What is the range of the function f(x) = |x – 5| – 3?
R: {f(x) ∈ ℝ | f(x) > 2}
R: {f(x) ∈ ℝ | f(x) < 2}
R: {f(x) ∈ ℝ | f(x) ≥ –3}
R: {f(x) ∈ ℝ | f(x) ≤ –3}
Reason:
The smallest |x-5| can get is 0 since the result of an absolute value is never negative (because it represents distance).
So the smallest f(x) = |x-5|-3 can get is 0-3 = -3
f(x) = -3 or f(x) > -3 are the only two options for the output f(x).
Condense that into [tex]f(\text{x}) \ge -3[/tex] to arrive at choice C as the final answer.
The fancy notation of f(x) ∈ ℝ translates to "f(x) is a real number".
If you were to graph this using a tool like Desmos, then notice how the lowest point occurs when y = -3
See the diagram below.
Answer:
R: {f(x) ∈ ℝ | f(x) ≥ –3}
Step-by-step explanation:
I got it right on the test.
The graph of y = f (x) is given. Graph the indicated function.Graph y = f (-x) - 4
Note the - sign in the evaluation of f(x), which changes the function directly, and the term -4 indicates a displacement vertically (down), but the graph goes up because of the sign -, therefore, the only option with these conditions is option b.
The correct answer is option b.
uestion 15(Multiple Choice Worth 4 points)
(02.05 MC)
What is the range of f(x) = |x| − 5?
−∞ < y ≤ −5
−5 ≤ y < ∞
0 ≤ y < ∞
5 ≤ y < ∞
Answer:
B) - 5 ≤ y < ∞============================
Given function:f(x) = |x| − 5This is an absolute value function and is the translation of f(x) = |x| down by 5 units.
We know that f(x) = |x| is never negative as per definition of absolute value. So its range is zero or positive numbers:
0 ≤ y < ∞
The given function (|x| - 5) can get values 5 less than the parent function (|x|), so its range is:
- 5 ≤ y < ∞This is option B.
You have a rectangular prism whose cross section is a square with side length
3 cm. You need to know its length, but you do not have a ruler. Luckily, you have a calibrated container of water nearby. The container has marks that measure cubic centimeters of liquid. It appears to have 70 cubic centimeters of water in it, but when you submerge the prism into the water, the water level rises to the 115-cubic-centimeter mark. Determine how long your prism is.
Answer:
side length = 5cm
Step-by-step explanation:
The volume of the prism is:
V = l × w × h
But we only know the width and height which are both 3cm. See image.
We put it in the calibrated container (container with markings on it) We find out the volume is 45. Because 115 - 70 is 45.
Divide to find the missing length. See image.
Vol
= 3 × 3 × sidelength
V = 9s
45 = 9s
5 = s
see image.
Help, write an equation in slope intercept form for slope -3 and y intercept -2
Hi :)
[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]
Q-u-e-s-t-i-o-n:what is an equation with slope -3 and y int. of -2A-n-s-w-e-r:[tex]\sf y=-3x-2[/tex]
- we just insert the number for slope before x in the y=mx+b formula and then write the y-intercept
[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]
how many 5 digit numbers can be created using the digits 2,3,4,7,8 and 9 without repeating any digits in that five digit number
Answer:
there are 720 three digit numbers that can be created from the digits provided given that no digit may be repeated.
Step-by-step explanation:
Write the sum. 54+63 as the product of a number and relatively prime addends
54 + 63 = 13 * 9 is the expression obtained as the product of a number and relatively prime addends.
A prime number is a number that can be divided only by 1 and itself.
54+63 (given)
We now have to find the sum of the given numbers as the product of relatively prime numbers.
In order to find the numbers we will find first sum and then factor
Sum=54+63=117
Factors of 117 are 13 and 9
117 = 13 * 9
13 and 9 are relatively prime because the factor of 13 and 9 is 1.
Therefore, 54 + 63 = 13 * 9 is the expression obtained as the product of a number and relatively prime addends.
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An agency charges $100 per person for a trip to a concert if 50 people travel in a group. But for each person above the 50, the amount charged for each traveler will be reduced by $3. If x represents the number of people above the 50, write the agency's revenue R as a function of x. (Assume that x is greater than zero.)
R(x)
The revenue of the the agency is given by the function
R(x) = 5000 - 50 x - 3x² .
A function is a relationship between an independent variable and a dependent variable which defines all points on a cartesian plane which satisfies the given condition.
The set of the independent variables is called a domain and the set of the dependent variable of the function is called a range.Each data in range is related to a particular data in the domain by the function.Now in the given Agency it is given that the charge of each tourist is $100 . Now for every tourist above 50 the charge is reduced by 3 dollars.
So for x people above 50 charge will be ( 100-3 x ) for all members.
The total revenue can be measured by the function
R(x) = ( 50 + x ) ( 100 - 3x )
or , R(x) = 5000 - 150 x + 100 x - 3x²
or, R(x) = 5000 - 50 x - 3x²
Hence the revenue function is given as : R(x) = 5000 - 50 x - 3x²
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need help with these due tomorrow morning do 1-6
Answer:
Step-by-step explanation:
5 over 12 is 5/17
the following table lists the ages and number of players per age group that are on a volleyball team. let A = (volleyball players who are younger than 8 years old) how many players are in the complement of A?
The number of elements in the complement of a set A is the total number of elements in the universal set minus the number of elements in the set A.
It is given that A={volleyball players who are younger than 8 years old}.
From the table, volleyball players who are younger than the age of 8, are players who are 7 years old.
Hence, the number of players in A is 5.
Add the number of players for each age to get the total number of players:
[tex]5+3+7+4=19\text{ players}[/tex]It follows that the number of players in the complement of A is:
[tex]19-5=14\text{ players}[/tex]Hence, the number of players in the comp
5 is to 7 as 15 is to x.
Answer:
x = 21
Step-by-step explanation:
To get your answer, you can turn these to fractions: 5/7 = 15/x
5 * 3 = 15
7 * 3 = x
x = 21
Describe how the change affects the volume of the prism or pyramid. Multiplying the height by 3/2.
Answer:
1512 cm²
Volume is also multiplied by [tex]\dfrac{3}{2}[/tex]
Step-by-step explanation:
The volume of a pyramid is given by the expression
[tex]V = \dfrac{1}{3} l\cdot w\cdot h[/tex]
where l = base length, w = base width and h = height
The volume of this pyramid
[tex]= \dfrac{18\cdot 12\cdot 14}{3} = 1008\; cm^3[/tex]
If we multiply the height by [tex]\dfrac{3}{2}[/tex] then new height
= [tex]14 \cdot \dfrac{3}{2} = 21 cm[/tex]
New Volume [tex]= \dfrac{18\cdot 12\cdot 21}{3} = 1512\; cm^3[/tex]
[tex]\dfrac{\text{NewVolume}}{\text{Old Volume}} = \dfrac{1512}{1008} = \dfrac{3}{2}[/tex]
So volume is also multiplied by 3/2
there are 60 mintnutes in one hour and 60 seconds in one minute using this imformation explain how you could convert 20 miles per hour to feet per second
Unit analysis is a helpful tool we can use to convert units.
All we have to do is multiply the original value by a fraction, to cancel out the units that we don't want.
Solving the QuestionWe're given:
Change [tex]\dfrac{20\hspace{4}miles}{hour}[/tex] to [tex]\dfrac{x\hspace{4}feet}{second}[/tex]There are a couple things we need to know before we tackle this question:
5280 in 1 mile: [tex]\dfrac{5280\hspace{4}feet}{mile}[/tex]60 seconds in 1 minute: [tex]\dfrac{60\hspace{4}seconds}{minute}[/tex]60 minutes in 1 hour: [tex]\dfrac{60\hspace{4}minutes}{hour}[/tex]Step 1 ⇒ Multiply [tex]\dfrac{20\hspace{4}miles}{hour}[/tex] by [tex]\dfrac{5280\hspace{4}feet}{mile}[/tex] to change miles to feet:
[tex]\dfrac{20\hspace{4}miles}{hour}\times\dfrac{5280\hspace{4}feet}{mile}\\\\= \dfrac{20\times5280\hspace{4}feet}{hour}\\\\= \dfrac{105600\hspace{4}feet}{hour}[/tex]
Step 2 ⇒ Multiply [tex]\dfrac{105600\hspace{4}feet}{hour}[/tex] by [tex]\dfrac{hour}{60\hspace{4}minutes}[/tex] to change hours to minutes:
[tex]\dfrac{105600\hspace{4}feet}{hour}\times\dfrac{hour}{60\hspace{4}minutes}\\\\=\dfrac{105600\hspace{4}feet}{60 minutes}\\\\=\dfrac{1760\hspace{4}feet}{minute}[/tex]
Step 2 ⇒ Multiply [tex]\dfrac{1760\hspace{4}feet}{minute}[/tex] by [tex]\dfrac{minute}{60\hspace{4}seconds}[/tex] to change minutes to seconds:
[tex]\dfrac{1760\hspace{4}feet}{minute}\times\dfrac{minute}{60\hspace{4}seconds}\\\\= \dfrac{1760\hspace{4}feet}{60\hspace{4}seconds}\\\\= \dfrac{29.3\hspace{4}feet}{second}[/tex]
Answer[tex]\dfrac{29.3\hspace{4}feet}{second}[/tex]
19. Write an ordered pair for the point in Quadrant II, that is 8 units away from the point Q
(0.75 -3.25) on a coordinate plane.
An ordered pair of point in Quadrant II is 8 units away from this point, the resulting point will be (-7.25, 4.25)
In this question, we need to find an ordered pair for the point in Quadrant II, that is 8 units away from the point Q(0.75 -3.25) on a coordinate plane.
If we have a coordinate point (x, y) in Quadrant ||, if the coordinate is 8 units away, the resulting coordinate will be expressed as (x - 8, y + 8)
Given the point Q(0.75, -3.25) on the coordinate the plane, if a point in Quadrant II is 8 units away from this point, the resulting point will be (0.75 - 8, -3.25 + 8) which is (-7.25, 4.25)
Therefore, an ordered pair a point in Quadrant II is 8 units away from this point, the resulting point will be (-7.25, 4.25)
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- 2(m - 2) = - 3(m = 5)
m = -19 is the solution to the equation -2(m - 2) = -3(m + 5).
What is the numerical value of m in the given equation?Given the data in the question;
-2(m - 2) = -3(m + 5)m = ?To determine the numerical value of m, remove the parenthesis and simplify.
-2(m - 2) = -3(m + 5)
Apply distributive property
-2(m - 2) = -3(m + 5)
m(-2) - 2(-2) = m(-3) + 5(-3)
-2m + 4 = -3m - 15
Now, collect like terms by bring all values containing variable m to the left and all constant to the right side of the equation.
-2m + 3m = -15 - 4
m = -15 - 4
m = -19
Therefore, the numerical value of m is -19.
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Heather, Ahmad, and Jim have a total of $68 in their wallets. Heather has $8 less than Jim. Ahmad has 2 times what Jim has. How much does each have?
Answer:
Step-by-step explanation:
1. Set x equal to the amount of money Jim has
Jim's money = x2. Create equations of the amount of money the other people have based on x
Heather's money = x - 8Ahmad's money = 2x3. Now, we set all of these equations as equal to 68
[tex](x)+(x-8)+(2x)=68[/tex]4. Combine the like terms, which means that the previous equation will simplify to:
[tex]4x-8=68[/tex]5. Add 8 to both sides
[tex]8+4x-8=68+8[/tex]This simplifies to: [tex]4x=76[/tex]6. Divide 76 by 4
[tex]\frac{4x}{4} =\frac{76}{4}[/tex]This equals: x = 197. Plug the value of x into the previous equations:
Jim's money: $19Heather's money: [tex]19-8=11[/tex] -> $11Ahmad's money: [tex]2*19=36[/tex] -> $36Final Answer:
Jim has $19Heather has $11Ahmad has $36I’m struggling finding the frequency, can anyone help me?
Which decimal is equivalent to39?
Answer: is 7
Step-by-step explanation: Its 7 cuz 14 weeks
5. Which of the following is a rational number that can be written as a decimal in which one or more nonzero digits repeat?
The rational number that can be written as a decimal in which one or more nonzero digits repeat is given by:
D. 5/9.
Which numbers compose the set of rational numbers?The set of rational numbers is composed by numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.
For this problem, we have a focus on numbers that have repeating decimal part. The most known case is the division by 9, as when an integer that is not a multiple of 9 is divided by 9, the result is a decimal with a repeating decimal part.
To find the equivalent decimal to 5/9, we divide the numerator of 5 by the denominator of 9, hence:
5/9 = 0.55555...
The decimal digit 5 repeats infinitely, hence option D is correct.
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when sarah planted a tree in her yard it was 24 inches tall it grew at a rate of 2.5 inches per month the tree is now 41.5 inches tall how many months has it been since sarah planted the tree
In linear equations, 103.75 inches per month tall has it been since sarah planted the tree.
What are instances of linear equations?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5.When an equation is given in this format, finding both intercepts is rather simple (x and y).When attempting to solve systems involving two linear equations, this form is also quite helpful.Sarah planted a tree in her yard = 24 inches tall
grew at a rate =2.5 inches per month
When tree is now 41.5 inches tall = 41 . 5 * 2.5
= 103.75
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Which fraction is in simplest form? A. 11 15 B. 12 18 C. 9 21 D. 14 24
Answer : 11 15
Reasoning : The fraction is in simplest form
9 21 is able to be simplified to 3 7,
12 18 is able to be simplified to 2 3
14 24 is able to be simplified to 7 12
I dont understand any of these functions please help on all!
1.The slope -intercept form of the function is y = 7x
2.The slope -intercept form of the function is y = x - 8
3.The slope -intercept form of the function is y = -2x +9
4.The slope -intercept form of the function is [tex]y = \frac{1}{3}x+9[/tex]
5.The slope -intercept form of the function is y = 0.5x - 1.5
6.The slope -intercept form of the function is y = 3x - 12
How is the slope -intercept form calculated?
1. The slope -intercept form of the equation of the function is y = 7x
Slope = m
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{0+7}{0+1} \\\\m= 7[/tex]
Substituting point (-1,-7) and m in the slope-intercept form of the equation,
y = mx+ c ----(1)
-7 = 7(-1) + c
c = 7 -7
c = 0
Substituting m and c in (1)
y = 7x
2. The slope -intercept form of the equation of the function is y = x - 8
Slope = m
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{-8+17}{0+9} \\\\m= \frac{9}{9} =1[/tex]
Substituting point (-9,-17) and m in the slope-intercept form of the equation,
y = mx+ c ----(1)
-17 = (-9) + c
c = -17 +9
c = -8
Substituting m and c in (1)
y = x - 8
3. The slope -intercept form of the equation of the function is y = -2x +9
Slope = m
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{5-9}{2-0} \\\\m= \frac{-4}{2} =-2[/tex]
Substituting point (0,9) and m in the slope-intercept form of the equation,
y = mx+ c ----(1)
9 = -2 (0) + c
c = 9
Substituting m and c in (1)
y = -2x +9
4.The slope -intercept form of the equation of the function is [tex]y = \frac{1}{3}x+9[/tex]
Slope = m
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{8-7}{-3+6} \\\\m= \frac{1}{3}[/tex]
Substituting point (0,9) and m in the slope-intercept form of the equation,
y = mx+ c ----(1)
9 = 1/3 (0) + c
c = 9
Substituting m and c in (1)
[tex]y = \frac{1}{3}x+9[/tex]
5. The slope -intercept form of the equation of the function is
y = 0.5x - 1.5
Slope = m
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{1-0.5}{5-4} \\\\m= \frac{0.5}{1}= 0.5[/tex]
Substituting point (5,1) and m in the slope-intercept form of the equation,
y = mx+ c ----(1)
1 =0.5 (5) + c
1 -2.5 = c
c = - 1.5
Substituting m and c in (1)
y = 0.5x - 1.5
6. The slope -intercept form of the equation of the function is y = 3x - 12
Slope = m
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{9-3}{7-5} \\\\m= \frac{6}{2}\\\\m= 3[/tex]
Substituting point (5,3) and m in the slope-intercept form of the equation,
y = mx+ c ----(1)
3 =3(5) + c
3 -15 = c
c = - 12
Substituting m and c in (1)
y = 3x - 12
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How to simplify:
[tex]\frac{5}{2\sqrt{5} }[/tex]
My textbook says the answer is [tex]\frac{\sqrt{5} }{2}[/tex], but I don't know to get there.
Someone pls help
hmmm first of all, let's keep in mind that any expression multiplied by 1 is always the same expression
[tex]12\cdot 1=12\qquad 13567\cdot 1=13567\qquad spaghetti\cdot 1=spaghetti[/tex]
and so on.
now, hmm 1 can be expressed as a rational, 1/1 = 1, but but but, we can really express it as
[tex]\cfrac{9999}{9999}\implies \cfrac{7857}{7357}\implies \cfrac{\sqrt[11]{1375}}{\sqrt[11]{1375}}\implies \cfrac{spaghetti}{spaghetti}\implies \cfrac{lettuce}{lettuce}\implies \text{\Huge 1}[/tex]
so let's do the so-called rationalizing of the denominator, we can also do it with the numerator btw, but we only need it for the denominator right now, by multiplying for 1 :), 1 is Da Bomb baby!!
[tex]\cfrac{5}{2\sqrt{5}}\cdot \text{\LARGE 1}\implies \cfrac{5}{2\sqrt{5}}\cdot \cfrac{\sqrt{5}}{\sqrt{5}}\implies \cfrac{5\sqrt{5}}{2\sqrt{5^2}}\implies \cfrac{5\sqrt{5}}{2(5)}\implies \cfrac{5\sqrt{5}}{10}\implies {\Large \begin{array}{llll} \cfrac{\sqrt{5}}{2} \end{array}}[/tex]
ANSWER FAST: 4 thumb drives and 1 compact disk have a total capacity of 18 gigabytes. 3 compact disks and 4 thumb drives have a total capacity of 22 gigabytes. find the capacity 1 thumb drive and the capacity of 1 compact disk.
Capacity of 1 thumb drives = 4 gigabytes.
Capacity of 1 compact disk = 2 gigabytes.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Let capacity of a thumb dives = x
And, Capacity of a compact disk = y
Then, For first condition;
''4 thumb drives and 1 compact disk have a total capacity of 18 gigabytes.''
We can formulate;
4x + y = 18 .... (i)
And, For second condition;
'3 compact disks and 4 thumb drives have a total capacity of 22 gigabytes.'
We can formulate;
4x + 3y = 22 .... (ii)
Solve the equation (i) and (ii) we get;
Subtract (ii) by equation (i) we get;
2y = 4
y = 2
And, 4x + 2 = 18
4x = 16
x = 4
So, Capacity of 1 thumb drives = 4 gigabytes.
Capacity of 1 compact disk = 2 gigabytes.
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A lawnmower with a 3-gallon gas tank uses an average of 0.6 gallons per hour. A function modeling this situation, where x represents the amount of gas in the tank, has a domain described by which inequality?
A. 0 ≤ x ≤ 5
B. 0 < x < 5
C. 0 < x < 3
D. 0 ≤ x ≤ 3
x represents the amount of gas in the tank, has a domain described by which inequality
[tex]0 \leq x \leq 3[/tex]
This is further explained below.
What is inequality?Generally, A typical 3-gallon lawnmower requires 0.6 gallons of petrol per hour.
This circumstance is modeled by a function, where x is the volume of gas in the tank.
The lawnmower's gas tank has a maximum capacity of gallons and may be completely empty (having 0 gallons of gas).
In conclusion, a function's domain is
[tex]0 \leq x \leq 3[/tex]
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a=3 and b=6 and c=5 what is ab+bc?
Answer:
you have the values of a, b and c
all you gotta do is just plug them in so
ab+bc is (3)(6)+(6)(5)
which equals 48.
Answer:
48
Step-by-step explanation:
since a=3, b=6 and c=5, you would replace the letters in ab+bc with their numbers, making it (3)(6)+(6)(5). then you would multiply 3 x 6 which would be 18, and 6 x 5, which would be 30, making your expression 18+30. finally you would add them together, making it 48.
Write an equation for the graph in slope-intercept form. Do not use spaces in the equation
Answer:
I think this is correct.
Step-by-step explanation:
y=-3x+10
You have $100 in a savings accoun and save an additional $40 each week. Your friend has $80 in a savings account and saves and addtional $10 each week. Find and intepret the sum and difference of the amounts of money in each of your savings accounts?
The sum and the difference in the amount saved in the accounts will be 180 + 50w and 20 + 30w respectively.
How to calculate the value?From the information, I have have $100 in a savings accoun and save an additional $40 each week.
Let the number of weeks be represented by w. The expression to represent this will be:
= 100 + 40w
My friend has $80 in a savings account and saves and addtional $10 each week. This will be:
= 80 + 10w
The sum will be:
= 100 + 40w + 80 + 10w
= 180 + 50w
The difference in the amount will be:
= 100 + 40w - (80 + 10w)
= 20 + 30w
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Given that (-6,-8) is on the graph of f(x), find
the corresponding point for the function
f(x) + 3.
Answer:
(-6, -5).
Step-by-step explanation:
f(x)+3 represents the graph of f(x) shifted up 3 units, meaning we add 3 to the y-coordinate
John has $10,000 in debt with Discover, $4,000 in debt with Chase, $9,000 in debt with Citi Bank, and $3,000 in debt with Wells Fargo, giving him a total debt of $26,000. What percentage of John's total debt is with Discover?*
John holds 26 percent of the debt from discover bank in its total debt obligation.
What is a total debt?The Total debt represents the obligations being taken by a company in the form of debt and yet to be repaid by them to the lender.
Given that the Debt hold in discover bank is $10,000
Total debt: $26,000
Computation of ratio of debt in discover bank:
Debt proportion = Debt hold in discover bank / Total debt
Debt proportion = 10,000/ 26,000
Debt proportion = 26%
Therefore, John holds 26 percent of the debt from discover bank in its total debt obligation.
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