated because a number multiplied by 0 gives 0
Evaluating the expression (-3)0From the question, we have the following parameters that can be used in our computation:
(-3)0
The above statement is a product expression that multiplies the values of -3 and 0
Also, there is no need to check if there are like terms in the expression or not
This is because we are multiplying the factors
So, we have
(-3)0 = 0
This means that the value of the expression is 0 i.e a number multiplied by 0 gives 0
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Titik ( 2,3 ) ditranslasi oleh (3 4) Koordinat bayangannya adalah
Answers
Answer:
6,2 kordinat 34,5 h2 semoga membanti