Which step is included in the graph of the function f(x)=[x-1] ?
O y=-5 for-4≤x <-3
O y=-2 for -2
Oy=-2 for 2
O y=-5 for -4
Answers
The step which is included in the graph of the function is Option(a)
y=-5 for -4≤ x <-3.
What is the greatest integer function?A function that yields an integer that is closest to the input real number is said to be the greatest integer function. The step function is another name for it. When rounding a number, the greatest integer function chooses the integer less than or equal to a given number. It is symbolized by the letter [x] where x can represent any number.The greatest integer function has R as its domain and Z as its range.From the properties of the greatest integer function y = [x], we know that
y = 0 for, 0 ≤ x < 1
y = -1 for, - 1 ≤ x < 0
y = -2 for, - 2 ≤ x < -1
Here,we are given a greatest integer function f(x) or y =[x-1]
Hence, the step which is included in the graph of the function is
y=-5 for -4 ≤ x <-3.
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Related Questions
Which value of x makes this inequality true? x+9<4x
A.4
B.1
C.3
D.2
Answers
Answer:
A. 4
Step-by-step explanation:
Given inequality:
\(x+9 < 4x\)
Rearrange the inequality to isolate x.
Subtract x from both sides of the inequality:
\(\begin{aligned}x+9-x & < 4x-x\\9& < 3x\end{aligned}\)
Divide both sides of the inequality by 3:
\(\begin{aligned}\dfrac{9}{3}& < \dfrac{3x}{3}\\\\3& < x\\\\x& > 3\end{aligned}\)
So the values of x that make the inequality true are:
Any value of x that is greater than 3.Therefore, from the given answer options, the value of x that makes the inequality true is x = 4.
To check this, substitute x = 4 into the inequality:
\(\begin{aligned}x+9& < 4x\\x=4\implies 4+9& < 4(4)\\13& < 16\end{aligned}\)
As 13 is less than 16, the inequality is true when x = 4.
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The EPA estimated that in 2013, the average amount of garbage produced in the United States was 4.4 pounds per person per day. At that rate, how long would it take YOUR family to produce a ton of garbage? (A ton is 2,000 pounds.)
Answers
hope this helped
The solid below is made from cubes.
Find Its volume.
Answers
Answer: The answer is 30 inches.
Answer:
36
Step-by-step explantion:
1 x 1 = 1 so each cube is 1 square inch
2 x 6= 12
12 x 3 = 36
pls answer will give brainliest answer
Answers
Answer:
∠A= ∠E, ∠H = ∠D
and the last one
Step-by-step explanation:
opposite angles are equal, alternative interior angle are equal.
Answer:
∠A = ∠E and ∠H = ∠D.
∠E = ∠H and ∠F = ∠G
Step-by-step explanation:
Angles A and E are one set of corresponding angles and angles H and D are another set. Corresponding angles are always congruent to each other and thus equal. Therefore, ∠A = ∠E and ∠H = ∠D.
Angles E and H are one set of vertical angles and angles F and G are another set. Vertical angles are also always congruent to each other and thus equal. Therefore ∠E = ∠H and ∠F = ∠G
!! Please help
Solve the system using substitution
x + 3y = 3
3y - 2x = 12
Answers
x + 3y = 3 and subtracting -3y from both sides which gives you
x = -3y +3 which you then substitute into the next equation
3y - 2(-3y +3) = 12 and then when you multiply you get
3y +6y -6 = 12 and when you’ve added like terms you get 9y -6 =12 adding +6 to both sides you get
9y =18 and then you solve and get
y=2 which you then substitute into the equation you’ve already solved for x ( x= -3y +3) which gives you x= -6+3 which means
y= 2 and x = -3
Hope this helps :)
The volume, of a rectangular solid with length L, width W, and height H is given by the formula V = LWH.
Use this formula to write a polynomial in standard form that models, or represents, the volume of the open box.
The volume of the open box is ____
Answers
Answer:
\(V(x) = 4x^3-34x^2+66x\)
Step-by-step explanation:
Polynomials
We'll apply the polynomials to geometry.
The volume of a rectangular box can be calculated as
V = LWH
Where L is the length, W is the width, and H is the height of the box.
The figure shows the three dimensions as a function of the variable x:
W = 6 - 2x
L = 11 - 2x
H = x
Substituting in the formula of the volume:
\(V(x) = (11-2x)(6-2x)(x)\)
Multiplying the first two factors:
\(V(x) = (66-22x-12x+4x^2)(x)\)
Simplifying:
\(V(x) = (66-34x+4x^2)(x)\)
Multiplying by x:
\(V(x) = 66x-34x^2+4x^3\)
Reordering:
\(\boxed{V(x) = 4x^3-34x^2+66x}\)
What is the surface area of a sphere with diameter 8 cm?
Answers
Answer:
As = 256\(\pi\) or 804.25cm
Step-by-step explanation:
By formula As = \(4\pi r^{2}\)
As = 256\(\pi\) or 804.25cm
Large Home Improvement Store: Total remodeling cost $13,200. Financing through the bank servicing the national home improvement company: 1 year 0% financing with a minimum monthly payment of $100; 16.99% APR for the remaining 3 years
Local Small Business Home Improvement Company: Total remodeling cost 11,800. Financing through her local credit union: 3% origination fee to be paid first then 7.5% APR for 5 years
Online Construction Business: Total remodeling costs $10,200. Financing through an online banking service: $1,000 applied toward the project before payback begins then 11.9% APR for 4 years.
Calculate the monthly payments for 2 of these options given that interest is compounded monthly.
What is the total amount that must be paid for each of the 2 options you chose?
In the 2 options you chose, what percentage of the total amounts to be paid back to each financial institution is interest?
How would you explain to Ramona the differences between these percentages and their corresponding APR’s?
Based on the financial outcomes for the 2 options you chose, which company would you suggest that Ramona choose to remodel her kitchen? Defend your suggestion.
Answers
1. The monthly payments for 2 of these options are:
Local Small Business Home Improvement Company is $236.45Online Construction Business is $294.39.2. The total payments for 2 of these options are:
Local Small Business Home Improvement Company is $14,540.87.Online Construction Business is $14,130.69.3. The percentage of the total amounts to be paid back as interest is:
Local Small Business Home Improvement Company is 16.41%.Online Construction Business is 20.74%.4. The percentages above represent the accumulated interests of the total payments.
The APR (annual percentage interest) represents the yearly financing cost of the financing institution for extending credit.
5. Ramona should choose the Online Construction Business to remodel her kitchen because the total cost she will incur is less than the total cost for the Local Small Business Home Improvement Company.
Large Home Improvement Store:Home improvement cost = $13,200
Financing:
Year 1 0% monthly payment of $100 = $1,200
Balance after Year 1 = $12,000
APR 16.99%
Remaining payment period = 3 years
N (# of periods) = 36 months
I/Y (Interest per year) = 16.99%
PV (Present Value) = $12,000
FV (Future Value) = $0
Results:
PMT = $427.77
Sum of all periodic payments = $15,399.83
Total Interest = $3,399.83
Total costs = $16,599.83 ($15,399.83 + $1,200)
Local Small Business Home Improvement Company:Home improvement cost = $11,800
Financing:
3% origination fee = $354 ($11,800 x 3%)
APR = 7.5%
Payment period = 5 years
N (# of periods) = 60 months (5 years x 12)
I/Y (Interest per year) = 7.5%
PV (Present Value) = $11,800
FV (Future Value) = $0
Results:
PMT = $236.45
Sum of all periodic payments = $14,186.87
Total Interest = $2,386.87
Total costs = $14,540.87 ($14,186.87 + $354)
Interest as a percentage of the total payment = 16.41% ($2,386.87/$14,540.87 x 100)
Online Construction Business:Home improvement cost = $10,200
Additional applied amount = $1,000
Total = $11,200
APR = 11.9%
Payment period = 4 years
N (# of periods) = 48 months (4 years x 12)
I/Y (Interest per year) = 11.9%
PV (Present Value) = $11,200
FV (Future Value) = $0
Results:
PMT = $294.39
Sum of all periodic payments = $14,130.69
Total Interest = $2,930.69
Total cost = $14,130.69
Interest as a percentage of the total payment = 20.74% ($2,930.69/$14,130.69 x 100)
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A 6-pack of ice cream sandwiches costs $3.86. What is the unit price, rounded to the nearest cent?
Answers
Answer: so either .64 or , .66,
Step-by-step explanation:
divide 3.86 by 6
find all values of a such that the following are independent in . {(1, 0, -2), (3, 2, a), (-3, -5, 1)}
Answers
The value of "a" that makes the set of vectors independent is 1.
In 3-dimensional space, a set of vectors is said to be independent if any one of the vectors cannot be represented as a linear combination of the other vectors.
We may utilize the idea of determinants to determine the value of "a" such that the set of vectors "(1, 0, -2), (3, 2, a), (-3, -5, 1)" is independent.
The linear dependence or independence of the given vectors can be assessed using the determinant of a 3x3 matrix, whose columns are the given vectors. If the vectors are linearly dependent, the determinant will be 0; if they are independent, it will be non-zero.
The determinant can be calculated as follows:
| 1 0 -2 |
| 3 2 a |
| -3 -5 1 | = 0
Expanding the determinant along the first row, we get:
1 * ((2 * 1) - (a * -5)) - 0 * ((-3 * 1) - (-2 * -5)) + (-2 * (2 * -3 - a * -3)) = 0
2 - 5a - 6 + 10 + 6a = 0
Expanding the equation and solving for a, we get:
8a = 8
a = 1
Thus, the set of vectors {(1, 0, -2), (3, 2, 1), (-3, -5, 1)} is independent.
So, the value of "a" that makes the set of vectors independent is 1.
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What is the circumference of this circle? Use π ≈ 3.14. Round your answer to the nearest tenth of a centimeter.
the diameter is 13
Answers
The circumference of the given circle is 41 cm
What is a circle?A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.
The circumference of a circle is the boundary length of the circle, it is basically the perimeter of the circle, in degree measure it can not exceed by 360°
Given that, a circle, with diameter, 13 cm, we need to find it circumference.
We know that, the circumference of a circle is given by,
Circumference of the circle = π × diameter
= 3.14 × 13
= 40.82
≈ 41 cm
Hence, the circumference of the given circle is 41 cm
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What's the output of a system modeled by the function ƒ(x) = x5 – x4 + 9 at x = 2?
Please Help
A)
24
B)
16
C)
30
D)
25
Answers
Answer:
a
Step-by-step explanation:
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Determine the percentile of 6.2 using the following data set.
4.2 4.6 5.1 6.2 6.3 6.6 6.7 6.8 7.1 7.2
Your answer should be an exact numerical value.
The percentile of 6.2 is |
%.
Answers
The percentile of 6.2 in the given data set is 40%.
To determine the percentile of 6.2 in the given data set, we can use the following steps:
Arrange the data set in ascending order:
4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2
Count the number of data points that are less than or equal to 6.2. In this case, there are 4 data points that satisfy this condition: 4.2, 4.6, 5.1, and 6.2.
Calculate the percentile using the formula:
Percentile = (Number of data points less than or equal to the given value / Total number of data points) × 100
In this case, the percentile of 6.2 can be calculated as:
Percentile = (4 / 10) × 100 = 40%
The percentile of 6.2 in the sample data set is therefore 40%.
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20 Points Please help me
Answers
Answer:
98 inches
Step-by-step explanation:
Multiply the top length by the bottom length
Find the whole. 40% of what number is 24? The whole is.
Answers
Answer:
60
Step-by-step explanation:
Learned this about a week ago
Answer:
60
Step-by-step explanation:
let the number be X
according to question,
40% of X = 24
(40/100) × X = 24
X=240/4
X = 60
You are washing cars over the summer. It costs you $3 to wash each car and a one-time cost of $35 for some supplies to market your car wash. You plan to charge $10 per wash. Write an equation and solve to determine the amount of cars you need to break even.
Answers
The amount of cars you need to break even is 5.
To determine the number of cars you need to break even, we can set up an equation where the revenue equals the total cost.
Let's denote the number of cars as x.
Revenue = Number of cars × Price per wash
= x × $10
Total cost = Cost per car × Number of cars + One-time cost
= $3x + $35
To break even, the revenue should be equal to the total cost:
x × $10 = $3x + $35
Now, let's solve this equation to find the value of x:
10x = 3x + 35
Subtract 3x from both sides:
10x - 3x = 3x + 35 - 3x
7x = 35
Divide both sides by 7:
x = 35 / 7
x = 5
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Find the value of y.
(6x - 13)
(3y + 1)
(8x - 61)
Answers
Answer:
y=1/3
Step-by-step explanation:
3y+1=0
3y=-1
3y/3=-1/3
y=-1/3
HELP! ITS DUE RIGHT NOW HELP
Answers
Answer:
Step-by-step explanation:
D
Answer:
x > 2
Step-by-step explanation:2 and under
verify each identity \( \frac{ \cos^{2}x }{ \csc{}^{2}x } = \frac{ \sin ^{2}x }{ \sec ^{2}x } \)
Answers
Answer:
Verified
Explanation:
Given the identity:
\(\frac{ \cos^{2}x }{ \csc{}^{2}x }=\frac{ \sin^{2}x }{ \sec^{2}x }\)We apply the following identity:
\(\begin{gathered} \csc =\frac{1}{\sin}\implies\sin =\frac{1}{\csc } \\ \sec =\frac{1}{\cos}\implies\cos =\frac{1}{\sec } \end{gathered}\)Therefore:
\(\begin{gathered} \frac{\cos^2x}{\csc{}^2x}\stackrel{?}{=}\frac{\sin^2x}{\sec^2x} \\ \cos ^2x\times\frac{1}{\csc{}^2x}\stackrel{?}{=}\sin ^2x\times\frac{1}{\sec ^2x} \\ \cos ^2x\times\sin ^2x\stackrel{?}{=}\sin ^2x\times\cos ^2x \\ \implies\sin ^2x\cos ^2x=\sin ^2x\cos ^2x \end{gathered}\)Thus, the identity is verified since both sides of the identity are equal.
On every 3rd day, Ivan goes to the gym to exercise. Every 5th day, Gavin goes to the gym to exercise. What is the first day Ivan and Gavin will be at the gym on the same day? Why isn't the answer day 1?
Answers
Answer:
Day 15
Step-by-step explanation: If you know how to find common denominators or numerators, you do that.
If you multiply 5 x 3, it equals 15 days. Does three go into 15? Yes! That means that they will first meet at day 15
{show steps please i’m begging it’s due in an hour }
PLEASE LET THIS GRAB UR ATTENTION IF UR AN EXPERT AT ALGEBRA I HAVE AN F
Answers
Hello!
\(slope = 2\\\\y-intercept = (0, 3)\\\\Equation: y = 2x + 3\)
We can find the slope using the slope formula:
\(slope = \frac{y_{2} - y_{1}}{x_{2}-x_{1}}\)
Plug in any two points from the table. We can use (0, 3) and (1, 5):
\(slope = \frac{5 - 3}{1-0}\)
\(slope = 2\)
Now, we can find the y-intercept by finding the y-value at which x = 0.
According to the table, when x = 0, y = 3. Thus, the y-intercept is:
\((0, 3)\)
We can write an equation using the slope and y-intercept in the format
y = mx + b where "m" is the slope and "b" is the y-intercept.
Plug in the solved values into the equation:
y = 2x + 3.
**Graphed below**
help in this plsssssssssss
Answers
Find the slope of the line above
Answers
Answer:
3/5
Step-by-step explanation:
Pick two points that are easy to read. pints that are easy to read are on the intersection of grid lines.
For example, pick (-2, 0) and (3, 3).
slope = rise/run
Rise is a vertical distance.
Run is a horizontal distance.
Start at (-2, 0). To go to (3, 3) by using only horizontal and vertical segments, go up 3 unit. Now go right 5 units.
The rise is 3. The runs is 5.
slope = rise/run = 3/5
Answer: 3/5
Calculate the surface area
Answers
To calculate the surface area of a rectangular prism, we need to find the area of each of its six faces and then add them up. In this case, the dimensions of the shape are:
Length = 8 cmWidth = 3 cmHeight = 6 cmRefer to the attachment below.
Three pairs of facesThere are three pairs of faces on a rectangular prism:
Two faces (top & bottom) with dimensions: Length × Width (8 cm × 3 cm).Two faces (front & back) with dimensions: Length × Height (8 cm × 6 cm).Two faces (left & right) with dimensions: Width × Height (3 cm × 6 cm).Finding the areaArea of Length × Width faces8 cm × 3 cm = 24 cm²
Since there are two of these faces, the total area is:
2 × 24 = 48 cm²
Area of Length × Height faces8 cm × 6 cm = 48 cm²
Since there are two of these faces, the total area is:
2 × 48 = 96 cm²
Area of Width × Height faces3 cm × 6 cm = 18 cm²
Since there are two of these faces, the total area is:
2 × 18 = 36 cm²
Adding the areas of the facesNow, add up the areas of all six faces:
Surface Area = 48 + 96 + 36 = 180 cm²
AnswerSo, the surface area of the rectangular prism is 180 cm².
________________________________________________________
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Clean Machine is Middletown's premier house cleaning service. The company used 2,920 gallons of soap last year, and 35% less this year. How many gallons of soap did the company use this year?
Answers
Answer:
Step-by-step explanation:)
Express 75 as a product of its prime factors write the prime factors in ascending order and give your answer in index form
Answers
Step-by-step explanation:
75 = 3 x 5 x 5 in prime factorization
Answer:
Step-by-step explanation:
3x5x5
What is the slope of the line that passes through the points
(
−
6
,
8
)
(−6,8) and
(
−
9
,
7
)
(−9,7)? Write your answer in simplest form.
Answers
Answer:
1/3 is the slope
Answer:
1 / 3
Step-by-step explanation:
Slope = y₂ - y₁ / x₂ - x
= 7 - 8 / -9 + 6
= - 1 / - 3
= 1 / 3
A 2 1/2 pound bag of grass seed covers 1/8 of an acre. How much grass seed is needed for 1 acre?
Answers
Answer:
it needs 234 grass seeds for the acre
The scale for this drawing is 3 in. = 8 ft. On the drawing, the length of the kitchen measures 7 in. What is the length of the actual Kitchen? Round your
answer to the nearest foot.
Answers
Answer:
19 feet
Step-by-step explanation:
First we must make the scale make sense, that is, it is in the same unit, therefore, we will pass 3 inches to feet, we know 1 foot is 12 inches, therefore:
3 inches * 1 foot / 12 inches = 0.25 feet
Which means that the real equivalence is 0.25: 8, now they are 7 inches, therefore:
7 inches * 1 foot / 12 inches = 0.583333
Now, we calculate the number of actual feet using the scale.
0.583333 * 8 / 0.25 = 18.66 feet
that is to say that the length of the current Kitchen is 19 feet if we round
Select the correct answer.
Which sentence correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14?
68% of the data points lie between 10 and 14.
68% of the data points lie between 8 and 12.
68% of the data points lie between 10 and 18.
68% of the data points lie between 10 and 16.
Answers
Answer:
68% of the data points lie between 10 and 18.
Step-by-step explanation:
one standard deviation to left of mean = 14 - 4 =10
one standard deviation to right of mean = 14 + 4 = 18
68% of data is in this region.
so the answer is 68% of the data points lie between 10 and 18.