Answers
The range of the given function is represented as {y | -5 ≤ y ≤ 5 , y ∈ R} .
Range of a function is defined as the possible values of y or the dependent variable in relation to the values of x.
Here from the graph we can see that the greatest value y achieves is 5.
The lowest value of y from the graph is -5 for all the values of x.
Hence the range will be {-5 ≤ y ≤ 5}
Now the graph is continuous, so we accept all values of y, hence y ∈ R .
Therefore the range will be: {y | -5 ≤ y ≤ 5 , y ∈ R} .
The set of all possible values for the results of the dependent variable, or the entire set of all possible values when the domain is substituted, is the range of a function.
The steps to find the range is:
The range of a function or similar object is the range of all y values, from least to greatest.We determine whether the provided expression of y is positive, negative, or equal to other values by substituting all possible values of x into it.We find the minimum and greatest values of y.To learn more about range visit:
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Related Questions
Write the slope-intercept form of a line with a slope of 12 and a y-intercept of (0, -7)
Answers
Answer:
y=12x-7
Step-by-step explanation:
Slope intercept is y=mx+b
y = slope+y-int
always start with variable y =
slope = 12
y=12
slope needs x
y=12x
y-int = -7 so just plug it in as is
y=12x-7
Which statement best reflects the solutions of the equation X over X minus one minus one over X -2 equals 2X -5 over X squared minus 3X +2
Answers
The statement which best reflects the solutions of the equation; as given in the task content is; x = 3 is a valid solution and x = 2 is an extraneous solution.
What is the solution of the equation?It follows from the task content that the statement which represents the solution of the given equation be determined.
Since the given equation can be written algebraically as follows;
x/(x - 1) - 1/(x - 2) = (2x - 5) / (x² - 3x + 2)
By observation; (x - 1) (x - 2) = x² - 3x + 2.
Therefore, by multiplying through the equation by; x² - 3x + 2; we have;
x (x - 2) - 1 (x - 1) = 2x - 5
x² - 2x - x + 1 = 2x - 5
x² - 5x + 6 = 0.
Hence, the equation above can be solved quadratically so that we have;
(x - 3) (x - 2) = 0.
Therefore, the solution to the given equation is; x = -3 Or x = 2.
However, the solution x = 2 renders the equation undefined, hence, it is not a valid solution but an extraneous solution.
Therefore, the statement which reflects the solutions to the given equation is; x = 3.
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You buy a basket of 24 strawberries. You eat them as you walk to the beach. It takes the same amount of time to walk each block. When you are halfway there, half of the berries are gone. After walking 3 more blocks, you still have 5 blocks to go. You reach the beach 28 minutes after you began. One-sixth of your strawberries are left.
You walked
blocks in 28 minutes. At this rate you walk 1 block in
minute(s)
second(s).
Answers
which of the following is a fair gamble? question 2 options: one coin toss: win $10 if heads, lose $10 if tails. two coin tosses: win $10 if two heads, lose $10 if two tails, no change of wealth otherwise. a game in which you win $100 with probability 50%, lose $200 with probability 25%, and gain nothing with probability 25%. all of the above are fair gambles.
Answers
Out of all the given situations, all are fair gambles,
Any gamble is considered to be a fair gamble if the expectation of it is 0. Here, gamble means any situation which has a probabilistic uncertainty attached to it.
The expectation of any game is
E(X) = ∑xp(x)
In the first case
The probability to get a had or tails on flipping a coin is 1/2
Hence the expectation will be
E(X) = 0.5 X 10 + 0.5 X (-10)
= 5 - 5
= 0
Hence this is a fair gamble
In the next gamble, two coins are tosses
The probability to get 2 head is 1/4
The probability to get 2 tails is 1/4
The probability to get one head and one tail is 1/2
Hence,
E(X) = 0.25 X 10 + 0.25 X (-10) + 0.5 X 0
= 2.5 - 2.5
= 0
Hence this too is a fair gamble
Here,it is given that
Probability Gain
0.5 $100
0.25 - $200
0.25 $0
Therefore,
E(X) = 0.5 X 100 + 0.25 X (-200) + 0.25 X 0
= 50 - 50
= 0
Hence, all are fair gambles.
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Correct Question
which of the following is a fair gamble?
one coin toss: win $10 if heads, lose $10 if tails.
two coin tosses: win $10 if two heads, lose $10 if two tails, and no change of wealth otherwise.
a game in which you win $100 with a probability of 50%, lose $200 with a probability of 25%, and gain nothing with a probability of 25%.
all of the above are fair gambles.
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The figure shows the reflex angle BOD measures 3,5y and AOB measures y. Find the measure of the non-felex DOB in degrees.
Answers
The measure of the non-felex DOB in degrees is 140°.
How to calculate the angle?It is important to note that the value of the angles at a point is 360°.
Therefore, it should be noted that also vertically opposite angles are equal.
Therefore, the angles will be:
3.5y + 3.5y + y + y = 360°
9y = 360°
Divide
y = 360° / 9
y = 40°
Therefore, DOB will be:
= 3.5y.
= 3.5 × 40
= 140°
DOB is 140°.
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Graph the line with y-intercept 3 and slope -4/3
Answers
The line graphed with the y-intercept 3 and slope -4/3 is shown in the graph added in the attachments.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
m=(y₂-y₁) / (x₂-x₁)
It is given that, the line is having the y-intercept 3 and slope -4/3.
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
The equation with the y-intercept 3 and slope -4/3 is,
y=mx+c
y= -4/3x+3
3y= -4x+9
Thus, the line graph with the y-intercept 3 and slope -4/3 is shown in the graph added in the attachments.
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On a scale drawing, a building has length 12.4 cm and width 9.4 cm. The real length of the building is 62 metres. Work out, in metres, the real width of the building.
Answers
The real width of the building is given by 47 meters.
Given that the actual length of the building is 62 meters.
In a scale drawing, the length of the building is 12.4 cm.
So, 12.4 cm = 62 meters
1 cm = 62/12.4 = 620/124 = 5 meters.
Also given that the width of building on scale drawing = 9.4 cm
Hence the real width of the building = 9.4 * 5 = 47 meters.
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Write a linear function f with f(5) =-1 and f(0) =-5
Answers
Answer: y = -4/5x - 5
Step-by-step explanation:
So you can view that fancy F with the parenthesis number inside of it as an input, just like X, and when -1 is the output, that means that y=-1, so your first set of numbers is (5,-1) now do the same with the second pair and you get (0,-5), we know that this is the Y intercept because X=0 in this pair.
-5 - (-1) = -4
0-5 = -5
slope = - 4/5
y intercept = -5
writr equivalnt fractions for 2 2/3 and 2 1/4 using common denominator.
2 2/3 + 2 1/4= 2 ?/? + 2 ?/?
Answers
The value of the fraction 2 2/3 + 2 1/4 is 4 11/12.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, the addition of the fraction will be:
= 2 2/3 + 2 1/4
= 2 8/12 + 2 3/12
= 4 11/12
The value is 4 11/12.
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4.43 overweight baggage. suppose weights of the checked baggage of airline passengers follow a nearly normal distribution with mean 45 pounds and standard deviation 3.2 pounds. most airlines charge a fee for baggage that weigh in excess of 50 pounds. determine what percent of airline passengers incur this fee.
Answers
The percentage of airline passengers covered by this fee is 85.99%.
If the distribution is normal, use the Z-score formula. For a set of means and standard deviations, the measure's z-score X is given by z-score measures how many standard deviations a measure is from its mean. After finding the Z-score, look at the Z-score table to find the p-value associated with that Z-score. This p-value is the probability that the value of the measure is
less than X, the percentile of X Subtracting 1 from the p-value gives the probability that the value of the measure is greater from X means 46 pounds with a standard deviation of 3.7 pounds.
This is the p-value of Z for X = 50 minus 1 as a
ratio. So the p-value of is 0.8599or 0.8599× 100 = 85.99%
So, 85.99% of the airline passengers pay this fee.
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What does an rectangle add up to
Answers
Answer:
360
Step-by-step explanation:
it has four right angles 90×4 =360
alfred tried to solve the system of equations shown below. he concluded that the system has an infinite number of solutions. which is the best evaluation of alfred's conclusion? a. he is incorrect. for any positive value of , the corresponding value of is negative, which means the system has no solution. b. he is correct. both equations describe lines that have infinitely many solutions. c. he is incorrect. if the first equation is multiplied by 4 and added to the second equation, the result is , which leads to exactly one solution. d. he is correct. if the first equation is multiplied by 4 and subtracted from the second equation, the result is , which means the system has an infinite number of solutions.
Answers
The Correct option is D .
System of linear equations,gives us the result that given system has unique solution such that 13x= 6 or x = 6/13 and y = -40/13 .
If a, b, and c are real numbers, the graph of the equation ax + by = c
is a straight line (unless both a and b are zero), so such an equation is called a linear equation in variables x and y. There are three possible types of solutions to a set of linear equations.
Unique Solution: A system of linear equations has a solution if the graphs intersect at a point.No Solution: If the graph is parallel, the system of linear equations has no solution.Infinitely Many Solutions: There are infinitely many solutions to a system of linear equations if the graph is exactly the same straight line.given system of equations is
2x - y = 4 --(1)
and 5x + 4y = -10 ---(2)
comparing the above equations with linear system , a1 x + b1 y = c1 and a2 x + b2y = c2
we get, a1 = 2 , a2= 5 , b1 = -1 , b2= 4 , c1= 4 ,
c2= -10
Now, the ratio are
a1/a2 = 2/5 ; b1/b2 = -1/4 ; c1/c2= -4/10 = 2/5
=> a1/a2 not equal to b1/ b2
therefore the given system of equations has unique solution.
Now , we find the soltion of given system using Elimination method,
multipling equation (1) by 4 to making same cofficient of y in both equations of system we get
8x - 4y = 16 --(3) and 5x +4y = -10
adding equation (2) from (3) we get,
8x -4y + 5x + 4y = 16 -10 => 13x = 6 => x = 6/13
putting this value of x in (1)
2×6/13 - y = 4 => y = 12/13-4 = -40/13
Hence , unique solution for given system of equations is x= 6/13 , y = -40/13.
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Complete Question:
Alfred tried to solve the system of equations shown below..
2x - y = 4 and 5x + 4y = -10
He concluded that the system has an infinite number of solutions. Which is the BEST evaluation of Alfred's conclusion?
He is correct. Both equations describe lines that have infinitely many solutions.
He is correct. If the first equation is multiplied by 4 and subtracted from the second equation, the result is -3x +8y = -14 , which means the system has an infinite number of solutions.
He is incorrect. For any positive value of , the corresponding value of is negative, which means the system has no solution.
He is incorrect. If the first equation is multiplied by 4 and added to the second equation, the result is 13x = 6 , which leads to exactly one solution.
The average annual rainfall for a town is 43.2 inches. What is the average monthly rainfall?
Answers
Answer: 3.6
Step-by-step explanation: Annual means yearly, therefore 43.2 divided by 12 is 3.6. So 3.6 inches monthly.
In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x)=log(x), to achieve the graph of g(x)=log(-3x+9) + 4
Answers
The graph g(x)=log(-3x + 9)+4 is the outcome of a transformation on the function, f (x) = log (x), which can be visualized as a reflection across the y-axis. Then you contract by a factor of 3 horizontally, 3 to the right, and 4 to the up.
What is a function?The connection between an independent variable and a dependent variable is established by a mathematical expression, rule, or law (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given function:
Parent function: f(x) = log(x)
Transformation function: g(x) = log(-3x + 9) + 4
Step 1 - Shift 3 unit right, to achieve the function
y = log (x - 3) (x - 3)
Step 2 - Reduce the graph by thrice by multiplying x by three:
y = log 3(x - 3) (x - 3)
Step 3 - The formula y = log 3(x - 3) to line -3 = x is to be reflected to obtain: y = -3 (x - 3)
Step 4 - The function y = log 1 - 3(x - 3) should be translated by four units to reach
Therefore, the function can be transformed by reflection and translation.
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-4|w-16|+9=39
solve for w
Answers
Answer:
There is no solution because after solving the absolute value, the number will be multiplied by -4 which would be getting positive 9 impossible.
A triangle has two sides of length 12 and 18. What is the smallest possible whole-number length for the third side?
Answers
Answer:
7
Step-by-step explanation:
You want the integer length of the shortest third side that will form a triangle with sides 12 and 18.
Triangle inequalityThe triangle inequality requires the sum of any two sides exceed the measure of the third side. If x is the short side, we want ...
x +12 > 18
x > 6 . . . . . . subtract 12
The smallest integer greater than 6 is 7.
The third side must be at least 7 units long.
__
Additional comment
Some authors write the triangle inequality as a+b≥c. If you use that version, then the shortest side can be 6 units. The resulting "triangle" will have zero area, and will look like a line segment 18 units long.
Increase 100kg by 25%
Answers
Answer: 125
Step-by-step explanation:
100% = 100
25% of 100 = 100/4 = 25
100 + 25% (25) = 125
Giovanni can read 250 words per minute. If there are approximately 300 words on a page, about how many pages can he read in 2 hours?
Answers
250*120 (words he can read per minute multiplied by 120 minutes or two hours)=30000
30000/300 (amount of words Giovanni can read in two hours divided by the words per page)=100
HELP PLEASEEEEEEEEEEEEEEEEEEEEEEEE
13. Write an equation of the graph in slope-intercept form.
14. If misty has been traveling for 9 hours, how many miles of the trip does she have remaining?
15. If there are 50 miles in the trip remaining, how many hours has misty been traveling?
Answers
The equation of the graph is a straight line written in slope-intercept form as y = -33.3x + 450. When Misty travelled for 9 hours, he drove 150.3 miles.
Equation of Straight LineThe general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept. It is the most common form of the equation of a straight line that is used in geometry. The equation of a straight line can be written in different forms such as point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a two-dimensional geometrical entity that extends on both its ends till infinity.
The equation of a straight line is a mathematical equation that gives the relation between the coordinate points lying on that straight line. It can be written in different forms and tells the slope, x-intercept, and y-intercept of the line. The most commonly used forms of the equation of straight line are y = mx + c and ax + by = c. Some other forms are point-slope form, slope-intercept form, general form, standard form, etc. Let us go through the formula for the equation of a straight line
13: The equation of graph in slope-intercept form
But for this case, we will represent our equation using point-slope formula which is y = mx + c
Let's find the slope of the line.
To do this, we will pick any two points and solve for the slope.
A = (0, 450), B = (6, 250)
The equation of slope of a line is given as
m = y₂ - y₁ / x₂ - x₁
m = 250 - 450 / 6 - 0
m = -200/6
m = -33.3
The y-intercept is the point which the line touches the y-axis or y-plane and in this case, the y-intercept is 450.
The equation of the line is y = -33.3x + 450
y = miles remainingx = hours travelled.14: If he has been travelling for 9 hours, how many miles left ?
Using the equation y = -33.3x + 450; put x = 9
y = -33.3(9) + 450
y = 150.3 miles
Misty has 150.3 miles left.
15: If there are 50 miles in the trip left, how many hours has Misty travelled.
Using the equation y = -33.3x + 450
50 = -33.3x + 450
-400 = -33.3x
x = 12 hours
Misty has approximately travelled 12 hours.
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Find the area of the triangle.
A=?in^2
Answers
Answer:
7.5 in²
Step-by-step explanation:
You want the area of a triangle shown as having a base of 6 inches and a height of 2.5 inches.
AreaThe formula for the area of a triangle is ...
A = 1/2bh
where b is the base length, and h is the height.
ApplicationThe figure shows the base of the triangle as 6 in, and the height as 2.5 in. This means the area is ...
A = 1/2(6 in)(2.5 in) = 7.5 in²
__
Additional comment
The attachments show the triangle to be overs-specified. If the side dimensions are correct, the area is actually about 7.48 square inches. If the base and height are correct, at least one side length is slightly off.
The temperature in a town increased 18°F in 4 hours. The temperature decreased 40°F in the next 6 hours. Write the total change in temperature as a rate in the form of a quotient of integers.
Answers
The total change in temperature is 58°F.
What is temperature?It should be noted that temperature simply means the degree of hotness and coldness in a body.
In this situation, the temperature in a town increased 18°F in 4 hours and the temperature decreased 40°F in the next 6 hours.
The change in temperature will be:
= Old temperature - New temperature
= 18°F - (-40°F)
= 18°F + 40°F
= 58°F
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the function h(x) is a transformation of the square root parent function
f(x)=[tex]\sqrt{x}[/tex]. what function is h(x)
Answers
The function h(x) is a translation of 4 units to the left, so the correct options is B.
h(x) = √(x + 4)
What is the rule for function h(x)?We know that h(x) is a transformation on the parent square root function:
f(x) = √x
If we look at the graphs, we can see h(x) is translated 4 units to the left.
Now, for a function f(x), we define a horizontal translation of N units as:
h(x) = f(x + N)
if N < 0, the translation is to the right.
if N > 0, the translation is to the left.
In this case we have a translation of 4 units to the left, then N = 4, so we can write:
h(x)= f(x + 4)
Replacing the function f(x) we get:
h(x) = √(x + 4)
So the correct option is B.
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Katherine drove home from college traveling an average speed of 65.1 mph and drove back to the college the following week at an average speed of 70.7 mph. If the total round trip took 7 hours, how much time did it take Katherine to drive from home back to college? Express the time in hours and minutes. Round to the nearest minute.
Answers
The number of time it take Katherine to drive from home back to college is: 3 hrs 21 min.
How to find the time?Going home:
Rate = 65.1 mph , distance = x miles ; time = distance /rate = x/ 65.1 hrs
Going to college:
Rate = 70.7 mph ; distance = x miles ; time = x/70.7 hrs
Equation:
x/70.7+ x/ 65.1= 11
70.7x + 65.1x = 7 × 65.1 × 70.7
Combine like terms
135.8x = 32,217.99
Divide both side by 135.8x
x = 32,217.99/ 135.8
x = 237.25 miles
Home back to college
= 237.25 /70.7
=3.35 hrs
= 3 hrs 21 min
Therefore it take Katherine 3 hrs 21 min.
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The average annual stock return is 11. 3%. If you begin your investment portfolio with $2,000, what will your portfolio be worth in 30 years if the average holds?.
Answers
If the average annual stock return is 11. 3%, the average holds a portfolio of $8600 worth 30 years.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
It is given that, the average annual stock return is 11. 3% and you begin your investment portfolio with $2,000,
Suppose the amount he earns in one year is x,
x= 11. 3%. of $2,000
x=220
The portfolio be worth 30 years if the average holds are,
=220 × 30
=$ 6600
The net cost is the sum of the return and the initial investment,
=$ 6600 + $ 2000
=$8600
Thus, if the average annual stock return is 11. 3%, the average holds a portfolio of $8600 worth 30 years.
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i need help with this question i will give brainliest!!
Answers
Answer:
Question 1 is G.
Question 2 is B
Question 3 is D
Question 4 is A.
Step-by-step explanation:
I have two turtles. Today, the older turtle's age is $11$ times that of the younger turtle. In $24$ years, the older turtle's age will only be $7$ times that of the younger turtle. If both turtles survive until then, how many years from today will the older turtle's age be $3$ times that of the younger turtle?
Answers
Answer: A number which is divided by 5, with the result as 50 less than if the number had been divided by 6 would be; -1500
How to solve Algebra Word Problems?
Let the number be x. We are asked that it is divided by 5, and the result is 50 less than if the number had been divided by 6;
(x/6) - (x/5) = 50
Multiply by 30 to get;
5x - 6x = 1500
-x = 1500
x = -1500
Let the older turtle be represented x and the younger one be y.
Todays age,
Older turtle = 11y years
Younger turtle = y years
Also the equation form as;
11y + 24 = 7(y + 24)
11y + 24 = 7y + 168
11y - 7y = 168 - 24
4y = 144
y = 144/4
y = 36
Thus;
Age of older turtle today = 396 years
Age of younger turtle today = 36 years
Therefore,
3(36 + t) = 396 + t
108 + 3t = 396 + t
2t = 292
t = 292/2
t = 146 years
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Step-by-step explanation:
Addison and some friends are going to the movies. At the theater, they sell a bag of
popcorn for $5 and a drink for $4.25. How much would it cost if they bought 8 bags
of popcorn and 4 drinks? How much would it cost if they bought p bags of popcorn
and d drinks?
Answers
Really hope this helps you!
Which angle is vertical to ∠BCH?
Please help!!!
Answers
Given that
4x:3=11:5
Calculate the value of x.
Answers
Answer:
THE ANSWER IS x= 33/20
hope it help
with the steps:
1) Multiply all terms by the same value to eliminate fraction denominators
2) Cancel multiplied terms that are in the denominator
3) Multiply the numbers
1) 4x//3==11/5 then 15 ✖️ 4x/3= 15 ✖️ 11/5
2) 5 ✖️ 4= 3 ✖️ 11
3) 5 ✖️ 4x=3 ✖️ 11
20x=3 ✖️ 11
solution : x= 33/20
Answer:
x = [tex]\frac{33}{20}[/tex]
Step-by-step explanation:
[tex]\frac{4x}{3}[/tex] = [tex]\frac{11}{5}[/tex] cross multiply and solve
20x = 33 divide both sides by 20
x = [tex]\frac{33}{20}[/tex]
how can i simplify this?
Answers
Answer:u dont
Step-by-step explanation: